@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#>.
@prefix log: <http://www.w3.org/2000/10/swap/log#>.

skolem:proof a r:Proof, r:Conjunction;
    r:component skolem:lemma1;
    r:component skolem:lemma2;
    r:component skolem:lemma3;
    r:gives {
        :Alice :loves :Bob.
        :Bob a :Person.
        :Alice :hates :Nobody.
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        :Alice :loves :Bob.
    };
    r:evidence (
        skolem:lemma4
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/loves"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/Alice"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/Bob"]];
    r:rule skolem:lemma5.

skolem:lemma2 a r:Inference;
    r:gives {
        :Bob a :Person.
    };
    r:evidence (
        skolem:lemma6
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://www.w3.org/1999/02/22-rdf-syntax-ns#type"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/Bob"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/Person"]];
    r:rule skolem:lemma5.

skolem:lemma3 a r:Inference;
    r:gives {
        :Alice :hates :Nobody.
    };
    r:evidence (
        skolem:lemma7
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/hates"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/Alice"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/Nobody"]];
    r:rule skolem:lemma5.

skolem:lemma4 a r:Extraction;
    r:gives {
        :Alice :loves :Bob.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/snaf/demo.n3>].

skolem:lemma5 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:lemma6 a r:Extraction;
    r:gives {
        :Bob a :Person.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/snaf/demo.n3>].

skolem:lemma7 a r:Inference;
    r:gives {
        :Alice :hates :Nobody.
    };
    r:evidence (
        [ a r:Fact; r:gives {((<https://eyereasoner.github.io/eye/reasoning/snaf/demo.n3> <https://eyereasoner.github.io/eye/reasoning/snaf/rules.n3>) 1) log:notIncludes {
            :Alice :hates :Bob.
        }}]
        skolem:lemma6
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo ((<https://eyereasoner.github.io/eye/reasoning/snaf/demo.n3> <https://eyereasoner.github.io/eye/reasoning/snaf/rules.n3>) 1)];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/Bob"]];
    r:rule skolem:lemma8.

skolem:lemma8 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 log:notIncludes {
                :Alice :hates var:x_1.
            }.
            var:x_1 a :Person.
        } => {
            :Alice :hates :Nobody.
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/snaf/rules.n3>].

