@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 : <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 {
        :angers :path :nantes.
        :lemans :path :nantes.
        :chartres :path :nantes.
        :paris :path :nantes.
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        :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 skolem:lemma6.

skolem:lemma2 a r:Inference;
    r:gives {
        :lemans :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/#lemans"]];
    r:rule skolem:lemma6.

skolem:lemma3 a r:Inference;
    r:gives {
        :chartres :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/#chartres"]];
    r:rule skolem:lemma6.

skolem:lemma4 a r:Inference;
    r:gives {
        :paris :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/#paris"]];
    r:rule skolem:lemma6.

skolem:lemma5 a r:Inference;
    r:gives {
        :angers :path :nantes.
    };
    r:evidence (
        skolem:lemma10
    );
    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 {@forSome var:x_0, var:x_1. {
        var:x_0 :oneway var:x_1.
    } => {
        var:x_0 :path var:x_1.
    }}].

skolem:lemma6 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            var:x_0 :path :nantes.
        } => {
            var:x_0 :path :nantes.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/graph.n3>].

skolem:lemma7 a r:Inference;
    r:gives {
        :lemans :path :nantes.
    };
    r:evidence (
        skolem:lemma11
        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 {@forSome var:x_0, var:x_1, var:x_2. {
        var:x_0 :oneway var:x_1.
        var:x_1 :path var:x_2.
    } => {
        var:x_0 :path var:x_2.
    }}].

skolem:lemma8 a r:Inference;
    r:gives {
        :chartres :path :nantes.
    };
    r:evidence (
        skolem:lemma12
        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: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 {@forSome var:x_0, var:x_1, var:x_2. {
        var:x_0 :oneway var:x_1.
        var:x_1 :path var:x_2.
    } => {
        var:x_0 :path var:x_2.
    }}].

skolem:lemma9 a r:Inference;
    r:gives {
        :paris :path :nantes.
    };
    r:evidence (
        skolem:lemma13
        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: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/#nantes"]];
    r:rule [ a r:Fact; r:gives {@forSome var:x_0, var:x_1, var:x_2. {
        var:x_0 :oneway var:x_1.
        var:x_1 :path var:x_2.
    } => {
        var:x_0 :path var:x_2.
    }}].

skolem:lemma10 a r:Extraction;
    r:gives {
        :angers :oneway :nantes.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/graph.n3>].

skolem:lemma11 a r:Extraction;
    r:gives {
        :lemans :oneway :angers.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/graph.n3>].

skolem:lemma12 a r:Extraction;
    r:gives {
        :chartres :oneway :lemans.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/graph.n3>].

skolem:lemma13 a r:Extraction;
    r:gives {
        :paris :oneway :chartres.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/graph.n3>].

