@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#>.
@prefix list: <http://www.w3.org/2000/10/swap/list#>.

skolem:proof a r:Proof, r:Conjunction;
    r:component skolem:lemma1;
    r:component skolem:lemma2;
    r:gives {
        {
            :Rex a :Bird.
        } => ($ $).
        {
            :Rex a :Chicken.
        } => ($ $).
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        {
            :Rex a :Bird.
        } => ($ $).
    };
    r:evidence (
        [ a r:Fact; r:gives {{
            :Rex a :Bird.
        } => ($ $)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#Bird"]];
    r:rule skolem:lemma3.

skolem:lemma2 a r:Inference;
    r:gives {
        {
            :Rex a :Chicken.
        } => ($ $).
    };
    r:evidence (
        skolem:lemma4
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#Chicken"]];
    r:rule skolem:lemma3.

skolem:lemma3 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            {
                :Rex a var:x_0.
            } => ($ $).
        } => {
            {
                :Rex a var:x_0.
            } => ($ $).
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/rex.n3>].

skolem:lemma4 a r:Inference;
    r:gives {
        {
            :Rex a :Chicken.
        } => ($ $).
    };
    r:evidence (
        [ a r:Fact; r:gives {{
            :Rex a :Chicken.
        } => {
            :Rex a :Bird.
        }}]
        [ a r:Fact; r:gives {{
            :Rex a :Bird.
        } list:isList false}]
        [ a r:Fact; r:gives {{
            :Rex a :Bird.
        } => ($ $)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo {
        :Rex a :Chicken.
    }];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo {
        :Rex a :Bird.
    }];
    r:rule skolem:lemma5.

skolem:lemma5 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 => var:x_1.
            var:x_1 list:isList false.
            var:x_1 => ($ $).
        } => {
            var:x_0 => ($ $).
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/sequents.n3>].

