Check if string is substring in Prolog

It is not clear what you mean by a string. But since you say you are converting it to a list, you could mean atoms. ISO Prolog offers atom_concat/3 and sub_atom/5 for this purpose.

| ?- atom_concat(X,Y,'abc').
  X = '', Y = abc
; X = a, Y = bc
; X = ab, Y = c
; X = abc, Y = ''.

| ?- sub_atom('abcbcbe',Before,Length,After,'bcb').
  Before = 1, Length = 3, After = 3
; Before = 3, Length = 3, After = 1.

Otherwise, use DCGs! Here's how

seq([]) --> [].
seq([E|Es]) --> [E], seq(Es).

... --> [] | [_], ... .

subseq([]) --> [].
subseq(Es) --> [_], subseq(Es).
subseq([E|Es]) --> [E], subseq(Es).

seq_substring(S, Sub) :-
   phrase((...,seq(Sub),...),S).

seq_subseq(S, Sub) :-
   phrase(subseq(Sub),S).

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Acknowledgements

The first appearance of above definition of ... is on p. 205, Note 1 of

David B. Searls, Investigating the Linguistics of DNA with Definite Clause Grammars. NACLP 1989, Volume 1.