#Processed by EYE v20.1020.2137 josd
#eye --no-genid --wcache http://josd.github.io/eye/reasoning/dqc . --no-distinct-input http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3 --query http://josd.github.io/eye/reasoning/dqc/sdcoding-query.n3

@prefix dqc: <http://josd.github.io/eye/reasoning/dqc#>.
@prefix e: <http://eulersharp.sourceforge.net/2003/03swap/log-rules#>.
@prefix math: <http://www.w3.org/2000/10/swap/math#>.
@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:gives {
    1 dqc:sdcoding 1 .
    3 dqc:sdcoding 3 .
    0 dqc:sdcoding 0 .
    2 dqc:sdcoding 2 .
  }.

<#lemma1> a r:Inference;
  r:gives {
    1 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma5>
    [ a r:Fact; r:gives {((<http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>) 1) e:findall (1 {1 dqc:sdcoding 1} (1))}]
    [ a r:Fact; r:gives {(1) math:sum 1}]
    [ a r:Fact; r:gives {(1 2) math:remainder 1}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo 1];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo 1];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo ((<http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>) 1)];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo (1)];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 1];
  r:rule <#lemma6>.

<#lemma2> a r:Inference;
  r:gives {
    3 dqc:sdcoding 3 .
  };
  r:evidence (
    <#lemma7>
    [ a r:Fact; r:gives {((<http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>) 1) e:findall (1 {3 dqc:sdcoding 3} (1))}]
    [ a r:Fact; r:gives {(1) math:sum 1}]
    [ a r:Fact; r:gives {(1 2) math:remainder 1}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo 3];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo 3];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo ((<http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>) 1)];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo (1)];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 1];
  r:rule <#lemma6>.

<#lemma3> a r:Inference;
  r:gives {
    0 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma8>
    [ a r:Fact; r:gives {((<http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>) 1) e:findall (1 {0 dqc:sdcoding 0} (1))}]
    [ a r:Fact; r:gives {(1) math:sum 1}]
    [ a r:Fact; r:gives {(1 2) math:remainder 1}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo 0];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo 0];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo ((<http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>) 1)];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo (1)];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 1];
  r:rule <#lemma6>.

<#lemma4> a r:Inference;
  r:gives {
    2 dqc:sdcoding 2 .
  };
  r:evidence (
    <#lemma9>
    [ a r:Fact; r:gives {((<http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>) 1) e:findall (1 {2 dqc:sdcoding 2} (1))}]
    [ a r:Fact; r:gives {(1) math:sum 1}]
    [ a r:Fact; r:gives {(1 2) math:remainder 1}]
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo 2];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo 2];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo ((<http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>) 1)];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo (1)];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 1];
  r:rule <#lemma6>.

<#lemma5> a r:Extraction;
  r:gives {
    1 dqc:sdcoding 1 .
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>].

<#lemma6> a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4. {var:x_0 dqc:sdcoding var:x_1.
     var:x_2 e:findall (1 {var:x_0 dqc:sdcoding var:x_1} var:x_3).
     var:x_3 math:sum var:x_4.
     (var:x_4 2) math:remainder 1} => {var:x_0 dqc:sdcoding var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding-query.n3>].

<#lemma7> a r:Extraction;
  r:gives {
    3 dqc:sdcoding 3 .
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>].

<#lemma8> a r:Extraction;
  r:gives {
    0 dqc:sdcoding 0 .
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>].

<#lemma9> a r:Extraction;
  r:gives {
    2 dqc:sdcoding 2 .
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding-a.n3>].

#2020-10-23T20:16:05.177Z in=25 out=4 ent=4 step=4 brake=2 inf=39507 sec=0.032 inf/sec=1234594
#ENDS

