@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 : <https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#>.
@prefix var: <http://www.w3.org/2000/10/swap/var#>.
@prefix n3: <http://www.w3.org/2004/06/rei#>.

skolem:proof a r:Proof, r:Conjunction;
    r:component skolem:lemma1;
    r:gives [ log:graph (
        [ log:triple (:b :re var:v_30)]
        [ log:triple (:c :re var:v_30)]
    )].

skolem:lemma1 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:b :re var:v_30)]
        [ log:triple (:c :re var:v_30)]
    )];
    r:evidence (
        skolem:lemma2
        skolem:lemma3
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_30"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (:b :re var:x_0)]
        [ log:triple (:c :re var:x_0)]
    )] log:implies [ log:graph (
        [ log:triple (:b :re var:x_0)]
        [ log:triple (:c :re var:x_0)]
    )])])]].

skolem:lemma2 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:b :re var:v_30)]
    )];
    r:evidence (
        skolem:lemma4
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_30"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :r var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :re var:x_1)]
    )])])]].

skolem:lemma3 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:c :re var:v_30)]
    )];
    r:evidence (
        skolem:lemma4
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_30"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :r var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :re var:x_1)]
    )])])]].

skolem:lemma4 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:b :r var:v_30)]
        [ log:triple (:c :r var:v_30)]
    )];
    r:evidence (
        skolem:lemma5
        skolem:lemma6
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_30"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :r var:x_1)]
        [ log:triple (var:x_0 :r var:x_2)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_1 :r var:x_3)]
        [ log:triple (var:x_2 :r var:x_3)]
    )])])]].

skolem:lemma5 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:a :r :b)]
    )];
    r:evidence (
        skolem:lemma7
        skolem:lemma8
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :re var:x_1)]
        [ log:triple (var:x_0 :not_e var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :r var:x_1)]
    )])])]].

skolem:lemma6 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:a :r :c)]
    )];
    r:evidence (
        skolem:lemma9
        skolem:lemma10
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :re var:x_1)]
        [ log:triple (var:x_0 :not_e var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :r var:x_1)]
    )])])]].

skolem:lemma7 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:a :re :b)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/diamond-property.ttl>].

skolem:lemma8 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:a :not_e :b)]
    )];
    r:evidence (
        skolem:lemma11
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :not_e var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_1 :not_e var:x_0)]
    )])])]].

skolem:lemma9 a r:Extraction;
    r:gives [ log:graph (
        [ log:triple (:a :re :c)]
    )];
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/diamond-property.ttl>].

skolem:lemma10 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:a :not_e :c)]
    )];
    r:evidence (
        skolem:lemma12
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :not_e var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_1 :not_e var:x_0)]
    )])])]].

skolem:lemma11 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:b :not_e :a)]
    )];
    r:evidence (
        skolem:lemma13
        skolem:lemma9
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :not_re var:x_1)]
        [ log:triple (var:x_2 :re var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :not_e var:x_2)]
    )])])]].

skolem:lemma12 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:c :not_e :a)]
    )];
    r:evidence (
        skolem:lemma14
        skolem:lemma7
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :not_re var:x_1)]
        [ log:triple (var:x_2 :re var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :not_e var:x_2)]
    )])])]].

skolem:lemma13 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:b :not_re :c)]
    )];
    r:evidence (
        skolem:lemma15
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (:c :re var:x_0)]
    )] log:implies [ log:graph (
        [ log:triple (:b :not_re var:x_0)]
    )])])]].

skolem:lemma14 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:c :not_re :b)]
    )];
    r:evidence (
        skolem:lemma16
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (:b :re var:x_0)]
    )] log:implies [ log:graph (
        [ log:triple (:c :not_re var:x_0)]
    )])])]].

skolem:lemma15 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:c :re :c)]
    )];
    r:evidence (
        skolem:lemma17
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :e var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :re var:x_1)]
    )])])]].

skolem:lemma16 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:b :re :b)]
    )];
    r:evidence (
        skolem:lemma18
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :e var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :re var:x_1)]
    )])])]].

skolem:lemma17 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:c :e :c)]
    )];
    r:evidence (
        skolem:lemma9
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#c"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :re var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_1 :e var:x_1)]
    )])])]].

skolem:lemma18 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:b :e :b)]
    )];
    r:evidence (
        skolem:lemma7
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#a"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning/arcus/diamond-property/dpe#b"]];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :re var:x_1)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_1 :e var:x_1)]
    )])])]].

