#Processed by EYE v20.0214.1629 josd
#eye --no-genid --plugin http://josd.github.io/brain/n3p/sample.pl --pass-all

@prefix e: <http://eulersharp.sourceforge.net/2003/03swap/log-rules#>.
@prefix : <http://example.org/try#>.
@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:component <#lemma11>;
  r:component <#lemma12>;
  r:gives {
    :s :p {:a :b :c}.
    :s :p {:a :b :c.
     :d :e :f}.
    <http://josd.github.io/.well-known/genid/0l4gZjrLokrTSMCaH1QcS_VZsC0#e_X_1> :p {<http://josd.github.io/.well-known/genid/0l4gZjrLokrTSMCaH1QcS_VZsC0#e_X_2> :b :c}.
    :s :p <http://www.w3.org/1999/02/22-rdf-syntax-ns#nil>.
    _:sk_0 :p :o.
    {:u :v ?U_1.
     ?U_2 :y :z} => {?U_1 a ?U_2}.
    {:u :p ?U_3} => false.
    {?U_4 :u ?U_5.
     ?U_4 :v ?U_6} => {_:sk_7 :x ?U_5.
     _:sk_7 :y ?U_6}.
    {:a :b ?U_8.
     ?U_8 :c :d.
     ?U_8 :e :f} => {:g :h :i}.
    {?U_9 :q ?U_10} <= {:u :v ?U_9.
     ?U_10 ?U_11 :z}.
    {?U_12 :y ?U_13} <= {?U_13 e:firstRest (?U_14 ?U_15).
     ?U_12 :p ?U_14.
     ?U_12 :y ?U_15}.
    {?U_16 :r ?U_17} <= {{?U_16 :q ?U_18} <= ?U_17}.
  }.

<#lemma1> a r:Inference;
  r:gives {
    :s :p {:a :b :c}.
  };
  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/try#p"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://example.org/try#s"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo {:a :b :c}];
  r:rule <#lemma14>.

<#lemma2> a r:Inference;
  r:gives {
    :s :p {:a :b :c.
     :d :e :f}.
  };
  r:evidence (
    <#lemma15>
    [ 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/try#p"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://example.org/try#s"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo {:a :b :c.
   :d :e :f}];
  r:rule <#lemma14>.

<#lemma3> a r:Inference;
  r:gives {
    <http://josd.github.io/.well-known/genid/0l4gZjrLokrTSMCaH1QcS_VZsC0#e_X_1> :p {<http://josd.github.io/.well-known/genid/0l4gZjrLokrTSMCaH1QcS_VZsC0#e_X_2> :b :c}.
  };
  r:evidence (
    <#lemma16>
    [ 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/try#p"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://josd.github.io/.well-known/genid/0l4gZjrLokrTSMCaH1QcS_VZsC0#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/0l4gZjrLokrTSMCaH1QcS_VZsC0#e_X_2> :b :c}];
  r:rule <#lemma14>.

<#lemma4> a r:Inference;
  r:gives {
    :s :p <http://www.w3.org/1999/02/22-rdf-syntax-ns#nil>.
  };
  r:evidence (
    <#lemma17>
    [ 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/try#p"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://example.org/try#s"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"]];
  r:rule <#lemma14>.

<#lemma5> a r:Inference;
  r:gives {
    _:sk_0 :p :o.
  };
  r:evidence (
    <#lemma18>
    [ 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/try#p"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://example.org/try#o"]];
  r:rule <#lemma14>.

<#lemma6> a r:Inference;
  r:gives {
    {:u :v ?U_1.
     ?U_2 :y :z} => {?U_1 a ?U_2}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{:u :v ?U_1.
     ?U_2 :y :z} => {?U_1 a ?U_2}}]
    [ a r:Fact; r:gives {{:u :v _:sk_1.
     _:sk_2 :y :z} <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 {:u :v _:sk_1.
   _:sk_2 :y :z}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {_:sk_1 a _:sk_2}];
  r:rule <#lemma19>.

<#lemma7> a r:Inference;
  r:gives {
    {:u :p ?U_3} => false.
  };
  r:evidence (
    [ a r:Fact; r:gives {{:u :p ?U_3} => false}]
    [ a r:Fact; r:gives {{:u :p _:sk_3} <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 {:u :p _:sk_3}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule <#lemma19>.

<#lemma8> a r:Inference;
  r:gives {
    {?U_4 :u ?U_5.
     ?U_4 :v ?U_6} => {_:sk_7 :x ?U_5.
     _:sk_7 :y ?U_6}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{?U_4 :u ?U_5.
     ?U_4 :v ?U_6} => {_:sk_7 :x ?U_5.
     _:sk_7 :y ?U_6}}]
    [ a r:Fact; r:gives {{_:sk_4 :u _:sk_5.
     _:sk_4 :v _:sk_6} <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 :u _:sk_5.
   _:sk_4 :v _:sk_6}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {_:sk_7 :x _:sk_5.
   _:sk_7 :y _:sk_6}];
  r:rule <#lemma19>.

<#lemma9> a r:Inference;
  r:gives {
    {:a :b ?U_8.
     ?U_8 :c :d.
     ?U_8 :e :f} => {:g :h :i}.
  };
  r:evidence (
    [ a r:Fact; r:gives {{:a :b ?U_8.
     ?U_8 :c :d.
     ?U_8 :e :f} => {:g :h :i}}]
    [ a r:Fact; r:gives {{:a :b _:sk_8.
     _:sk_8 :c :d.
     _:sk_8 :e :f} <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 {:a :b _:sk_8.
   _:sk_8 :c :d.
   _:sk_8 :e :f}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {:g :h :i}];
  r:rule <#lemma19>.

<#lemma10> a r:Inference;
  r:gives {
    {?U_9 :q ?U_10} <= {:u :v ?U_9.
     ?U_10 ?U_11 :z}.
  };
  r:evidence (
    <#lemma20>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {_:sk_9 :q _:sk_10}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {:u :v _:sk_9.
   _:sk_10 _:sk_11 :z}];
  r:rule <#lemma21>.

<#lemma11> a r:Inference;
  r:gives {
    {?U_12 :y ?U_13} <= {?U_13 e:firstRest (?U_14 ?U_15).
     ?U_12 :p ?U_14.
     ?U_12 :y ?U_15}.
  };
  r:evidence (
    <#lemma22>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {_:sk_12 :y _:sk_13}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {_:sk_13 e:firstRest (_:sk_14 _:sk_15).
   _:sk_12 :p _:sk_14.
   _:sk_12 :y _:sk_15}];
  r:rule <#lemma21>.

<#lemma12> a r:Inference;
  r:gives {
    {?U_16 :r ?U_17} <= {{?U_16 :q ?U_18} <= ?U_17}.
  };
  r:evidence (
    <#lemma23>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo {_:sk_16 :r _:sk_17}];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo {{_:sk_16 :q _:sk_18} <= _:sk_17}];
  r:rule <#lemma21>.

<#lemma13> a r:Extraction;
  r:gives {
    :s :p {:a :b :c}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/n3p/sample.n3>].

<#lemma14> 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>].

<#lemma15> a r:Extraction;
  r:gives {
    :s :p {:a :b :c.
     :d :e :f}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/n3p/sample.n3>].

<#lemma16> a r:Extraction;
  r:gives {
    <http://josd.github.io/.well-known/genid/0l4gZjrLokrTSMCaH1QcS_VZsC0#e_X_1> :p {<http://josd.github.io/.well-known/genid/0l4gZjrLokrTSMCaH1QcS_VZsC0#e_X_2> :b :c}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/n3p/sample.n3>].

<#lemma17> a r:Extraction;
  r:gives {
    :s :p <http://www.w3.org/1999/02/22-rdf-syntax-ns#nil>.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/n3p/sample.n3>].

<#lemma18> a r:Inference;
  r:gives {
    _:sk_0 :p :o.
  };
  r:evidence (
    [ a r:Fact; r:gives true]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]];
  r:rule <#lemma24>.

<#lemma19> 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>].

<#lemma20> a r:Extraction;
  r:gives {
    {?U_9 :q ?U_10} <= {:u :v ?U_9.
     ?U_10 ?U_11 :z}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/n3p/sample.n3>].

<#lemma21> a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {var:x_0 <= var:x_1} => {var:x_0 <= var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://eulersharp.sourceforge.net/2003/03swap/pass-all>].

<#lemma22> a r:Extraction;
  r:gives {
    {?U_12 :y ?U_13} <= {?U_13 e:firstRest (?U_14 ?U_15).
     ?U_12 :p ?U_14.
     ?U_12 :y ?U_15}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/n3p/sample.n3>].

<#lemma23> a r:Extraction;
  r:gives {
    {?U_16 :r ?U_17} <= {{?U_16 :q ?U_18} <= ?U_17}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/n3p/sample.n3>].

<#lemma24> a r:Extraction;
  r:gives {
    @forSome var:x_0. true => {var:x_0 :p :o}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/n3p/sample.n3>].

#2020-02-15T20:06:23.307Z in=12 out=12 ent=13 step=29 brake=2 inf=51037 sec=0.097 inf/sec=526155
#ENDS

