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 {
    {?U_0 :p ?U_1} => {?U_0 :q ?U_1}.
    {?U_2 :q ?U_3} => {?U_2 :r ?U_3}.
  }.

<#lemma1> a r:Inference;
  r:gives {
    {?U_0 :p ?U_1} => {?U_0 :q ?U_1}.
  };
  r:evidence (
    [ a r:Fact; r:gives true]
  );
  r:rule <#lemma3>.

<#lemma2> a r:Inference;
  r:gives {
    {?U_2 :q ?U_3} => {?U_2 :r ?U_3}.
  };
  r:evidence (
    [ a r:Fact; r:gives true]
  );
  r:rule <#lemma4>.

<#lemma3> a r:Extraction;
  r:gives {
    true => {{_:x_0_5 :p _:x_1_5} => {_:x_0_5 :q _:x_1_5}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/rgb/greenquery003.n3>].

<#lemma4> a r:Extraction;
  r:gives {
    true => {{_:x_0_6 :q _:x_1_6} => {_:x_0_6 :r _:x_1_6}}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/rgb/greenquery003.n3>].

