PREFIX : <http://josd.github.io/eye/reasoning/dpe/dpe#>
PREFIX r: <http://www.w3.org/2000/10/swap/reason#>

[] a r:Proof, r:Conjunction;
  r:component <#lemma1>;
  r:gives {
    :b :re _:sk_1.
    :c :re _:sk_1.
  }.

<#lemma1> a r:Inference;
  r:gives {
    :b :re _:sk_1.
    :c :re _:sk_1.
  };
  r:evidence (
    <#lemma2>
    <#lemma3>
  );
  r:rule <#lemma4>.

<#lemma2> a r:Inference;
  r:gives {
    :b :re _:sk_1.
  };
  r:evidence (
    <#lemma5>
  );
  r:rule <#lemma6>.

<#lemma3> a r:Inference;
  r:gives {
    :c :re _:sk_1.
  };
  r:evidence (
    <#lemma5>
  );
  r:rule <#lemma6>.

<#lemma4> a r:Extraction;
  r:gives {
    {:b :re ?x_0_1.
     :c :re ?x_0_1} => {:b :re ?x_0_1.
     :c :re ?x_0_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_query.n3>].

<#lemma5> a r:Inference;
  r:gives {
    :b :r _:sk_1.
    :c :r _:sk_1.
  };
  r:evidence (
    <#lemma7>
    <#lemma8>
  );
  r:rule <#lemma9>.

<#lemma6> a r:Extraction;
  r:gives {
    {?x_0_2 :r ?x_1_2} => {?x_0_2 :re ?x_1_2}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

<#lemma7> a r:Inference;
  r:gives {
    :a :r :b.
  };
  r:evidence (
    <#lemma10>
    <#lemma11>
  );
  r:rule <#lemma12>.

<#lemma8> a r:Inference;
  r:gives {
    :a :r :c.
  };
  r:evidence (
    <#lemma13>
    <#lemma14>
  );
  r:rule <#lemma12>.

<#lemma9> a r:Extraction;
  r:gives {
    {?x_0_3 :r ?x_1_3.
     ?x_0_3 :r ?x_2_3} => {?x_1_3 :r _:x_3_3.
     ?x_2_3 :r _:x_3_3}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

<#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>].

<#lemma11> a r:Inference;
  r:gives {
    :a :not_e :b.
  };
  r:evidence (
    <#lemma15>
  );
  r:rule <#lemma16>.

<#lemma12> a r:Extraction;
  r:gives {
    {?x_0_4 :re ?x_1_4.
     ?x_0_4 :not_e ?x_1_4} => {?x_0_4 :r ?x_1_4}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

<#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>].

<#lemma14> a r:Inference;
  r:gives {
    :a :not_e :c.
  };
  r:evidence (
    <#lemma17>
  );
  r:rule <#lemma16>.

<#lemma15> a r:Inference;
  r:gives {
    :b :not_e :a.
  };
  r:evidence (
    <#lemma18>
    <#lemma13>
  );
  r:rule <#lemma19>.

<#lemma16> a r:Extraction;
  r:gives {
    {?x_0_5 :not_e ?x_1_5} => {?x_1_5 :not_e ?x_0_5}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

<#lemma17> a r:Inference;
  r:gives {
    :c :not_e :a.
  };
  r:evidence (
    <#lemma20>
    <#lemma10>
  );
  r:rule <#lemma19>.

<#lemma18> a r:Inference;
  r:gives {
    :b :not_re :c.
  };
  r:evidence (
    <#lemma21>
  );
  r:rule <#lemma22>.

<#lemma19> a r:Extraction;
  r:gives {
    {?x_0_6 :not_re ?x_1_6.
     ?x_2_6 :re ?x_1_6} => {?x_0_6 :not_e ?x_2_6}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

<#lemma20> a r:Inference;
  r:gives {
    :c :not_re :b.
  };
  r:evidence (
    <#lemma23>
  );
  r:rule <#lemma24>.

<#lemma21> a r:Inference;
  r:gives {
    :c :re :c.
  };
  r:evidence (
    <#lemma25>
  );
  r:rule <#lemma26>.

<#lemma22> a r:Extraction;
  r:gives {
    {:c :re ?x_0_7} => {:b :not_re ?x_0_7}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_assumption.n3>].

<#lemma23> a r:Inference;
  r:gives {
    :b :re :b.
  };
  r:evidence (
    <#lemma27>
  );
  r:rule <#lemma26>.

<#lemma24> a r:Extraction;
  r:gives {
    {:b :re ?x_0_8} => {:c :not_re ?x_0_8}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_assumption.n3>].

<#lemma25> a r:Inference;
  r:gives {
    :c :e :c.
  };
  r:evidence (
    <#lemma13>
  );
  r:rule <#lemma28>.

<#lemma26> a r:Extraction;
  r:gives {
    {?x_0_9 :e ?x_1_9} => {?x_0_9 :re ?x_1_9}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

<#lemma27> a r:Inference;
  r:gives {
    :b :e :b.
  };
  r:evidence (
    <#lemma10>
  );
  r:rule <#lemma28>.

<#lemma28> a r:Extraction;
  r:gives {
    {?x_0_10 :re ?x_1_10} => {?x_1_10 :e ?x_1_10}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3>].

