@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/eye/reasoning#>.
@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 {
        3 :answer ((:left :right) (:left :center) (:right :center) (:left :right) (:center :left) (:center :right) (:left :right)).
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        3 :answer ((:left :right) (:left :center) (:right :center) (:left :right) (:center :left) (:center :right) (:left :right)).
    };
    r:evidence (
        skolem:lemma2
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "https://eyereasoner.github.io/eye/reasoning#answer"]];
    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_2"]; r:boundTo ((:left :right) (:left :center) (:right :center) (:left :right) (:center :left) (:center :right) (:left :right))];
    r:rule skolem:lemma3.

skolem:lemma2 a r:Inference;
    r:gives {
        3 :answer ((:left :right) (:left :center) (:right :center) (:left :right) (:center :left) (:center :right) (:left :right)).
    };
    r:evidence (
        [ a r:Fact; r:gives {(3 :left :right :center) :moves ((:left :right) (:left :center) (:right :center) (:left :right) (:center :left) (:center :right) (:left :right))}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo ((:left :right) (:left :center) (:right :center) (:left :right) (:center :left) (:center :right) (:left :right))];
    r:rule skolem:lemma4.

skolem:lemma3 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1, var:x_2. {
            var:x_1 var:x_0 var:x_2.
        } => {
            var:x_1 var:x_0 var:x_2.
        }.
    };
    r:because [ a r:Parsing; r:source <http://eulersharp.sourceforge.net/2003/03swap/pass>].

skolem:lemma4 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            (3 :left :right :center) :moves var:x_0.
        } => {
            3 :answer var:x_0.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/hanoi/hanoi.n3>].

