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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 : Tue Apr 30 11:42:35 EDT 2024

% Result   : Theorem 0.23s 0.40s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  119 (  13 unt;   0 def)
%            Number of atoms       :  443 (  82 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  505 ( 181   ~; 160   |; 122   &)
%                                         (  15 <=>;  19  =>;   0  <=;   8 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   25 (  23 usr;  11 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :  262 ( 226   !;  36   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f275,plain,
    $false,
    inference(avatar_sat_refutation,[],[f178,f186,f188,f210,f219,f224,f229,f256,f265,f274]) ).

fof(f274,plain,
    ~ spl16_10,
    inference(avatar_contradiction_clause,[],[f273]) ).

fof(f273,plain,
    ( $false
    | ~ spl16_10 ),
    inference(subsumption_resolution,[],[f266,f234]) ).

fof(f234,plain,
    ! [X0,X1] :
      ( ~ precedes(X1,X0,sK8)
      | ~ precedes(X0,X1,sK8) ),
    inference(resolution,[],[f149,f95]) ).

fof(f95,plain,
    shortest_path(sK4,sK5,sK8),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ( ( ~ path(sK4,sK5,sK8)
      | sK6 = sK7
      | ~ edge(sK7)
      | ~ edge(sK6)
      | sK4 = sK5
      | ~ vertex(sK5)
      | ~ vertex(sK4) )
    & precedes(sK6,sK7,sK8)
    & shortest_path(sK4,sK5,sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f39,f68]) ).

fof(f68,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(sK4,sK5,sK8)
        | sK6 = sK7
        | ~ edge(sK7)
        | ~ edge(sK6)
        | sK4 = sK5
        | ~ vertex(sK5)
        | ~ vertex(sK4) )
      & precedes(sK6,sK7,sK8)
      & shortest_path(sK4,sK5,sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,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,[],[f38]) ).

fof(f38,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,[],[f20]) ).

fof(f20,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/benchmark/theBenchmark.p',vertices_and_edges) ).

fof(f149,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ precedes(X2,X3,X4)
      | ~ precedes(X3,X2,X4) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,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,[],[f59]) ).

fof(f59,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,[],[f35]) ).

fof(f35,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/benchmark/theBenchmark.p',shortest_path_properties) ).

fof(f266,plain,
    ( precedes(sK6,sK6,sK8)
    | ~ spl16_10 ),
    inference(superposition,[],[f96,f255]) ).

fof(f255,plain,
    ( sK6 = sK7
    | ~ spl16_10 ),
    inference(avatar_component_clause,[],[f253]) ).

fof(f253,plain,
    ( spl16_10
  <=> sK6 = sK7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_10])]) ).

fof(f96,plain,
    precedes(sK6,sK7,sK8),
    inference(cnf_transformation,[],[f69]) ).

fof(f265,plain,
    ~ spl16_9,
    inference(avatar_contradiction_clause,[],[f264]) ).

fof(f264,plain,
    ( $false
    | ~ spl16_9 ),
    inference(subsumption_resolution,[],[f257,f159]) ).

fof(f159,plain,
    ! [X0,X1] : ~ shortest_path(X0,X0,X1),
    inference(resolution,[],[f140,f158]) ).

fof(f158,plain,
    ! [X2,X0] : ~ sP3(X0,X2,X2),
    inference(equality_resolution,[],[f136]) ).

fof(f136,plain,
    ! [X2,X0,X1] :
      ( X1 != X2
      | ~ sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ( sP3(X0,X1,X2)
        | ( ~ less_or_equal(length_of(X0),length_of(sK14(X0,X1,X2)))
          & path(X2,X1,sK14(X0,X1,X2)) )
        | X1 = X2
        | ~ path(X2,X1,X0) )
      & ( ( ! [X4] :
              ( less_or_equal(length_of(X0),length_of(X4))
              | ~ path(X2,X1,X4) )
          & X1 != X2
          & path(X2,X1,X0) )
        | ~ sP3(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f89,f90]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ less_or_equal(length_of(X0),length_of(X3))
          & path(X2,X1,X3) )
     => ( ~ less_or_equal(length_of(X0),length_of(sK14(X0,X1,X2)))
        & path(X2,X1,sK14(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ( sP3(X0,X1,X2)
        | ? [X3] :
            ( ~ less_or_equal(length_of(X0),length_of(X3))
            & path(X2,X1,X3) )
        | X1 = X2
        | ~ path(X2,X1,X0) )
      & ( ( ! [X4] :
              ( less_or_equal(length_of(X0),length_of(X4))
              | ~ path(X2,X1,X4) )
          & X1 != X2
          & path(X2,X1,X0) )
        | ~ sP3(X0,X1,X2) ) ),
    inference(rectify,[],[f88]) ).

fof(f88,plain,
    ! [X2,X1,X0] :
      ( ( sP3(X2,X1,X0)
        | ? [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) )
        | ~ sP3(X2,X1,X0) ) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ! [X2,X1,X0] :
      ( ( sP3(X2,X1,X0)
        | ? [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) )
        | ~ sP3(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X2,X1,X0] :
      ( sP3(X2,X1,X0)
    <=> ( ! [X3] :
            ( less_or_equal(length_of(X2),length_of(X3))
            | ~ path(X0,X1,X3) )
        & X0 != X1
        & path(X0,X1,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f140,plain,
    ! [X2,X0,X1] :
      ( sP3(X2,X1,X0)
      | ~ shortest_path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( ( shortest_path(X0,X1,X2)
        | ~ sP3(X2,X1,X0) )
      & ( sP3(X2,X1,X0)
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( shortest_path(X0,X1,X2)
    <=> sP3(X2,X1,X0) ),
    inference(definition_folding,[],[f54,f66]) ).

fof(f54,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,[],[f32]) ).

fof(f32,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/benchmark/theBenchmark.p',shortest_path_defn) ).

fof(f257,plain,
    ( shortest_path(sK4,sK4,sK8)
    | ~ spl16_9 ),
    inference(superposition,[],[f95,f251]) ).

fof(f251,plain,
    ( sK4 = sK5
    | ~ spl16_9 ),
    inference(avatar_component_clause,[],[f249]) ).

fof(f249,plain,
    ( spl16_9
  <=> sK4 = sK5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_9])]) ).

fof(f256,plain,
    ( spl16_9
    | spl16_10
    | ~ spl16_2
    | ~ spl16_3 ),
    inference(avatar_split_clause,[],[f247,f183,f175,f253,f249]) ).

fof(f175,plain,
    ( spl16_2
  <=> on_path(sK6,sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).

fof(f183,plain,
    ( spl16_3
  <=> on_path(sK7,sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).

fof(f247,plain,
    ( sK6 = sK7
    | sK4 = sK5
    | ~ spl16_2
    | ~ spl16_3 ),
    inference(subsumption_resolution,[],[f246,f164]) ).

fof(f164,plain,
    vertex(sK4),
    inference(resolution,[],[f162,f117]) ).

fof(f117,plain,
    ! [X2,X0,X1] :
      ( ~ path(X0,X1,X2)
      | vertex(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X1,X2,X0)
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(definition_folding,[],[f44,f62,f61]) ).

fof(f61,plain,
    ! [X2,X3,X1] :
      ( ( ( path_cons(X3,empty) = X2
          & head_of(X3) = X1 )
      <~> ? [X4] :
            ( path_cons(X3,X4) = X2
            & path(head_of(X3),X1,X4) ) )
      | ~ sP0(X2,X3,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f62,plain,
    ! [X1,X2,X0] :
      ( ? [X3] :
          ( sP0(X2,X3,X1)
          & tail_of(X3) = X0
          & edge(X3) )
      | ~ sP1(X1,X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f44,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,[],[f26]) ).

fof(f26,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/benchmark/theBenchmark.p',path_properties) ).

fof(f162,plain,
    path(sK4,sK5,sK8),
    inference(resolution,[],[f160,f95]) ).

fof(f160,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X0,X1,X2)
      | path(X0,X1,X2) ),
    inference(resolution,[],[f140,f135]) ).

fof(f135,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X0,X1,X2)
      | path(X2,X1,X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f246,plain,
    ( sK6 = sK7
    | sK4 = sK5
    | ~ vertex(sK4)
    | ~ spl16_2
    | ~ spl16_3 ),
    inference(subsumption_resolution,[],[f245,f163]) ).

fof(f163,plain,
    vertex(sK5),
    inference(resolution,[],[f162,f118]) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( ~ path(X0,X1,X2)
      | vertex(X1) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f245,plain,
    ( sK6 = sK7
    | sK4 = sK5
    | ~ vertex(sK5)
    | ~ vertex(sK4)
    | ~ spl16_2
    | ~ spl16_3 ),
    inference(subsumption_resolution,[],[f244,f179]) ).

fof(f179,plain,
    ( edge(sK6)
    | ~ spl16_2 ),
    inference(resolution,[],[f177,f166]) ).

fof(f166,plain,
    ! [X0] :
      ( ~ on_path(X0,sK8)
      | edge(X0) ),
    inference(resolution,[],[f145,f162]) ).

fof(f145,plain,
    ! [X2,X3,X0,X1] :
      ( ~ path(X0,X1,X2)
      | ~ on_path(X3,X2)
      | edge(X3) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,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,[],[f57]) ).

fof(f57,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,[],[f34]) ).

fof(f34,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/benchmark/theBenchmark.p',on_path_properties) ).

fof(f177,plain,
    ( on_path(sK6,sK8)
    | ~ spl16_2 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f244,plain,
    ( sK6 = sK7
    | ~ edge(sK6)
    | sK4 = sK5
    | ~ vertex(sK5)
    | ~ vertex(sK4)
    | ~ spl16_3 ),
    inference(subsumption_resolution,[],[f243,f189]) ).

fof(f189,plain,
    ( edge(sK7)
    | ~ spl16_3 ),
    inference(resolution,[],[f185,f166]) ).

fof(f185,plain,
    ( on_path(sK7,sK8)
    | ~ spl16_3 ),
    inference(avatar_component_clause,[],[f183]) ).

fof(f243,plain,
    ( sK6 = sK7
    | ~ edge(sK7)
    | ~ edge(sK6)
    | sK4 = sK5
    | ~ vertex(sK5)
    | ~ vertex(sK4) ),
    inference(subsumption_resolution,[],[f97,f162]) ).

fof(f97,plain,
    ( ~ path(sK4,sK5,sK8)
    | sK6 = sK7
    | ~ edge(sK7)
    | ~ edge(sK6)
    | sK4 = sK5
    | ~ vertex(sK5)
    | ~ vertex(sK4) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f229,plain,
    ( spl16_1
    | spl16_8 ),
    inference(avatar_split_clause,[],[f221,f226,f172]) ).

fof(f172,plain,
    ( spl16_1
  <=> ! [X0,X1] : ~ path(X0,X1,sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).

fof(f226,plain,
    ( spl16_8
  <=> sP2(sK8,sK7,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( sP2(sK8,sK7,sK6)
      | ~ path(X0,X1,sK8) ),
    inference(resolution,[],[f125,f96]) ).

fof(f125,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X0)
      | sP2(X0,X4,X3)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( sP2(X0,X4,X3)
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(definition_folding,[],[f45,f64]) ).

fof(f64,plain,
    ! [X0,X4,X3] :
      ( ( sequential(X3,X4)
      <~> ? [X5] :
            ( precedes(X5,X4,X0)
            & sequential(X3,X5) ) )
      | ~ sP2(X0,X4,X3) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f45,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/benchmark/theBenchmark.p',precedes_properties) ).

fof(f224,plain,
    spl16_6,
    inference(avatar_contradiction_clause,[],[f223]) ).

fof(f223,plain,
    ( $false
    | spl16_6 ),
    inference(subsumption_resolution,[],[f222,f162]) ).

fof(f222,plain,
    ( ~ path(sK4,sK5,sK8)
    | spl16_6 ),
    inference(resolution,[],[f220,f119]) ).

fof(f119,plain,
    ! [X2,X0,X1] :
      ( sP1(X1,X2,X0)
      | ~ path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f220,plain,
    ( ~ sP1(sK5,sK8,sK4)
    | spl16_6 ),
    inference(resolution,[],[f214,f109]) ).

fof(f109,plain,
    ! [X2,X0,X1] :
      ( edge(sK9(X0,X1,X2))
      | ~ sP1(X0,X1,X2) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X1,sK9(X0,X1,X2),X0)
        & tail_of(sK9(X0,X1,X2)) = X2
        & edge(sK9(X0,X1,X2)) )
      | ~ sP1(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f73,f74]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( sP0(X1,X3,X0)
          & tail_of(X3) = X2
          & edge(X3) )
     => ( sP0(X1,sK9(X0,X1,X2),X0)
        & tail_of(sK9(X0,X1,X2)) = X2
        & edge(sK9(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( sP0(X1,X3,X0)
          & tail_of(X3) = X2
          & edge(X3) )
      | ~ sP1(X0,X1,X2) ),
    inference(rectify,[],[f72]) ).

fof(f72,plain,
    ! [X1,X2,X0] :
      ( ? [X3] :
          ( sP0(X2,X3,X1)
          & tail_of(X3) = X0
          & edge(X3) )
      | ~ sP1(X1,X2,X0) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f214,plain,
    ( ~ edge(sK9(sK5,sK8,sK4))
    | spl16_6 ),
    inference(avatar_component_clause,[],[f212]) ).

fof(f212,plain,
    ( spl16_6
  <=> edge(sK9(sK5,sK8,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).

fof(f219,plain,
    ( ~ spl16_6
    | ~ spl16_7 ),
    inference(avatar_split_clause,[],[f200,f216,f212]) ).

fof(f216,plain,
    ( spl16_7
  <=> sK4 = head_of(sK9(sK5,sK8,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_7])]) ).

fof(f200,plain,
    ( sK4 != head_of(sK9(sK5,sK8,sK4))
    | ~ edge(sK9(sK5,sK8,sK4)) ),
    inference(superposition,[],[f98,f198]) ).

fof(f198,plain,
    sK4 = tail_of(sK9(sK5,sK8,sK4)),
    inference(resolution,[],[f169,f162]) ).

fof(f169,plain,
    ! [X2,X0,X1] :
      ( ~ path(X2,X0,X1)
      | tail_of(sK9(X0,X1,X2)) = X2 ),
    inference(resolution,[],[f110,f119]) ).

fof(f110,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X1,X2)
      | tail_of(sK9(X0,X1,X2)) = X2 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f98,plain,
    ! [X0] :
      ( head_of(X0) != tail_of(X0)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,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(f210,plain,
    ( ~ spl16_4
    | spl16_5 ),
    inference(avatar_split_clause,[],[f199,f207,f203]) ).

fof(f203,plain,
    ( spl16_4
  <=> on_path(sK9(sK5,sK8,sK4),sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).

fof(f207,plain,
    ( spl16_5
  <=> in_path(sK4,sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).

fof(f199,plain,
    ( in_path(sK4,sK8)
    | ~ on_path(sK9(sK5,sK8,sK4),sK8) ),
    inference(superposition,[],[f193,f198]) ).

fof(f193,plain,
    ! [X0] :
      ( in_path(tail_of(X0),sK8)
      | ~ on_path(X0,sK8) ),
    inference(resolution,[],[f147,f162]) ).

fof(f147,plain,
    ! [X2,X3,X0,X1] :
      ( ~ path(X0,X1,X2)
      | ~ on_path(X3,X2)
      | in_path(tail_of(X3),X2) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f188,plain,
    ~ spl16_1,
    inference(avatar_contradiction_clause,[],[f187]) ).

fof(f187,plain,
    ( $false
    | ~ spl16_1 ),
    inference(resolution,[],[f173,f162]) ).

fof(f173,plain,
    ( ! [X0,X1] : ~ path(X0,X1,sK8)
    | ~ spl16_1 ),
    inference(avatar_component_clause,[],[f172]) ).

fof(f186,plain,
    ( spl16_1
    | spl16_3 ),
    inference(avatar_split_clause,[],[f180,f183,f172]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( on_path(sK7,sK8)
      | ~ path(X0,X1,sK8) ),
    inference(resolution,[],[f124,f96]) ).

fof(f124,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X0)
      | on_path(X4,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f178,plain,
    ( spl16_1
    | spl16_2 ),
    inference(avatar_split_clause,[],[f170,f175,f172]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( on_path(sK6,sK8)
      | ~ path(X0,X1,sK8) ),
    inference(resolution,[],[f123,f96]) ).

fof(f123,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X0)
      | on_path(X3,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f65]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n020.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Tue Apr 30 02:10:32 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (10314)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.39  % (10317)WARNING: value z3 for option sas not known
% 0.23/0.39  % (10315)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.39  % (10316)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.39  % (10318)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.39  % (10317)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.23/0.39  % (10320)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.23/0.39  % (10319)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.23/0.39  % (10321)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.23/0.40  TRYING [1]
% 0.23/0.40  TRYING [1]
% 0.23/0.40  TRYING [2]
% 0.23/0.40  TRYING [2]
% 0.23/0.40  % (10317)First to succeed.
% 0.23/0.40  TRYING [1]
% 0.23/0.40  TRYING [2]
% 0.23/0.40  % (10317)Refutation found. Thanks to Tanya!
% 0.23/0.40  % SZS status Theorem for theBenchmark
% 0.23/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.41  % (10317)------------------------------
% 0.23/0.41  % (10317)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.23/0.41  % (10317)Termination reason: Refutation
% 0.23/0.41  
% 0.23/0.41  % (10317)Memory used [KB]: 973
% 0.23/0.41  % (10317)Time elapsed: 0.013 s
% 0.23/0.41  % (10317)Instructions burned: 16 (million)
% 0.23/0.41  % (10317)------------------------------
% 0.23/0.41  % (10317)------------------------------
% 0.23/0.41  % (10314)Success in time 0.029 s
%------------------------------------------------------------------------------