@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/eye/reasoning#>.
@prefix gps: <https://eyereasoner.github.io/eye/reasoning/gps/gps-schema#>.
@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:gives {
        :i1 gps:path ((:drive_gent_brugge :drive_brugge_oostende) 2400.0 0.01 0.9408 0.99).
        :i1 gps:path ((:drive_gent_kortrijk :drive_kortrijk_brugge :drive_brugge_oostende) 4100.0 0.018000000000000002 0.903168 0.9801).
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        :i1 gps:path ((:drive_gent_brugge :drive_brugge_oostende) 2400.0 0.01 0.9408 0.99).
    };
    r:evidence (
        [ a r:Fact; r:gives {((<https://eyereasoner.github.io/eye/reasoning/gps/gps-plugin.n3> <https://eyereasoner.github.io/eye/reasoning/gps/gps-example1.n3>) 1) gps:findpath ({
            :i1 :location :Oostende.
        } (:drive_gent_brugge :drive_brugge_oostende) 2400.0 0.01 0.9408 0.99 (5000.0 5.0 0.2 0.4 1))}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo ((<https://eyereasoner.github.io/eye/reasoning/gps/gps-plugin.n3> <https://eyereasoner.github.io/eye/reasoning/gps/gps-example1.n3>) 1)];
    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#i1"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:drive_gent_brugge :drive_brugge_oostende)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2400.0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0.01];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0.9408];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0.99];
    r:rule skolem:lemma3.

skolem:lemma2 a r:Inference;
    r:gives {
        :i1 gps:path ((:drive_gent_kortrijk :drive_kortrijk_brugge :drive_brugge_oostende) 4100.0 0.018000000000000002 0.903168 0.9801).
    };
    r:evidence (
        [ a r:Fact; r:gives {((<https://eyereasoner.github.io/eye/reasoning/gps/gps-plugin.n3> <https://eyereasoner.github.io/eye/reasoning/gps/gps-example1.n3>) 1) gps:findpath ({
            :i1 :location :Oostende.
        } (:drive_gent_kortrijk :drive_kortrijk_brugge :drive_brugge_oostende) 4100.0 0.018000000000000002 0.903168 0.9801 (5000.0 5.0 0.2 0.4 1))}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo ((<https://eyereasoner.github.io/eye/reasoning/gps/gps-plugin.n3> <https://eyereasoner.github.io/eye/reasoning/gps/gps-example1.n3>) 1)];
    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#i1"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:drive_gent_kortrijk :drive_kortrijk_brugge :drive_brugge_oostende)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4100.0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0.018000000000000002];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0.903168];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0.9801];
    r:rule skolem:lemma3.

skolem:lemma3 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4, var:x_5, var:x_6. {
            var:x_0 gps:findpath ({
                var:x_1 :location :Oostende.
            } var:x_2 var:x_3 var:x_4 var:x_5 var:x_6 (5000.0 5.0 0.2 0.4 1)).
        } => {
            var:x_1 gps:path (var:x_2 var:x_3 var:x_4 var:x_5 var:x_6).
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/gps/gps-query1.n3>].

