TSTP Solution File: GRA003+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : GRA003+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 : n005.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 : Wed May  1 02:25:11 EDT 2024

% Result   : Theorem 0.79s 0.94s
% Output   : Refutation 0.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   96 (   9 unt;   0 def)
%            Number of atoms       :  462 (  98 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  558 ( 192   ~; 169   |; 158   &)
%                                         (  13 <=>;  20  =>;   0  <=;   6 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   21 (  19 usr;  11 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :  247 ( 203   !;  44   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f301,plain,
    $false,
    inference(avatar_sat_refutation,[],[f171,f178,f181,f182,f210,f212,f216,f236,f240,f287,f300]) ).

fof(f300,plain,
    ~ spl12_3,
    inference(avatar_contradiction_clause,[],[f297]) ).

fof(f297,plain,
    ( $false
    | ~ spl12_3 ),
    inference(resolution,[],[f290,f141]) ).

fof(f141,plain,
    ! [X2,X1] : ~ shortest_path(X1,X1,X2),
    inference(equality_resolution,[],[f118]) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | ~ shortest_path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ( shortest_path(X0,X1,X2)
        | ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
          & path(X0,X1,sK4(X0,X1,X2)) )
        | X0 = X1
        | ~ path(X0,X1,X2) )
      & ( ( ! [X4] :
              ( less_or_equal(length_of(X2),length_of(X4))
              | ~ path(X0,X1,X4) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f78,f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ less_or_equal(length_of(X2),length_of(X3))
          & path(X0,X1,X3) )
     => ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
        & path(X0,X1,sK4(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,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) )
      & ( ( ! [X4] :
              ( less_or_equal(length_of(X2),length_of(X4))
              | ~ path(X0,X1,X4) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(rectify,[],[f77]) ).

fof(f77,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) )
      & ( ( ! [X3] :
              ( less_or_equal(length_of(X2),length_of(X3))
              | ~ path(X0,X1,X3) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(flattening,[],[f76]) ).

fof(f76,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) )
      & ( ( ! [X3] :
              ( less_or_equal(length_of(X2),length_of(X3))
              | ~ path(X0,X1,X3) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,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,[],[f28]) ).

fof(f28,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.tCxUp0tGsv/Vampire---4.8_7945',shortest_path_defn) ).

fof(f290,plain,
    ( shortest_path(sK7,sK7,sK11)
    | ~ spl12_3 ),
    inference(superposition,[],[f132,f154]) ).

fof(f154,plain,
    ( sK7 = sK8
    | ~ spl12_3 ),
    inference(avatar_component_clause,[],[f152]) ).

fof(f152,plain,
    ( spl12_3
  <=> sK7 = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).

fof(f132,plain,
    shortest_path(sK7,sK8,sK11),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ( ( ~ path(sK7,sK8,sK11)
      | sK9 = sK10
      | ~ edge(sK10)
      | ~ edge(sK9)
      | sK7 = sK8
      | ~ vertex(sK8)
      | ~ vertex(sK7) )
    & precedes(sK9,sK10,sK11)
    & shortest_path(sK7,sK8,sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f60,f83]) ).

fof(f83,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( ( ~ path(X0,X1,X4)
          | X2 = X3
          | ~ edge(X3)
          | ~ edge(X2)
          | X0 = X1
          | ~ vertex(X1)
          | ~ vertex(X0) )
        & precedes(X2,X3,X4)
        & shortest_path(X0,X1,X4) )
   => ( ( ~ path(sK7,sK8,sK11)
        | sK9 = sK10
        | ~ edge(sK10)
        | ~ edge(sK9)
        | sK7 = sK8
        | ~ vertex(sK8)
        | ~ vertex(sK7) )
      & precedes(sK9,sK10,sK11)
      & shortest_path(sK7,sK8,sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ? [X0,X1,X2,X3,X4] :
      ( ( ~ path(X0,X1,X4)
        | X2 = X3
        | ~ edge(X3)
        | ~ edge(X2)
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
      & precedes(X2,X3,X4)
      & shortest_path(X0,X1,X4) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ? [X0,X1,X2,X3,X4] :
      ( ( ~ path(X0,X1,X4)
        | X2 = X3
        | ~ edge(X3)
        | ~ edge(X2)
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
      & precedes(X2,X3,X4)
      & shortest_path(X0,X1,X4) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,plain,
    ~ ! [X0,X1,X2,X3,X4] :
        ( ( precedes(X2,X3,X4)
          & shortest_path(X0,X1,X4) )
       => ( path(X0,X1,X4)
          & X2 != X3
          & edge(X3)
          & edge(X2)
          & X0 != X1
          & vertex(X1)
          & vertex(X0) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ! [X1,X2,X6,X7,X3] :
        ( ( precedes(X6,X7,X3)
          & shortest_path(X1,X2,X3) )
       => ( path(X1,X2,X3)
          & X6 != X7
          & edge(X7)
          & edge(X6)
          & X1 != X2
          & vertex(X2)
          & vertex(X1) ) ),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ! [X1,X2,X6,X7,X3] :
      ( ( precedes(X6,X7,X3)
        & shortest_path(X1,X2,X3) )
     => ( path(X1,X2,X3)
        & X6 != X7
        & edge(X7)
        & edge(X6)
        & X1 != X2
        & vertex(X2)
        & vertex(X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',vertices_and_edges) ).

fof(f287,plain,
    ~ spl12_6,
    inference(avatar_contradiction_clause,[],[f286]) ).

fof(f286,plain,
    ( $false
    | ~ spl12_6 ),
    inference(resolution,[],[f285,f253]) ).

fof(f253,plain,
    ( precedes(sK9,sK9,sK11)
    | ~ spl12_6 ),
    inference(superposition,[],[f133,f166]) ).

fof(f166,plain,
    ( sK9 = sK10
    | ~ spl12_6 ),
    inference(avatar_component_clause,[],[f164]) ).

fof(f164,plain,
    ( spl12_6
  <=> sK9 = sK10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).

fof(f133,plain,
    precedes(sK9,sK10,sK11),
    inference(cnf_transformation,[],[f84]) ).

fof(f285,plain,
    ( ~ precedes(sK9,sK9,sK11)
    | ~ spl12_6 ),
    inference(forward_demodulation,[],[f283,f166]) ).

fof(f283,plain,
    ~ precedes(sK10,sK9,sK11),
    inference(resolution,[],[f282,f133]) ).

fof(f282,plain,
    ! [X0,X1] :
      ( ~ precedes(X0,X1,sK11)
      | ~ precedes(X1,X0,sK11) ),
    inference(resolution,[],[f123,f132]) ).

fof(f123,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ precedes(X2,X3,X4)
      | ~ precedes(X3,X2,X4) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ precedes(X3,X2,X4)
        & ! [X5] :
            ( head_of(X3) != head_of(X5)
            | tail_of(X2) != tail_of(X5) ) )
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ precedes(X3,X2,X4)
        & ! [X5] :
            ( head_of(X3) != head_of(X5)
            | tail_of(X2) != tail_of(X5) ) )
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( precedes(X2,X3,X4)
        & shortest_path(X0,X1,X4) )
     => ( ~ precedes(X3,X2,X4)
        & ~ ? [X5] :
              ( head_of(X3) = head_of(X5)
              & 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.tCxUp0tGsv/Vampire---4.8_7945',shortest_path_properties) ).

fof(f240,plain,
    ( spl12_5
    | ~ spl12_7
    | ~ spl12_14 ),
    inference(avatar_split_clause,[],[f237,f233,f168,f160]) ).

fof(f160,plain,
    ( spl12_5
  <=> edge(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).

fof(f168,plain,
    ( spl12_7
  <=> path(sK7,sK8,sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).

fof(f233,plain,
    ( spl12_14
  <=> on_path(sK10,sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).

fof(f237,plain,
    ( edge(sK10)
    | ~ spl12_7
    | ~ spl12_14 ),
    inference(resolution,[],[f235,f183]) ).

fof(f183,plain,
    ( ! [X0] :
        ( ~ on_path(X0,sK11)
        | edge(X0) )
    | ~ spl12_7 ),
    inference(resolution,[],[f99,f169]) ).

fof(f169,plain,
    ( path(sK7,sK8,sK11)
    | ~ spl12_7 ),
    inference(avatar_component_clause,[],[f168]) ).

fof(f99,plain,
    ! [X2,X3,X0,X1] :
      ( ~ path(X0,X1,X2)
      | ~ on_path(X3,X2)
      | edge(X3) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1,X2,X3] :
      ( ( in_path(tail_of(X3),X2)
        & in_path(head_of(X3),X2)
        & edge(X3) )
      | ~ on_path(X3,X2)
      | ~ path(X0,X1,X2) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2,X3] :
      ( ( in_path(tail_of(X3),X2)
        & in_path(head_of(X3),X2)
        & edge(X3) )
      | ~ on_path(X3,X2)
      | ~ path(X0,X1,X2) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3] :
      ( ( on_path(X3,X2)
        & path(X0,X1,X2) )
     => ( in_path(tail_of(X3),X2)
        & in_path(head_of(X3),X2)
        & edge(X3) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X2,X3,X0] :
      ( ( on_path(X0,X3)
        & path(X1,X2,X3) )
     => ( in_path(tail_of(X0),X3)
        & in_path(head_of(X0),X3)
        & edge(X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',on_path_properties) ).

fof(f235,plain,
    ( on_path(sK10,sK11)
    | ~ spl12_14 ),
    inference(avatar_component_clause,[],[f233]) ).

fof(f236,plain,
    ( spl12_10
    | spl12_14 ),
    inference(avatar_split_clause,[],[f231,f233,f204]) ).

fof(f204,plain,
    ( spl12_10
  <=> ! [X0,X1] : ~ path(X0,X1,sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).

fof(f231,plain,
    ! [X0,X1] :
      ( on_path(sK10,sK11)
      | ~ path(X0,X1,sK11) ),
    inference(resolution,[],[f113,f133]) ).

fof(f113,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X0)
      | on_path(X4,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( ! [X5] :
                  ( ~ precedes(X5,X4,X0)
                  | ~ sequential(X3,X5) )
              | ~ sequential(X3,X4) )
            & ( ( precedes(sK3(X0,X3,X4),X4,X0)
                & sequential(X3,sK3(X0,X3,X4)) )
              | sequential(X3,X4) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f73,f74]) ).

fof(f74,plain,
    ! [X0,X3,X4] :
      ( ? [X6] :
          ( precedes(X6,X4,X0)
          & sequential(X3,X6) )
     => ( precedes(sK3(X0,X3,X4),X4,X0)
        & sequential(X3,sK3(X0,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( ! [X5] :
                  ( ~ precedes(X5,X4,X0)
                  | ~ sequential(X3,X5) )
              | ~ sequential(X3,X4) )
            & ( ? [X6] :
                  ( precedes(X6,X4,X0)
                  & sequential(X3,X6) )
              | sequential(X3,X4) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(rectify,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( ! [X5] :
                  ( ~ precedes(X5,X4,X0)
                  | ~ sequential(X3,X5) )
              | ~ sequential(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) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( ! [X5] :
                  ( ~ precedes(X5,X4,X0)
                  | ~ sequential(X3,X5) )
              | ~ sequential(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) )
      | ~ path(X1,X2,X0) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( sequential(X3,X4)
            <~> ? [X5] :
                  ( precedes(X5,X4,X0)
                  & sequential(X3,X5) ) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( path(X1,X2,X0)
     => ! [X3,X4] :
          ( precedes(X3,X4,X0)
         => ( ( sequential(X3,X4)
            <~> ? [X5] :
                  ( precedes(X5,X4,X0)
                  & sequential(X3,X5) ) )
            & on_path(X4,X0)
            & on_path(X3,X0) ) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X3,X1,X2] :
      ( path(X1,X2,X3)
     => ! [X6,X7] :
          ( precedes(X6,X7,X3)
         => ( ( sequential(X6,X7)
            <~> ? [X8] :
                  ( precedes(X8,X7,X3)
                  & sequential(X6,X8) ) )
            & on_path(X7,X3)
            & on_path(X6,X3) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',precedes_properties) ).

fof(f216,plain,
    ( spl12_4
    | ~ spl12_7
    | ~ spl12_11 ),
    inference(avatar_split_clause,[],[f213,f207,f168,f156]) ).

fof(f156,plain,
    ( spl12_4
  <=> edge(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).

fof(f207,plain,
    ( spl12_11
  <=> on_path(sK9,sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).

fof(f213,plain,
    ( edge(sK9)
    | ~ spl12_7
    | ~ spl12_11 ),
    inference(resolution,[],[f209,f183]) ).

fof(f209,plain,
    ( on_path(sK9,sK11)
    | ~ spl12_11 ),
    inference(avatar_component_clause,[],[f207]) ).

fof(f212,plain,
    ( ~ spl12_7
    | ~ spl12_10 ),
    inference(avatar_contradiction_clause,[],[f211]) ).

fof(f211,plain,
    ( $false
    | ~ spl12_7
    | ~ spl12_10 ),
    inference(resolution,[],[f205,f169]) ).

fof(f205,plain,
    ( ! [X0,X1] : ~ path(X0,X1,sK11)
    | ~ spl12_10 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f210,plain,
    ( spl12_10
    | spl12_11 ),
    inference(avatar_split_clause,[],[f202,f207,f204]) ).

fof(f202,plain,
    ! [X0,X1] :
      ( on_path(sK9,sK11)
      | ~ path(X0,X1,sK11) ),
    inference(resolution,[],[f112,f133]) ).

fof(f112,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X0)
      | on_path(X3,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f182,plain,
    ( spl12_1
    | ~ spl12_7 ),
    inference(avatar_split_clause,[],[f180,f168,f144]) ).

fof(f144,plain,
    ( spl12_1
  <=> vertex(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f180,plain,
    ( vertex(sK7)
    | ~ spl12_7 ),
    inference(resolution,[],[f169,f90]) ).

fof(f90,plain,
    ! [X2,X0,X1] :
      ( ~ path(X0,X1,X2)
      | vertex(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ( ( ! [X4] :
              ( path_cons(sK0(X0,X1,X2),X4) != X2
              | ~ path(head_of(sK0(X0,X1,X2)),X1,X4) )
          | path_cons(sK0(X0,X1,X2),empty) != X2
          | head_of(sK0(X0,X1,X2)) != X1 )
        & ( ( path_cons(sK0(X0,X1,X2),sK1(X0,X1,X2)) = X2
            & path(head_of(sK0(X0,X1,X2)),X1,sK1(X0,X1,X2)) )
          | ( path_cons(sK0(X0,X1,X2),empty) = X2
            & head_of(sK0(X0,X1,X2)) = X1 ) )
        & tail_of(sK0(X0,X1,X2)) = X0
        & edge(sK0(X0,X1,X2))
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f63,f65,f64]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4] :
                ( path_cons(X3,X4) != X2
                | ~ path(head_of(X3),X1,X4) )
            | path_cons(X3,empty) != X2
            | head_of(X3) != X1 )
          & ( ? [X5] :
                ( path_cons(X3,X5) = X2
                & path(head_of(X3),X1,X5) )
            | ( path_cons(X3,empty) = X2
              & head_of(X3) = X1 ) )
          & tail_of(X3) = X0
          & edge(X3) )
     => ( ( ! [X4] :
              ( path_cons(sK0(X0,X1,X2),X4) != X2
              | ~ path(head_of(sK0(X0,X1,X2)),X1,X4) )
          | path_cons(sK0(X0,X1,X2),empty) != X2
          | head_of(sK0(X0,X1,X2)) != X1 )
        & ( ? [X5] :
              ( path_cons(sK0(X0,X1,X2),X5) = X2
              & path(head_of(sK0(X0,X1,X2)),X1,X5) )
          | ( path_cons(sK0(X0,X1,X2),empty) = X2
            & head_of(sK0(X0,X1,X2)) = X1 ) )
        & tail_of(sK0(X0,X1,X2)) = X0
        & edge(sK0(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( path_cons(sK0(X0,X1,X2),X5) = X2
          & path(head_of(sK0(X0,X1,X2)),X1,X5) )
     => ( path_cons(sK0(X0,X1,X2),sK1(X0,X1,X2)) = X2
        & path(head_of(sK0(X0,X1,X2)),X1,sK1(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] :
            ( ( ! [X4] :
                  ( path_cons(X3,X4) != X2
                  | ~ path(head_of(X3),X1,X4) )
              | path_cons(X3,empty) != X2
              | head_of(X3) != X1 )
            & ( ? [X5] :
                  ( path_cons(X3,X5) = X2
                  & path(head_of(X3),X1,X5) )
              | ( path_cons(X3,empty) = X2
                & head_of(X3) = X1 ) )
            & tail_of(X3) = X0
            & edge(X3) )
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(rectify,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] :
            ( ( ! [X4] :
                  ( path_cons(X3,X4) != X2
                  | ~ path(head_of(X3),X1,X4) )
              | path_cons(X3,empty) != X2
              | head_of(X3) != X1 )
            & ( ? [X4] :
                  ( path_cons(X3,X4) = X2
                  & path(head_of(X3),X1,X4) )
              | ( path_cons(X3,empty) = X2
                & head_of(X3) = X1 ) )
            & tail_of(X3) = X0
            & edge(X3) )
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] :
            ( ( ! [X4] :
                  ( path_cons(X3,X4) != X2
                  | ~ path(head_of(X3),X1,X4) )
              | path_cons(X3,empty) != X2
              | head_of(X3) != X1 )
            & ( ? [X4] :
                  ( path_cons(X3,X4) = X2
                  & path(head_of(X3),X1,X4) )
              | ( path_cons(X3,empty) = X2
                & head_of(X3) = X1 ) )
            & tail_of(X3) = X0
            & edge(X3) )
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] :
            ( ( ( path_cons(X3,empty) = X2
                & head_of(X3) = X1 )
            <~> ? [X4] :
                  ( path_cons(X3,X4) = X2
                  & path(head_of(X3),X1,X4) ) )
            & tail_of(X3) = X0
            & edge(X3) )
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( path(X0,X1,X2)
     => ( ? [X3] :
            ( ( ( path_cons(X3,empty) = X2
                & head_of(X3) = X1 )
            <~> ? [X4] :
                  ( path_cons(X3,X4) = X2
                  & path(head_of(X3),X1,X4) ) )
            & tail_of(X3) = X0
            & edge(X3) )
        & vertex(X1)
        & vertex(X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X2,X3] :
      ( path(X1,X2,X3)
     => ( ? [X0] :
            ( ( ( path_cons(X0,empty) = X3
                & head_of(X0) = X2 )
            <~> ? [X4] :
                  ( path_cons(X0,X4) = X3
                  & path(head_of(X0),X2,X4) ) )
            & tail_of(X0) = X1
            & edge(X0) )
        & vertex(X2)
        & vertex(X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',path_properties) ).

fof(f181,plain,
    ( spl12_2
    | ~ spl12_7 ),
    inference(avatar_split_clause,[],[f179,f168,f148]) ).

fof(f148,plain,
    ( spl12_2
  <=> vertex(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f179,plain,
    ( vertex(sK8)
    | ~ spl12_7 ),
    inference(resolution,[],[f169,f91]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( ~ path(X0,X1,X2)
      | vertex(X1) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f178,plain,
    spl12_7,
    inference(avatar_split_clause,[],[f177,f168]) ).

fof(f177,plain,
    path(sK7,sK8,sK11),
    inference(resolution,[],[f117,f132]) ).

fof(f117,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X0,X1,X2)
      | path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f171,plain,
    ( ~ spl12_1
    | ~ spl12_2
    | spl12_3
    | ~ spl12_4
    | ~ spl12_5
    | spl12_6
    | ~ spl12_7 ),
    inference(avatar_split_clause,[],[f134,f168,f164,f160,f156,f152,f148,f144]) ).

fof(f134,plain,
    ( ~ path(sK7,sK8,sK11)
    | sK9 = sK10
    | ~ edge(sK10)
    | ~ edge(sK9)
    | sK7 = sK8
    | ~ vertex(sK8)
    | ~ vertex(sK7) ),
    inference(cnf_transformation,[],[f84]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.15  % 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
% 0.16/0.37  % Computer : n005.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Tue Apr 30 17:31:41 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  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.tCxUp0tGsv/Vampire---4.8_7945
% 0.77/0.93  % (8261)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2994ds/78Mi)
% 0.77/0.93  % (8259)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 (2994ds/34Mi)
% 0.77/0.93  % (8265)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 (2994ds/83Mi)
% 0.77/0.93  % (8262)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2994ds/33Mi)
% 0.77/0.93  % (8260)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 (2994ds/51Mi)
% 0.77/0.93  % (8264)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2994ds/45Mi)
% 0.77/0.93  % (8263)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 (2994ds/34Mi)
% 0.77/0.93  % (8266)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 (2994ds/56Mi)
% 0.77/0.93  % (8266)Refutation not found, incomplete strategy% (8266)------------------------------
% 0.77/0.93  % (8266)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.77/0.93  % (8264)Refutation not found, incomplete strategy% (8264)------------------------------
% 0.77/0.93  % (8264)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.77/0.93  % (8264)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.93  
% 0.77/0.93  % (8264)Memory used [KB]: 979
% 0.77/0.93  % (8264)Time elapsed: 0.003 s
% 0.77/0.93  % (8264)Instructions burned: 2 (million)
% 0.77/0.93  % (8264)------------------------------
% 0.77/0.93  % (8264)------------------------------
% 0.77/0.93  % (8266)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.93  
% 0.77/0.93  % (8266)Memory used [KB]: 1044
% 0.77/0.93  % (8266)Time elapsed: 0.003 s
% 0.77/0.93  % (8266)Instructions burned: 2 (million)
% 0.77/0.93  % (8266)------------------------------
% 0.77/0.93  % (8266)------------------------------
% 0.77/0.93  % (8262)Refutation not found, incomplete strategy% (8262)------------------------------
% 0.77/0.93  % (8262)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.77/0.93  % (8262)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.93  
% 0.77/0.93  % (8262)Memory used [KB]: 981
% 0.77/0.93  % (8262)Time elapsed: 0.003 s
% 0.77/0.93  % (8262)Instructions burned: 3 (million)
% 0.77/0.93  % (8262)------------------------------
% 0.77/0.93  % (8262)------------------------------
% 0.77/0.94  % (8267)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 (2994ds/55Mi)
% 0.77/0.94  % (8260)First to succeed.
% 0.77/0.94  % (8268)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 (2994ds/50Mi)
% 0.77/0.94  % (8269)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 (2994ds/208Mi)
% 0.77/0.94  % (8267)Refutation not found, incomplete strategy% (8267)------------------------------
% 0.77/0.94  % (8267)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.77/0.94  % (8267)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.94  
% 0.77/0.94  % (8267)Memory used [KB]: 1134
% 0.77/0.94  % (8267)Time elapsed: 0.005 s
% 0.79/0.94  % (8267)Instructions burned: 6 (million)
% 0.79/0.94  % (8267)------------------------------
% 0.79/0.94  % (8267)------------------------------
% 0.79/0.94  % (8260)Refutation found. Thanks to Tanya!
% 0.79/0.94  % SZS status Theorem for Vampire---4
% 0.79/0.94  % SZS output start Proof for Vampire---4
% See solution above
% 0.79/0.94  % (8260)------------------------------
% 0.79/0.94  % (8260)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.79/0.94  % (8260)Termination reason: Refutation
% 0.79/0.94  
% 0.79/0.94  % (8260)Memory used [KB]: 1180
% 0.79/0.94  % (8260)Time elapsed: 0.010 s
% 0.79/0.94  % (8260)Instructions burned: 13 (million)
% 0.79/0.94  % (8260)------------------------------
% 0.79/0.94  % (8260)------------------------------
% 0.79/0.94  % (8186)Success in time 0.565 s
% 0.79/0.94  % Vampire---4.8 exiting
%------------------------------------------------------------------------------