@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/diamond-property/dpe#>.
@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:gives {
        :b :re _:sk_1.
        :c :re _:sk_1.
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        :b :re _:sk_1.
        :c :re _:sk_1.
    };
    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_1"]];
    r:rule skolem:lemma4.

skolem:lemma2 a r:Inference;
    r:gives {
        :b :re _:sk_1.
    };
    r:evidence (
        skolem:lemma5
    );
    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/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_1"]];
    r:rule skolem:lemma6.

skolem:lemma3 a r:Inference;
    r:gives {
        :c :re _:sk_1.
    };
    r:evidence (
        skolem:lemma5
    );
    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/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_1"]];
    r:rule skolem:lemma6.

skolem:lemma4 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            :b :re var:x_0.
            :c :re var:x_0.
        } => {
            :b :re var:x_0.
            :c :re var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property-query.n3>].

skolem:lemma5 a r:Inference;
    r:gives {
        :b :r _:sk_1.
        :c :r _:sk_1.
    };
    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/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/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/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_1"]];
    r:rule skolem:lemma9.

skolem:lemma6 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 :r var:x_1.
        } => {
            var:x_0 :re var:x_1.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma7 a r:Inference;
    r:gives {
        :a :r :b.
    };
    r:evidence (
        skolem:lemma10
        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/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/diamond-property/dpe#b"]];
    r:rule skolem:lemma12.

skolem:lemma8 a r:Inference;
    r:gives {
        :a :r :c.
    };
    r:evidence (
        skolem:lemma13
        skolem:lemma14
    );
    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/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/diamond-property/dpe#c"]];
    r:rule skolem:lemma12.

skolem:lemma9 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2. @forSome var:x_3. {
            var:x_0 :r var:x_1.
            var:x_0 :r var:x_2.
        } => {
            var:x_1 :r var:x_3.
            var:x_2 :r var:x_3.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma10 a r:Extraction;
    r:gives {
        :a :re :b.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma11 a r:Inference;
    r:gives {
        :a :not_e :b.
    };
    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/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/diamond-property/dpe#a"]];
    r:rule skolem:lemma16.

skolem:lemma12 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 :re var:x_1.
            var:x_0 :not_e var:x_1.
        } => {
            var:x_0 :r var:x_1.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma13 a r:Extraction;
    r:gives {
        :a :re :c.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma14 a r:Inference;
    r:gives {
        :a :not_e :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/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/diamond-property/dpe#a"]];
    r:rule skolem:lemma16.

skolem:lemma15 a r:Inference;
    r:gives {
        :b :not_e :a.
    };
    r:evidence (
        skolem:lemma18
        skolem:lemma13
    );
    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/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/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/diamond-property/dpe#a"]];
    r:rule skolem:lemma19.

skolem:lemma16 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 :not_e var:x_1.
        } => {
            var:x_1 :not_e var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma17 a r:Inference;
    r:gives {
        :c :not_e :a.
    };
    r:evidence (
        skolem:lemma20
        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/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/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/diamond-property/dpe#a"]];
    r:rule skolem:lemma19.

skolem:lemma18 a r:Inference;
    r:gives {
        :b :not_re :c.
    };
    r:evidence (
        skolem:lemma21
    );
    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/diamond-property/dpe#c"]];
    r:rule skolem:lemma22.

skolem:lemma19 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2. {
            var:x_0 :not_re var:x_1.
            var:x_2 :re var:x_1.
        } => {
            var:x_0 :not_e var:x_2.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma20 a r:Inference;
    r:gives {
        :c :not_re :b.
    };
    r:evidence (
        skolem:lemma23
    );
    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/diamond-property/dpe#b"]];
    r:rule skolem:lemma24.

skolem:lemma21 a r:Inference;
    r:gives {
        :c :re :c.
    };
    r:evidence (
        skolem:lemma25
    );
    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/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/diamond-property/dpe#c"]];
    r:rule skolem:lemma26.

skolem:lemma22 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            :c :re var:x_0.
        } => {
            :b :not_re var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma23 a r:Inference;
    r:gives {
        :b :re :b.
    };
    r:evidence (
        skolem:lemma27
    );
    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/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/diamond-property/dpe#b"]];
    r:rule skolem:lemma26.

skolem:lemma24 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            :b :re var:x_0.
        } => {
            :c :not_re var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma25 a r:Inference;
    r:gives {
        :c :e :c.
    };
    r:evidence (
        skolem:lemma13
    );
    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/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/diamond-property/dpe#c"]];
    r:rule skolem:lemma28.

skolem:lemma26 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 :e var:x_1.
        } => {
            var:x_0 :re var:x_1.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

skolem:lemma27 a r:Inference;
    r:gives {
        :b :e :b.
    };
    r:evidence (
        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/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/diamond-property/dpe#b"]];
    r:rule skolem:lemma28.

skolem:lemma28 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 :re var:x_1.
        } => {
            var:x_1 :e var:x_1.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/diamond-property/diamond-property.n3>].

