@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 math: <http://www.w3.org/2000/10/swap/math#>.
@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 {
        5 :moreInterestingThan 3 .
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        5 :moreInterestingThan 3 .
    };
    r:evidence (
        skolem:lemma2
    );
    r:rule [ a r:Fact; r:gives {{
        5 :moreInterestingThan 3.
    } => {
        5 :moreInterestingThan 3.
    }}].

skolem:lemma2 a r:Inference;
    r:gives {
        5 :moreInterestingThan 3 .
    };
    r:evidence (
        [ a r:Fact; r:gives {5 math:greaterThan 3}]
    );
    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 3];
    r:rule skolem:lemma3.

skolem:lemma3 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 :moreInterestingThan var:x_1.
        } <= {
            var:x_0 math:greaterThan var:x_1.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/backward/backward.n3>].

