PREFIX dqc: <http://josd.github.io/eye/reasoning/dqc#>
PREFIX r: <http://www.w3.org/2000/10/swap/reason#>

[] 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:component <#lemma13>;
  r:component <#lemma14>;
  r:gives {
    0 dqc:sdcoding 1 .
    0 dqc:sdcoding 3 .
    1 dqc:sdcoding 0 .
    1 dqc:sdcoding 1 .
    1 dqc:sdcoding 2 .
    2 dqc:sdcoding 1 .
    2 dqc:sdcoding 3 .
    3 dqc:sdcoding 1 .
    3 dqc:sdcoding 3 .
    3 dqc:sdcoding 0 .
    3 dqc:sdcoding 2 .
    0 dqc:sdcoding 0 .
    2 dqc:sdcoding 0 .
    2 dqc:sdcoding 2 .
  }.

<#lemma1> a r:Inference;
  r:gives {
    0 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma15>
  );
  r:rule <#lemma16>.

<#lemma2> a r:Inference;
  r:gives {
    0 dqc:sdcoding 3 .
  };
  r:evidence (
    <#lemma17>
  );
  r:rule <#lemma16>.

<#lemma3> a r:Inference;
  r:gives {
    1 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma18>
  );
  r:rule <#lemma16>.

<#lemma4> a r:Inference;
  r:gives {
    1 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma19>
  );
  r:rule <#lemma16>.

<#lemma5> a r:Inference;
  r:gives {
    1 dqc:sdcoding 2 .
  };
  r:evidence (
    <#lemma20>
  );
  r:rule <#lemma16>.

<#lemma6> a r:Inference;
  r:gives {
    2 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma21>
  );
  r:rule <#lemma16>.

<#lemma7> a r:Inference;
  r:gives {
    2 dqc:sdcoding 3 .
  };
  r:evidence (
    <#lemma22>
  );
  r:rule <#lemma16>.

<#lemma8> a r:Inference;
  r:gives {
    3 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma23>
  );
  r:rule <#lemma16>.

<#lemma9> a r:Inference;
  r:gives {
    3 dqc:sdcoding 3 .
  };
  r:evidence (
    <#lemma24>
  );
  r:rule <#lemma16>.

<#lemma10> a r:Inference;
  r:gives {
    3 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma25>
  );
  r:rule <#lemma16>.

<#lemma11> a r:Inference;
  r:gives {
    3 dqc:sdcoding 2 .
  };
  r:evidence (
    <#lemma26>
  );
  r:rule <#lemma16>.

<#lemma12> a r:Inference;
  r:gives {
    0 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma27>
  );
  r:rule <#lemma16>.

<#lemma13> a r:Inference;
  r:gives {
    2 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma28>
  );
  r:rule <#lemma16>.

<#lemma14> a r:Inference;
  r:gives {
    2 dqc:sdcoding 2 .
  };
  r:evidence (
    <#lemma29>
  );
  r:rule <#lemma16>.

<#lemma15> a r:Inference;
  r:gives {
    0 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma30>
    <#lemma31>
    <#lemma32>
  );
  r:rule <#lemma33>.

<#lemma16> a r:Extraction;
  r:gives {
    {?x_0_1 dqc:sdcoding ?x_1_1} => {?x_0_1 dqc:sdcoding ?x_1_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding-q.n3>].

<#lemma17> a r:Inference;
  r:gives {
    0 dqc:sdcoding 3 .
  };
  r:evidence (
    <#lemma30>
    <#lemma31>
    <#lemma34>
  );
  r:rule <#lemma33>.

<#lemma18> a r:Inference;
  r:gives {
    1 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma30>
    <#lemma35>
    <#lemma36>
  );
  r:rule <#lemma33>.

<#lemma19> a r:Inference;
  r:gives {
    1 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma30>
    <#lemma35>
    <#lemma37>
  );
  r:rule <#lemma33>.

<#lemma20> a r:Inference;
  r:gives {
    1 dqc:sdcoding 2 .
  };
  r:evidence (
    <#lemma30>
    <#lemma35>
    <#lemma38>
  );
  r:rule <#lemma33>.

<#lemma21> a r:Inference;
  r:gives {
    2 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma30>
    <#lemma39>
    <#lemma32>
  );
  r:rule <#lemma33>.

<#lemma22> a r:Inference;
  r:gives {
    2 dqc:sdcoding 3 .
  };
  r:evidence (
    <#lemma30>
    <#lemma39>
    <#lemma34>
  );
  r:rule <#lemma33>.

<#lemma23> a r:Inference;
  r:gives {
    3 dqc:sdcoding 1 .
  };
  r:evidence (
    <#lemma30>
    <#lemma40>
    <#lemma32>
  );
  r:rule <#lemma33>.

<#lemma24> a r:Inference;
  r:gives {
    3 dqc:sdcoding 3 .
  };
  r:evidence (
    <#lemma30>
    <#lemma40>
    <#lemma34>
  );
  r:rule <#lemma33>.

<#lemma25> a r:Inference;
  r:gives {
    3 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma30>
    <#lemma41>
    <#lemma36>
  );
  r:rule <#lemma33>.

<#lemma26> a r:Inference;
  r:gives {
    3 dqc:sdcoding 2 .
  };
  r:evidence (
    <#lemma30>
    <#lemma41>
    <#lemma38>
  );
  r:rule <#lemma33>.

<#lemma27> a r:Inference;
  r:gives {
    0 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma42>
    <#lemma43>
    <#lemma44>
  );
  r:rule <#lemma33>.

<#lemma28> a r:Inference;
  r:gives {
    2 dqc:sdcoding 0 .
  };
  r:evidence (
    <#lemma42>
    <#lemma45>
    <#lemma46>
  );
  r:rule <#lemma33>.

<#lemma29> a r:Inference;
  r:gives {
    2 dqc:sdcoding 2 .
  };
  r:evidence (
    <#lemma42>
    <#lemma45>
    <#lemma47>
  );
  r:rule <#lemma33>.

<#lemma30> a r:Extraction;
  r:gives {
    false dqc:r false.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma31> a r:Inference;
  r:gives {
    0 dqc:alice (false false).
  };
  r:evidence (
    <#lemma48>
  );
  r:rule <#lemma49>.

<#lemma32> a r:Inference;
  r:gives {
    (false false) dqc:bob 1 .
  };
  r:evidence (
    <#lemma50>
  );
  r:rule <#lemma51>.

<#lemma33> a r:Extraction;
  r:gives {
    {?x_2_2 dqc:sdcoding ?x_4_2} <= {?x_0_2 dqc:r ?x_1_2.
     ?x_2_2 dqc:alice (?x_0_2 ?x_3_2).
     (?x_3_2 ?x_1_2) dqc:bob ?x_4_2}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma34> a r:Inference;
  r:gives {
    (false false) dqc:bob 3 .
  };
  r:evidence (
    <#lemma48>
  );
  r:rule <#lemma52>.

<#lemma35> a r:Inference;
  r:gives {
    1 dqc:alice (false true).
  };
  r:evidence (
    <#lemma53>
  );
  r:rule <#lemma54>.

<#lemma36> a r:Inference;
  r:gives {
    (true false) dqc:bob 0 .
  };
  r:evidence (
    <#lemma55>
  );
  r:rule <#lemma56>.

<#lemma37> a r:Inference;
  r:gives {
    (true false) dqc:bob 1 .
  };
  r:evidence (
    <#lemma57>
  );
  r:rule <#lemma51>.

<#lemma38> a r:Inference;
  r:gives {
    (true false) dqc:bob 2 .
  };
  r:evidence (
    <#lemma58>
  );
  r:rule <#lemma59>.

<#lemma39> a r:Inference;
  r:gives {
    2 dqc:alice (false false).
  };
  r:evidence (
    <#lemma50>
  );
  r:rule <#lemma60>.

<#lemma40> a r:Inference;
  r:gives {
    3 dqc:alice (false false).
  };
  r:evidence (
    <#lemma61>
  );
  r:rule <#lemma62>.

<#lemma41> a r:Inference;
  r:gives {
    3 dqc:alice (false true).
  };
  r:evidence (
    <#lemma63>
  );
  r:rule <#lemma62>.

<#lemma42> a r:Extraction;
  r:gives {
    true dqc:r true.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma43> a r:Inference;
  r:gives {
    0 dqc:alice (true true).
  };
  r:evidence (
    <#lemma64>
  );
  r:rule <#lemma49>.

<#lemma44> a r:Inference;
  r:gives {
    (true true) dqc:bob 0 .
  };
  r:evidence (
    <#lemma65>
  );
  r:rule <#lemma56>.

<#lemma45> a r:Inference;
  r:gives {
    2 dqc:alice (true false).
  };
  r:evidence (
    <#lemma57>
  );
  r:rule <#lemma60>.

<#lemma46> a r:Inference;
  r:gives {
    (false true) dqc:bob 0 .
  };
  r:evidence (
    <#lemma66>
  );
  r:rule <#lemma56>.

<#lemma47> a r:Inference;
  r:gives {
    (false true) dqc:bob 2 .
  };
  r:evidence (
    <#lemma53>
  );
  r:rule <#lemma59>.

<#lemma48> a r:Extraction;
  r:gives {
    false dqc:id false.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma49> a r:Extraction;
  r:gives {
    {0 dqc:alice (?x_0_3 ?x_1_3)} <= {?x_0_3 dqc:id ?x_1_3}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma50> a r:Extraction;
  r:gives {
    false dqc:k false.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma51> a r:Extraction;
  r:gives {
    {(?x_0_4 ?x_1_4) dqc:bob 1} <= {?x_0_4 dqc:k ?x_1_4}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma52> a r:Extraction;
  r:gives {
    {(?x_0_5 ?x_1_5) dqc:bob 3} <= {?x_0_5 dqc:id ?x_1_5}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma53> a r:Extraction;
  r:gives {
    false dqc:g true.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma54> a r:Extraction;
  r:gives {
    {1 dqc:alice (?x_0_6 ?x_1_6)} <= {?x_0_6 dqc:g ?x_1_6}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma55> a r:Inference;
  r:gives {
    true dqc:gk false.
  };
  r:evidence (
    <#lemma67>
    <#lemma58>
  );
  r:rule <#lemma68>.

<#lemma56> a r:Extraction;
  r:gives {
    {(?x_0_7 ?x_1_7) dqc:bob 0} <= {?x_0_7 dqc:gk ?x_1_7}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma57> a r:Extraction;
  r:gives {
    true dqc:k false.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma58> a r:Extraction;
  r:gives {
    true dqc:g false.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma59> a r:Extraction;
  r:gives {
    {(?x_0_8 ?x_1_8) dqc:bob 2} <= {?x_0_8 dqc:g ?x_1_8}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma60> a r:Extraction;
  r:gives {
    {2 dqc:alice (?x_0_9 ?x_1_9)} <= {?x_0_9 dqc:k ?x_1_9}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma61> a r:Inference;
  r:gives {
    false dqc:kg false.
  };
  r:evidence (
    <#lemma53>
    <#lemma57>
  );
  r:rule <#lemma69>.

<#lemma62> a r:Extraction;
  r:gives {
    {3 dqc:alice (?x_0_10 ?x_1_10)} <= {?x_0_10 dqc:kg ?x_1_10}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma63> a r:Inference;
  r:gives {
    false dqc:kg true.
  };
  r:evidence (
    <#lemma53>
    <#lemma67>
  );
  r:rule <#lemma69>.

<#lemma64> a r:Extraction;
  r:gives {
    true dqc:id true.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma65> a r:Inference;
  r:gives {
    true dqc:gk true.
  };
  r:evidence (
    <#lemma57>
    <#lemma53>
  );
  r:rule <#lemma68>.

<#lemma66> a r:Inference;
  r:gives {
    false dqc:gk true.
  };
  r:evidence (
    <#lemma50>
    <#lemma53>
  );
  r:rule <#lemma68>.

<#lemma67> a r:Extraction;
  r:gives {
    true dqc:k true.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma68> a r:Extraction;
  r:gives {
    {?x_0_11 dqc:gk ?x_2_11} <= {?x_0_11 dqc:k ?x_1_11.
     ?x_1_11 dqc:g ?x_2_11}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

<#lemma69> a r:Extraction;
  r:gives {
    {?x_0_12 dqc:kg ?x_2_12} <= {?x_0_12 dqc:g ?x_1_12.
     ?x_1_12 dqc:k ?x_2_12}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

