@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 : <https://eyereasoner.github.io/ns#>.
@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:component skolem:lemma5;
    r:component skolem:lemma6;
    r:component skolem:lemma7;
    r:gives {
        (:a :f) :dijkstra ((:a :c :b :d :e :f) 13).
        (:a :f) :dijkstra ((:a :c :b :d :f) 14).
        (:a :f) :dijkstra ((:a :b :d :e :f) 14).
        (:a :f) :dijkstra ((:a :b :d :f) 15).
        (:a :f) :dijkstra ((:a :c :e :f) 15).
        (:a :f) :dijkstra ((:a :c :d :e :f) 15).
        (:a :f) :dijkstra ((:a :c :d :f) 16).
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        (:a :f) :dijkstra ((:a :c :b :d :e :f) 13).
    };
    r:evidence (
        [ a r:Fact; r:gives {(:a :f) :dijkstra ((:a :c :b :d :e :f) 13)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:a :c :b :d :e :f)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 13];
    r:rule skolem:lemma8.

skolem:lemma2 a r:Inference;
    r:gives {
        (:a :f) :dijkstra ((:a :c :b :d :f) 14).
    };
    r:evidence (
        [ a r:Fact; r:gives {(:a :f) :dijkstra ((:a :c :b :d :f) 14)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:a :c :b :d :f)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 14];
    r:rule skolem:lemma8.

skolem:lemma3 a r:Inference;
    r:gives {
        (:a :f) :dijkstra ((:a :b :d :e :f) 14).
    };
    r:evidence (
        [ a r:Fact; r:gives {(:a :f) :dijkstra ((:a :b :d :e :f) 14)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:a :b :d :e :f)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 14];
    r:rule skolem:lemma8.

skolem:lemma4 a r:Inference;
    r:gives {
        (:a :f) :dijkstra ((:a :b :d :f) 15).
    };
    r:evidence (
        [ a r:Fact; r:gives {(:a :f) :dijkstra ((:a :b :d :f) 15)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:a :b :d :f)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 15];
    r:rule skolem:lemma8.

skolem:lemma5 a r:Inference;
    r:gives {
        (:a :f) :dijkstra ((:a :c :e :f) 15).
    };
    r:evidence (
        [ a r:Fact; r:gives {(:a :f) :dijkstra ((:a :c :e :f) 15)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:a :c :e :f)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 15];
    r:rule skolem:lemma8.

skolem:lemma6 a r:Inference;
    r:gives {
        (:a :f) :dijkstra ((:a :c :d :e :f) 15).
    };
    r:evidence (
        [ a r:Fact; r:gives {(:a :f) :dijkstra ((:a :c :d :e :f) 15)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:a :c :d :e :f)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 15];
    r:rule skolem:lemma8.

skolem:lemma7 a r:Inference;
    r:gives {
        (:a :f) :dijkstra ((:a :c :d :f) 16).
    };
    r:evidence (
        [ a r:Fact; r:gives {(:a :f) :dijkstra ((:a :c :d :f) 16)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:a :c :d :f)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 16];
    r:rule skolem:lemma8.

skolem:lemma8 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            (:a :f) :dijkstra (var:x_0 var:x_1).
        } => {
            (:a :f) :dijkstra (var:x_0 var:x_1).
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/dijkstra/dijkstra-query.n3>].

