Disambiguation of a sentence

Solution 1:

(1) tells me that there is a student who attended every lecture. The use of “a ...” suggests “one and only one” or may just mean “any one of many”. Hence the ambiguity, which may only be resolved by logical argument or convention.

(2) is similar. “There was a student present” is open to ambiguity, depending too much on the logical abilities of the reader to resolve it.

Can I do any better? It’s not easy because so much depends on the readers’ thinking habits and on their logical training.

Let’s try “One or more students attended each lecture” and see what other site members think. I suggest that “one or more” overcomes the ambiguity that may be read in by “a”.