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In systems without reflexivity, the transitivity (axiom 4) and euclidean (axiom 5) are applied incorrectly.
These should all obviously be true, but MOLTAP considers them false.

system K4; K K (p&q) -> K K p
system K5; K K (p&q) -> K K p
system KD4; K K (p&q) -> K K p
system KD5; K K (p&q) -> K K p

MOLTAP only considers the transitive case, so it tries to prove K K p by proving K p instead. With reflexivity that would be valid, because then K K p -> K p, but without it we need to do something else.

Note: we need K K (p&q) instead of K K p on the left of the implication, because otherwise the formulas match syntactically.

The following two formulas should both be true, since in system K4 (also S4 and S5), K1 p -> K1 K1 p.

system K4; (K1 p & K1 K2 p) -> K1 K{1,2} p
system K4; (K1 p & K1 K2 p) -> K1 (K1 p & K2 p)

But MOLTAP incorrectly claims that the first is false. The produced counterexample is (obviously) incorrect.

This is caused by tabLocalUpIf, which only moves up in the tree if the agent set matches exactly, and 1 does not equal {1,2}, so the axiom is not applied. The correct solution would be to split into two worlds as is done in the second formula.