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_width14_height14
object(input1_idPz7ea0g_t1_l1_b14_r14_w14_h14_mass52_shapeUnclassified_scaleUnknown, transform(all)).
object(input1_idPj8kdf4_t1_l6_b4_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(input1_idP33ffe7_t7_l2_b8_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input1_idPfe7a8k_t2_l2_b3_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input1_idP3d53ef_t12_l2_b13_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).

% Example 1 output grid_width14_height14
object(output1_idPz7ea0g_t1_l1_b14_r14_w14_h14_mass52_shapeUnclassified_scaleUnknown, transform(all)).
object(output1_idP33ffe7_t6_l11_b9_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(output1_idP33ffe7_t6_l6_b9_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(output1_idP33ffe7_t6_l1_b9_r4_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(output1_idPfe7a8k_t1_l11_b4_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(output1_idPfe7a8k_t1_l6_b4_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(output1_idPfe7a8k_t1_l1_b4_r4_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(output1_idP3d53ef_t11_l11_b14_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(output1_idP3d53ef_t11_l6_b14_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).
object(output1_idP3d53ef_t11_l1_b14_r4_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(flip270)).

% Example 2 input grid_width19_height19
object(input2_idPz7ea0g_t12_l2_b13_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input2_idP48kmo7_t17_l9_b17_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_idP48kmo7_t17_l6_b19_r8_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(input2_idP989a7f_t2_l2_b3_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input2_idP33ffe7_t1_l1_b19_r19_w19_h19_mass105_shapeUnclassified_scaleUnknown, transform(all)).
object(input2_idPfe7a8k_t7_l2_b8_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input2_idP3d53ef_t17_l2_b18_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).

% Example 2 output grid_width19_height19
object(output2_idPz7ea0g_t12_l19_b12_r19_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPz7ea0g_t12_l16_b14_r18_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idPz7ea0g_t12_l14_b12_r14_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPz7ea0g_t12_l11_b14_r13_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idPz7ea0g_t12_l9_b12_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPz7ea0g_t12_l6_b14_r8_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idPz7ea0g_t12_l4_b12_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPz7ea0g_t12_l1_b14_r3_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP989a7f_t2_l19_b2_r19_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP989a7f_t2_l16_b4_r18_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP989a7f_t2_l14_b2_r14_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP989a7f_t2_l11_b4_r13_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP989a7f_t2_l9_b2_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP989a7f_t2_l6_b4_r8_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP989a7f_t2_l4_b2_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP989a7f_t2_l1_b4_r3_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP33ffe7_t1_l1_b19_r19_w19_h19_mass105_shapeUnclassified_scaleUnknown, transform(all)).
object(output2_idPfe7a8k_t7_l19_b7_r19_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPfe7a8k_t7_l16_b9_r18_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idPfe7a8k_t7_l14_b7_r14_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPfe7a8k_t7_l11_b9_r13_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idPfe7a8k_t7_l9_b7_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPfe7a8k_t7_l6_b9_r8_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idPfe7a8k_t7_l4_b7_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idPfe7a8k_t7_l1_b9_r3_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP3d53ef_t17_l19_b17_r19_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP3d53ef_t17_l16_b19_r18_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP3d53ef_t17_l14_b17_r14_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP3d53ef_t17_l11_b19_r13_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP3d53ef_t17_l9_b17_r9_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP3d53ef_t17_l6_b19_r8_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
object(output2_idP3d53ef_t17_l4_b17_r4_w1_h1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_idP3d53ef_t17_l1_b19_r3_w3_h3_mass5_shapeLowerLeftTriangleWithoutCorner_scalex1_scaley1, transform(rot180_flip270)).
```


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_width24_height24
object(input3_idP847fa3_t22_l2_b23_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_idP48kmo7_t17_l2_b18_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_idPj8kdf4_t1_l1_b24_r24_w24_h24_mass176_shapeUnclassified_scaleUnknown, transform(all)).
object(input3_idP989a7f_t12_l2_b13_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_idP33ffe7_t7_l2_b8_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_idPfe7a8k_t2_l2_b3_r3_w2_h2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_idP3d53ef_t6_l11_b9_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).

% Example 3 output grid_width24_height24
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.

---

Analyzing the transformation between input and output in the examples you've given, I observed that the transformation is based on the flipping and shifting of the objects. Here is what I've understood:

1. The 'idPz7ea0g' object remains the same in both input and output.
2. The other objects are flip270 transformed and positioned multiple times on the grid. The width and height remain constant, but their positions change.
3. It seems each object is duplicated based on the width of 'idPz7ea0g' object (which acts like a kind of grid within the grid). The positions (Top-Left Bottom-Right) are changed in such a way that the objects are evenly distributed within the 'idPz7ea0g' object.
4. As we can see in Example 2, the positioning of the objects also takes into account the object's dimensions, so it's not overlapping with others.

Applying these rules to the third example, the output would be:

```prolog
% Example 3 output grid_width24_height24
object(output3_idPj8kdf4_t1_l1_b24_r24_w24_h24_mass176_shapeUnclassified_scaleUnknown, transform(all)).
object(output3_idP847fa3_t21_l11_b24_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP847fa3_t21_l6_b24_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP847fa3_t21_l1_b24_r4_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP48kmo7_t16_l11_b19_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP48kmo7_t16_l6_b19_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP48kmo7_t16_l1_b19_r4_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP989a7f_t11_l11_b14_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP989a7f_t11_l6_b14_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP989a7f_t11_l1_b14_r4_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP33ffe7_t6_l11_b9_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP33ffe7_t6_l6_b9_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idP33ffe7_t6_l1_b9_r4_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idPfe7a8k_t1_l11_b4_r14_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idPfe7a8k_t1_l6_b4_r9_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
object(output3_idPfe7a8k_t1_l1_b4_r4_w4_h4_mass8_shapeUnclassified_scalex1_scaley1, transform(rot180_flip270)).
```

I've made these predictions based on the pattern identified from the previous examples, and assuming that these transformations will follow the same pattern in the new example.

