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 `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_width15_height13
object(input1_idPz7ea0g_t2_l3_b9_r10_w8_h8_mass56_shapeUnclassified_scaleUnknown, transform(rot0_rot180_flip90_flip270)).
object(input1_idP33ffe7_t7_l8_b8_r9_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input1_idPfe7a8k_t3_l4_b4_r5_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).

% Example 1 output grid_width2_height2
object(output1_idP33ffe7_t2_l2_b2_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idPfe7a8k_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 2 input grid_width15_height16
object(input2_idPz7ea0g_t3_l2_b12_r14_w13_h10_mass118_shapeUnclassified_scaleUnknown, transform(rot0_flip90)).
object(input2_idP33ffe7_t5_l9_b6_r10_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input2_idPfe7a8k_t8_l9_b9_r10_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input2_idP3d53ef_t5_l4_b6_r5_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).

% Example 2 output grid_width2_height2
object(output2_idP33ffe7_t1_l2_b1_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPfe7a8k_t2_l2_b2_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP3d53ef_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 3 input grid_width16_height14
object(input3_idPz7ea0g_t2_l2_b13_r10_w9_h12_mass96_shapeUnclassified_scaleUnknown, transform(rot90_flip)).
object(input3_idPj8kdf4_t4_l3_b5_r4_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_idP989a7f_t4_l7_b5_r8_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_idP33ffe7_t9_l3_b10_r4_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).

% Example 3 output grid_width2_height2
object(output3_idPj8kdf4_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idP989a7f_t1_l2_b1_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idP33ffe7_t2_l1_b2_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
```
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.


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_width15_height14
object(input4_idPz7ea0g_t4_l3_b13_r14_w12_h10_mass104_shapeBoxWith2x2Holes_scaleUnknown, transform(all)).
object(input4_idP48kmo7_t7_l11_b8_r12_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input4_idP33ffe7_t11_l11_b12_r12_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input4_idPfe7a8k_t7_l5_b8_r6_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input4_idP3d53ef_t11_l5_b12_r6_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).

% Example 4 output grid_width2_height2
PREDICT the text that starts with object(output4_
```
Repeat the previous example prolog code, with PREDICT replaced with your predictions.

---

Based on the given examples, it seems like the transformation process reduces the size of all objects to 1x1 (width=1, height=1), places them at their relative positions within a 2x2 grid, and also reduces their mass to 1.

The transformation process also appears to discard the objects prefixed with "idPz", as those objects are not present in the output.

Given these observations, the output for the Example 4 would look like this:

```prolog
% Example 4 input grid_width15_height14
object(input4_idPz7ea0g_t4_l3_b13_r14_w12_h10_mass104_shapeBoxWith2x2Holes_scaleUnknown, transform(all)).
object(input4_idP48kmo7_t7_l11_b8_r12_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input4_idP33ffe7_t11_l11_b12_r12_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input4_idPfe7a8k_t7_l5_b8_r6_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input4_idP3d53ef_t11_l5_b12_r6_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).

% Example 4 output grid_width2_height2
object(output4_idP48kmo7_t1_l2_b1_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output4_idP33ffe7_t2_l2_b2_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output4_idPfe7a8k_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output4_idP3d53ef_t2_l1_b2_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
```

Please note that I preserved the relative positions of the objects on a smaller 2x2 grid, transformed their sizes and mass to 1, and disregarded the object prefixed with "idPz". The order of the objects in the output is maintained based on their positions (top-bottom, left-right).

