This is the problem (formulated in my Popper example equation)

It's the infamous equation.

11x11=4 
22x22=16 
33x33=?

One of the intended solutions is that X=36:

  f(a,b,c,d,X)  
  (a+a)*(a+a)

i.e
  (1+1)*(1+1) = 2*2=4
  (2+2)*(2+2) = 4*4=16
  (3+3)*(3+3) = 6*6=36)

There are different interpretations, see for example
* https://mindyourdecisions.com/blog/2016/09/21/viral-puzzle-11x11-4-the-correct-answer-explained/
* http://hakank.org/picat/symbolic_regression.pi
  The comments for data(infamous_equation,...)


hakank:
'''
pos(f(1,1,1,1,4)).
pos(f(2,2,2,2,16)).
neg(f(1,1,1,1,2)).
'''

GPT4:
'''
Based on the given examples, it seems that the pattern is related to raising a number to the power of 4. For the positive examples:

pos(f(1,1,1,1,4)): 1^4 = 111*1 = 4
pos(f(2,2,2,2,16)): 2^4 = 222*2 = 16
For the negative example:

neg(f(1,1,1,1,2)): 1^4 = 111*1 = 4, which is not equal to 2, so it is a negative example.



hakank:
'''
What would then X be in 
pos(f(3,3,3,3,X))
'''

GPT4:
'''
For the given example:

pos(f(3,3,3,3,X)): 3^4 = 333*3 = 81

So, X would be 81.
'''

So I tried to make GPT4 figure this out:

hakank:
'''
Hmm, the intended solution for X is 36. Can you think of another pattern
that works with this?
'''

GPT4:
'''
I see. Considering the new information, the pattern seems to be as follows:

f(A, B, C, D, X) :- X = (A * B) + (C * D)

For the given example:

pos(f(3,3,3,3,X)): (33) + (33) = 9 + 9 = 18

I previously made a mistake in my response. The correct value for X in this case is 18, not 36. Apologies for the confusion.
'''


hakank.
'''
You are on the right track. Please have another go.
'''

GPT4:
'''
Thank you for your patience. Given the new information, let's try another pattern:

f(A, B, C, D, X) :- X = A * (B + C) * D

For the given example:

pos(f(3,3,3,3,X)): 3 * (3 + 3) * 3 = 3 * 6 * 3 = 54

So, the correct value for X in this case is 54.
'''

hakank:
'''
But X should be 36, remember?
'''

GPT4:
'''
I apologize for the confusion. Let's attempt another pattern:

f(A, B, C, D, X) :- X = A * B * C - D

For the given example:

pos(f(3, 3, 3, 3, X)): 3 * 3 * 3 - 3 = 27 - 3 = 24

My previous response contained an error, and upon reevaluation, the correct value for X in this case should be 24, not 36.
'''

hakank:
'''
No, please try again.
'''

GPT4:
'''
I apologize for my previous attempts. Let's try another pattern:

f(A, B, C, D, X) :- X = (A * B * C) / D

For the given example:

pos(f(3, 3, 3, 3, X)): (3 * 3 * 3) / 3 = 27 / 3 = 9

However, this pattern results in X being 9, not 36 as required. I will continue searching for a correct pattern.
'''

Here - and above - GPT4 don't seems to "think" about the problem before
it writes the answer, but "thinks" along as it writes the answer (think as
it speaks).

Sometimes it realizes that it's an incorrect solution, sometimes it don't...
We had some round of errouneous tries and I gave it a last chance:

hakank.
'''
Still not the intended solution. Do you want a hint or perhaps do you want to try again?
'''

GPT4:
I would appreciate a hint to help me find the correct pattern. Thank you.
'''

hakank:
'''
It's two additions and one multiplication.
'''

GPT4:
'''
I see. Based on the hint, the pattern could be as follows:

f(A, B, C, D, E) is true if E = (A + B) * (C + D).

With this pattern:
pos(f(1, 1, 1, 1, 4)).
pos(f(2, 2, 2, 2, 16)).
pos(f(3, 3, 3, 3, 36)).

'''

And I would say it's a hit (with some help).