Thanks for confirming that it is just a smart brute force, erveryone! 

The algorithm is not implemented.

Best regards,
Marlo Bruder
On Tuesday, September 30, 2025 at 10:26:38 PM UTC+2 [email protected] 
wrote:

> > My understanding is that it really is just a smart brute force: the 
> worst-case time complexity is something like O((# of theorems) × (# of 
> preceding steps) ^ (# of hypotheses per theorem)). That's why 4syl is 
> discouraged, since both its hypotheses and conclusion are very broad and 
> can potentially match many different steps. In my experience with 
> metamath-lamp's unifier, it tends to time out on theorems like syl333anc 
> with loads of hypotheses, since there are simply too many possibilities for 
> matching.
>
> Yes, that’s correct, in metamath-lamp it is just a smart brute force. I 
> need to check, but I feel like the inability to unify syl333anc and similar 
> assertions in some cases is not the browser limitation, it is rather not 
> enough optimized implementation.
>
> Maybe this will be useful:
>
>    1. In this comment 
>    <https://github.com/expln/metamath-lamp/issues/77#issuecomment-1577804381> 
>    Mario summarized his implementation of the unification algorithm in MM1.
>    2. This comment 
>    <https://github.com/expln/metamath-lamp/issues/77#issuecomment-1608487072> 
>    contains a few interesting examples of unification.
>
>
> -
> Igor
>
>

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