gpt4

---

I'm doing Prolog experiments.


The grid is 1-indexed and does allow negative indices.


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 `id` prefixed text has no integer value and should not be considered.


```prolog
% Example 1 input grid_width15_height15
object(input1_idP3d53ef_t6_l6_b6_r6_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_idP3d53ef_t4_l4_b4_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_idP3d53ef_t2_l2_b2_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 1 output grid_width15_height15
object(output1_idPfe7a8k_t14_l14_b14_r14_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idPfe7a8k_t12_l12_b12_r12_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idPfe7a8k_t10_l10_b10_r10_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idPfe7a8k_t8_l8_b8_r8_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idP3d53ef_t6_l6_b6_r6_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idP3d53ef_t4_l4_b4_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idP3d53ef_t2_l2_b2_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 2 input grid_width15_height15
object(input2_idP3d53ef_t9_l9_b9_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_idP3d53ef_t5_l5_b5_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_idP3d53ef_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 2 output grid_width15_height15
object(output2_idPfe7a8k_t13_l13_b13_r13_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP3d53ef_t9_l9_b9_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP3d53ef_t5_l5_b5_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP3d53ef_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
```


Think step by step, what are the transformations across all the examples, that goes from the input to the output.
With the following example, I want you to predict what the output should be


```prolog

% Example 3 input grid_width15_height15
object(input3_idP3d53ef_t7_l7_b7_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input3_idP3d53ef_t4_l4_b4_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input3_idP3d53ef_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 3 output grid_width15_height15
PREDICT the text that starts with object(output3_
```
Repeat the previous example prolog code, with PREDICT replaced with your predictions.
There number of output objects may be different than the input objects.
The output objects may have to be sorted by coordinates or mass or some other property.

---

Based on the examples provided, it seems that the transformation is creating one or more new objects at a certain interval above the topmost object in the input set, while preserving the input objects in the output. This interval appears to be equal to the distance between the highest and lowest object in the input set.

The new objects added have id "idPfe7a8k" and are placed above the topmost input object in the grid. The top, left, bottom, and right coordinates of the new object are the same as the topmost input object's, and incremented by the difference of the top coordinates of the highest and lowest input objects.

Following this pattern, for example 3, the topmost object is at t7 and the bottommost object is at t1. The difference between these two is 6. Therefore, the new object should be at t13. 

Here's the output:

```prolog
% Example 3 output grid_width15_height15
object(output3_idPfe7a8k_t13_l13_b13_r13_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idP3d53ef_t7_l7_b7_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idP3d53ef_t4_l4_b4_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idP3d53ef_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
```

