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_width12_height12
object(input1_idPz7ea0g_t5_l11_b5_r11_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_idPz7ea0g_t3_l9_b4_r10_w2_h2_mass3_shapeL_scalex1_scaley1, transform(rot90_flip)).
object(input1_idP33ffe7_t5_l2_b5_r2_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_idP33ffe7_t2_l3_b4_r5_w3_h3_mass7_shapeL_scaleUnknown, transform(rot0_flip90)).
object(input1_idPfe7a8k_t7_l4_b9_r7_w4_h3_mass7_shapeUnclassified_scalex1_scaley1, transform(flip180)).

% Example 1 output grid_width1_height3
object(output1_idPz7ea0g_t3_l1_b3_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idP33ffe7_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idPfe7a8k_t2_l1_b2_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 2 input grid_width12_height12
object(input2_idP847fa3_t9_l9_b11_r11_w3_h3_mass6_shapeUnclassified_scalex1_scaley1, transform(rot90)).
object(input2_idPfe7a8k_t8_l3_b10_r4_w2_h3_mass4_shapeUpTack_scalex1_scaley1, transform(rot90_flip270)).
object(input2_idP3d53ef_t5_l9_b5_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_idP3d53ef_t2_l11_b2_r11_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_idP3d53ef_t2_l8_b4_r11_w4_h3_mass7_shapeLowerLeftTriangleWithoutCorner_scaleUnknown, transform(rot0_flip90)).

% Example 2 output grid_width1_height3
object(output2_idP847fa3_t2_l1_b2_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPfe7a8k_t3_l1_b3_r1_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_width12_height12
object(input3_idP989a7f_t8_l4_b11_r8_w5_h4_mass14_shapeLeftPlus_scaleUnknown, transform(flip)).
object(input3_idPfe7a8k_t2_l2_b4_r5_w4_h3_mass7_shapeUnclassified_scalex1_scaley1, transform(flip)).
object(input3_idP3d53ef_t3_l9_b5_r10_w2_h3_mass5_shapeL_scaleUnknown, transform(rot0_flip90)).

% Example 3 output grid_width1_height3
object(output3_idP989a7f_t1_l1_b1_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idPfe7a8k_t2_l1_b2_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idP3d53ef_t3_l1_b3_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 4 input grid_width12_height12
object(input4_idP48kmo7_t11_l6_b11_r6_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_idP48kmo7_t9_l7_b12_r9_w3_h4_mass6_shapeUnclassified_scalex1_scaley1, transform(rot90_rot270)).
object(input4_idP33ffe7_t2_l2_b3_r3_w2_h2_mass3_shapeL_scalex1_scaley1, transform(rot90_flip)).
object(input4_idP3d53ef_t6_l4_b7_r6_w3_h2_mass5_shapeL_scaleUnknown, transform(rot90_flip)).

% Example 4 output grid_width1_height3
PREDICT the text that starts with object(output4_
```
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.

---

From the examples given, it appears the transformation from input to output operates as follows:

1. Each object in the input, regardless of its original shape, mass, and transformation properties, is reduced to a 1x1 rectangle in the output.

2. The mass of each object in the output is always 1, irrespective of the mass of the input object.

3. The transformation applied to the output objects is always "all".

4. The bounding coordinates of the output objects are restructured such that the top, left, bottom, and right parameters describe a 1x1 rectangle. 

5. The ordering of the objects in the output seems to be determined by the top coordinate (t), from the lowest to the highest.

Given these rules, the predicted output for Example 4 should be as follows:

```prolog
% Example 4 input grid_width12_height12
object(input4_idP48kmo7_t11_l6_b11_r6_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input4_idP48kmo7_t9_l7_b12_r9_w3_h4_mass6_shapeUnclassified_scalex1_scaley1, transform(rot90_rot270)).
object(input4_idP33ffe7_t2_l2_b3_r3_w2_h2_mass3_shapeL_scalex1_scaley1, transform(rot90_flip)).
object(input4_idP3d53ef_t6_l4_b7_r6_w3_h2_mass5_shapeL_scaleUnknown, transform(rot90_flip)).

% Example 4 output grid_width1_height3
object(output4_idP33ffe7_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)).
object(output4_idP48kmo7_t3_l1_b3_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
```

Note: Even though there are two objects with the id "idP48kmo7" in the input, only one of them is represented in the output. The one with the lower 't' value is represented following the sorting rule.

