#Processed by EYE v20.1020.2137 josd
#eye --no-genid http://josd.github.io/eye/reasoning/rgb/redgraph002.n3 --query http://josd.github.io/eye/reasoning/rgb/greenquery002.n3

@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:gives {
    {:s :p _:sk_0} :u {:s :q _:sk_0}.
    {:s :q _:sk_1} :u {:s :r _:sk_1}.
  }.

<#lemma1> a r:Inference;
  r:gives {
    {:s :p _:sk_0} :u {:s :q _:sk_0}.
  };
  r:evidence (
    <#lemma3>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://example.org/try#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 <#lemma4>.

<#lemma2> a r:Inference;
  r:gives {
    {:s :q _:sk_1} :u {:s :r _:sk_1}.
  };
  r:evidence (
    <#lemma3>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://example.org/try#s"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_1"]];
  r:rule <#lemma5>.

<#lemma3> a r:Extraction;
  r:gives {
    :s :p :o.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/rgb/redgraph002.n3>].

<#lemma4> a r:Extraction;
  r:gives {
    @forAll var:x_0. @forSome var:x_1. {var:x_0 :p :o} => {{var:x_0 :p var:x_1} :u {var:x_0 :q var:x_1}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/rgb/greenquery002.n3>].

<#lemma5> a r:Extraction;
  r:gives {
    @forAll var:x_0. @forSome var:x_1. {var:x_0 :p :o} => {{var:x_0 :q var:x_1} :u {var:x_0 :r var:x_1}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/rgb/greenquery002.n3>].

#2020-10-23T20:17:10.751Z in=5 out=2 ent=2 step=2 brake=1 inf=20091 sec=0.035 inf/sec=574029
#ENDS

