I am not providing the hands or the actual auction, because the bidding was silly and the result absurd. Suffice it to say that the opponents ended up in 6NT doubled, missing three Aces.
However, the problem was intriguing. I'll give the patterns:
Assuming that Opener is strong enough to open a strong forcing 2♣ (standard), how is this pattern resolved (also assuming that Responder's majors are too weak to positive)?
This is not all that difficult if 2♣ tends to deny a four-card spade suit and 2♦ shows a hand with four spades (strong), with my methods.
3♦(natural, no 4-card major)-P-3♥(five hearts)-P-
3♠(no heart fit, three spades)-P-4♠(or cue if stronger)
Easy. (Opener would have bid 2♠ with four hearts and a longer minor or 1-4-4-4.)
The actual problem faced by my opponents was a 4♦ overcall of 2♣. Now what?!?!?
This also is rather simple:
4♠(spade fragment)-all pass
Now, maybe 4♥ is wrong, and maybe Opener should pass 4♥. But, you see the point. If Opener has four spades, he must be balanced, where he could pass 4♥. If he bids spades, then, he must have only three of them but unbalanced.
I liked 6NTX, though.