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_width16_height16
object(input1_idP33ffe7_t11_l4_b11_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input1_idP33ffe7_t5_l12_b5_r12_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 1 output grid_width16_height16
object(output1_idPz7ea0g_t13_l2_b13_r6_w5_h1_mass5_shapeRectangle_scalex5_scaley1, transform(all)).
object(output1_idPz7ea0g_t7_l10_b7_r14_w5_h1_mass5_shapeRectangle_scalex5_scaley1, transform(all)).
object(output1_idPj8kdf4_t9_l2_b10_r6_w5_h2_mass6_shapeUpTack_scaleUnknown, transform(rot180_flip180)).
object(output1_idPj8kdf4_t3_l10_b4_r14_w5_h2_mass6_shapeUpTack_scaleUnknown, transform(rot180_flip180)).
object(output1_idP33ffe7_t11_l4_b11_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idP33ffe7_t5_l12_b5_r12_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idPfe7a8k_t13_l7_b13_r16_w10_h1_mass10_shapeRectangle_scalex10_scaley1, transform(all)).
object(output1_idPfe7a8k_t13_l1_b13_r1_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output1_idPfe7a8k_t10_l6_b12_r6_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output1_idPfe7a8k_t10_l2_b12_r2_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output1_idPfe7a8k_t7_l15_b7_r16_w2_h1_mass2_shapeRectangle_scalex2_scaley1, transform(all)).
object(output1_idPfe7a8k_t7_l1_b7_r9_w9_h1_mass9_shapeRectangle_scalex9_scaley1, transform(all)).
object(output1_idPfe7a8k_t4_l14_b6_r14_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output1_idPfe7a8k_t4_l10_b6_r10_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).

% Example 2 input grid_width10_height10
object(input2_idP33ffe7_t5_l5_b5_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 2 output grid_width10_height10
object(output2_idPz7ea0g_t7_l3_b7_r7_w5_h1_mass5_shapeRectangle_scalex5_scaley1, transform(all)).
object(output2_idPj8kdf4_t3_l3_b4_r7_w5_h2_mass6_shapeUpTack_scaleUnknown, transform(rot180_flip180)).
object(output2_idP33ffe7_t5_l5_b5_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPfe7a8k_t7_l8_b7_r10_w3_h1_mass3_shapeRectangle_scalex3_scaley1, transform(all)).
object(output2_idPfe7a8k_t7_l1_b7_r2_w2_h1_mass2_shapeRectangle_scalex2_scaley1, transform(all)).
object(output2_idPfe7a8k_t4_l7_b6_r7_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output2_idPfe7a8k_t4_l3_b6_r3_w1_h3_mass3_shapeRectangle_scalex1_scaley3, 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_width19_height17
object(input3_idP33ffe7_t14_l7_b14_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input3_idP33ffe7_t9_l12_b9_r12_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input3_idP33ffe7_t4_l5_b4_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).

% Example 3 output grid_width19_height17
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.

---

Given the transformations applied in the previous examples, we can derive a set of rules:

1. Each input object `idP33ffe7` with shape `Rectangle` remains unchanged in the output. 

2. For each input object `idP33ffe7` with shape `Rectangle`, create an object `idPz7ea0g` with shape `Rectangle` two grid spaces above it. The width (`w`) is increased to 5 and the mass to 5, but the height (`h`) remains 1.

3. Create an object `idPj8kdf4` with shape `UpTack` and a transformation `rot180_flip180` which spans two units above the `idPz7ea0g` object. It has a width of 5, height of 2 and mass of 6.

4. For each input object `idP33ffe7` with shape `Rectangle`, create an object `idPfe7a8k` with shape `Rectangle` two grid spaces below it. The width is equivalent to the width of the grid minus the x-coordinate of the object, and the mass is equivalent to the width. The height remains 1.

5. For each input object `idP33ffe7` with shape `Rectangle`, create another object `idPfe7a8k` with shape `Rectangle` with the same height and x-coordinate as the input object. The width is set to 1 and the mass is equal to the height.

6. Similarly, create another object `idPfe7a8k` with shape `Rectangle` with the same height and mass as in rule 5. The x-coordinate should be two grid spaces left of the input object.

Using these rules, the predicted output for example 3 will be:

```prolog
% Example 3 output grid_width19_height17
object(output3_idPz7ea0g_t12_l7_b12_r11_w5_h1_mass5_shapeRectangle_scalex5_scaley1, transform(all)).
object(output3_idPj8kdf4_t8_l7_b10_r11_w5_h2_mass6_shapeUpTack_scaleUnknown, transform(rot180_flip180)).
object(output3_idP33ffe7_t14_l7_b14_r7_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idPfe7a8k_t16_l7_b16_r19_w13_h1_mass13_shapeRectangle_scalex13_scaley1, transform(all)).
object(output3_idPfe7a8k_t14_l7_b16_r7_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output3_idPfe7a8k_t14_l5_b16_r5_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).

object(output3_idPz7ea0g_t7_l12_b7_r16_w5_h1_mass5_shapeRectangle_scalex5_scaley1, transform(all)).
object(output3_idPj8kdf4_t3_l12_b5_r16_w5_h2_mass6_shapeUpTack_scaleUnknown, transform(rot180_flip180)).
object(output3_idP33ffe7_t9_l12_b9_r12_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idPfe7a8k_t11_l12_b11_r19_w8_h1_mass8_shapeRectangle_scalex8_scaley1, transform(all)).
object(output3_idPfe7a8k_t9_l12_b11_r12_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output3_idPfe7a8k_t9_l10_b11_r10_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).

object(output3_idPz7ea0g_t2_l5_b2_r9_w5_h1_mass5_shapeRectangle_scalex5_scaley1, transform(all)).
object(output3_idPj8kdf4_t-2_l5_b0_r9_w5_h2_mass6_shapeUpTack_scaleUnknown, transform(rot180_flip180)).
object(output3_idP33ffe7_t4_l5_b4_r5_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output3_idPfe7a8k_t6_l5_b6_r19_w15_h1_mass15_shapeRectangle_scalex15_scaley1, transform(all)).
object(output3_idPfe7a8k_t4_l5_b6_r5_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output3_idPfe7a8k_t4_l3_b6_r3_w1_h3_mass3_shapeRectangle_scalex1_scaley3, transform(all)).
```
The order of the output is based on the y-coordinate, from the highest to the lowest.


