At first I thought it's just brute forcing, but after reaching the solution it becomes obvious that the flzzrgel (rot13) of the condition simplifies the solving. Alas it's just like working on math problems. The result of an arduous calculation sometimes point to an elegant shortcut.
T216
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At this point it can still be cheesed, because e.g. the game incorrectly allows N(L,N(L,L)) to predate N(L,N(N(L,L))), where N is an inner node and L is a leaf. I think the correct inf-embedding allows for embeddings with gaps as long as the order of tree nodes is preserved, but now the game only checks for contiguous subtrees, which is strictly stronger.
The correct embedding checking should be easy to implement, but to check embedding of T into S, each branching node in T will create a possibility of permutation, together with all the backtracking, I guess will blow up the complexity?