@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/ns#>.
@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 (:xxx rdf:type :aaa)]
    )].

skolem:lemma1 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:xxx rdf:type :aaa)]
    )];
    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/ns#xxx"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/ns#aaa"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 rdf:type var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 rdf:type var:x_1)]
    )])])]].

skolem:lemma2 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:xxx rdf:type :aaa)]
    )];
    r:evidence (
        skolem:lemma3
        skolem:lemma4
        [ a r:Fact; r:gives [ log:graph ([ log:triple ((skolem:e_y_1) log:onNegativeSurface [ log:graph (
            [ log:triple (:xxx :bbb skolem:e_y_1)]
            [ log:triple (() log:onNegativeSurface [ log:graph (
                [ log:triple (skolem:e_y_1 rdf:type :ccc)]
            )])]
        )])])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/ns#aaa"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/ns#bbb"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/ns#ccc"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo [ a r:Existential; n3:nodeId "https://eyereasoner.github.io/.well-known/genid/8b98b360-9a70-4845-b52c-c675af60ad01#e_y_1"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo [ n3:uri "http://example.org/ns#xxx"]];
    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:allValuesFrom var:x_2)]
        [ log:triple ((var:x_3) log:onNegativeSurface [ log:graph (
            [ log:triple (var:x_4 var:x_1 var:x_3)]
            [ log:triple (() log:onNegativeSurface [ log:graph (
                [ log:triple (var:x_3 rdf:type var:x_2)]
            )])]
        )])]
    )] log:implies [ log:graph (
        [ log:triple (var:x_4 rdf:type var:x_0)]
    )])])]].

skolem:lemma3 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:aaa owl:onProperty :bbb)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/slide33/slide33.ttl>].

skolem:lemma4 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:aaa owl:allValuesFrom :ccc)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/slide33/slide33.ttl>].

