$ pl
Welcome to SWI-Prolog (Multi-threaded, Version 5.6.24)
Copyright (c) 1990-2006 University of Amsterdam.
SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
and you are welcome to redistribute it under certain conditions.
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For help, use ?- help(Topic). or ?- apropos(Word).

?- ['crypto.pro'].
%  combosets.pro compiled 0.00 sec, 7,448 bytes
% crypto.pro compiled 0.01 sec, 10,496 bytes

Yes
?- crypto(2,2,4,Solution).

Solution = ex(2, +, 2) ;

Solution = ex(2, *, 2) ;

No
?- crypto(2,2,2,2,Solution).

Solution = ex(2, -, ex(2, +, 2)) ;

Solution = ex(2, /, ex(2, +, 2)) ;

Solution = ex(2, -, ex(2, *, 2)) ;

Solution = ex(2, /, ex(2, *, 2)) ;

Solution = ex(2, +, ex(2, -, 2)) ;

Solution = ex(2, -, ex(2, -, 2)) ;

Solution = ex(2, +, ex(2, -, 2)) ;

Solution = ex(2, -, ex(2, -, 2)) ;

Solution = ex(2, *, ex(2, /, 2)) ;

Solution = ex(2, /, ex(2, /, 2)) ;

Solution = ex(2, *, ex(2, /, 2)) ;

Solution = ex(2, /, ex(2, /, 2)) ;

Solution = ex(2, -, ex(2, +, 2)) ;

Solution = ex(2, /, ex(2, +, 2)) ;

Solution = ex(2, -, ex(2, *, 2)) 

Yes
?- crypto(2,2,2,2,2,Solution).

Solution = ex(2, +, ex(2, *, ex(2, -, 2))) ;

Solution = ex(2, -, ex(2, *, ex(2, -, 2))) ;

Solution = ex(2, +, ex(2, /, ex(2, -, 2))) ;

Solution = ex(2, -, ex(2, /, ex(2, -, 2))) ;

Solution = ex(2, +, ex(2, *, ex(2, -, 2))) ;

Solution = ex(2, -, ex(2, *, ex(2, -, 2))) ;

Solution = ex(2, +, ex(2, /, ex(2, -, 2))) ;

Solution = ex(2, -, ex(2, /, ex(2, -, 2))) ;

Solution = ex(2, +, ex(2, *, ex(2, -, 2))) ;

Solution = ex(2, -, ex(2, *, ex(2, -, 2))) ;

Solution = ex(2, +, ex(2, /, ex(2, -, 2))) ;

Solution = ex(2, -, ex(2, /, ex(2, -, 2))) ;

Solution = ex(2, +, ex(2, *, ex(2, -, 2))) 

Yes
?-