#Processed by EYE v20.0218.2044 josd
#eye --no-genid http://josd.github.io/brain/iq/iq.n3 --pass-all

@prefix : <http://example.org/test#>.
@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:component <#lemma2>;
  r:component <#lemma3>;
  r:component <#lemma4>;
  r:component <#lemma5>;
  r:component <#lemma6>;
  r:component <#lemma7>;
  r:component <#lemma8>;
  r:component <#lemma9>;
  r:component <#lemma10>;
  r:gives {
    <http://josd.github.io/.well-known/genid/#e_x_1> :says {<http://josd.github.io/.well-known/genid/#e_x_2> :knows :Albert}.
    :s :p :o.
    :s :pp {:s :ppp :ooo}.
    {?U_1 :knows :Albert} => {var:x_0 :knows :Kurt}.
    {:e :p :a} => {:e :q :b}.
    {{?U_2 :p :a} => {?U_2 :q :b}} => {{?U_2 :r :c} => {?U_2 :s :d}}.
    {?U_3 :p :o} => {?U_3 :pp {?U_3 :ppp :ooo}}.
    {?U_4 :p :o} => {{{?U_4 :p2 _:sk_5} => {?U_4 :p3 _:sk_5}} => {{?U_4 :p4 _:sk_5} => {?U_4 :p5 _:sk_5}}}.
    {:e :r :c} => {:e :s :d}.
    {{:s :p2 ?U_0} => {:s :p3 ?U_0}} => {{:s :p4 ?U_0} => {:s :p5 ?U_0}}.
  }.

<#lemma1> a r:Inference;
  r:gives {
    <http://josd.github.io/.well-known/genid/#e_x_1> :says {<http://josd.github.io/.well-known/genid/#e_x_2> :knows :Albert}.
  };
  r:evidence (
    <#lemma11>
    [ a r:Fact; r:gives {:says <http://www.w3.org/2000/10/swap/log#notEqualTo> <http://www.w3.org/2000/10/swap/log#implies>}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://example.org/test#says"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "http://josd.github.io/.well-known/genid/#e_x_1"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo {<http://josd.github.io/.well-known/genid/#e_x_2> :knows :Albert}];
  r:rule <#lemma12>.

<#lemma2> a r:Inference;
  r:gives {
    :s :p :o.
  };
  r:evidence (
    <#lemma13>
    [ a r:Fact; r:gives {:p <http://www.w3.org/2000/10/swap/log#notEqualTo> <http://www.w3.org/2000/10/swap/log#implies>}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://example.org/test#p"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://example.org/test#s"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://example.org/test#o"]];
  r:rule <#lemma12>.

<#lemma3> a r:Inference;
  r:gives {
    :s :pp {:s :ppp :ooo}.
  };
  r:evidence (
    <#lemma14>
    [ a r:Fact; r:gives {:pp <http://www.w3.org/2000/10/swap/log#notEqualTo> <http://www.w3.org/2000/10/swap/log#implies>}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://example.org/test#pp"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://example.org/test#s"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo {:s :ppp :ooo}];
  r:rule <#lemma12>.

<#lemma4> a r:Inference;
  r:gives {
    {?U_1 :knows :Albert} => {var:x_0 :knows :Kurt}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{?U_1 :knows :Albert} => {var:x_0 :knows :Kurt}}]
    [ a r:Fact; r:gives {{_:sk_1 :knows :Albert} <http://www.w3.org/2000/10/swap/log#notEqualTo> true}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {_:sk_1 :knows :Albert}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {var:x_0 :knows :Kurt}];
  r:rule <#lemma15>.

<#lemma5> a r:Inference;
  r:gives {
    {:e :p :a} => {:e :q :b}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{:e :p :a} => {:e :q :b}}]
    [ a r:Fact; r:gives {{:e :p :a} <http://www.w3.org/2000/10/swap/log#notEqualTo> true}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {:e :p :a}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {:e :q :b}];
  r:rule <#lemma15>.

<#lemma6> a r:Inference;
  r:gives {
    {{?U_2 :p :a} => {?U_2 :q :b}} => {{?U_2 :r :c} => {?U_2 :s :d}}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{{?U_2 :p :a} => {?U_2 :q :b}} => {{?U_2 :r :c} => {?U_2 :s :d}}}]
    [ a r:Fact; r:gives {{{_:sk_2 :p :a} => {_:sk_2 :q :b}} <http://www.w3.org/2000/10/swap/log#notEqualTo> true}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {{_:sk_2 :p :a} => {_:sk_2 :q :b}}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {{_:sk_2 :r :c} => {_:sk_2 :s :d}}];
  r:rule <#lemma15>.

<#lemma7> a r:Inference;
  r:gives {
    {?U_3 :p :o} => {?U_3 :pp {?U_3 :ppp :ooo}}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{?U_3 :p :o} => {?U_3 :pp {?U_3 :ppp :ooo}}}]
    [ a r:Fact; r:gives {{_:sk_3 :p :o} <http://www.w3.org/2000/10/swap/log#notEqualTo> true}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {_:sk_3 :p :o}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {_:sk_3 :pp {_:sk_3 :ppp :ooo}}];
  r:rule <#lemma15>.

<#lemma8> a r:Inference;
  r:gives {
    {?U_4 :p :o} => {{{?U_4 :p2 _:sk_5} => {?U_4 :p3 _:sk_5}} => {{?U_4 :p4 _:sk_5} => {?U_4 :p5 _:sk_5}}}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{?U_4 :p :o} => {{{?U_4 :p2 _:sk_5} => {?U_4 :p3 _:sk_5}} => {{?U_4 :p4 _:sk_5} => {?U_4 :p5 _:sk_5}}}}]
    [ a r:Fact; r:gives {{_:sk_4 :p :o} <http://www.w3.org/2000/10/swap/log#notEqualTo> true}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {_:sk_4 :p :o}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {{{_:sk_4 :p2 _:sk_5} => {_:sk_4 :p3 _:sk_5}} => {{_:sk_4 :p4 _:sk_5} => {_:sk_4 :p5 _:sk_5}}}];
  r:rule <#lemma15>.

<#lemma9> a r:Inference;
  r:gives {
    {:e :r :c} => {:e :s :d}.
  };
  r:evidence (
    <#lemma16>
    [ a r:Fact; r:gives {{:e :r :c} <http://www.w3.org/2000/10/swap/log#notEqualTo> true}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {:e :r :c}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {:e :s :d}];
  r:rule <#lemma15>.

<#lemma10> a r:Inference;
  r:gives {
    {{:s :p2 ?U_0} => {:s :p3 ?U_0}} => {{:s :p4 ?U_0} => {:s :p5 ?U_0}}.
  };
  r:evidence (
    <#lemma17>
    [ a r:Fact; r:gives {{{:s :p2 _:sk_0} => {:s :p3 _:sk_0}} <http://www.w3.org/2000/10/swap/log#notEqualTo> true}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {{:s :p2 _:sk_0} => {:s :p3 _:sk_0}}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {{:s :p4 _:sk_0} => {:s :p5 _:sk_0}}];
  r:rule <#lemma15>.

<#lemma11> a r:Extraction;
  r:gives {
    <http://josd.github.io/.well-known/genid/#e_x_1> :says {<http://josd.github.io/.well-known/genid/#e_x_2> :knows :Albert}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/iq/iq.n3>].

<#lemma12> 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_0 <http://www.w3.org/2000/10/swap/log#notEqualTo> <http://www.w3.org/2000/10/swap/log#implies>} => {var:x_1 var:x_0 var:x_2}.
  };
  r:because [ a r:Parsing; r:source <http://eulersharp.sourceforge.net/2003/03swap/pass-all>].

<#lemma13> a r:Extraction;
  r:gives {
    :s :p :o.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/iq/iq.n3>].

<#lemma14> a r:Inference;
  r:gives {
    :s :pp {:s :ppp :ooo}.
  };
  r:evidence (
    <#lemma13>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://example.org/test#s"]];
  r:rule <#lemma18>.

<#lemma15> a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {var:x_0 => var:x_1.
     var:x_0 <http://www.w3.org/2000/10/swap/log#notEqualTo> true} => {var:x_0 => var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://eulersharp.sourceforge.net/2003/03swap/pass-all>].

<#lemma16> a r:Inference;
  r:gives {
    {:e :r :c} => {:e :s :d}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{:e :p :a} => {:e :q :b}}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://example.org/test#e"]];
  r:rule <#lemma19>.

<#lemma17> a r:Inference;
  r:gives {
    {{:s :p2 ?U_0} => {:s :p3 ?U_0}} => {{:s :p4 ?U_0} => {:s :p5 ?U_0}}.
  };
  r:evidence (
    <#lemma13>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://example.org/test#s"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]];
  r:rule <#lemma20>.

<#lemma18> a r:Extraction;
  r:gives {
    @forAll var:x_0. {var:x_0 :p :o} => {var:x_0 :pp {var:x_0 :ppp :ooo}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/iq/iq.n3>].

<#lemma19> a r:Extraction;
  r:gives {
    @forAll var:x_0. {{var:x_0 :p :a} => {var:x_0 :q :b}} => {{var:x_0 :r :c} => {var:x_0 :s :d}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/iq/iq.n3>].

<#lemma20> a r:Extraction;
  r:gives {
    @forAll var:x_0. @forSome var:x_1. {var:x_0 :p :o} => {{{var:x_0 :p2 var:x_1} => {var:x_0 :p3 var:x_1}} => {{var:x_0 :p4 var:x_1} => {var:x_0 :p5 var:x_1}}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/iq/iq.n3>].

#2020-02-22T21:51:57.116Z in=7 out=10 ent=13 step=26 brake=2 inf=59779 sec=0.119 inf/sec=502345
#ENDS

