I notice that queries using values like
SELECT ?item ?item2 ?inv WHERE {
VALUES ?collection {wd:Q28045665 wd:Q28045660 wd:Q28045674 wd:Q2066737 wd:Q18600731 } . # The different collections
?item p:P217 ?inv1statement .
?inv1statement ps:P217 ?inv .
?inv1statement pq:P195 ?collection .
?item2 p:P217 ?inv2statement .
?inv2statement ps:P217 ?inv .
?inv2statement pq:P195 ?collection .
FILTER(?item!=?item2)
} LIMIT 500often time out.
if you unpack it in a bunch of unions it completes in less than a second:
SELECT ?item ?item2 ?inv WHERE {
{ ?inv1statement pq:P195 wd:Q28045665 . } union
{ ?inv1statement pq:P195 wd:Q28045660 . } union
{ ?inv1statement pq:P195 wd:Q28045674 . } union
{ ?inv1statement pq:P195 wd:Q2066737 . } union
{ ?inv1statement pq:P195 wd:Q18600731 . }
?item p:P217 ?inv1statement .
?inv1statement ps:P217 ?inv .
{ ?inv2statement pq:P195 wd:Q28045665 . } union
{ ?inv2tatement pq:P195 wd:Q28045660 . } union
{ ?inv2statement pq:P195 wd:Q28045674 . } union
{ ?inv2statement pq:P195 wd:Q2066737 . } union
{ ?inv2statement pq:P195 wd:Q18600731 . }
?item2 p:P217 ?inv2statement .
?inv2statement ps:P217 ?inv .
FILTER(?item!=?item2)
} LIMIT 500