@prefix dqc: <http://josd.github.io/eye/reasoning/dqc#>.
@prefix r: <http://www.w3.org/2000/10/swap/reason#>.
@prefix var: <http://josd.github.io/var#>.
@prefix skolem: <http://josd.github.io/.well-known/genid/3917894951695475063#>.
@prefix n3: <http://www.w3.org/2004/06/rei#>.

skolem:proof a r:Proof, r:Conjunction;
  r:component skolem:lemma1;
  r:component skolem:lemma2;
  r:component skolem:lemma3;
  r:component skolem:lemma4;
  r:component skolem:lemma5;
  r:component skolem:lemma6;
  r:component skolem:lemma7;
  r:component skolem:lemma8;
  r:component skolem:lemma9;
  r:component skolem:lemma10;
  r:component skolem:lemma11;
  r:component skolem:lemma12;
  r:component skolem:lemma13;
  r:component skolem: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 .
  }.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

skolem:lemma15 a r:Inference;
  r:gives {
    0 dqc:sdcoding 1 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma31
    skolem:lemma32
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 0];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 1];
  r:rule skolem:lemma33.

skolem:lemma16 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {var:x_0 dqc:sdcoding var:x_1} => {var:x_0 dqc:sdcoding var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding-q.n3>].

skolem:lemma17 a r:Inference;
  r:gives {
    0 dqc:sdcoding 3 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma31
    skolem:lemma34
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 0];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 3];
  r:rule skolem:lemma33.

skolem:lemma18 a r:Inference;
  r:gives {
    1 dqc:sdcoding 0 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma35
    skolem:lemma36
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 1];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 0];
  r:rule skolem:lemma33.

skolem:lemma19 a r:Inference;
  r:gives {
    1 dqc:sdcoding 1 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma35
    skolem:lemma37
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 1];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 1];
  r:rule skolem:lemma33.

skolem:lemma20 a r:Inference;
  r:gives {
    1 dqc:sdcoding 2 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma35
    skolem:lemma38
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 1];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 2];
  r:rule skolem:lemma33.

skolem:lemma21 a r:Inference;
  r:gives {
    2 dqc:sdcoding 1 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma39
    skolem:lemma32
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 2];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 1];
  r:rule skolem:lemma33.

skolem:lemma22 a r:Inference;
  r:gives {
    2 dqc:sdcoding 3 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma39
    skolem:lemma34
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 2];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 3];
  r:rule skolem:lemma33.

skolem:lemma23 a r:Inference;
  r:gives {
    3 dqc:sdcoding 1 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma40
    skolem:lemma32
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 3];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 1];
  r:rule skolem:lemma33.

skolem:lemma24 a r:Inference;
  r:gives {
    3 dqc:sdcoding 3 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma40
    skolem:lemma34
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 3];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 3];
  r:rule skolem:lemma33.

skolem:lemma25 a r:Inference;
  r:gives {
    3 dqc:sdcoding 0 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma41
    skolem:lemma36
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 3];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 0];
  r:rule skolem:lemma33.

skolem:lemma26 a r:Inference;
  r:gives {
    3 dqc:sdcoding 2 .
  };
  r:evidence (
    skolem:lemma30
    skolem:lemma41
    skolem:lemma38
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 3];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 2];
  r:rule skolem:lemma33.

skolem:lemma27 a r:Inference;
  r:gives {
    0 dqc:sdcoding 0 .
  };
  r:evidence (
    skolem:lemma42
    skolem:lemma43
    skolem:lemma44
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 0];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 0];
  r:rule skolem:lemma33.

skolem:lemma28 a r:Inference;
  r:gives {
    2 dqc:sdcoding 0 .
  };
  r:evidence (
    skolem:lemma42
    skolem:lemma45
    skolem:lemma46
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 2];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 0];
  r:rule skolem:lemma33.

skolem:lemma29 a r:Inference;
  r:gives {
    2 dqc:sdcoding 2 .
  };
  r:evidence (
    skolem:lemma42
    skolem:lemma45
    skolem:lemma47
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo 2];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_4"]; r:boundTo 2];
  r:rule skolem:lemma33.

skolem: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>].

skolem:lemma31 a r:Inference;
  r:gives {
    0 dqc:alice (false false).
  };
  r:evidence (
    skolem:lemma48
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma49.

skolem:lemma32 a r:Inference;
  r:gives {
    (false false) dqc:bob 1 .
  };
  r:evidence (
    skolem:lemma50
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma51.

skolem:lemma33 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4. {var:x_2 dqc:sdcoding var:x_4} <= {var:x_0 dqc:r var:x_1.
     var:x_2 dqc:alice (var:x_0 var:x_3).
     (var:x_3 var:x_1) dqc:bob var:x_4}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem:lemma34 a r:Inference;
  r:gives {
    (false false) dqc:bob 3 .
  };
  r:evidence (
    skolem:lemma48
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma52.

skolem:lemma35 a r:Inference;
  r:gives {
    1 dqc:alice (false true).
  };
  r:evidence (
    skolem:lemma53
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:rule skolem:lemma54.

skolem:lemma36 a r:Inference;
  r:gives {
    (true false) dqc:bob 0 .
  };
  r:evidence (
    skolem:lemma55
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma56.

skolem:lemma37 a r:Inference;
  r:gives {
    (true false) dqc:bob 1 .
  };
  r:evidence (
    skolem:lemma57
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma51.

skolem:lemma38 a r:Inference;
  r:gives {
    (true false) dqc:bob 2 .
  };
  r:evidence (
    skolem:lemma58
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma59.

skolem:lemma39 a r:Inference;
  r:gives {
    2 dqc:alice (false false).
  };
  r:evidence (
    skolem:lemma50
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma60.

skolem:lemma40 a r:Inference;
  r:gives {
    3 dqc:alice (false false).
  };
  r:evidence (
    skolem:lemma61
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma62.

skolem:lemma41 a r:Inference;
  r:gives {
    3 dqc:alice (false true).
  };
  r:evidence (
    skolem:lemma63
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:rule skolem:lemma62.

skolem: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>].

skolem:lemma43 a r:Inference;
  r:gives {
    0 dqc:alice (true true).
  };
  r:evidence (
    skolem:lemma64
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:rule skolem:lemma49.

skolem:lemma44 a r:Inference;
  r:gives {
    (true true) dqc:bob 0 .
  };
  r:evidence (
    skolem:lemma65
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:rule skolem:lemma56.

skolem:lemma45 a r:Inference;
  r:gives {
    2 dqc:alice (true false).
  };
  r:evidence (
    skolem:lemma57
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:rule skolem:lemma60.

skolem:lemma46 a r:Inference;
  r:gives {
    (false true) dqc:bob 0 .
  };
  r:evidence (
    skolem:lemma66
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:rule skolem:lemma56.

skolem:lemma47 a r:Inference;
  r:gives {
    (false true) dqc:bob 2 .
  };
  r:evidence (
    skolem:lemma53
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:rule skolem:lemma59.

skolem: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>].

skolem:lemma49 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {0 dqc:alice (var:x_0 var:x_1)} <= {var:x_0 dqc:id var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem: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>].

skolem:lemma51 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {(var:x_0 var:x_1) dqc:bob 1} <= {var:x_0 dqc:k var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem:lemma52 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {(var:x_0 var:x_1) dqc:bob 3} <= {var:x_0 dqc:id var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem: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>].

skolem:lemma54 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {1 dqc:alice (var:x_0 var:x_1)} <= {var:x_0 dqc:g var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem:lemma55 a r:Inference;
  r:gives {
    true dqc:gk false.
  };
  r:evidence (
    skolem:lemma67
    skolem:lemma58
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo false];
  r:rule skolem:lemma68.

skolem:lemma56 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {(var:x_0 var:x_1) dqc:bob 0} <= {var:x_0 dqc:gk var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem: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>].

skolem: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>].

skolem:lemma59 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {(var:x_0 var:x_1) dqc:bob 2} <= {var:x_0 dqc:g var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem:lemma60 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {2 dqc:alice (var:x_0 var:x_1)} <= {var:x_0 dqc:k var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem:lemma61 a r:Inference;
  r:gives {
    false dqc:kg false.
  };
  r:evidence (
    skolem:lemma53
    skolem:lemma57
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo false];
  r:rule skolem:lemma69.

skolem:lemma62 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1. {3 dqc:alice (var:x_0 var:x_1)} <= {var:x_0 dqc:kg var:x_1}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem:lemma63 a r:Inference;
  r:gives {
    false dqc:kg true.
  };
  r:evidence (
    skolem:lemma53
    skolem:lemma67
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo true];
  r:rule skolem:lemma69.

skolem: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>].

skolem:lemma65 a r:Inference;
  r:gives {
    true dqc:gk true.
  };
  r:evidence (
    skolem:lemma57
    skolem:lemma53
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo true];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo true];
  r:rule skolem:lemma68.

skolem:lemma66 a r:Inference;
  r:gives {
    false dqc:gk true.
  };
  r:evidence (
    skolem:lemma50
    skolem:lemma53
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo false];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo true];
  r:rule skolem:lemma68.

skolem: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>].

skolem:lemma68 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1, var:x_2. {var:x_0 dqc:gk var:x_2} <= {var:x_0 dqc:k var:x_1.
     var:x_1 dqc:g var:x_2}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

skolem:lemma69 a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1, var:x_2. {var:x_0 dqc:kg var:x_2} <= {var:x_0 dqc:g var:x_1.
     var:x_1 dqc:k var:x_2}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/dqc/sdcoding.n3>].

