Query plan for count based intersection

count-plan

# select ?s ?inter
# from <tag:stardog:api:context:default>
# from :entailed
# WHERE
#   { { SELECT  ?inter (COUNT(DISTINCT ?c) AS ?inter_cnt)
#       WHERE
#         { ?inter owl:intersectionOf/rdf:rest*/rdf:first ?c }
#       GROUP BY ?inter
#     }
#     { SELECT  ?s ?inter (COUNT(DISTINCT ?c) AS ?instance_cnt)
#       WHERE
#         { ?inter owl:intersectionOf/rdf:rest*/rdf:first ?c .
#           ?s  rdf:type  ?c
#         }
#       GROUP BY ?s ?inter
#     }
#     FILTER ( ?instance_cnt = ?inter_cnt )
#   }

From entailed
From default
Slice(offset=0, limit=1000) [#1.0K]
`─ Projection(?s, ?inter) [#7531.9M]
   `─ Filter(?instance_cnt = ?inter_cnt) [#7531.9M]
      `─ HashJoin(?inter) [#15063.9M]
         +─ Projection(?s, ?inter, ?instance_cnt) [#11518.7M]
         │  `─ Group(by=[?inter, ?s] aggregates=[(COUNT(DISTINCT ?c) AS ?instance_cnt)]) [#11518.7M]
         │     `─ MergeJoin(?c) [#28796.8M]
         │        +─ Scan[POSC](?s, rdf:type, ?c) [#2.2M]
         │        `─ Sort(?c) [#641K]
         │           `─ MergeJoin(?ozpgzmze) [#641K]
         │              +─ Scan[PSOC](?ozpgzmze, rdf:first, ?c) [#891K]
         │              `─ Sort(?ozpgzmze) [#853K]
         │                 `─ MergeJoin(?iielhfjt) [#853K]
         │                    +─ PropertyPath(?iielhfjt -> ?ozpgzmze, minLength=0, sortedBy=?iielhfjt) [#868K]
         │                    │  +─ Distinct [#332K]
         │                    │  │  `─ Projection(?iielhfjt) [#332K]
         │                    │  │     `─ Scan[POSC](?inter, owl:intersectionOf, ?iielhfjt) [#332K]
         │                    │  `─ Scan[PSOC](?iielhfjt, rdf:rest, ?ozpgzmze) [#891K]
         │                    `─ Scan[POSC](?inter, owl:intersectionOf, ?iielhfjt) [#332K]
         `─ Projection(?inter, ?inter_cnt) [#641K]
            `─ Group(by=[?inter] aggregates=[(COUNT(DISTINCT ?c) AS ?inter_cnt)]) [#641K]
               `─ MergeJoin(?bqvrwwep) [#641K]
                  +─ Scan[PSOC](?bqvrwwep, rdf:first, ?c) [#891K]
                  `─ Sort(?bqvrwwep) [#853K]
                     `─ MergeJoin(?hjfbpnht) [#853K]
                        +─ PropertyPath(?hjfbpnht -> ?bqvrwwep, minLength=0, sortedBy=?hjfbpnht) [#868K]
                        │  +─ Distinct [#332K]
                        │  │  `─ Projection(?hjfbpnht) [#332K]
                        │  │     `─ Scan[POSC](?inter, owl:intersectionOf, ?hjfbpnht) [#332K]
                        │  `─ Scan[PSOC](?hjfbpnht, rdf:rest, ?bqvrwwep) [#891K]
                        `─ Scan[POSC](?inter, owl:intersectionOf, ?hjfbpnht) [#332K]

minus-plan

# select ?x ?i
# from <tag:stardog:api:context:default>
# from :entailed
# where { ?i owl:intersectionOf ?l .
#         ?l rdf:rest*/rdf:first ?c .
#         ?x a ?c
#         MINUS {
#           ?l rdf:rest*/rdf:first ?d .
#           ?l rdf:rest*/rdf:first ?d2 .
#           FILTER ( ?d != ?d2 )
#           ?x a ?d MINUS { ?x a ?d2 }
#         } }

# reused
From entailed
From default
Slice(offset=0, limit=1000) [#1.0K]
`─ Projection(?x, ?i) [#28796.8M]
   `─ Minus(HashLookup) [#28796.8M]
      +─ MergeJoin(?c) [#28796.8M]
      │  +─ Scan[POSC](?x, rdf:type, ?c) [#2.2M]
      │  `─ Sort(?c) [#641K]
      │     `─ MergeJoin(?tddiphpw) [#641K]
      │        +─ Scan[PSOC](?tddiphpw, rdf:first, ?c) [#891K]
      │        `─ Sort(?tddiphpw) [#853K]
      │           `─ MergeJoin(?l) [#853K]
      │              +─ PropertyPath(?l -> ?tddiphpw, minLength=0, sortedBy=?l) [#868K]
      │              │  +─ Distinct [#332K]
      │              │  │  `─ Projection(?l) [#332K]
      │              │  │     `─ Scan[POSC](?i, owl:intersectionOf, ?l) [#332K]
      │              │  `─ Scan[POSC](?l, rdf:rest, ?tddiphpw) [#891K]
      │              `─ Scan[POSC](?i, owl:intersectionOf, ?l) [#332K]
      `─ Minus(HashLookup) [#53277.7M]
         +─ MergeJoin(?d) [#53277.7M]
         │  +─ Scan[POSC](?x, rdf:type, ?d) [#2.2M]
         │  `─ Filter(?d != ?d2) [#1.8M]
         │     `─ HashJoin(?lvdvlmvc) [#3.6M]
         │        +─ Scan[POSC](?lvdvlmvc, rdf:first, ?d) [#891K]
         │        `─ HashJoin(?l) [#3.6M]
         │           +─ MergeJoin(?gsdohjpd) [#1.8M]
         │           │  +─ PropertyPath(?l -> ?gsdohjpd, minLength=0, sortedBy=?gsdohjpd, reversed) [#2.3M]
         │           │  │  +─ Distinct [#891K]
         │           │  │  │  `─ Projection(?gsdohjpd) [#891K]
         │           │  │  │     `─ Scan[PSOC](?gsdohjpd, rdf:first, ?d2) [#891K]
         │           │  │  `─ Scan[PSOC](?l, rdf:rest, ?gsdohjpd) [#891K]
         │           │  `─ Scan[PSOC](?gsdohjpd, rdf:first, ?d2) [#891K]
         │           `─ PropertyPath(?l -> ?lvdvlmvc, minLength=0, sortedBy=?lvdvlmvc, reversed) [#2.3M]
         │              +─ Distinct [#891K]
         │              │  `─ Projection(?lvdvlmvc) [#891K]
         │              │     `─ Scan[PSOC](?lvdvlmvc, rdf:first, ?d) [#891K]
         │              `─ Scan[POSC](?l, rdf:rest, ?lvdvlmvc) [#891K]
         `─ Scan[PSOC](?x, rdf:type, ?d2) [#2.2M]