@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/ns#>.
@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 {
        (0 0) :ackermann 1 .
        (0 6) :ackermann 7 .
        (1 2) :ackermann 4 .
        (1 7) :ackermann 9 .
        (2 2) :ackermann 7 .
        (2 9) :ackermann 21 .
        (3 4) :ackermann 125 .
        (3 14) :ackermann 131069 .
        (4 0) :ackermann 13 .
        (4 1) :ackermann 65533 .
        (4 2) :ackermann [encoded data, 19729 characters] .
        (5 0) :ackermann 65533 .
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        (0 0) :ackermann 1 .
        (0 6) :ackermann 7 .
        (1 2) :ackermann 4 .
        (1 7) :ackermann 9 .
        (2 2) :ackermann 7 .
        (2 9) :ackermann 21 .
        (3 4) :ackermann 125 .
        (3 14) :ackermann 131069 .
        (4 0) :ackermann 13 .
        (4 1) :ackermann 65533 .
        (4 2) :ackermann [encoded data, 19729 characters] .
        (5 0) :ackermann 65533 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(0 0) :ackermann 1}]
        [ a r:Fact; r:gives {(0 6) :ackermann 7}]
        [ a r:Fact; r:gives {(1 2) :ackermann 4}]
        [ a r:Fact; r:gives {(1 7) :ackermann 9}]
        [ a r:Fact; r:gives {(2 2) :ackermann 7}]
        [ a r:Fact; r:gives {(2 9) :ackermann 21}]
        [ a r:Fact; r:gives {(3 4) :ackermann 125}]
        [ a r:Fact; r:gives {(3 14) :ackermann 131069}]
        [ a r:Fact; r:gives {(4 0) :ackermann 13}]
        [ a r:Fact; r:gives {(4 1) :ackermann 65533}]
        [ a r:Fact; r:gives {(4 2) :ackermann [encoded data, 19729 characters]}]
        [ a r:Fact; r:gives {(5 0) :ackermann 65533}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 21];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 125];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 131069];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 13];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 65533];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo [encoded data, 19729 characters]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_11"]; r:boundTo 65533];
    r:rule skolem:lemma2.

skolem:lemma2 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4, var:x_5, var:x_6, var:x_7, var:x_8, var:x_9, var:x_10, var:x_11. {
            (0 0) :ackermann var:x_0.
            (0 6) :ackermann var:x_1.
            (1 2) :ackermann var:x_2.
            (1 7) :ackermann var:x_3.
            (2 2) :ackermann var:x_4.
            (2 9) :ackermann var:x_5.
            (3 4) :ackermann var:x_6.
            (3 14) :ackermann var:x_7.
            (4 0) :ackermann var:x_8.
            (4 1) :ackermann var:x_9.
            (4 2) :ackermann var:x_10.
            (5 0) :ackermann var:x_11.
        } => {
            (0 0) :ackermann var:x_0.
            (0 6) :ackermann var:x_1.
            (1 2) :ackermann var:x_2.
            (1 7) :ackermann var:x_3.
            (2 2) :ackermann var:x_4.
            (2 9) :ackermann var:x_5.
            (3 4) :ackermann var:x_6.
            (3 14) :ackermann var:x_7.
            (4 0) :ackermann var:x_8.
            (4 1) :ackermann var:x_9.
            (4 2) :ackermann var:x_10.
            (5 0) :ackermann var:x_11.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/ackermann/ackermann-query.n3>].

