@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 : <urn:example:>.
@prefix n3: <http://www.w3.org/2004/06/rei#>.
@prefix math: <http://www.w3.org/2000/10/swap/math#>.
@prefix var: <http://www.w3.org/2000/10/swap/var#>.
@prefix log: <http://www.w3.org/2000/10/swap/log#>.

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 .
        (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 .
        (5 0) :ackermann 65533 .
    };
    r:evidence (
        skolem:lemma2
        skolem:lemma3
        skolem:lemma4
        skolem:lemma5
        skolem:lemma6
        skolem:lemma7
        skolem:lemma8
        skolem:lemma9
        skolem:lemma10
        skolem:lemma11
        skolem:lemma12
    );
    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 65533];
    r:rule skolem:lemma13.

skolem:lemma2 a r:Inference;
    r:gives {
        (0 0) :ackermann 1 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(0 3) math:sum 3}]
        skolem:lemma14
        [ a r:Fact; r:gives {(4 3) math:difference 1}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1];
    r:rule skolem:lemma15.

skolem:lemma3 a r:Inference;
    r:gives {
        (0 6) :ackermann 7 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(6 3) math:sum 9}]
        skolem:lemma16
        [ a r:Fact; r:gives {(10 3) math:difference 7}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 10];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7];
    r:rule skolem:lemma15.

skolem:lemma4 a r:Inference;
    r:gives {
        (1 2) :ackermann 4 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 3) math:sum 5}]
        skolem:lemma17
        [ a r:Fact; r:gives {(7 3) math:difference 4}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4];
    r:rule skolem:lemma15.

skolem:lemma5 a r:Inference;
    r:gives {
        (1 7) :ackermann 9 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(7 3) math:sum 10}]
        skolem:lemma18
        [ a r:Fact; r:gives {(12 3) math:difference 9}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 10];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 12];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9];
    r:rule skolem:lemma15.

skolem:lemma6 a r:Inference;
    r:gives {
        (2 2) :ackermann 7 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 3) math:sum 5}]
        skolem:lemma19
        [ a r:Fact; r:gives {(10 3) math:difference 7}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 10];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7];
    r:rule skolem:lemma15.

skolem:lemma7 a r:Inference;
    r:gives {
        (2 9) :ackermann 21 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(9 3) math:sum 12}]
        skolem:lemma20
        [ a r:Fact; r:gives {(24 3) math:difference 21}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 12];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 24];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21];
    r:rule skolem:lemma15.

skolem:lemma8 a r:Inference;
    r:gives {
        (3 4) :ackermann 125 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(4 3) math:sum 7}]
        skolem:lemma21
        [ a r:Fact; r:gives {(128 3) math:difference 125}]
    );
    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_0"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 128];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125];
    r:rule skolem:lemma15.

skolem:lemma9 a r:Inference;
    r:gives {
        (3 14) :ackermann 131069 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(14 3) math:sum 17}]
        skolem:lemma22
        [ a r:Fact; r:gives {(131072 3) math:difference 131069}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 17];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 14];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 131072];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 131069];
    r:rule skolem:lemma15.

skolem:lemma10 a r:Inference;
    r:gives {
        (4 0) :ackermann 13 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(0 3) math:sum 3}]
        skolem:lemma23
        [ a r:Fact; r:gives {(16 3) math:difference 13}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 16];
    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_4"]; r:boundTo 13];
    r:rule skolem:lemma15.

skolem:lemma11 a r:Inference;
    r:gives {
        (4 1) :ackermann 65533 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 3) math:sum 4}]
        skolem:lemma24
        [ a r:Fact; r:gives {(65536 3) math:difference 65533}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4];
    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_3"]; r:boundTo 65536];
    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_4"]; r:boundTo 65533];
    r:rule skolem:lemma15.

skolem:lemma12 a r:Inference;
    r:gives {
        (5 0) :ackermann 65533 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(0 3) math:sum 3}]
        skolem:lemma25
        [ a r:Fact; r:gives {(65536 3) math:difference 65533}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 65536];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65533];
    r:rule skolem:lemma15.

skolem:lemma13 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. {
            (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.
            (5 0) :ackermann var:x_10.
        } => {
            (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.
            (5 0) :ackermann var:x_10.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/ackermann/ackermann-query2.n3>].

skolem:lemma14 a r:Inference;
    r:gives {
        (0 3 2) :ackermann 4 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(3 1) math:sum 4}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2];
    r:rule skolem:lemma26.

skolem:lemma15 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4. {
            (var:x_2 var:x_0) :ackermann var:x_4.
        } <= {
            (var:x_0 3) math:sum var:x_1.
            (var:x_2 var:x_1 2) :ackermann var:x_3.
            (var:x_3 3) math:difference var:x_4.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/ackermann/ackermann.n3>].

skolem:lemma16 a r:Inference;
    r:gives {
        (0 9 2) :ackermann 10 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(9 1) math:sum 10}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 10];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2];
    r:rule skolem:lemma26.

skolem:lemma17 a r:Inference;
    r:gives {
        (1 5 2) :ackermann 7 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(5 2) math:sum 7}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma27.

skolem:lemma18 a r:Inference;
    r:gives {
        (1 10 2) :ackermann 12 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(10 2) math:sum 12}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 12];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 10];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma27.

skolem:lemma19 a r:Inference;
    r:gives {
        (2 5 2) :ackermann 10 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(5 2) math:product 10}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 10];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma20 a r:Inference;
    r:gives {
        (2 12 2) :ackermann 24 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(12 2) math:product 24}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 24];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 12];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma21 a r:Inference;
    r:gives {
        (3 7 2) :ackermann 128 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(7 1) math:difference 6}]
        skolem:lemma29
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma30
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 128];
    r:rule skolem:lemma31.

skolem:lemma22 a r:Inference;
    r:gives {
        (3 17 2) :ackermann 131072 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(17 1) math:difference 16}]
        skolem:lemma32
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma33
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 16];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 17];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65536];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 131072];
    r:rule skolem:lemma31.

skolem:lemma23 a r:Inference;
    r:gives {
        (4 3 2) :ackermann 16 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma34
        [ a r:Fact; r:gives {(4 1) math:difference 3}]
        skolem:lemma35
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4];
    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 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 16];
    r:rule skolem:lemma31.

skolem:lemma24 a r:Inference;
    r:gives {
        (4 4 2) :ackermann 65536 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(4 1) math:difference 3}]
        skolem:lemma23
        [ a r:Fact; r:gives {(4 1) math:difference 3}]
        skolem:lemma32
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16];
    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 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 65536];
    r:rule skolem:lemma31.

skolem:lemma25 a r:Inference;
    r:gives {
        (5 3 2) :ackermann 65536 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma36
        [ a r:Fact; r:gives {(5 1) math:difference 4}]
        skolem:lemma24
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 65536];
    r:rule skolem:lemma31.

skolem:lemma26 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. @forSome var:x_2. {
            (0 var:x_0 var:x_2) :ackermann var:x_1.
        } <= {
            true log:callWithCut true.
            (var:x_0 1) math:sum var:x_1.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/ackermann/ackermann.n3>].

skolem:lemma27 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2. {
            (1 var:x_0 var:x_1) :ackermann var:x_2.
        } <= {
            true log:callWithCut true.
            (var:x_0 var:x_1) math:sum var:x_2.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/ackermann/ackermann.n3>].

skolem:lemma28 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2. {
            (2 var:x_0 var:x_1) :ackermann var:x_2.
        } <= {
            true log:callWithCut true.
            (var:x_0 var:x_1) math:product var:x_2.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/ackermann/ackermann.n3>].

skolem:lemma29 a r:Inference;
    r:gives {
        (3 6 2) :ackermann 64 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(6 1) math:difference 5}]
        skolem:lemma37
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma38
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 64];
    r:rule skolem:lemma31.

skolem:lemma30 a r:Inference;
    r:gives {
        (2 64 2) :ackermann 128 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(64 2) math:product 128}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 128];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 64];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma31 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_2 var:x_0 var:x_3) :ackermann var:x_6.
        } <= {
            (var:x_0 1) math:difference var:x_1.
            (var:x_2 var:x_1 var:x_3) :ackermann var:x_4.
            (var:x_2 1) math:difference var:x_5.
            (var:x_5 var:x_4 var:x_3) :ackermann var:x_6.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/ackermann/ackermann.n3>].

skolem:lemma32 a r:Inference;
    r:gives {
        (3 16 2) :ackermann 65536 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(16 1) math:difference 15}]
        skolem:lemma39
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma40
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 15];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32768];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 65536];
    r:rule skolem:lemma31.

skolem:lemma33 a r:Inference;
    r:gives {
        (2 65536 2) :ackermann 131072 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(65536 2) math:product 131072}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 131072];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 65536];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma34 a r:Inference;
    r:gives {
        (4 2 2) :ackermann 4 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 1) math:difference 1}]
        skolem:lemma41
        [ a r:Fact; r:gives {(4 1) math:difference 3}]
        skolem:lemma42
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2];
    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 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4];
    r:rule skolem:lemma31.

skolem:lemma35 a r:Inference;
    r:gives {
        (3 4 2) :ackermann 16 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(4 1) math:difference 3}]
        skolem:lemma43
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma44
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 16];
    r:rule skolem:lemma31.

skolem:lemma36 a r:Inference;
    r:gives {
        (5 2 2) :ackermann 4 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 1) math:difference 1}]
        skolem:lemma45
        [ a r:Fact; r:gives {(5 1) math:difference 4}]
        skolem:lemma34
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4];
    r:rule skolem:lemma31.

skolem:lemma37 a r:Inference;
    r:gives {
        (3 5 2) :ackermann 32 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(5 1) math:difference 4}]
        skolem:lemma35
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma46
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 32];
    r:rule skolem:lemma31.

skolem:lemma38 a r:Inference;
    r:gives {
        (2 32 2) :ackermann 64 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(32 2) math:product 64}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 64];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 32];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma39 a r:Inference;
    r:gives {
        (3 15 2) :ackermann 32768 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(15 1) math:difference 14}]
        skolem:lemma47
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma48
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 14];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 15];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16384];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 32768];
    r:rule skolem:lemma31.

skolem:lemma40 a r:Inference;
    r:gives {
        (2 32768 2) :ackermann 65536 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(32768 2) math:product 65536}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 65536];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 32768];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma41 a r:Inference;
    r:gives {
        (4 1 2) :ackermann 2 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 1) math:difference 0}]
        skolem:lemma49
        [ a r:Fact; r:gives {(4 1) math:difference 3}]
        skolem:lemma50
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0];
    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_4"]; r:boundTo 1];
    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 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2];
    r:rule skolem:lemma31.

skolem:lemma42 a r:Inference;
    r:gives {
        (3 2 2) :ackermann 4 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 1) math:difference 1}]
        skolem:lemma50
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma51
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4];
    r:rule skolem:lemma31.

skolem:lemma43 a r:Inference;
    r:gives {
        (3 3 2) :ackermann 8 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma42
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma52
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8];
    r:rule skolem:lemma31.

skolem:lemma44 a r:Inference;
    r:gives {
        (2 8 2) :ackermann 16 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(8 2) math:product 16}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 16];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma45 a r:Inference;
    r:gives {
        (5 1 2) :ackermann 2 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 1) math:difference 0}]
        skolem:lemma53
        [ a r:Fact; r:gives {(5 1) math:difference 4}]
        skolem:lemma41
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0];
    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_4"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2];
    r:rule skolem:lemma31.

skolem:lemma46 a r:Inference;
    r:gives {
        (2 16 2) :ackermann 32 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(16 2) math:product 32}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 32];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma47 a r:Inference;
    r:gives {
        (3 14 2) :ackermann 16384 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(14 1) math:difference 13}]
        skolem:lemma54
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma55
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 13];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 14];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8192];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 16384];
    r:rule skolem:lemma31.

skolem:lemma48 a r:Inference;
    r:gives {
        (2 16384 2) :ackermann 32768 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(16384 2) math:product 32768}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 32768];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16384];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma49 a r:Inference;
    r:gives {
        (4 0 2) :ackermann 1 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma56.

skolem:lemma50 a r:Inference;
    r:gives {
        (3 1 2) :ackermann 2 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 1) math:difference 0}]
        skolem:lemma57
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma58
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0];
    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_4"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2];
    r:rule skolem:lemma31.

skolem:lemma51 a r:Inference;
    r:gives {
        (2 2 2) :ackermann 4 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(2 2) math:product 4}]
    );
    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_0"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma52 a r:Inference;
    r:gives {
        (2 4 2) :ackermann 8 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(4 2) math:product 8}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma53 a r:Inference;
    r:gives {
        (5 0 2) :ackermann 1 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma56.

skolem:lemma54 a r:Inference;
    r:gives {
        (3 13 2) :ackermann 8192 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(13 1) math:difference 12}]
        skolem:lemma59
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma60
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 12];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 13];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4096];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8192];
    r:rule skolem:lemma31.

skolem:lemma55 a r:Inference;
    r:gives {
        (2 8192 2) :ackermann 16384 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(8192 2) math:product 16384}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 16384];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8192];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma56 a r:Extraction;
    r:gives {
        @forSome var:x_0, var:x_1. {
            (var:x_0 0 var:x_1) :ackermann 1.
        } <= {
            true log:callWithCut true.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/ackermann/ackermann.n3>].

skolem:lemma57 a r:Inference;
    r:gives {
        (3 0 2) :ackermann 1 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma56.

skolem:lemma58 a r:Inference;
    r:gives {
        (2 1 2) :ackermann 2 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(1 2) math:product 2}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2];
    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 2];
    r:rule skolem:lemma28.

skolem:lemma59 a r:Inference;
    r:gives {
        (3 12 2) :ackermann 4096 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(12 1) math:difference 11}]
        skolem:lemma61
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma62
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 11];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 12];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2048];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4096];
    r:rule skolem:lemma31.

skolem:lemma60 a r:Inference;
    r:gives {
        (2 4096 2) :ackermann 8192 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(4096 2) math:product 8192}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8192];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4096];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma61 a r:Inference;
    r:gives {
        (3 11 2) :ackermann 2048 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(11 1) math:difference 10}]
        skolem:lemma63
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma64
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 10];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 11];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1024];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2048];
    r:rule skolem:lemma31.

skolem:lemma62 a r:Inference;
    r:gives {
        (2 2048 2) :ackermann 4096 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(2048 2) math:product 4096}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4096];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2048];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma63 a r:Inference;
    r:gives {
        (3 10 2) :ackermann 1024 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(10 1) math:difference 9}]
        skolem:lemma65
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma66
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 10];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 512];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1024];
    r:rule skolem:lemma31.

skolem:lemma64 a r:Inference;
    r:gives {
        (2 1024 2) :ackermann 2048 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(1024 2) math:product 2048}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2048];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1024];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma65 a r:Inference;
    r:gives {
        (3 9 2) :ackermann 512 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(9 1) math:difference 8}]
        skolem:lemma67
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma68
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 512];
    r:rule skolem:lemma31.

skolem:lemma66 a r:Inference;
    r:gives {
        (2 512 2) :ackermann 1024 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(512 2) math:product 1024}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1024];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 512];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma67 a r:Inference;
    r:gives {
        (3 8 2) :ackermann 256 .
    };
    r:evidence (
        [ a r:Fact; r:gives {(8 1) math:difference 7}]
        skolem:lemma21
        [ a r:Fact; r:gives {(3 1) math:difference 2}]
        skolem:lemma69
    );
    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_0"]; r:boundTo 8];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 256];
    r:rule skolem:lemma31.

skolem:lemma68 a r:Inference;
    r:gives {
        (2 256 2) :ackermann 512 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(256 2) math:product 512}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 512];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 256];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

skolem:lemma69 a r:Inference;
    r:gives {
        (2 128 2) :ackermann 256 .
    };
    r:evidence (
        [ a r:Fact; r:gives {true log:callWithCut true}]
        [ a r:Fact; r:gives {(128 2) math:product 256}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 256];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 128];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2];
    r:rule skolem:lemma28.

