#Processed by EYE v20.1020.2137 josd
#eye --no-genid --tactic limited-answer 1 http://josd.github.io/eye/reasoning/dpe/dpe_theory.n3 http://josd.github.io/eye/reasoning/dpe/dpe_assumption.n3 --query http://josd.github.io/eye/reasoning/dpe/dpe_query.n3

@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 n3: <http://www.w3.org/2004/06/rei#>.

[] 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:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_1"]];
  r:rule <#lemma4>.

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

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

<#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>].

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

<#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>].

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

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

<#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>].

<#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: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 <#lemma16>.

<#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>].

<#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: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 <#lemma16>.

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

<#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>].

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

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

<#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>].

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

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

<#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>].

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

<#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>].

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

<#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>].

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

<#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>].

#2020-10-23T20:16:04.602Z in=16 out=2 ent=32 step=120 brake=4 inf=56530 sec=0.043 inf/sec=1314651
#ENDS

