@prefix : <http://josd.github.io/eye/reasoning/dpe/dpe#>.
@prefix r: <http://www.w3.org/2000/10/swap/reason#>.
@prefix var: <http://josd.github.io/var#>.
@prefix skolem: <http://josd.github.io/.well-known/genid/3917894951695475063#>.
@prefix n3: <http://www.w3.org/2004/06/rei#>.

skolem:proof a r:Proof, r:Conjunction;
  r:component skolem:lemma1;
  r:gives {
    :b :re _:sk_1.
    :c :re _:sk_1.
  }.

skolem:lemma1 a r:Inference;
  r:gives {
    :b :re _:sk_1.
    :c :re _:sk_1.
  };
  r:evidence (
    skolem:lemma2
    skolem:lemma3
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_1"]];
  r:rule skolem:lemma4.

skolem:lemma2 a r:Inference;
  r:gives {
    :b :re _:sk_1.
  };
  r:evidence (
    skolem:lemma5
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_1"]];
  r:rule skolem:lemma6.

skolem:lemma3 a r:Inference;
  r:gives {
    :c :re _:sk_1.
  };
  r:evidence (
    skolem:lemma5
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_1"]];
  r:rule skolem:lemma6.

skolem:lemma4 a r:Extraction;
  r:gives {
    @forAll var:x_0. {:b :re var:x_0.
     :c :re var:x_0} => {:b :re var:x_0.
     :c :re var:x_0}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_query.n3>].

skolem:lemma5 a r:Inference;
  r:gives {
    :b :r _:sk_1.
    :c :r _:sk_1.
  };
  r:evidence (
    skolem:lemma7
    skolem:lemma8
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_1"]];
  r:rule skolem:lemma9.

skolem:lemma6 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {var:x_0 :r var:x_1} => {var:x_0 :re var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

skolem:lemma7 a r:Inference;
  r:gives {
    :a :r :b.
  };
  r:evidence (
    skolem:lemma10
    skolem:lemma11
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:rule skolem:lemma12.

skolem:lemma8 a r:Inference;
  r:gives {
    :a :r :c.
  };
  r:evidence (
    skolem:lemma13
    skolem:lemma14
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:rule skolem:lemma12.

skolem:lemma9 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1, var:x_2. @forSome var:x_3. {var:x_0 :r var:x_1.
     var:x_0 :r var:x_2} => {var:x_1 :r var:x_3.
     var:x_2 :r var:x_3}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

skolem:lemma10 a r:Extraction;
  r:gives {
    :a :re :b.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

skolem:lemma11 a r:Inference;
  r:gives {
    :a :not_e :b.
  };
  r:evidence (
    skolem:lemma15
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:rule skolem:lemma16.

skolem:lemma12 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {var:x_0 :re var:x_1.
     var:x_0 :not_e var:x_1} => {var:x_0 :r var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

skolem:lemma13 a r:Extraction;
  r:gives {
    :a :re :c.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

skolem:lemma14 a r:Inference;
  r:gives {
    :a :not_e :c.
  };
  r:evidence (
    skolem:lemma17
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:rule skolem:lemma16.

skolem:lemma15 a r:Inference;
  r:gives {
    :b :not_e :a.
  };
  r:evidence (
    skolem:lemma18
    skolem:lemma13
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:rule skolem:lemma19.

skolem:lemma16 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {var:x_0 :not_e var:x_1} => {var:x_1 :not_e var:x_0}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

skolem:lemma17 a r:Inference;
  r:gives {
    :c :not_e :a.
  };
  r:evidence (
    skolem:lemma20
    skolem:lemma10
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:rule skolem:lemma19.

skolem:lemma18 a r:Inference;
  r:gives {
    :b :not_re :c.
  };
  r:evidence (
    skolem:lemma21
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:rule skolem:lemma22.

skolem:lemma19 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1, var:x_2. {var:x_0 :not_re var:x_1.
     var:x_2 :re var:x_1} => {var:x_0 :not_e var:x_2}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

skolem:lemma20 a r:Inference;
  r:gives {
    :c :not_re :b.
  };
  r:evidence (
    skolem:lemma23
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:rule skolem:lemma24.

skolem:lemma21 a r:Inference;
  r:gives {
    :c :re :c.
  };
  r:evidence (
    skolem:lemma25
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:rule skolem:lemma26.

skolem:lemma22 a r:Extraction;
  r:gives {
    @forAll var:x_0. {:c :re var:x_0} => {:b :not_re var:x_0}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_assumption.n3>].

skolem:lemma23 a r:Inference;
  r:gives {
    :b :re :b.
  };
  r:evidence (
    skolem:lemma27
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:rule skolem:lemma26.

skolem:lemma24 a r:Extraction;
  r:gives {
    @forAll var:x_0. {:b :re var:x_0} => {:c :not_re var:x_0}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_assumption.n3>].

skolem:lemma25 a r:Inference;
  r:gives {
    :c :e :c.
  };
  r:evidence (
    skolem:lemma13
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#c"]];
  r:rule skolem:lemma28.

skolem:lemma26 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {var:x_0 :e var:x_1} => {var:x_0 :re var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

skolem:lemma27 a r:Inference;
  r:gives {
    :b :e :b.
  };
  r:evidence (
    skolem:lemma10
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#a"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/eye/reasoning/dpe/dpe#b"]];
  r:rule skolem:lemma28.

skolem:lemma28 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {var:x_0 :re var:x_1} => {var:x_1 :e var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

