@prefix skolem: <https://eyereasoner.github.io/.well-known/genid/8b98b360-9a70-4845-b52c-c675af60ad01#>.
@prefix r: <http://www.w3.org/2000/10/swap/reason#>.
@prefix log: <http://www.w3.org/2000/10/swap/log#>.
@prefix : <http://example.org/#>.
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>.
@prefix n3: <http://www.w3.org/2004/06/rei#>.
@prefix var: <http://www.w3.org/2000/10/swap/var#>.
@prefix owl: <http://www.w3.org/2002/07/owl#>.

skolem:proof a r:Proof, r:Conjunction;
    r:component skolem:lemma1;
    r:gives [ log:graph (
        [ log:triple (:P1 rdf:type :HasCardinalityCheck)]
    )].

skolem:lemma1 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:P1 rdf:type :HasCardinalityCheck)]
    )];
    r:evidence (
        skolem:lemma2
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#P1"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 rdf:type :HasCardinalityCheck)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 rdf:type :HasCardinalityCheck)]
    )])])]].

skolem:lemma2 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:P1 rdf:type :HasCardinalityCheck)]
    )];
    r:evidence (
        skolem:lemma3
        skolem:lemma4
        skolem:lemma5
        skolem:lemma6
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple (:P1 :name var:v_12)]
        )] :cardinalCount 3)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#HasCardinalityCheck"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#name"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo [ n3:uri "http://example.org/#P1"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo "Patrick"];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo [ n3:uri "http://example.org/#cardinalCount"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_12"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 owl:onProperty var:x_1)]
        [ log:triple (var:x_0 owl:cardinality var:x_2)]
        [ log:triple (var:x_3 var:x_1 var:x_4)]
        [ log:triple (var:x_5 rdf:type log:GraphCounter)]
        [ log:triple ([ log:graph (
            [ log:triple (var:x_3 var:x_1 var:x_6)]
        )] var:x_5 var:x_2)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_3 rdf:type var:x_0)]
    )])])]].

skolem:lemma3 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:HasCardinalityCheck owl:onProperty :name)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/cardinality/cardinality.ttl>].

skolem:lemma4 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:HasCardinalityCheck owl:cardinality 3)] 
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/cardinality/cardinality.ttl>].

skolem:lemma5 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:P1 :name "Patrick")]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/cardinality/cardinality.ttl>].

skolem:lemma6 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:cardinalCount rdf:type log:GraphCounter)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/cardinality/cardinality.ttl>].

