@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:component skolem:lemma4;
    r:component skolem:lemma5;
    r:component skolem:lemma6;
    r:component skolem:lemma7;
    r:component skolem:lemma8;
    r:gives {
        :Joe a :Runner.
        :Vic a :Runner.
        :Ray a :Runner.
        :Tom a :Runner.
        :Vic a :Winner.
        {
            :Joe a :Winner.
        } => ($ $).
        {
            :Ray a :Winner.
        } => ($ $).
        {
            :Tom a :Winner.
        } => ($ $).
    }.

skolem:lemma1 a r:Inference;
    r:gives {
        :Joe a :Runner.
    };
    r:evidence (
        skolem:lemma9
    );
    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/#Joe"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#Runner"]];
    r:rule skolem:lemma10.

skolem:lemma2 a r:Inference;
    r:gives {
        :Vic a :Runner.
    };
    r:evidence (
        skolem:lemma11
    );
    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/#Vic"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#Runner"]];
    r:rule skolem:lemma10.

skolem:lemma3 a r:Inference;
    r:gives {
        :Ray a :Runner.
    };
    r:evidence (
        skolem:lemma12
    );
    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/#Ray"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#Runner"]];
    r:rule skolem:lemma10.

skolem:lemma4 a r:Inference;
    r:gives {
        :Tom a :Runner.
    };
    r:evidence (
        skolem:lemma13
    );
    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/#Tom"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#Runner"]];
    r:rule skolem:lemma10.

skolem:lemma5 a r:Inference;
    r:gives {
        :Vic a :Winner.
    };
    r:evidence (
        skolem:lemma14
    );
    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/#Vic"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ n3:uri "http://example.org/#Winner"]];
    r:rule skolem:lemma10.

skolem:lemma6 a r:Inference;
    r:gives {
        {
            :Joe a :Winner.
        } => ($ $).
    };
    r:evidence (
        skolem:lemma15
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#Joe"]];
    r:rule skolem:lemma16.

skolem:lemma7 a r:Inference;
    r:gives {
        {
            :Ray a :Winner.
        } => ($ $).
    };
    r:evidence (
        skolem:lemma17
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#Ray"]];
    r:rule skolem:lemma16.

skolem:lemma8 a r:Inference;
    r:gives {
        {
            :Tom a :Winner.
        } => ($ $).
    };
    r:evidence (
        skolem:lemma18
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#Tom"]];
    r:rule skolem:lemma16.

skolem:lemma9 a r:Extraction;
    r:gives {
        :Joe a :Runner.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/winner.n3>].

skolem:lemma10 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 <https://eyereasoner.github.io/eye/reasoning/sequents/input/winner.n3>].

skolem:lemma11 a r:Extraction;
    r:gives {
        :Vic a :Runner.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/winner.n3>].

skolem:lemma12 a r:Extraction;
    r:gives {
        :Ray a :Runner.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/winner.n3>].

skolem:lemma13 a r:Extraction;
    r:gives {
        :Tom a :Runner.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/winner.n3>].

skolem:lemma14 a r:Extraction;
    r:gives {
        :Vic a :Winner.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/winner.n3>].

skolem:lemma15 a r:Inference;
    r:gives {
        {
            :Joe a :Winner.
        } => ($ $).
    };
    r:evidence (
        skolem:lemma11
        skolem:lemma14
        skolem:lemma9
        [ a r:Fact; r:gives {:Joe log:notEqualTo :Vic}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#Vic"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#Joe"]];
    r:rule skolem:lemma19.

skolem:lemma16 a r:Extraction;
    r:gives {
        @forAll var:x_0. {
            {
                var:x_0 a :Winner.
            } => ($ $).
        } => {
            {
                var:x_0 a :Winner.
            } => ($ $).
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/winner.n3>].

skolem:lemma17 a r:Inference;
    r:gives {
        {
            :Ray a :Winner.
        } => ($ $).
    };
    r:evidence (
        skolem:lemma11
        skolem:lemma14
        skolem:lemma12
        [ a r:Fact; r:gives {:Ray log:notEqualTo :Vic}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#Vic"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#Ray"]];
    r:rule skolem:lemma19.

skolem:lemma18 a r:Inference;
    r:gives {
        {
            :Tom a :Winner.
        } => ($ $).
    };
    r:evidence (
        skolem:lemma11
        skolem:lemma14
        skolem:lemma13
        [ a r:Fact; r:gives {:Tom log:notEqualTo :Vic}]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo [ n3:uri "http://example.org/#Vic"]];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo [ n3:uri "http://example.org/#Tom"]];
    r:rule skolem:lemma19.

skolem:lemma19 a r:Extraction;
    r:gives {
        @forAll var:x_0, var:x_1. {
            var:x_0 a :Runner.
            var:x_0 a :Winner.
            var:x_1 a :Runner.
            var:x_1 log:notEqualTo var:x_0.
        } => {
            {
                var:x_1 a :Winner.
            } => ($ $).
        }.
    };
    r:because [ a r:Parsing; r:source <https://eyereasoner.github.io/eye/reasoning/sequents/input/winner.n3>].

