@prefix skolem: <https://eyereasoner.github.io/.well-known/genid/8b98b360-9a70-4845-b52c-c675af60ad01#>.
@prefix r: <http://www.w3.org/2000/10/swap/reason#>.
@prefix log: <http://www.w3.org/2000/10/swap/log#>.
@prefix : <https://eyereasoner.github.io/eye/reasoning#>.
@prefix math: <http://www.w3.org/2000/10/swap/math#>.
@prefix n3: <http://www.w3.org/2004/06/rei#>.
@prefix var: <http://www.w3.org/2000/10/swap/var#>.

skolem:proof a r:Proof, r:Conjunction;
    r:component skolem:lemma1;
    r:gives [ log:graph (
        [ log:triple (:s :is :3outof5)]
    )].

skolem:lemma1 a r:Inference;
    r:gives [ log:graph (
        [ log:triple (:s :is :3outof5)]
    )];
    r:evidence (
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p1 true)]
            [ log:triple (1 log:equalTo 1)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (1 log:equalTo 0)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p2 true)]
            [ log:triple (0 log:equalTo 1)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (0 log:equalTo 0)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p3 true)]
            [ log:triple (1 log:equalTo 1)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (1 log:equalTo 0)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p4 true)]
            [ log:triple (1 log:equalTo 1)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (1 log:equalTo 0)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p5 true)]
            [ log:triple (0 log:equalTo 1)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (0 log:equalTo 0)]
        )])])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple ((1 0 1 1 0) math:sum 3)])]]
        [ a r:Fact; r:gives [ log:graph ([ log:triple (3 math:notLessThan 3)])]]
    );
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0];
    r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3];
    r:rule [ a r:Fact; r:gives [ log:graph ([ log:triple ([ log:graph (
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p1 true)]
            [ log:triple (var:x_0 log:equalTo 1)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (var:x_0 log:equalTo 0)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p2 true)]
            [ log:triple (var:x_1 log:equalTo 1)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (var:x_1 log:equalTo 0)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p3 true)]
            [ log:triple (var:x_2 log:equalTo 1)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (var:x_2 log:equalTo 0)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p4 true)]
            [ log:triple (var:x_3 log:equalTo 1)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (var:x_3 log:equalTo 0)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (:s :p5 true)]
            [ log:triple (var:x_4 log:equalTo 1)]
        )])]
        [ log:triple (true log:callWithOptional [ log:graph (
            [ log:triple (var:x_4 log:equalTo 0)]
        )])]
        [ log:triple ((var:x_0 var:x_1 var:x_2 var:x_3 var:x_4) math:sum var:x_5)]
        [ log:triple (var:x_5 math:notLessThan 3)]
    )] log:implies [ log:graph (
        [ log:triple (:s :is :3outof5)]
    )])])]].

