gpt4

---

I'm doing Prolog experiments.


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


```prolog
% Example 0 input grid 12cols_11rows
object(input0_color4_x9_y8_width3_height3_mass9_shapeRectangle_scalex3_scaley3, transform(all)).
object(input0_color4_x3_y8_width4_height3_mass12_shapeRectangle_scalex4_scaley3, transform(all)).
object(input0_color4_x3_y1_width4_height3_mass12_shapeRectangle_scalex4_scaley3, transform(all)).
object(input0_color2_x0_y6_width12_height1_mass12_shapeRectangle_scalex12_scaley1, transform(all)).

% Example 0 output grid 12cols_11rows
object(output0_color4_x3_y1_width4_height3_mass12_shapeRectangle_scalex4_scaley3, transform(all)).
object(output0_color2_x0_y6_width12_height1_mass12_shapeRectangle_scalex12_scaley1, transform(all)).

% Example 1 input grid 16cols_10rows
object(input1_color6_x6_y7_width2_height3_mass6_shapeRectangle_scalex2_scaley3, transform(all)).
object(input1_color6_x2_y7_width2_height3_mass6_shapeRectangle_scalex2_scaley3, transform(all)).
object(input1_color6_x10_y3_width4_height5_mass20_shapeRectangle_scalex4_scaley5, transform(all)).
object(input1_color6_x2_y3_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(input1_color6_x14_y0_width2_height2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input1_color6_x9_y0_width4_height2_mass8_shapeRectangle_scalex4_scaley2, transform(all)).
object(input1_color6_x3_y0_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(input1_color3_x0_y2_width16_height1_mass16_shapeRectangle_scalex16_scaley1, transform(all)).

% Example 1 output grid 16cols_10rows
object(output1_color6_x14_y0_width2_height2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(output1_color6_x9_y0_width4_height2_mass8_shapeRectangle_scalex4_scaley2, transform(all)).
object(output1_color6_x3_y0_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(output1_color3_x0_y2_width16_height1_mass16_shapeRectangle_scalex16_scaley1, transform(all)).

% Example 2 input grid 16cols_9rows
object(input2_color8_x14_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color8_x12_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color8_x10_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color8_x8_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color8_x6_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color8_x4_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color8_x2_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color8_x0_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(input2_color1_x9_y4_width3_height3_mass9_shapeRectangle_scalex3_scaley3, transform(all)).
object(input2_color1_x3_y4_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(input2_color1_x0_y4_width2_height3_mass6_shapeRectangle_scalex2_scaley3, transform(all)).
object(input2_color1_x7_y1_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(input2_color1_x12_y0_width2_height2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input2_color1_x2_y0_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).

% Example 2 output grid 16cols_9rows
object(output2_color8_x14_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color8_x12_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color8_x10_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color8_x8_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color8_x6_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color8_x4_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color8_x2_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color8_x0_y3_width1_height1_mass1_shapeRectangle_scalex1_scaley1, transform(all)).
object(output2_color1_x7_y1_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(output2_color1_x12_y0_width2_height2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(output2_color1_x2_y0_width3_height2_mass6_shapeRectangle_scalex3_scaley2, 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 10cols_14rows
object(input3_color6_x1_y11_width4_height3_mass12_shapeRectangle_scalex4_scaley3, transform(all)).
object(input3_color6_x6_y6_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(input3_color6_x1_y6_width3_height3_mass9_shapeRectangle_scalex3_scaley3, transform(all)).
object(input3_color6_x9_y0_width1_height2_mass2_shapeRectangle_scalex1_scaley2, transform(all)).
object(input3_color6_x5_y0_width3_height3_mass9_shapeRectangle_scalex3_scaley3, transform(all)).
object(input3_color6_x1_y0_width2_height2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_color4_x0_y3_width10_height1_mass10_shapeRectangle_scalex10_scaley1, transform(all)).

% Example 3 output grid 10cols_14rows
PREDICT the lines that starts with object(output3_
```
Repeat the previous example prolog code, with the PREDICT replaced with your predictions.

---

Based on the patterns I see from examples 0 to 2, it seems the transformation removes rectangles with a mass greater than the width multiplied by height (or in other words, the area). For example, in example 0, the rectangle with mass 9 and area (width * height) 3*3=9 was removed, while rectangles with equal or lesser mass were retained. 

Applying this rule to example 3, we would remove the objects with mass 12 and mass 9 and retain the rest. Therefore, the output would be as follows:

```prolog
% Example 3 input grid 10cols_14rows
object(input3_color6_x1_y11_width4_height3_mass12_shapeRectangle_scalex4_scaley3, transform(all)).
object(input3_color6_x6_y6_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(input3_color6_x1_y6_width3_height3_mass9_shapeRectangle_scalex3_scaley3, transform(all)).
object(input3_color6_x9_y0_width1_height2_mass2_shapeRectangle_scalex1_scaley2, transform(all)).
object(input3_color6_x5_y0_width3_height3_mass9_shapeRectangle_scalex3_scaley3, transform(all)).
object(input3_color6_x1_y0_width2_height2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(input3_color4_x0_y3_width10_height1_mass10_shapeRectangle_scalex10_scaley1, transform(all)).

% Example 3 output grid 10cols_14rows
object(output3_color6_x6_y6_width3_height2_mass6_shapeRectangle_scalex3_scaley2, transform(all)).
object(output3_color6_x9_y0_width1_height2_mass2_shapeRectangle_scalex1_scaley2, transform(all)).
object(output3_color6_x1_y0_width2_height2_mass4_shapeRectangle_scalex2_scaley2, transform(all)).
object(output3_color4_x0_y3_width10_height1_mass10_shapeRectangle_scalex10_scaley1, transform(all)).
```

---

One of the objects is below the dividing line.

