TSTP Solution File: GRA012+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : GRA012+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 05:43:20 EDT 2024

% Result   : Theorem 0.57s 0.76s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  187 (  14 unt;   0 def)
%            Number of atoms       :  671 ( 144 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  839 ( 355   ~; 352   |;  75   &)
%                                         (  26 <=>;  27  =>;   0  <=;   4 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   32 (  30 usr;  13 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :  286 ( 269   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f711,plain,
    $false,
    inference(avatar_sat_refutation,[],[f168,f173,f178,f183,f220,f257,f471,f651,f676,f685,f707,f710]) ).

fof(f710,plain,
    ( ~ spl29_4
    | ~ spl29_6
    | ~ spl29_7 ),
    inference(avatar_contradiction_clause,[],[f709]) ).

fof(f709,plain,
    ( $false
    | ~ spl29_4
    | ~ spl29_6
    | ~ spl29_7 ),
    inference(subsumption_resolution,[],[f708,f208]) ).

fof(f208,plain,
    ( head_of(sK6(sK0)) != tail_of(sK6(sK0))
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f201,f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ edge(X0)
      | head_of(X0) != tail_of(X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( head_of(X0) != tail_of(X0)
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( edge(X0)
     => head_of(X0) != tail_of(X0) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',no_loops) ).

fof(f201,plain,
    ( edge(sK6(sK0))
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f177,f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ~ sequential(X0,X1)
      | edge(X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( sequential(X0,X1)
    <=> ( head_of(X0) = tail_of(X1)
        & X0 != X1
        & edge(X1)
        & edge(X0) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X6,X7] :
      ( sequential(X6,X7)
    <=> ( head_of(X6) = tail_of(X7)
        & X6 != X7
        & edge(X7)
        & edge(X6) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',sequential_defn) ).

fof(f177,plain,
    ( sequential(sK6(sK0),sK7(sK0))
    | ~ spl29_4 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f175,plain,
    ( spl29_4
  <=> sequential(sK6(sK0),sK7(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_4])]) ).

fof(f708,plain,
    ( head_of(sK6(sK0)) = tail_of(sK6(sK0))
    | ~ spl29_6
    | ~ spl29_7 ),
    inference(forward_demodulation,[],[f251,f256]) ).

fof(f256,plain,
    ( sK6(sK0) = sK7(sK0)
    | ~ spl29_7 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f254,plain,
    ( spl29_7
  <=> sK6(sK0) = sK7(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_7])]) ).

fof(f251,plain,
    ( tail_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ spl29_6 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f250,plain,
    ( spl29_6
  <=> tail_of(sK6(sK0)) = head_of(sK7(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_6])]) ).

fof(f707,plain,
    ( ~ spl29_4
    | spl29_6
    | ~ spl29_22 ),
    inference(avatar_contradiction_clause,[],[f706]) ).

fof(f706,plain,
    ( $false
    | ~ spl29_4
    | spl29_6
    | ~ spl29_22 ),
    inference(subsumption_resolution,[],[f705,f217]) ).

fof(f217,plain,
    ( head_of(sK6(sK0)) != head_of(sK7(sK0))
    | ~ spl29_4 ),
    inference(forward_demodulation,[],[f212,f203]) ).

fof(f203,plain,
    ( head_of(sK6(sK0)) = tail_of(sK7(sK0))
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f177,f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ~ sequential(X0,X1)
      | head_of(X0) = tail_of(X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f212,plain,
    ( tail_of(sK7(sK0)) != head_of(sK7(sK0))
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f202,f50]) ).

fof(f202,plain,
    ( edge(sK7(sK0))
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f177,f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ~ sequential(X0,X1)
      | edge(X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f705,plain,
    ( head_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ spl29_4
    | spl29_6
    | ~ spl29_22 ),
    inference(subsumption_resolution,[],[f704,f49]) ).

fof(f49,plain,
    complete,
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( ? [X0,X1,X2] :
        ( minus(length_of(X0),n1) != number_of_in(triangles,X0)
        & shortest_path(X1,X2,X0) )
    & complete ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ( complete
     => ! [X0,X1,X2] :
          ( shortest_path(X1,X2,X0)
         => minus(length_of(X0),n1) = number_of_in(triangles,X0) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ( complete
     => ! [X3,X1,X2] :
          ( shortest_path(X1,X2,X3)
         => minus(length_of(X3),n1) = number_of_in(triangles,X3) ) ),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ( complete
   => ! [X3,X1,X2] :
        ( shortest_path(X1,X2,X3)
       => minus(length_of(X3),n1) = number_of_in(triangles,X3) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',triangles_on_a_path) ).

fof(f704,plain,
    ( ~ complete
    | head_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ spl29_4
    | spl29_6
    | ~ spl29_22 ),
    inference(subsumption_resolution,[],[f703,f252]) ).

fof(f252,plain,
    ( tail_of(sK6(sK0)) != head_of(sK7(sK0))
    | spl29_6 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f703,plain,
    ( tail_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ complete
    | head_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ spl29_4
    | ~ spl29_22 ),
    inference(subsumption_resolution,[],[f702,f210]) ).

fof(f210,plain,
    ( vertex(tail_of(sK6(sK0)))
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f201,f71]) ).

fof(f71,plain,
    ! [X0] :
      ( vertex(tail_of(X0))
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( vertex(tail_of(X0))
        & vertex(head_of(X0)) )
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( edge(X0)
     => ( vertex(tail_of(X0))
        & vertex(head_of(X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',edge_ends_are_vertices) ).

fof(f702,plain,
    ( ~ vertex(tail_of(sK6(sK0)))
    | tail_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ complete
    | head_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ spl29_4
    | ~ spl29_22 ),
    inference(subsumption_resolution,[],[f701,f213]) ).

fof(f213,plain,
    ( vertex(head_of(sK7(sK0)))
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f202,f70]) ).

fof(f70,plain,
    ! [X0] :
      ( vertex(head_of(X0))
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f701,plain,
    ( ~ vertex(head_of(sK7(sK0)))
    | ~ vertex(tail_of(sK6(sK0)))
    | tail_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ complete
    | head_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ spl29_4
    | ~ spl29_22 ),
    inference(subsumption_resolution,[],[f695,f269]) ).

fof(f269,plain,
    ( ! [X0] : ~ sP4(sK6(sK0),tail_of(sK6(sK0)),X0)
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f208,f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( ~ sP4(X2,X1,X0)
      | head_of(X2) = X1 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ( ! [X0,X1] :
        ( ? [X2] :
            ( ( ( tail_of(X2) = X1
                & head_of(X2) = X0 )
            <~> ( tail_of(X2) = X0
                & head_of(X2) = X1 ) )
            & edge(X2) )
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
    | ~ complete ),
    inference(flattening,[],[f33]) ).

fof(f33,plain,
    ( ! [X0,X1] :
        ( ? [X2] :
            ( ( ( tail_of(X2) = X1
                & head_of(X2) = X0 )
            <~> ( tail_of(X2) = X0
                & head_of(X2) = X1 ) )
            & edge(X2) )
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
    | ~ complete ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ( complete
   => ! [X0,X1] :
        ( ( X0 != X1
          & vertex(X1)
          & vertex(X0) )
       => ? [X2] :
            ( ( ( tail_of(X2) = X1
                & head_of(X2) = X0 )
            <~> ( tail_of(X2) = X0
                & head_of(X2) = X1 ) )
            & edge(X2) ) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ( complete
   => ! [X1,X2] :
        ( ( X1 != X2
          & vertex(X2)
          & vertex(X1) )
       => ? [X0] :
            ( ( ( tail_of(X0) = X2
                & head_of(X0) = X1 )
            <~> ( tail_of(X0) = X1
                & head_of(X0) = X2 ) )
            & edge(X0) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',complete_properties) ).

fof(f695,plain,
    ( sP4(sK6(sK0),tail_of(sK6(sK0)),head_of(sK7(sK0)))
    | ~ vertex(head_of(sK7(sK0)))
    | ~ vertex(tail_of(sK6(sK0)))
    | tail_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ complete
    | head_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ spl29_22 ),
    inference(superposition,[],[f55,f466]) ).

fof(f466,plain,
    ( sK6(sK0) = sK3(head_of(sK7(sK0)),tail_of(sK6(sK0)))
    | ~ spl29_22 ),
    inference(avatar_component_clause,[],[f464]) ).

fof(f464,plain,
    ( spl29_22
  <=> sK6(sK0) = sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_22])]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( sP4(sK3(X0,X1),X1,X0)
      | ~ vertex(X0)
      | ~ vertex(X1)
      | X0 = X1
      | ~ complete
      | head_of(sK3(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f685,plain,
    ( ~ spl29_4
    | ~ spl29_20
    | ~ spl29_21 ),
    inference(avatar_contradiction_clause,[],[f684]) ).

fof(f684,plain,
    ( $false
    | ~ spl29_4
    | ~ spl29_20
    | ~ spl29_21 ),
    inference(subsumption_resolution,[],[f683,f217]) ).

fof(f683,plain,
    ( head_of(sK6(sK0)) = head_of(sK7(sK0))
    | ~ spl29_4
    | ~ spl29_20
    | ~ spl29_21 ),
    inference(forward_demodulation,[],[f682,f203]) ).

fof(f682,plain,
    ( tail_of(sK7(sK0)) = head_of(sK7(sK0))
    | ~ spl29_20
    | ~ spl29_21 ),
    inference(forward_demodulation,[],[f457,f462]) ).

fof(f462,plain,
    ( sK7(sK0) = sK3(head_of(sK7(sK0)),tail_of(sK6(sK0)))
    | ~ spl29_21 ),
    inference(avatar_component_clause,[],[f460]) ).

fof(f460,plain,
    ( spl29_21
  <=> sK7(sK0) = sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_21])]) ).

fof(f457,plain,
    ( head_of(sK7(sK0)) = tail_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_20 ),
    inference(avatar_component_clause,[],[f456]) ).

fof(f456,plain,
    ( spl29_20
  <=> head_of(sK7(sK0)) = tail_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_20])]) ).

fof(f676,plain,
    ( ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4
    | spl29_6
    | spl29_20 ),
    inference(avatar_contradiction_clause,[],[f675]) ).

fof(f675,plain,
    ( $false
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4
    | spl29_6
    | spl29_20 ),
    inference(subsumption_resolution,[],[f666,f663]) ).

fof(f663,plain,
    ( tail_of(sK6(sK0)) = tail_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_4
    | spl29_6
    | spl29_20 ),
    inference(unit_resulting_resolution,[],[f49,f213,f210,f252,f656,f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( sP4(sK3(X0,X1),X1,X0)
      | ~ vertex(X0)
      | ~ vertex(X1)
      | X0 = X1
      | ~ complete
      | tail_of(sK3(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f656,plain,
    ( ! [X0] : ~ sP4(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))),X0,head_of(sK7(sK0)))
    | spl29_20 ),
    inference(unit_resulting_resolution,[],[f458,f53]) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( ~ sP4(X2,X1,X0)
      | tail_of(X2) = X0 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f458,plain,
    ( head_of(sK7(sK0)) != tail_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | spl29_20 ),
    inference(avatar_component_clause,[],[f456]) ).

fof(f666,plain,
    ( tail_of(sK6(sK0)) != tail_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4
    | spl29_6
    | spl29_20 ),
    inference(unit_resulting_resolution,[],[f662,f243]) ).

fof(f243,plain,
    ( ! [X0] :
        ( tail_of(X0) != tail_of(sK6(sK0))
        | head_of(X0) != head_of(sK7(sK0)) )
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(resolution,[],[f228,f98]) ).

fof(f98,plain,
    ! [X2,X3,X5] :
      ( ~ sP13(X3,X2)
      | head_of(X5) != head_of(X3)
      | tail_of(X2) != tail_of(X5) ),
    inference(general_splitting,[],[f96,f97_D]) ).

fof(f97,plain,
    ! [X2,X3,X4] :
      ( ~ precedes(X2,X3,X4)
      | ~ sP12(X4)
      | sP13(X3,X2) ),
    inference(cnf_transformation,[],[f97_D]) ).

fof(f97_D,plain,
    ! [X2,X3] :
      ( ! [X4] :
          ( ~ precedes(X2,X3,X4)
          | ~ sP12(X4) )
    <=> ~ sP13(X3,X2) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP13])]) ).

fof(f96,plain,
    ! [X2,X3,X4,X5] :
      ( ~ precedes(X2,X3,X4)
      | tail_of(X2) != tail_of(X5)
      | head_of(X5) != head_of(X3)
      | ~ sP12(X4) ),
    inference(general_splitting,[],[f94,f95_D]) ).

fof(f95,plain,
    ! [X1,X4] :
      ( ~ sP11(X4,X1)
      | sP12(X4) ),
    inference(cnf_transformation,[],[f95_D]) ).

fof(f95_D,plain,
    ! [X4] :
      ( ! [X1] : ~ sP11(X4,X1)
    <=> ~ sP12(X4) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP12])]) ).

fof(f94,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ precedes(X2,X3,X4)
      | tail_of(X2) != tail_of(X5)
      | head_of(X5) != head_of(X3)
      | ~ sP11(X4,X1) ),
    inference(general_splitting,[],[f59,f93_D]) ).

fof(f93,plain,
    ! [X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | sP11(X4,X1) ),
    inference(cnf_transformation,[],[f93_D]) ).

fof(f93_D,plain,
    ! [X1,X4] :
      ( ! [X0] : ~ shortest_path(X0,X1,X4)
    <=> ~ sP11(X4,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP11])]) ).

fof(f59,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ precedes(X2,X3,X4)
      | tail_of(X2) != tail_of(X5)
      | head_of(X5) != head_of(X3) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ precedes(X3,X2,X4)
        & ! [X5] :
            ( head_of(X5) != head_of(X3)
            | tail_of(X2) != tail_of(X5) ) )
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ precedes(X3,X2,X4)
        & ! [X5] :
            ( head_of(X5) != head_of(X3)
            | tail_of(X2) != tail_of(X5) ) )
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( precedes(X2,X3,X4)
        & shortest_path(X0,X1,X4) )
     => ( ~ precedes(X3,X2,X4)
        & ~ ? [X5] :
              ( head_of(X5) = head_of(X3)
              & tail_of(X2) = tail_of(X5) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X1,X2,X6,X7,X3] :
      ( ( precedes(X6,X7,X3)
        & shortest_path(X1,X2,X3) )
     => ( ~ precedes(X7,X6,X3)
        & ~ ? [X8] :
              ( head_of(X8) = head_of(X7)
              & tail_of(X8) = tail_of(X6) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',shortest_path_properties) ).

fof(f228,plain,
    ( sP13(sK7(sK0),sK6(sK0))
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f137,f204,f97]) ).

fof(f204,plain,
    ( precedes(sK6(sK0),sK7(sK0),sK0)
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f197,f167,f172,f177,f124]) ).

fof(f124,plain,
    ! [X3,X0,X4] :
      ( precedes(X3,X4,X0)
      | ~ on_path(X4,X0)
      | ~ sequential(X3,X4)
      | ~ on_path(X3,X0)
      | ~ sP26(X0) ),
    inference(general_splitting,[],[f122,f123_D]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ~ sP25(X0,X1)
      | sP26(X0) ),
    inference(cnf_transformation,[],[f123_D]) ).

fof(f123_D,plain,
    ! [X0] :
      ( ! [X1] : ~ sP25(X0,X1)
    <=> ~ sP26(X0) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP26])]) ).

fof(f122,plain,
    ! [X3,X0,X1,X4] :
      ( ~ on_path(X3,X0)
      | ~ on_path(X4,X0)
      | ~ sequential(X3,X4)
      | precedes(X3,X4,X0)
      | ~ sP25(X0,X1) ),
    inference(general_splitting,[],[f78,f121_D]) ).

fof(f121,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | sP25(X0,X1) ),
    inference(cnf_transformation,[],[f121_D]) ).

fof(f121_D,plain,
    ! [X1,X0] :
      ( ! [X2] : ~ path(X1,X2,X0)
    <=> ~ sP25(X0,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP25])]) ).

fof(f78,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ path(X1,X2,X0)
      | ~ on_path(X3,X0)
      | ~ on_path(X4,X0)
      | ~ sequential(X3,X4)
      | precedes(X3,X4,X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( precedes(X3,X4,X0)
          | ( ! [X5] :
                ( ~ precedes(X5,X4,X0)
                | ~ sequential(X3,X5) )
            & ~ sequential(X3,X4) )
          | ~ on_path(X4,X0)
          | ~ on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( precedes(X3,X4,X0)
          | ( ! [X5] :
                ( ~ precedes(X5,X4,X0)
                | ~ sequential(X3,X5) )
            & ~ sequential(X3,X4) )
          | ~ on_path(X4,X0)
          | ~ on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( path(X1,X2,X0)
     => ! [X3,X4] :
          ( ( ( ? [X5] :
                  ( precedes(X5,X4,X0)
                  & sequential(X3,X5) )
              | sequential(X3,X4) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
         => precedes(X3,X4,X0) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X3,X1,X2] :
      ( path(X1,X2,X3)
     => ! [X6,X7] :
          ( ( ( ? [X8] :
                  ( precedes(X8,X7,X3)
                  & sequential(X6,X8) )
              | sequential(X6,X7) )
            & on_path(X7,X3)
            & on_path(X6,X3) )
         => precedes(X6,X7,X3) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',precedes_defn) ).

fof(f172,plain,
    ( on_path(sK7(sK0),sK0)
    | ~ spl29_3 ),
    inference(avatar_component_clause,[],[f170]) ).

fof(f170,plain,
    ( spl29_3
  <=> on_path(sK7(sK0),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).

fof(f167,plain,
    ( on_path(sK6(sK0),sK0)
    | ~ spl29_2 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f165,plain,
    ( spl29_2
  <=> on_path(sK6(sK0),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_2])]) ).

fof(f197,plain,
    sP26(sK0),
    inference(unit_resulting_resolution,[],[f146,f123]) ).

fof(f146,plain,
    sP25(sK0,sK1),
    inference(unit_resulting_resolution,[],[f129,f121]) ).

fof(f129,plain,
    path(sK1,sK2,sK0),
    inference(unit_resulting_resolution,[],[f47,f64]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X0,X1,X2)
      | path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( shortest_path(X0,X1,X2)
    <=> ( ! [X3] :
            ( less_or_equal(length_of(X2),length_of(X3))
            | ~ path(X0,X1,X3) )
        & X0 != X1
        & path(X0,X1,X2) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( shortest_path(X0,X1,X2)
    <=> ( ! [X3] :
            ( path(X0,X1,X3)
           => less_or_equal(length_of(X2),length_of(X3)) )
        & X0 != X1
        & path(X0,X1,X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X2,X9] :
      ( shortest_path(X1,X2,X9)
    <=> ( ! [X3] :
            ( path(X1,X2,X3)
           => less_or_equal(length_of(X9),length_of(X3)) )
        & X1 != X2
        & path(X1,X2,X9) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',shortest_path_defn) ).

fof(f47,plain,
    shortest_path(sK1,sK2,sK0),
    inference(cnf_transformation,[],[f31]) ).

fof(f137,plain,
    sP12(sK0),
    inference(unit_resulting_resolution,[],[f131,f95]) ).

fof(f131,plain,
    sP11(sK0,sK2),
    inference(unit_resulting_resolution,[],[f47,f93]) ).

fof(f662,plain,
    ( head_of(sK7(sK0)) = head_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_4
    | spl29_6
    | spl29_20 ),
    inference(unit_resulting_resolution,[],[f49,f213,f210,f252,f656,f55]) ).

fof(f651,plain,
    ( ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4
    | spl29_6
    | spl29_23 ),
    inference(avatar_contradiction_clause,[],[f650]) ).

fof(f650,plain,
    ( $false
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4
    | spl29_6
    | spl29_23 ),
    inference(subsumption_resolution,[],[f641,f580]) ).

fof(f580,plain,
    ( tail_of(sK6(sK0)) = tail_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_4
    | spl29_6
    | spl29_23 ),
    inference(unit_resulting_resolution,[],[f49,f213,f210,f252,f544,f56]) ).

fof(f544,plain,
    ( ! [X0] : ~ sP4(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))),tail_of(sK6(sK0)),X0)
    | spl29_23 ),
    inference(unit_resulting_resolution,[],[f470,f52]) ).

fof(f470,plain,
    ( tail_of(sK6(sK0)) != head_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | spl29_23 ),
    inference(avatar_component_clause,[],[f468]) ).

fof(f468,plain,
    ( spl29_23
  <=> tail_of(sK6(sK0)) = head_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_23])]) ).

fof(f641,plain,
    ( tail_of(sK6(sK0)) != tail_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4
    | spl29_6
    | spl29_23 ),
    inference(unit_resulting_resolution,[],[f579,f243]) ).

fof(f579,plain,
    ( head_of(sK7(sK0)) = head_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_4
    | spl29_6
    | spl29_23 ),
    inference(unit_resulting_resolution,[],[f49,f213,f210,f252,f544,f55]) ).

fof(f471,plain,
    ( ~ spl29_20
    | spl29_21
    | spl29_22
    | ~ spl29_23
    | ~ spl29_4
    | spl29_5
    | spl29_6 ),
    inference(avatar_split_clause,[],[f398,f250,f180,f175,f468,f464,f460,f456]) ).

fof(f180,plain,
    ( spl29_5
  <=> sP14(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_5])]) ).

fof(f398,plain,
    ( tail_of(sK6(sK0)) != head_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | sK6(sK0) = sK3(head_of(sK7(sK0)),tail_of(sK6(sK0)))
    | sK7(sK0) = sK3(head_of(sK7(sK0)),tail_of(sK6(sK0)))
    | head_of(sK7(sK0)) != tail_of(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_4
    | spl29_5
    | spl29_6 ),
    inference(resolution,[],[f338,f283]) ).

fof(f283,plain,
    ( edge(sK3(head_of(sK7(sK0)),tail_of(sK6(sK0))))
    | ~ spl29_4
    | spl29_6 ),
    inference(unit_resulting_resolution,[],[f49,f213,f210,f252,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( edge(sK3(X0,X1))
      | ~ vertex(X0)
      | ~ vertex(X1)
      | X0 = X1
      | ~ complete ),
    inference(cnf_transformation,[],[f34]) ).

fof(f338,plain,
    ( ! [X0] :
        ( ~ edge(X0)
        | head_of(X0) != tail_of(sK6(sK0))
        | sK6(sK0) = X0
        | sK7(sK0) = X0
        | tail_of(X0) != head_of(sK7(sK0)) )
    | ~ spl29_4
    | spl29_5 ),
    inference(subsumption_resolution,[],[f337,f202]) ).

fof(f337,plain,
    ( ! [X0] :
        ( sK6(sK0) = X0
        | head_of(X0) != tail_of(sK6(sK0))
        | ~ edge(X0)
        | sK7(sK0) = X0
        | tail_of(X0) != head_of(sK7(sK0))
        | ~ edge(sK7(sK0)) )
    | ~ spl29_4
    | spl29_5 ),
    inference(resolution,[],[f286,f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( sequential(X0,X1)
      | ~ edge(X1)
      | X0 = X1
      | head_of(X0) != tail_of(X1)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f286,plain,
    ( ! [X0] :
        ( ~ sequential(sK7(sK0),X0)
        | sK6(sK0) = X0
        | head_of(X0) != tail_of(sK6(sK0)) )
    | ~ spl29_4
    | spl29_5 ),
    inference(subsumption_resolution,[],[f285,f80]) ).

fof(f285,plain,
    ( ! [X0] :
        ( ~ sequential(sK7(sK0),X0)
        | sK6(sK0) = X0
        | head_of(X0) != tail_of(sK6(sK0))
        | ~ edge(X0) )
    | ~ spl29_4
    | spl29_5 ),
    inference(subsumption_resolution,[],[f284,f201]) ).

fof(f284,plain,
    ( ! [X0] :
        ( ~ sequential(sK7(sK0),X0)
        | ~ edge(sK6(sK0))
        | sK6(sK0) = X0
        | head_of(X0) != tail_of(sK6(sK0))
        | ~ edge(X0) )
    | ~ spl29_4
    | spl29_5 ),
    inference(resolution,[],[f225,f83]) ).

fof(f225,plain,
    ( ! [X0] :
        ( ~ sequential(X0,sK6(sK0))
        | ~ sequential(sK7(sK0),X0) )
    | ~ spl29_4
    | spl29_5 ),
    inference(subsumption_resolution,[],[f224,f80]) ).

fof(f224,plain,
    ( ! [X0] :
        ( ~ edge(X0)
        | ~ sequential(sK7(sK0),X0)
        | ~ sequential(X0,sK6(sK0)) )
    | ~ spl29_4
    | spl29_5 ),
    inference(subsumption_resolution,[],[f223,f201]) ).

fof(f223,plain,
    ( ! [X0] :
        ( ~ edge(X0)
        | ~ sequential(sK7(sK0),X0)
        | ~ sequential(X0,sK6(sK0))
        | ~ edge(sK6(sK0)) )
    | ~ spl29_4
    | spl29_5 ),
    inference(subsumption_resolution,[],[f222,f177]) ).

fof(f222,plain,
    ( ! [X0] :
        ( ~ edge(X0)
        | ~ sequential(sK6(sK0),sK7(sK0))
        | ~ sequential(sK7(sK0),X0)
        | ~ sequential(X0,sK6(sK0))
        | ~ edge(sK6(sK0)) )
    | ~ spl29_4
    | spl29_5 ),
    inference(subsumption_resolution,[],[f221,f202]) ).

fof(f221,plain,
    ( ! [X0] :
        ( ~ edge(sK7(sK0))
        | ~ edge(X0)
        | ~ sequential(sK6(sK0),sK7(sK0))
        | ~ sequential(sK7(sK0),X0)
        | ~ sequential(X0,sK6(sK0))
        | ~ edge(sK6(sK0)) )
    | spl29_5 ),
    inference(resolution,[],[f186,f84]) ).

fof(f84,plain,
    ! [X2,X0,X1] :
      ( triangle(X0,X1,X2)
      | ~ edge(X1)
      | ~ edge(X2)
      | ~ sequential(X0,X1)
      | ~ sequential(X1,X2)
      | ~ sequential(X2,X0)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( triangle(X0,X1,X2)
      | ~ sequential(X2,X0)
      | ~ sequential(X1,X2)
      | ~ sequential(X0,X1)
      | ~ edge(X2)
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( triangle(X0,X1,X2)
      | ~ sequential(X2,X0)
      | ~ sequential(X1,X2)
      | ~ sequential(X0,X1)
      | ~ edge(X2)
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( sequential(X2,X0)
        & sequential(X1,X2)
        & sequential(X0,X1)
        & edge(X2)
        & edge(X1)
        & edge(X0) )
     => triangle(X0,X1,X2) ),
    inference(unused_predicate_definition_removal,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( triangle(X0,X1,X2)
    <=> ( sequential(X2,X0)
        & sequential(X1,X2)
        & sequential(X0,X1)
        & edge(X2)
        & edge(X1)
        & edge(X0) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X6,X7,X8] :
      ( triangle(X6,X7,X8)
    <=> ( sequential(X8,X6)
        & sequential(X7,X8)
        & sequential(X6,X7)
        & edge(X8)
        & edge(X7)
        & edge(X6) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',triangle_defn) ).

fof(f186,plain,
    ( ! [X0] : ~ triangle(sK6(sK0),sK7(sK0),X0)
    | spl29_5 ),
    inference(unit_resulting_resolution,[],[f182,f99]) ).

fof(f99,plain,
    ! [X0,X5] :
      ( ~ triangle(sK6(X0),sK7(X0),X5)
      | sP14(X0) ),
    inference(cnf_transformation,[],[f99_D]) ).

fof(f99_D,plain,
    ! [X0] :
      ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
    <=> ~ sP14(X0) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP14])]) ).

fof(f182,plain,
    ( ~ sP14(sK0)
    | spl29_5 ),
    inference(avatar_component_clause,[],[f180]) ).

fof(f257,plain,
    ( ~ spl29_6
    | spl29_7
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(avatar_split_clause,[],[f248,f175,f170,f165,f254,f250]) ).

fof(f248,plain,
    ( sK6(sK0) = sK7(sK0)
    | tail_of(sK6(sK0)) != head_of(sK7(sK0))
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(subsumption_resolution,[],[f247,f202]) ).

fof(f247,plain,
    ( sK6(sK0) = sK7(sK0)
    | tail_of(sK6(sK0)) != head_of(sK7(sK0))
    | ~ edge(sK7(sK0))
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(subsumption_resolution,[],[f246,f201]) ).

fof(f246,plain,
    ( ~ edge(sK6(sK0))
    | sK6(sK0) = sK7(sK0)
    | tail_of(sK6(sK0)) != head_of(sK7(sK0))
    | ~ edge(sK7(sK0))
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(resolution,[],[f244,f83]) ).

fof(f244,plain,
    ( ~ sequential(sK7(sK0),sK6(sK0))
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f197,f172,f167,f227,f124]) ).

fof(f227,plain,
    ( ~ precedes(sK7(sK0),sK6(sK0),sK0)
    | ~ spl29_2
    | ~ spl29_3
    | ~ spl29_4 ),
    inference(unit_resulting_resolution,[],[f136,f204,f89]) ).

fof(f89,plain,
    ! [X2,X3,X4] :
      ( ~ precedes(X3,X2,X4)
      | ~ precedes(X2,X3,X4)
      | sP9(X4,X3) ),
    inference(cnf_transformation,[],[f89_D]) ).

fof(f89_D,plain,
    ! [X3,X4] :
      ( ! [X2] :
          ( ~ precedes(X3,X2,X4)
          | ~ precedes(X2,X3,X4) )
    <=> ~ sP9(X4,X3) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).

fof(f136,plain,
    ! [X0] : ~ sP9(sK0,X0),
    inference(unit_resulting_resolution,[],[f130,f91]) ).

fof(f91,plain,
    ! [X3,X4] :
      ( ~ sP9(X4,X3)
      | sP10(X4) ),
    inference(cnf_transformation,[],[f91_D]) ).

fof(f91_D,plain,
    ! [X4] :
      ( ! [X3] : ~ sP9(X4,X3)
    <=> ~ sP10(X4) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP10])]) ).

fof(f130,plain,
    ~ sP10(sK0),
    inference(unit_resulting_resolution,[],[f47,f92]) ).

fof(f92,plain,
    ! [X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ sP10(X4) ),
    inference(general_splitting,[],[f90,f91_D]) ).

fof(f90,plain,
    ! [X3,X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ sP9(X4,X3) ),
    inference(general_splitting,[],[f60,f89_D]) ).

fof(f60,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ precedes(X2,X3,X4)
      | ~ precedes(X3,X2,X4) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f220,plain,
    ~ spl29_1,
    inference(avatar_split_clause,[],[f219,f161]) ).

fof(f161,plain,
    ( spl29_1
  <=> number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_1])]) ).

fof(f219,plain,
    number_of_in(triangles,sK0) != number_of_in(sequential_pairs,sK0),
    inference(superposition,[],[f48,f139]) ).

fof(f139,plain,
    minus(length_of(sK0),n1) = number_of_in(sequential_pairs,sK0),
    inference(unit_resulting_resolution,[],[f129,f58]) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( ~ path(X0,X1,X2)
      | number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
      | ~ path(X0,X1,X2) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( path(X0,X1,X2)
     => number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X1,X2,X3] :
      ( path(X1,X2,X3)
     => number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',path_length_sequential_pairs) ).

fof(f48,plain,
    minus(length_of(sK0),n1) != number_of_in(triangles,sK0),
    inference(cnf_transformation,[],[f31]) ).

fof(f183,plain,
    ( ~ spl29_5
    | spl29_1 ),
    inference(avatar_split_clause,[],[f152,f161,f180]) ).

fof(f152,plain,
    ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0)
    | ~ sP14(sK0) ),
    inference(resolution,[],[f129,f100]) ).

fof(f100,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0)
      | ~ sP14(X0) ),
    inference(general_splitting,[],[f69,f99_D]) ).

fof(f69,plain,
    ! [X2,X0,X1,X5] :
      ( ~ path(X1,X2,X0)
      | ~ triangle(sK6(X0),sK7(X0),X5)
      | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3,X4] :
            ( ( sequential(X3,X4)
              & on_path(X4,X0)
              & on_path(X3,X0) )
           => ? [X5] : triangle(X3,X4,X5) )
        & path(X1,X2,X0) )
     => number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X3,X1,X2] :
      ( ( ! [X6,X7] :
            ( ( sequential(X6,X7)
              & on_path(X7,X3)
              & on_path(X6,X3) )
           => ? [X8] : triangle(X6,X7,X8) )
        & path(X1,X2,X3) )
     => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929',sequential_pairs_and_triangles) ).

fof(f178,plain,
    ( spl29_1
    | spl29_4 ),
    inference(avatar_split_clause,[],[f151,f175,f161]) ).

fof(f151,plain,
    ( sequential(sK6(sK0),sK7(sK0))
    | number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ),
    inference(resolution,[],[f129,f68]) ).

fof(f68,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | sequential(sK6(X0),sK7(X0))
      | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f173,plain,
    ( spl29_1
    | spl29_3 ),
    inference(avatar_split_clause,[],[f150,f170,f161]) ).

fof(f150,plain,
    ( on_path(sK7(sK0),sK0)
    | number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ),
    inference(resolution,[],[f129,f67]) ).

fof(f67,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | on_path(sK7(X0),X0)
      | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f168,plain,
    ( spl29_1
    | spl29_2 ),
    inference(avatar_split_clause,[],[f149,f165,f161]) ).

fof(f149,plain,
    ( on_path(sK6(sK0),sK0)
    | number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ),
    inference(resolution,[],[f129,f66]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | on_path(sK6(X0),X0)
      | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) ),
    inference(cnf_transformation,[],[f40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : GRA012+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31  % Computer : n003.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 18:25:22 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.31  This is a FOF_THM_RFO_SEQ problem
% 0.10/0.31  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.7qujHhX6iF/Vampire---4.8_18929
% 0.57/0.74  % (19043)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.57/0.74  % (19040)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.57/0.74  % (19044)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.57/0.74  % (19041)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.57/0.74  % (19038)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.57/0.74  % (19042)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.57/0.74  % (19039)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.57/0.74  % (19045)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.57/0.74  % (19041)Refutation not found, incomplete strategy% (19041)------------------------------
% 0.57/0.74  % (19041)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.74  % (19041)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.74  
% 0.57/0.74  % (19041)Memory used [KB]: 964
% 0.57/0.74  % (19041)Time elapsed: 0.003 s
% 0.57/0.74  % (19041)Instructions burned: 2 (million)
% 0.57/0.74  % (19043)Refutation not found, incomplete strategy% (19043)------------------------------
% 0.57/0.74  % (19043)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.74  % (19043)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.74  
% 0.57/0.74  % (19043)Memory used [KB]: 1034
% 0.57/0.74  % (19043)Time elapsed: 0.003 s
% 0.57/0.74  % (19043)Instructions burned: 2 (million)
% 0.57/0.74  % (19041)------------------------------
% 0.57/0.74  % (19041)------------------------------
% 0.57/0.74  % (19045)Refutation not found, incomplete strategy% (19045)------------------------------
% 0.57/0.74  % (19045)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.74  % (19043)------------------------------
% 0.57/0.74  % (19043)------------------------------
% 0.57/0.74  % (19045)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.74  
% 0.57/0.74  % (19045)Memory used [KB]: 1041
% 0.57/0.74  % (19038)Refutation not found, incomplete strategy% (19038)------------------------------
% 0.57/0.74  % (19038)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.74  % (19045)Time elapsed: 0.002 s
% 0.57/0.74  % (19045)Instructions burned: 3 (million)
% 0.57/0.74  % (19038)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.74  
% 0.57/0.74  % (19038)Memory used [KB]: 1051
% 0.57/0.74  % (19038)Time elapsed: 0.003 s
% 0.57/0.74  % (19038)Instructions burned: 3 (million)
% 0.57/0.74  % (19045)------------------------------
% 0.57/0.74  % (19045)------------------------------
% 0.57/0.74  % (19038)------------------------------
% 0.57/0.74  % (19038)------------------------------
% 0.57/0.75  % (19048)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.57/0.75  % (19047)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.57/0.75  % (19046)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.57/0.75  % (19049)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.57/0.75  % (19048)Refutation not found, incomplete strategy% (19048)------------------------------
% 0.57/0.75  % (19048)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75  % (19048)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (19048)Memory used [KB]: 1035
% 0.57/0.75  % (19048)Time elapsed: 0.002 s
% 0.57/0.75  % (19048)Instructions burned: 3 (million)
% 0.57/0.75  % (19048)------------------------------
% 0.57/0.75  % (19048)------------------------------
% 0.57/0.75  % (19046)Refutation not found, incomplete strategy% (19046)------------------------------
% 0.57/0.75  % (19046)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75  % (19046)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (19046)Memory used [KB]: 1071
% 0.57/0.75  % (19046)Time elapsed: 0.004 s
% 0.57/0.75  % (19046)Instructions burned: 4 (million)
% 0.57/0.75  % (19046)------------------------------
% 0.57/0.75  % (19046)------------------------------
% 0.57/0.75  % (19050)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.57/0.75  % (19051)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.57/0.76  % (19042)Instruction limit reached!
% 0.57/0.76  % (19042)------------------------------
% 0.57/0.76  % (19042)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76  % (19042)Termination reason: Unknown
% 0.57/0.76  % (19042)Termination phase: Saturation
% 0.57/0.76  
% 0.57/0.76  % (19042)Memory used [KB]: 1364
% 0.57/0.76  % (19042)Time elapsed: 0.018 s
% 0.57/0.76  % (19042)Instructions burned: 34 (million)
% 0.57/0.76  % (19042)------------------------------
% 0.57/0.76  % (19042)------------------------------
% 0.57/0.76  % (19044)First to succeed.
% 0.57/0.76  % (19044)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19037"
% 0.57/0.76  % (19052)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.57/0.76  % (19044)Refutation found. Thanks to Tanya!
% 0.57/0.76  % SZS status Theorem for Vampire---4
% 0.57/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.76  % (19044)------------------------------
% 0.57/0.76  % (19044)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76  % (19044)Termination reason: Refutation
% 0.57/0.76  
% 0.57/0.76  % (19044)Memory used [KB]: 1396
% 0.57/0.76  % (19044)Time elapsed: 0.021 s
% 0.57/0.76  % (19044)Instructions burned: 44 (million)
% 0.57/0.76  % (19037)Success in time 0.448 s
% 0.57/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------