@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 n3: <http://www.w3.org/2004/06/rei#>.
@prefix var: <http://www.w3.org/2000/10/swap/var#>.

skolem:proof a r:Proof, r:Conjunction;
    r:component skolem:lemma1;
    r:component skolem:lemma2;
    r:component skolem:lemma3;
    r:component skolem:lemma4;
    r:gives [ log:graph (
        [ log:triple (:angers :path :nantes)]
        [ log:triple (:lemans :path :nantes)]
        [ log:triple (:chartres :path :nantes)]
        [ log:triple (:paris :path :nantes)]
    )].

skolem:lemma1 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:angers :path :nantes)]
    )];
    r:evidence (
        skolem:lemma5
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#angers"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :path :nantes)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path :nantes)]
    )])])]].

skolem:lemma2 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:lemans :path :nantes)]
    )];
    r:evidence (
        skolem:lemma6
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#lemans"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :path :nantes)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path :nantes)]
    )])])]].

skolem:lemma3 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:chartres :path :nantes)]
    )];
    r:evidence (
        skolem:lemma7
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#chartres"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :path :nantes)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path :nantes)]
    )])])]].

skolem:lemma4 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:paris :path :nantes)]
    )];
    r:evidence (
        skolem:lemma8
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#paris"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :path :nantes)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path :nantes)]
    )])])]].

skolem:lemma5 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:angers :path :nantes)]
    )];
    r:evidence (
        skolem:lemma9
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#angers"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#nantes"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :oneway var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path var:x_1)]
    )])])]].

skolem:lemma6 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:lemans :path :nantes)]
    )];
    r:evidence (
        skolem:lemma10
        skolem:lemma5
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#lemans"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#angers"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#nantes"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :path var:x_1)]
        [ log:triple (var:x_1 :path var:x_2)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path var:x_2)]
    )])])]].

skolem:lemma7 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:chartres :path :nantes)]
    )];
    r:evidence (
        skolem:lemma11
        skolem:lemma6
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#chartres"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#lemans"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#nantes"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :path var:x_1)]
        [ log:triple (var:x_1 :path var:x_2)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path var:x_2)]
    )])])]].

skolem:lemma8 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:paris :path :nantes)]
    )];
    r:evidence (
        skolem:lemma12
        skolem:lemma6
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#paris"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#lemans"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#nantes"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :path var:x_1)]
        [ log:triple (var:x_1 :path var:x_2)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path var:x_2)]
    )])])]].

skolem:lemma9 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:angers :oneway :nantes)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/graph/graph.ttl>].

skolem:lemma10 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:lemans :path :angers)]
    )];
    r:evidence (
        skolem:lemma13
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#lemans"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#angers"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :oneway var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path var:x_1)]
    )])])]].

skolem:lemma11 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:chartres :path :lemans)]
    )];
    r:evidence (
        skolem:lemma14
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#chartres"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#lemans"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :oneway var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path var:x_1)]
    )])])]].

skolem:lemma12 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:paris :path :lemans)]
    )];
    r:evidence (
        skolem:lemma15
        skolem:lemma11
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#paris"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#chartres"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#lemans"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :path var:x_1)]
        [ log:triple (var:x_1 :path var:x_2)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path var:x_2)]
    )])])]].

skolem:lemma13 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:lemans :oneway :angers)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/graph/graph.ttl>].

skolem:lemma14 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:chartres :oneway :lemans)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/graph/graph.ttl>].

skolem:lemma15 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:paris :path :chartres)]
    )];
    r:evidence (
        skolem:lemma16
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#paris"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#chartres"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :oneway var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :path var:x_1)]
    )])])]].

skolem:lemma16 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:paris :oneway :chartres)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/graph/graph.ttl>].

