TSTP Solution File: GRA004+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GRA004+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n009.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 Aug 31 16:13:20 EDT 2022

% Result   : Theorem 1.58s 0.56s
% Output   : Refutation 1.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   92 (  13 unt;   0 def)
%            Number of atoms       :  408 ( 109 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  488 ( 172   ~; 151   |; 131   &)
%                                         (   9 <=>;  22  =>;   0  <=;   3 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   5 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  256 ( 212   !;  44   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f308,plain,
    $false,
    inference(avatar_sat_refutation,[],[f173,f181,f246,f279,f304]) ).

fof(f304,plain,
    ( ~ spl13_1
    | ~ spl13_4 ),
    inference(avatar_contradiction_clause,[],[f303]) ).

fof(f303,plain,
    ( $false
    | ~ spl13_1
    | ~ spl13_4 ),
    inference(subsumption_resolution,[],[f296,f245]) ).

fof(f245,plain,
    ( head_of(sK4) = head_of(sK5)
    | ~ spl13_4 ),
    inference(avatar_component_clause,[],[f243]) ).

fof(f243,plain,
    ( spl13_4
  <=> head_of(sK4) = head_of(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

fof(f296,plain,
    ( head_of(sK4) != head_of(sK5)
    | ~ spl13_1 ),
    inference(unit_resulting_resolution,[],[f102,f105,f164,f97]) ).

fof(f97,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ shortest_path(X1,X3,X2)
      | ~ precedes(X4,X0,X2)
      | tail_of(X5) != tail_of(X4)
      | head_of(X0) != head_of(X5) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ precedes(X0,X4,X2)
        & ! [X5] :
            ( tail_of(X5) != tail_of(X4)
            | head_of(X0) != head_of(X5) ) )
      | ~ shortest_path(X1,X3,X2)
      | ~ precedes(X4,X0,X2) ),
    inference(rectify,[],[f43]) ).

fof(f43,plain,
    ! [X3,X2,X4,X1,X0] :
      ( ( ~ precedes(X3,X0,X4)
        & ! [X5] :
            ( tail_of(X0) != tail_of(X5)
            | head_of(X3) != head_of(X5) ) )
      | ~ shortest_path(X2,X1,X4)
      | ~ precedes(X0,X3,X4) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ! [X0,X3,X4,X2,X1] :
      ( ( ~ precedes(X3,X0,X4)
        & ! [X5] :
            ( tail_of(X0) != tail_of(X5)
            | head_of(X3) != head_of(X5) ) )
      | ~ shortest_path(X2,X1,X4)
      | ~ precedes(X0,X3,X4) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X3,X4,X2,X1] :
      ( ( shortest_path(X2,X1,X4)
        & precedes(X0,X3,X4) )
     => ( ~ ? [X5] :
              ( tail_of(X0) = tail_of(X5)
              & head_of(X3) = head_of(X5) )
        & ~ precedes(X3,X0,X4) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X6,X2,X1,X7,X3] :
      ( ( shortest_path(X1,X2,X3)
        & precedes(X6,X7,X3) )
     => ( ~ precedes(X7,X6,X3)
        & ~ ? [X8] :
              ( tail_of(X8) = tail_of(X6)
              & head_of(X8) = head_of(X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).

fof(f164,plain,
    ( tail_of(sK5) = tail_of(sK2)
    | ~ spl13_1 ),
    inference(avatar_component_clause,[],[f162]) ).

fof(f162,plain,
    ( spl13_1
  <=> tail_of(sK5) = tail_of(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

fof(f105,plain,
    precedes(sK2,sK4,sK1),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ( precedes(sK2,sK4,sK1)
    & ( head_of(sK4) = tail_of(sK2)
      | ( head_of(sK4) = head_of(sK5)
        & tail_of(sK5) = tail_of(sK2) )
      | head_of(sK4) = head_of(sK2) )
    & shortest_path(sK0,sK3,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f63,f65,f64]) ).

fof(f64,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( precedes(X2,X4,X1)
        & ( head_of(X4) = tail_of(X2)
          | ? [X5] :
              ( head_of(X4) = head_of(X5)
              & tail_of(X5) = tail_of(X2) )
          | head_of(X4) = head_of(X2) )
        & shortest_path(X0,X3,X1) )
   => ( precedes(sK2,sK4,sK1)
      & ( head_of(sK4) = tail_of(sK2)
        | ? [X5] :
            ( head_of(sK4) = head_of(X5)
            & tail_of(X5) = tail_of(sK2) )
        | head_of(sK4) = head_of(sK2) )
      & shortest_path(sK0,sK3,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ( ? [X5] :
        ( head_of(sK4) = head_of(X5)
        & tail_of(X5) = tail_of(sK2) )
   => ( head_of(sK4) = head_of(sK5)
      & tail_of(sK5) = tail_of(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ? [X0,X1,X2,X3,X4] :
      ( precedes(X2,X4,X1)
      & ( head_of(X4) = tail_of(X2)
        | ? [X5] :
            ( head_of(X4) = head_of(X5)
            & tail_of(X5) = tail_of(X2) )
        | head_of(X4) = head_of(X2) )
      & shortest_path(X0,X3,X1) ),
    inference(rectify,[],[f51]) ).

fof(f51,plain,
    ? [X3,X1,X4,X0,X2] :
      ( precedes(X4,X2,X1)
      & ( tail_of(X4) = head_of(X2)
        | ? [X5] :
            ( head_of(X2) = head_of(X5)
            & tail_of(X5) = tail_of(X4) )
        | head_of(X4) = head_of(X2) )
      & shortest_path(X3,X0,X1) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ? [X3,X0,X4,X2,X1] :
      ( ( tail_of(X4) = head_of(X2)
        | ? [X5] :
            ( head_of(X2) = head_of(X5)
            & tail_of(X5) = tail_of(X4) )
        | head_of(X4) = head_of(X2) )
      & precedes(X4,X2,X1)
      & shortest_path(X3,X0,X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ! [X3,X0,X4,X2,X1] :
        ( ( precedes(X4,X2,X1)
          & shortest_path(X3,X0,X1) )
       => ( head_of(X4) != head_of(X2)
          & tail_of(X4) != head_of(X2)
          & ~ ? [X5] :
                ( head_of(X2) = head_of(X5)
                & tail_of(X5) = tail_of(X4) ) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ! [X2,X3,X7,X1,X6] :
        ( ( shortest_path(X1,X2,X3)
          & precedes(X6,X7,X3) )
       => ( ~ ? [X8] :
                ( tail_of(X8) = tail_of(X6)
                & head_of(X8) = head_of(X7) )
          & head_of(X6) != head_of(X7)
          & tail_of(X6) != head_of(X7) ) ),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ! [X2,X3,X7,X1,X6] :
      ( ( shortest_path(X1,X2,X3)
        & precedes(X6,X7,X3) )
     => ( ~ ? [X8] :
              ( tail_of(X8) = tail_of(X6)
              & head_of(X8) = head_of(X7) )
        & head_of(X6) != head_of(X7)
        & tail_of(X6) != head_of(X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties_lemma) ).

fof(f102,plain,
    shortest_path(sK0,sK3,sK1),
    inference(cnf_transformation,[],[f66]) ).

fof(f279,plain,
    ~ spl13_3,
    inference(avatar_contradiction_clause,[],[f278]) ).

fof(f278,plain,
    ( $false
    | ~ spl13_3 ),
    inference(subsumption_resolution,[],[f258,f240]) ).

fof(f240,plain,
    head_of(sK2) != tail_of(sK2),
    inference(resolution,[],[f234,f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ~ edge(X0)
      | head_of(X0) != tail_of(X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,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/benchmark/theBenchmark.p',no_loops) ).

fof(f234,plain,
    edge(sK2),
    inference(unit_resulting_resolution,[],[f149,f190,f101]) ).

fof(f101,plain,
    ! [X2,X3,X0,X1] :
      ( ~ path(X2,X1,X3)
      | edge(X0)
      | ~ on_path(X0,X3) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2,X3] :
      ( ( edge(X0)
        & in_path(tail_of(X0),X3)
        & in_path(head_of(X0),X3) )
      | ~ path(X2,X1,X3)
      | ~ on_path(X0,X3) ),
    inference(rectify,[],[f49]) ).

fof(f49,plain,
    ! [X1,X2,X3,X0] :
      ( ( edge(X1)
        & in_path(tail_of(X1),X0)
        & in_path(head_of(X1),X0) )
      | ~ path(X3,X2,X0)
      | ~ on_path(X1,X0) ),
    inference(flattening,[],[f48]) ).

fof(f48,plain,
    ! [X3,X1,X0,X2] :
      ( ( edge(X1)
        & in_path(tail_of(X1),X0)
        & in_path(head_of(X1),X0) )
      | ~ path(X3,X2,X0)
      | ~ on_path(X1,X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X3,X1,X0,X2] :
      ( ( path(X3,X2,X0)
        & on_path(X1,X0) )
     => ( edge(X1)
        & in_path(tail_of(X1),X0)
        & in_path(head_of(X1),X0) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X3,X0,X2,X1] :
      ( ( 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/benchmark/theBenchmark.p',on_path_properties) ).

fof(f190,plain,
    on_path(sK2,sK1),
    inference(unit_resulting_resolution,[],[f105,f149,f112]) ).

fof(f112,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X2)
      | ~ path(X0,X1,X2)
      | on_path(X3,X2) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ~ path(X0,X1,X2)
      | ! [X3,X4] :
          ( ( on_path(X3,X2)
            & ( ! [X5] :
                  ( ~ sequential(X3,X5)
                  | ~ precedes(X5,X4,X2) )
              | ~ sequential(X3,X4) )
            & ( ( sequential(X3,sK6(X2,X3,X4))
                & precedes(sK6(X2,X3,X4),X4,X2) )
              | sequential(X3,X4) )
            & on_path(X4,X2) )
          | ~ precedes(X3,X4,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f70,f71]) ).

fof(f71,plain,
    ! [X2,X3,X4] :
      ( ? [X6] :
          ( sequential(X3,X6)
          & precedes(X6,X4,X2) )
     => ( sequential(X3,sK6(X2,X3,X4))
        & precedes(sK6(X2,X3,X4),X4,X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ~ path(X0,X1,X2)
      | ! [X3,X4] :
          ( ( on_path(X3,X2)
            & ( ! [X5] :
                  ( ~ sequential(X3,X5)
                  | ~ precedes(X5,X4,X2) )
              | ~ sequential(X3,X4) )
            & ( ? [X6] :
                  ( sequential(X3,X6)
                  & precedes(X6,X4,X2) )
              | sequential(X3,X4) )
            & on_path(X4,X2) )
          | ~ precedes(X3,X4,X2) ) ),
    inference(rectify,[],[f69]) ).

fof(f69,plain,
    ! [X2,X1,X0] :
      ( ~ path(X2,X1,X0)
      | ! [X3,X4] :
          ( ( on_path(X3,X0)
            & ( ! [X5] :
                  ( ~ sequential(X3,X5)
                  | ~ precedes(X5,X4,X0) )
              | ~ sequential(X3,X4) )
            & ( ? [X5] :
                  ( sequential(X3,X5)
                  & precedes(X5,X4,X0) )
              | sequential(X3,X4) )
            & on_path(X4,X0) )
          | ~ precedes(X3,X4,X0) ) ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X2,X1,X0] :
      ( ~ path(X2,X1,X0)
      | ! [X3,X4] :
          ( ( on_path(X3,X0)
            & ( ! [X5] :
                  ( ~ sequential(X3,X5)
                  | ~ precedes(X5,X4,X0) )
              | ~ sequential(X3,X4) )
            & ( ? [X5] :
                  ( sequential(X3,X5)
                  & precedes(X5,X4,X0) )
              | sequential(X3,X4) )
            & on_path(X4,X0) )
          | ~ precedes(X3,X4,X0) ) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X2,X1,X0] :
      ( ~ path(X2,X1,X0)
      | ! [X3,X4] :
          ( ( on_path(X3,X0)
            & ( sequential(X3,X4)
            <~> ? [X5] :
                  ( sequential(X3,X5)
                  & precedes(X5,X4,X0) ) )
            & on_path(X4,X0) )
          | ~ precedes(X3,X4,X0) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X1,X0,X2] :
      ( path(X2,X1,X0)
     => ! [X3,X4] :
          ( precedes(X3,X4,X0)
         => ( on_path(X3,X0)
            & ( sequential(X3,X4)
            <~> ? [X5] :
                  ( sequential(X3,X5)
                  & precedes(X5,X4,X0) ) )
            & on_path(X4,X0) ) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X3,X2,X1] :
      ( path(X1,X2,X3)
     => ! [X6,X7] :
          ( precedes(X6,X7,X3)
         => ( ( sequential(X6,X7)
            <~> ? [X8] :
                  ( sequential(X6,X8)
                  & precedes(X8,X7,X3) ) )
            & on_path(X7,X3)
            & on_path(X6,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).

fof(f149,plain,
    path(sK0,sK3,sK1),
    inference(unit_resulting_resolution,[],[f102,f117]) ).

fof(f117,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X1,X0,X2)
      | path(X1,X0,X2) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 != X1
          & ! [X3] :
              ( less_or_equal(length_of(X2),length_of(X3))
              | ~ path(X1,X0,X3) )
          & path(X1,X0,X2) )
        | ~ shortest_path(X1,X0,X2) )
      & ( shortest_path(X1,X0,X2)
        | X0 = X1
        | ( ~ less_or_equal(length_of(X2),length_of(sK7(X0,X1,X2)))
          & path(X1,X0,sK7(X0,X1,X2)) )
        | ~ path(X1,X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f76,f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ~ less_or_equal(length_of(X2),length_of(X4))
          & path(X1,X0,X4) )
     => ( ~ less_or_equal(length_of(X2),length_of(sK7(X0,X1,X2)))
        & path(X1,X0,sK7(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ( ( X0 != X1
          & ! [X3] :
              ( less_or_equal(length_of(X2),length_of(X3))
              | ~ path(X1,X0,X3) )
          & path(X1,X0,X2) )
        | ~ shortest_path(X1,X0,X2) )
      & ( shortest_path(X1,X0,X2)
        | X0 = X1
        | ? [X4] :
            ( ~ less_or_equal(length_of(X2),length_of(X4))
            & path(X1,X0,X4) )
        | ~ path(X1,X0,X2) ) ),
    inference(rectify,[],[f75]) ).

fof(f75,plain,
    ! [X0,X2,X1] :
      ( ( ( X0 != X2
          & ! [X3] :
              ( less_or_equal(length_of(X1),length_of(X3))
              | ~ path(X2,X0,X3) )
          & path(X2,X0,X1) )
        | ~ shortest_path(X2,X0,X1) )
      & ( shortest_path(X2,X0,X1)
        | X0 = X2
        | ? [X3] :
            ( ~ less_or_equal(length_of(X1),length_of(X3))
            & path(X2,X0,X3) )
        | ~ path(X2,X0,X1) ) ),
    inference(flattening,[],[f74]) ).

fof(f74,plain,
    ! [X0,X2,X1] :
      ( ( ( X0 != X2
          & ! [X3] :
              ( less_or_equal(length_of(X1),length_of(X3))
              | ~ path(X2,X0,X3) )
          & path(X2,X0,X1) )
        | ~ shortest_path(X2,X0,X1) )
      & ( shortest_path(X2,X0,X1)
        | X0 = X2
        | ? [X3] :
            ( ~ less_or_equal(length_of(X1),length_of(X3))
            & path(X2,X0,X3) )
        | ~ path(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X2,X1] :
      ( ( X0 != X2
        & ! [X3] :
            ( less_or_equal(length_of(X1),length_of(X3))
            | ~ path(X2,X0,X3) )
        & path(X2,X0,X1) )
    <=> shortest_path(X2,X0,X1) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X2,X1] :
      ( ( X0 != X2
        & path(X2,X0,X1)
        & ! [X3] :
            ( path(X2,X0,X3)
           => less_or_equal(length_of(X1),length_of(X3)) ) )
    <=> shortest_path(X2,X0,X1) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X2,X9,X1] :
      ( ( ! [X3] :
            ( path(X1,X2,X3)
           => less_or_equal(length_of(X9),length_of(X3)) )
        & X1 != X2
        & path(X1,X2,X9) )
    <=> shortest_path(X1,X2,X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).

fof(f258,plain,
    ( head_of(sK2) = tail_of(sK2)
    | ~ spl13_3 ),
    inference(backward_demodulation,[],[f172,f251]) ).

fof(f251,plain,
    ( sK2 = sK4
    | ~ spl13_3 ),
    inference(subsumption_resolution,[],[f250,f172]) ).

fof(f250,plain,
    ( head_of(sK4) != tail_of(sK2)
    | sK2 = sK4 ),
    inference(subsumption_resolution,[],[f249,f227]) ).

fof(f227,plain,
    edge(sK4),
    inference(unit_resulting_resolution,[],[f149,f189,f101]) ).

fof(f189,plain,
    on_path(sK4,sK1),
    inference(unit_resulting_resolution,[],[f105,f149,f108]) ).

fof(f108,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X2)
      | ~ path(X0,X1,X2)
      | on_path(X4,X2) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f249,plain,
    ( ~ edge(sK4)
    | sK2 = sK4
    | head_of(sK4) != tail_of(sK2) ),
    inference(subsumption_resolution,[],[f248,f234]) ).

fof(f248,plain,
    ( ~ edge(sK2)
    | sK2 = sK4
    | ~ edge(sK4)
    | head_of(sK4) != tail_of(sK2) ),
    inference(resolution,[],[f235,f127]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( sequential(X0,X1)
      | head_of(X0) != tail_of(X1)
      | ~ edge(X0)
      | X0 = X1
      | ~ edge(X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( sequential(X0,X1)
        | X0 = X1
        | head_of(X0) != tail_of(X1)
        | ~ edge(X0)
        | ~ edge(X1) )
      & ( ( X0 != X1
          & head_of(X0) = tail_of(X1)
          & edge(X0)
          & edge(X1) )
        | ~ sequential(X0,X1) ) ),
    inference(rectify,[],[f81]) ).

fof(f81,plain,
    ! [X1,X0] :
      ( ( sequential(X1,X0)
        | X0 = X1
        | tail_of(X0) != head_of(X1)
        | ~ edge(X1)
        | ~ edge(X0) )
      & ( ( X0 != X1
          & tail_of(X0) = head_of(X1)
          & edge(X1)
          & edge(X0) )
        | ~ sequential(X1,X0) ) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X1,X0] :
      ( ( sequential(X1,X0)
        | X0 = X1
        | tail_of(X0) != head_of(X1)
        | ~ edge(X1)
        | ~ edge(X0) )
      & ( ( X0 != X1
          & tail_of(X0) = head_of(X1)
          & edge(X1)
          & edge(X0) )
        | ~ sequential(X1,X0) ) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X1,X0] :
      ( sequential(X1,X0)
    <=> ( X0 != X1
        & tail_of(X0) = head_of(X1)
        & edge(X1)
        & edge(X0) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X7,X6] :
      ( sequential(X6,X7)
    <=> ( head_of(X6) = tail_of(X7)
        & X6 != X7
        & edge(X7)
        & edge(X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).

fof(f235,plain,
    ~ sequential(sK4,sK2),
    inference(unit_resulting_resolution,[],[f149,f189,f155,f190,f107]) ).

fof(f107,plain,
    ! [X2,X3,X0,X1,X4] :
      ( precedes(X4,X3,X2)
      | ~ sequential(X4,X3)
      | ~ path(X0,X1,X2)
      | ~ on_path(X3,X2)
      | ~ on_path(X4,X2) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ~ path(X0,X1,X2)
      | ! [X3,X4] :
          ( ~ on_path(X4,X2)
          | ~ on_path(X3,X2)
          | ( ~ sequential(X4,X3)
            & ! [X5] :
                ( ~ sequential(X4,X5)
                | ~ precedes(X5,X3,X2) ) )
          | precedes(X4,X3,X2) ) ),
    inference(rectify,[],[f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ path(X2,X0,X1)
      | ! [X3,X4] :
          ( ~ on_path(X4,X1)
          | ~ on_path(X3,X1)
          | ( ~ sequential(X4,X3)
            & ! [X5] :
                ( ~ sequential(X4,X5)
                | ~ precedes(X5,X3,X1) ) )
          | precedes(X4,X3,X1) ) ),
    inference(flattening,[],[f44]) ).

fof(f44,plain,
    ! [X1,X2,X0] :
      ( ! [X4,X3] :
          ( precedes(X4,X3,X1)
          | ~ on_path(X4,X1)
          | ~ on_path(X3,X1)
          | ( ~ sequential(X4,X3)
            & ! [X5] :
                ( ~ sequential(X4,X5)
                | ~ precedes(X5,X3,X1) ) ) )
      | ~ path(X2,X0,X1) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X1,X2,X0] :
      ( path(X2,X0,X1)
     => ! [X4,X3] :
          ( ( on_path(X4,X1)
            & on_path(X3,X1)
            & ( ? [X5] :
                  ( sequential(X4,X5)
                  & precedes(X5,X3,X1) )
              | sequential(X4,X3) ) )
         => precedes(X4,X3,X1) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X2,X3,X1] :
      ( path(X1,X2,X3)
     => ! [X7,X6] :
          ( ( ( ? [X8] :
                  ( precedes(X8,X7,X3)
                  & sequential(X6,X8) )
              | sequential(X6,X7) )
            & on_path(X6,X3)
            & on_path(X7,X3) )
         => precedes(X6,X7,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).

fof(f155,plain,
    ~ precedes(sK4,sK2,sK1),
    inference(unit_resulting_resolution,[],[f102,f105,f98]) ).

fof(f98,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ shortest_path(X1,X3,X2)
      | ~ precedes(X0,X4,X2)
      | ~ precedes(X4,X0,X2) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f172,plain,
    ( head_of(sK4) = tail_of(sK2)
    | ~ spl13_3 ),
    inference(avatar_component_clause,[],[f170]) ).

fof(f170,plain,
    ( spl13_3
  <=> head_of(sK4) = tail_of(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

fof(f246,plain,
    ( spl13_4
    | spl13_3
    | spl13_2 ),
    inference(avatar_split_clause,[],[f104,f166,f170,f243]) ).

fof(f166,plain,
    ( spl13_2
  <=> head_of(sK4) = head_of(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

fof(f104,plain,
    ( head_of(sK4) = head_of(sK2)
    | head_of(sK4) = tail_of(sK2)
    | head_of(sK4) = head_of(sK5) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f181,plain,
    ~ spl13_2,
    inference(avatar_contradiction_clause,[],[f180]) ).

fof(f180,plain,
    ( $false
    | ~ spl13_2 ),
    inference(trivial_inequality_removal,[],[f174]) ).

fof(f174,plain,
    ( tail_of(sK2) != tail_of(sK2)
    | ~ spl13_2 ),
    inference(unit_resulting_resolution,[],[f102,f105,f168,f97]) ).

fof(f168,plain,
    ( head_of(sK4) = head_of(sK2)
    | ~ spl13_2 ),
    inference(avatar_component_clause,[],[f166]) ).

fof(f173,plain,
    ( spl13_1
    | spl13_2
    | spl13_3 ),
    inference(avatar_split_clause,[],[f103,f170,f166,f162]) ).

fof(f103,plain,
    ( head_of(sK4) = tail_of(sK2)
    | head_of(sK4) = head_of(sK2)
    | tail_of(sK5) = tail_of(sK2) ),
    inference(cnf_transformation,[],[f66]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GRA004+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 29 21:58:05 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.51  % (4332)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.52  % (4345)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (4354)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.52  % (4352)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.52  % (4346)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.52  % (4335)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (4333)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.53  % (4351)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.53  % (4336)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.53  % (4343)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53  % (4346)Instruction limit reached!
% 0.19/0.53  % (4346)------------------------------
% 0.19/0.53  % (4346)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (4346)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (4346)Termination reason: Unknown
% 0.19/0.53  % (4346)Termination phase: Clausification
% 0.19/0.53  
% 0.19/0.53  % (4346)Memory used [KB]: 1535
% 0.19/0.53  % (4346)Time elapsed: 0.003 s
% 0.19/0.53  % (4346)Instructions burned: 3 (million)
% 0.19/0.53  % (4346)------------------------------
% 0.19/0.53  % (4346)------------------------------
% 0.19/0.53  % (4334)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.53  % (4339)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.53  % (4337)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.53  % (4338)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.53  % (4348)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53  % (4355)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.53  % (4334)Instruction limit reached!
% 0.19/0.53  % (4334)------------------------------
% 0.19/0.53  % (4334)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (4334)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (4334)Termination reason: Unknown
% 0.19/0.53  % (4334)Termination phase: Property scanning
% 0.19/0.53  
% 0.19/0.53  % (4338)Refutation not found, incomplete strategy% (4338)------------------------------
% 0.19/0.53  % (4338)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (4334)Memory used [KB]: 1535
% 0.19/0.53  % (4334)Time elapsed: 0.004 s
% 0.19/0.53  % (4334)Instructions burned: 3 (million)
% 0.19/0.54  % (4334)------------------------------
% 0.19/0.54  % (4334)------------------------------
% 0.19/0.54  % (4336)Refutation not found, incomplete strategy% (4336)------------------------------
% 0.19/0.54  % (4336)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54  % (4336)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54  % (4336)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.54  
% 0.19/0.54  % (4336)Memory used [KB]: 6012
% 0.19/0.54  % (4336)Time elapsed: 0.133 s
% 0.19/0.54  % (4336)Instructions burned: 2 (million)
% 0.19/0.54  % (4336)------------------------------
% 0.19/0.54  % (4336)------------------------------
% 0.19/0.54  % (4353)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.54  % (4359)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.54  % (4360)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.54  % (4338)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54  % (4338)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.54  
% 0.19/0.54  % (4338)Memory used [KB]: 6012
% 0.19/0.54  % (4338)Time elapsed: 0.094 s
% 0.19/0.54  % (4338)Instructions burned: 3 (million)
% 0.19/0.54  % (4338)------------------------------
% 0.19/0.54  % (4338)------------------------------
% 0.19/0.54  % (4347)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.54  % (4349)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.54  % (4350)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.54  % (4350)Instruction limit reached!
% 0.19/0.54  % (4350)------------------------------
% 0.19/0.54  % (4350)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54  % (4350)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54  % (4350)Termination reason: Unknown
% 0.19/0.54  % (4350)Termination phase: Preprocessing 3
% 0.19/0.54  
% 0.19/0.54  % (4350)Memory used [KB]: 1407
% 0.19/0.54  % (4350)Time elapsed: 0.002 s
% 0.19/0.54  % (4350)Instructions burned: 2 (million)
% 0.19/0.54  % (4350)------------------------------
% 0.19/0.54  % (4350)------------------------------
% 0.19/0.54  % (4353)First to succeed.
% 0.19/0.54  % (4356)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.54  % (4340)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.54  % (4358)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.55  % (4344)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.55  % (4361)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.55  % (4342)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.55  % (4333)Instruction limit reached!
% 0.19/0.55  % (4333)------------------------------
% 0.19/0.55  % (4333)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (4333)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (4333)Termination reason: Unknown
% 0.19/0.55  % (4333)Termination phase: Saturation
% 0.19/0.55  
% 0.19/0.55  % (4333)Memory used [KB]: 6268
% 0.19/0.55  % (4333)Time elapsed: 0.154 s
% 0.19/0.55  % (4333)Instructions burned: 13 (million)
% 0.19/0.55  % (4333)------------------------------
% 0.19/0.55  % (4333)------------------------------
% 0.19/0.55  % (4343)Instruction limit reached!
% 0.19/0.55  % (4343)------------------------------
% 0.19/0.55  % (4343)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (4343)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (4343)Termination reason: Unknown
% 0.19/0.55  % (4343)Termination phase: Saturation
% 0.19/0.55  
% 0.19/0.55  % (4343)Memory used [KB]: 6140
% 0.19/0.55  % (4343)Time elapsed: 0.160 s
% 0.19/0.55  % (4343)Instructions burned: 8 (million)
% 0.19/0.55  % (4343)------------------------------
% 0.19/0.55  % (4343)------------------------------
% 0.19/0.55  % (4341)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.55  % (4357)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 1.58/0.55  % (4337)Instruction limit reached!
% 1.58/0.55  % (4337)------------------------------
% 1.58/0.55  % (4337)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.55  % (4337)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.55  % (4337)Termination reason: Unknown
% 1.58/0.55  % (4337)Termination phase: Saturation
% 1.58/0.55  
% 1.58/0.55  % (4337)Memory used [KB]: 1663
% 1.58/0.55  % (4337)Time elapsed: 0.139 s
% 1.58/0.55  % (4337)Instructions burned: 16 (million)
% 1.58/0.55  % (4337)------------------------------
% 1.58/0.55  % (4337)------------------------------
% 1.58/0.56  % (4351)Instruction limit reached!
% 1.58/0.56  % (4351)------------------------------
% 1.58/0.56  % (4351)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.56  % (4353)Refutation found. Thanks to Tanya!
% 1.58/0.56  % SZS status Theorem for theBenchmark
% 1.58/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 1.58/0.56  % (4353)------------------------------
% 1.58/0.56  % (4353)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.56  % (4353)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.56  % (4353)Termination reason: Refutation
% 1.58/0.56  
% 1.58/0.56  % (4353)Memory used [KB]: 6268
% 1.58/0.56  % (4353)Time elapsed: 0.153 s
% 1.58/0.56  % (4353)Instructions burned: 11 (million)
% 1.58/0.56  % (4353)------------------------------
% 1.58/0.56  % (4353)------------------------------
% 1.58/0.56  % (4331)Success in time 0.207 s
%------------------------------------------------------------------------------