@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/try#>.
@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 {
        {
            :s :p _:sk_0.
        } :u {
            :s :q _:sk_0.
        }.
        {
            :s :q _:sk_1.
        } :u {
            :s :r _:sk_1.
        }.
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        {
            :s :p _:sk_0.
        } :u {
            :s :q _:sk_0.
        }.
    };
    r:evidence (
        skolem:lemma3
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/try#s"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]];
    r:rule skolem:lemma4.

skolem:lemma2 a r:Inference;
    r:gives {
        {
            :s :q _:sk_1.
        } :u {
            :s :r _:sk_1.
        }.
    };
    r:evidence (
        skolem:lemma3
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/try#s"]];
    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:lemma5.

skolem:lemma3 a r:Extraction;
    r:gives {
        :s :p :o.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/rgb/redgraph002.n3>].

skolem:lemma4 a r:Extraction;
    r:gives {
        @forAll var:x_0. @forSome var:x_1. {
            var:x_0 :p :o.
        } => {
            {
                var:x_0 :p var:x_1.
            } :u {
                var:x_0 :q var:x_1.
            }.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/rgb/greenquery002.n3>].

skolem:lemma5 a r:Extraction;
    r:gives {
        @forAll var:x_0. @forSome var:x_1. {
            var:x_0 :p :o.
        } => {
            {
                var:x_0 :q var:x_1.
            } :u {
                var:x_0 :r var:x_1.
            }.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/rgb/greenquery002.n3>].

