@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:gives {
        (1 0 1 0 0 1) :compute (1 0 1 0 1 0 "#").
        (1 0 1 1 1 1) :compute (1 1 0 0 0 0 "#").
        (1 1 1 1 1 1) :compute (1 0 0 0 0 0 0 "#").
        () :compute (1 "#").
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        (1 0 1 0 0 1) :compute (1 0 1 0 1 0 "#").
        (1 0 1 1 1 1) :compute (1 1 0 0 0 0 "#").
        (1 1 1 1 1 1) :compute (1 0 0 0 0 0 0 "#").
        () :compute (1 "#").
    };
    r:evidence (
        [ a r:Fact; r:gives {(1 0 1 0 0 1) :compute (1 0 1 0 1 0 "#")}]
        [ a r:Fact; r:gives {(1 0 1 1 1 1) :compute (1 1 0 0 0 0 "#")}]
        [ a r:Fact; r:gives {(1 1 1 1 1 1) :compute (1 0 0 0 0 0 0 "#")}]
        [ a r:Fact; r:gives {() :compute (1 "#")}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 1 0 1 0 "#")];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (1 1 0 0 0 0 "#")];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0 0 0 0 0 0 "#")];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 "#")];
    r:rule skolem:lemma2.

skolem:lemma2 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2, var:x_3. {
            (1 0 1 0 0 1) :compute var:x_0.
            (1 0 1 1 1 1) :compute var:x_1.
            (1 1 1 1 1 1) :compute var:x_2.
            () :compute var:x_3.
        } => {
            (1 0 1 0 0 1) :compute var:x_0.
            (1 0 1 1 1 1) :compute var:x_1.
            (1 1 1 1 1 1) :compute var:x_2.
            () :compute var:x_3.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/turing/turing-query.n3>].

