PREFIX : <http://example.org/try#>
PREFIX r: <http://www.w3.org/2000/10/swap/reason#>

[] 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:rule <#lemma4>.

<#lemma2> a r:Inference;
  r:gives {
    {:s :q _:sk_1} :u {:s :r _:sk_1}.
  };
  r:evidence (
    <#lemma3>
  );
  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 {
    {?x_0_1 :p :o} => {{?x_0_1 :p _:x_1_1} :u {?x_0_1 :q _:x_1_1}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/rgb/greenquery002.n3>].

<#lemma5> a r:Extraction;
  r:gives {
    {?x_0_2 :p :o} => {{?x_0_2 :q _:x_1_2} :u {?x_0_2 :r _:x_1_2}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/rgb/greenquery002.n3>].

