@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#>.

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:component skolem:lemma11;
    r:component skolem:lemma12;
    r:component skolem:lemma13;
    r:component skolem:lemma14;
    r:component skolem:lemma15;
    r:component skolem:lemma16;
    r:component skolem:lemma17;
    r:component skolem:lemma18;
    r:component skolem:lemma19;
    r:component skolem:lemma20;
    r:component skolem:lemma21;
    r:component skolem:lemma22;
    r:component skolem:lemma23;
    r:component skolem:lemma24;
    r:component skolem:lemma25;
    r:component skolem:lemma26;
    r:component skolem:lemma27;
    r:component skolem:lemma28;
    r:component skolem:lemma29;
    r:component skolem:lemma30;
    r:component skolem:lemma31;
    r:component skolem:lemma32;
    r:gives {
        (0 (1 2 3 4 5)) :combination ().
        (1 (1 2 3 4 5)) :combination (1).
        (1 (1 2 3 4 5)) :combination (2).
        (1 (1 2 3 4 5)) :combination (3).
        (1 (1 2 3 4 5)) :combination (4).
        (1 (1 2 3 4 5)) :combination (5).
        (2 (1 2 3 4 5)) :combination (1 2).
        (2 (1 2 3 4 5)) :combination (1 3).
        (2 (1 2 3 4 5)) :combination (1 4).
        (2 (1 2 3 4 5)) :combination (1 5).
        (2 (1 2 3 4 5)) :combination (2 3).
        (2 (1 2 3 4 5)) :combination (2 4).
        (2 (1 2 3 4 5)) :combination (2 5).
        (2 (1 2 3 4 5)) :combination (3 4).
        (2 (1 2 3 4 5)) :combination (3 5).
        (2 (1 2 3 4 5)) :combination (4 5).
        (3 (1 2 3 4 5)) :combination (1 2 3).
        (3 (1 2 3 4 5)) :combination (1 2 4).
        (3 (1 2 3 4 5)) :combination (1 2 5).
        (3 (1 2 3 4 5)) :combination (1 3 4).
        (3 (1 2 3 4 5)) :combination (1 3 5).
        (3 (1 2 3 4 5)) :combination (1 4 5).
        (3 (1 2 3 4 5)) :combination (2 3 4).
        (3 (1 2 3 4 5)) :combination (2 3 5).
        (3 (1 2 3 4 5)) :combination (2 4 5).
        (3 (1 2 3 4 5)) :combination (3 4 5).
        (4 (1 2 3 4 5)) :combination (1 2 3 4).
        (4 (1 2 3 4 5)) :combination (1 2 3 5).
        (4 (1 2 3 4 5)) :combination (1 2 4 5).
        (4 (1 2 3 4 5)) :combination (1 3 4 5).
        (4 (1 2 3 4 5)) :combination (2 3 4 5).
        (5 (1 2 3 4 5)) :combination (1 2 3 4 5).
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        (0 (1 2 3 4 5)) :combination ().
    };
    r:evidence (
        [ a r:Fact; r:gives {(0 (1 2 3 4 5)) :combination ()}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo ()];
    r:rule skolem:lemma33.

skolem:lemma2 a r:Inference;
    r:gives {
        (1 (1 2 3 4 5)) :combination (1).
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 (1 2 3 4 5)) :combination (1)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1)];
    r:rule skolem:lemma34.

skolem:lemma3 a r:Inference;
    r:gives {
        (1 (1 2 3 4 5)) :combination (2).
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 (1 2 3 4 5)) :combination (2)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2)];
    r:rule skolem:lemma34.

skolem:lemma4 a r:Inference;
    r:gives {
        (1 (1 2 3 4 5)) :combination (3).
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 (1 2 3 4 5)) :combination (3)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3)];
    r:rule skolem:lemma34.

skolem:lemma5 a r:Inference;
    r:gives {
        (1 (1 2 3 4 5)) :combination (4).
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 (1 2 3 4 5)) :combination (4)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4)];
    r:rule skolem:lemma34.

skolem:lemma6 a r:Inference;
    r:gives {
        (1 (1 2 3 4 5)) :combination (5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 (1 2 3 4 5)) :combination (5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5)];
    r:rule skolem:lemma34.

skolem:lemma7 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (1 2).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (1 2)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2)];
    r:rule skolem:lemma35.

skolem:lemma8 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (1 3).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (1 3)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3)];
    r:rule skolem:lemma35.

skolem:lemma9 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (1 4).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (1 4)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4)];
    r:rule skolem:lemma35.

skolem:lemma10 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (1 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (1 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5)];
    r:rule skolem:lemma35.

skolem:lemma11 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (2 3).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (2 3)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3)];
    r:rule skolem:lemma35.

skolem:lemma12 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (2 4).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (2 4)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4)];
    r:rule skolem:lemma35.

skolem:lemma13 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (2 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (2 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5)];
    r:rule skolem:lemma35.

skolem:lemma14 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (3 4).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (3 4)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)];
    r:rule skolem:lemma35.

skolem:lemma15 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (3 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (3 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5)];
    r:rule skolem:lemma35.

skolem:lemma16 a r:Inference;
    r:gives {
        (2 (1 2 3 4 5)) :combination (4 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(2 (1 2 3 4 5)) :combination (4 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)];
    r:rule skolem:lemma35.

skolem:lemma17 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (1 2 3).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (1 2 3)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 3)];
    r:rule skolem:lemma36.

skolem:lemma18 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (1 2 4).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (1 2 4)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 4)];
    r:rule skolem:lemma36.

skolem:lemma19 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (1 2 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (1 2 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 5)];
    r:rule skolem:lemma36.

skolem:lemma20 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (1 3 4).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (1 3 4)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 4)];
    r:rule skolem:lemma36.

skolem:lemma21 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (1 3 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (1 3 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 5)];
    r:rule skolem:lemma36.

skolem:lemma22 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (1 4 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (1 4 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 5)];
    r:rule skolem:lemma36.

skolem:lemma23 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (2 3 4).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (2 3 4)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4)];
    r:rule skolem:lemma36.

skolem:lemma24 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (2 3 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (2 3 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5)];
    r:rule skolem:lemma36.

skolem:lemma25 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (2 4 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (2 4 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5)];
    r:rule skolem:lemma36.

skolem:lemma26 a r:Inference;
    r:gives {
        (3 (1 2 3 4 5)) :combination (3 4 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 (1 2 3 4 5)) :combination (3 4 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 5)];
    r:rule skolem:lemma36.

skolem:lemma27 a r:Inference;
    r:gives {
        (4 (1 2 3 4 5)) :combination (1 2 3 4).
    };
    r:evidence (
        [ a r:Fact; r:gives {(4 (1 2 3 4 5)) :combination (1 2 3 4)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 3 4)];
    r:rule skolem:lemma37.

skolem:lemma28 a r:Inference;
    r:gives {
        (4 (1 2 3 4 5)) :combination (1 2 3 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(4 (1 2 3 4 5)) :combination (1 2 3 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 3 5)];
    r:rule skolem:lemma37.

skolem:lemma29 a r:Inference;
    r:gives {
        (4 (1 2 3 4 5)) :combination (1 2 4 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(4 (1 2 3 4 5)) :combination (1 2 4 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 4 5)];
    r:rule skolem:lemma37.

skolem:lemma30 a r:Inference;
    r:gives {
        (4 (1 2 3 4 5)) :combination (1 3 4 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(4 (1 2 3 4 5)) :combination (1 3 4 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 4 5)];
    r:rule skolem:lemma37.

skolem:lemma31 a r:Inference;
    r:gives {
        (4 (1 2 3 4 5)) :combination (2 3 4 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(4 (1 2 3 4 5)) :combination (2 3 4 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 5)];
    r:rule skolem:lemma37.

skolem:lemma32 a r:Inference;
    r:gives {
        (5 (1 2 3 4 5)) :combination (1 2 3 4 5).
    };
    r:evidence (
        [ a r:Fact; r:gives {(5 (1 2 3 4 5)) :combination (1 2 3 4 5)}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 3 4 5)];
    r:rule skolem:lemma38.

skolem:lemma33 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            (0 (1 2 3 4 5)) :combination var:x_0.
        } => {
            (0 (1 2 3 4 5)) :combination var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/combinatorics/combination-query.n3>].

skolem:lemma34 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            (1 (1 2 3 4 5)) :combination var:x_0.
        } => {
            (1 (1 2 3 4 5)) :combination var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/combinatorics/combination-query.n3>].

skolem:lemma35 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            (2 (1 2 3 4 5)) :combination var:x_0.
        } => {
            (2 (1 2 3 4 5)) :combination var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/combinatorics/combination-query.n3>].

skolem:lemma36 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            (3 (1 2 3 4 5)) :combination var:x_0.
        } => {
            (3 (1 2 3 4 5)) :combination var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/combinatorics/combination-query.n3>].

skolem:lemma37 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            (4 (1 2 3 4 5)) :combination var:x_0.
        } => {
            (4 (1 2 3 4 5)) :combination var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/combinatorics/combination-query.n3>].

skolem:lemma38 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            (5 (1 2 3 4 5)) :combination var:x_0.
        } => {
            (5 (1 2 3 4 5)) :combination var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/combinatorics/combination-query.n3>].

