gpt4

---

I'm doing Prolog experiments.


The x and y coordinates represent a 0-indexed grid.


```prolog
% Example 0 input grid 5cols_5rows
object(input0_color8_x1_y3_width2_height2_mass3_shapeL).
object(input0_color4_x3_y2_width2_height1_mass2_shapeRectangle).
object(input0_color3_x1_y0_width3_height2_mass4_shapeUpTack).
object(input0_color2_x0_y2_width1_height1_mass1_shapeRectangle).

% Example 0 output grid 5cols_5rows
object(output0_color8_x0_y2_width1_height1_mass1_shapeRectangle).
object(output0_color4_x1_y3_width2_height2_mass3_shapeL).
object(output0_color3_x3_y2_width2_height1_mass2_shapeRectangle).
object(output0_color2_x1_y0_width3_height2_mass4_shapeUpTack).

% Example 1 input grid 5cols_5rows
object(input1_color6_x3_y3_width2_height2_mass3_shapeL).
object(input1_color5_x0_y0_width1_height1_mass1_shapeRectangle).
object(input1_color3_x2_y0_width2_height2_mass4_shapeRectangle).
object(input1_color2_x0_y2_width1_height3_mass3_shapeRectangle).

% Example 1 output grid 5cols_5rows
object(output1_color6_x0_y2_width1_height3_mass3_shapeRectangle).
object(output1_color5_x2_y0_width2_height2_mass4_shapeRectangle).
object(output1_color3_x3_y3_width2_height2_mass3_shapeL).
object(output1_color2_x0_y0_width1_height1_mass1_shapeRectangle).

% Example 2 input grid 5cols_5rows
object(input2_color9_x2_y3_width1_height2_mass2_shapeRectangle).
object(input2_color7_x3_y0_width2_height3_mass4_shapeL).
object(input2_color4_x0_y0_width2_height2_mass4_shapeRectangle).

% Example 2 output grid 5cols_5rows
object(output2_color9_x0_y0_width2_height2_mass4_shapeRectangle).
object(output2_color7_x2_y3_width1_height2_mass2_shapeRectangle).
object(output2_color4_x3_y0_width2_height3_mass4_shapeL).
```


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 5cols_5rows
object(input3_color8_x3_y1_width2_height3_mass4_shapeUpTack).
object(input3_color5_x0_y0_width2_height2_mass4_shapeRectangle).
object(input3_color1_x0_y4_width2_height1_mass2_shapeRectangle).

% Example 3 output grid 5cols_5rows
PREDICT the lines that starts with object(output3_
```
Repeat the previous example prolog code, with the PREDICT replaced with your predictions.

---


The transformation seems to be a combination of moves, resizes, and color swaps, not necessarily preserving the shape. After studying the transformations from input to output in your examples, it seems like the following transformations have been made:

1. Objects are shifted to different positions. 
2. Width and height might swap places.
3. Mass and color stay the same.
4. Shapes are not preserved.

For instance, in example 0:

- The `object(input0_color8_x1_y3_width2_height2_mass3_shapeL)` moved from `(1,3)` to `(0,2)` and its width and height changed from `(2,2)` to `(1,1)`.
- The `object(input0_color4_x3_y2_width2_height1_mass2_shapeRectangle)` moved from `(3,2)` to `(1,3)` and its width and height changed from `(2,1)` to `(2,2)`.
- The `object(input0_color3_x1_y0_width3_height2_mass4_shapeUpTack)` moved from `(1,0)` to `(3,2)` and its width and height changed from `(3,2)` to `(2,1)`.
- The `object(input0_color2_x0_y2_width1_height1_mass1_shapeRectangle)` moved from `(0,2)` to `(1,0)` and its width and height changed from `(1,1)` to `(3,2)`.

Applying the similar transformation pattern to Example 3, we would have:

```prolog
% Example 3 input grid 5cols_5rows
object(input3_color8_x3_y1_width2_height3_mass4_shapeUpTack).
object(input3_color5_x0_y0_width2_height2_mass4_shapeRectangle).
object(input3_color1_x0_y4_width2_height1_mass2_shapeRectangle).

% Example 3 output grid 5cols_5rows
object(output3_color8_x0_y0_width2_height2_mass4_shapeRectangle).
object(output3_color5_x3_y1_width2_height3_mass4_shapeUpTack).
object(output3_color1_x0_y4_width2_height1_mass2_shapeRectangle).
```
Here are the transformations:

- The `object(input3_color8_x3_y1_width2_height3_mass4_shapeUpTack)` moved from `(3,1)` to `(0,0)` and its width and height changed from `(2,3)` to `(2,2)`.
- The `object(input3_color5_x0_y0_width2_height2_mass4_shapeRectangle)` moved from `(0,0)` to `(3,1)` and its width and height changed from `(2,2)` to `(2,3)`.
- The `object(input3_color1_x0_y4_width2_height1_mass2_shapeRectangle)` stayed the same as its position, mass, color, shape and dimensions did not change.

