@prefix log: <http://www.w3.org/2000/10/swap/log#>.
@prefix math: <http://www.w3.org/2000/10/swap/math#>.
@prefix : <https://eyereasoner.github.io/ns#>.
@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 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:component skolem:lemma5;
    r:component skolem:lemma6;
    r:component skolem:lemma7;
    r:component skolem:lemma8;
    r:component skolem:lemma9;
    r:component skolem:lemma10;
    r:gives [ log:graph (
        [ log:triple (0 :is :Positive)]
        [ log:triple (1 :is :Positive)]
        [ log:triple (2 :is :Positive)]
        [ log:triple (3 :is :Positive)]
        [ log:triple (4 :is :Positive)]
        [ log:triple (5 :is :Positive)]
        [ log:triple (6 :is :Positive)]
        [ log:triple (7 :is :Positive)]
        [ log:triple (8 :is :Positive)]
        [ log:triple (9 :is :Positive)]
    )].

skolem:lemma1 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (0 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma11
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma2 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (1 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma12
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma3 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (2 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma13
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma4 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (3 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma14
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma5 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (4 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma15
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma6 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (5 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma16
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma7 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (6 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma17
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma8 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (7 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma18
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma9 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (8 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma19
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma10 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (9 :is :Positive)]
    )];
    r:evidence (
        skolem:lemma20
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma11 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (0 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 0)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma12 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (1 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 1)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (1 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (1 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (1 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma13 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (2 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 2)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (2 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (2 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (2 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma14 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (3 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 3)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (3 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (3 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (3 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma15 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (4 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 4)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (4 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (4 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (4 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma16 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (5 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 5)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (5 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (5 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (5 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma17 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (6 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 6)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (6 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (6 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (6 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma18 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (7 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 7)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (7 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (7 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (7 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma19 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (8 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 8)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (8 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (8 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (8 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

skolem:lemma20 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (9 :is :Positive)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (10 log:repeat 9)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (9 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (9 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (9 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (10 log:repeat var:x_0)]
        [ log:triple ([ log:graph (
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 math:notLessThan 0)]
            )] log:implies [ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )])]
            [ log:triple ([ log:graph (
                [ log:triple (var:x_0 :is :Positive)]
            )] log:implies false)]
        )] log:satisfiable false)]
    )] log:implies [ log:graph (
        [ log:triple (var:x_0 :is :Positive)]
    )])])]].

