@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 rdfs: <http://www.w3.org/2000/01/rdf-schema#>.
@prefix n3: <http://www.w3.org/2004/06/rei#>.
@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 {
        :pat a rdfs:Resource.
        :bob :loves skolem:t_0.
        skolem:t_0 :is :lonely.
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        :pat a rdfs:Resource.
        :bob :loves skolem:t_0.
        skolem:t_0 :is :lonely.
    };
    r:evidence (
        skolem:lemma2
        skolem:lemma3
        skolem:lemma4
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ a r:Existential; n3:nodeId "https://eyereasoner.github.io/.well-known/genid/8b98b360-9a70-4845-b52c-c675af60ad01#t_0"]];
    r:rule [ a r:Fact; r:gives {@forSome var:x_0. {
        :pat a rdfs:Resource.
        :bob :loves var:x_0.
        var:x_0 :is :lonely.
    } => {
        :pat a rdfs:Resource.
        :bob :loves var:x_0.
        var:x_0 :is :lonely.
    }}].

skolem:lemma2 a r:Inference;
    r:gives {
        :pat a rdfs:Resource.
    };
    r:evidence (
        [ a r:Fact; r:gives true]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#pat"]];
    r:rule skolem:lemma5.

skolem:lemma3 a r:Inference;
    r:gives {
        :bob :loves skolem:t_0.
    };
    r:evidence (
        [ a r:Fact; r:gives {(:bob) log:skolem skolem:t_0}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "https://eyereasoner.github.io/.well-known/genid/8b98b360-9a70-4845-b52c-c675af60ad01#t_0"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#bob"]];
    r:rule skolem:lemma6.

skolem:lemma4 a r:Inference;
    r:gives {
        skolem:t_0 :is :lonely.
    };
    r:evidence (
        [ a r:Fact; r:gives {(:bob) log:skolem skolem:t_0}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "https://eyereasoner.github.io/.well-known/genid/8b98b360-9a70-4845-b52c-c675af60ad01#t_0"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#bob"]];
    r:rule skolem:lemma7.

skolem:lemma5 a r:Extraction;
    r:gives {
        @forSome var:x_0. {
            var:x_0 a rdfs:Resource.
        } <= true.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/universal/universal.n3>].

skolem:lemma6 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 :loves var:x_1.
        } <= {
            (var:x_0) log:skolem var:x_1.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/universal/universal.n3>].

skolem:lemma7 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_1 :is :lonely.
        } <= {
            (var:x_0) log:skolem var:x_1.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/universal/universal.n3>].

