TSTP Solution File: GRA003+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GRA003+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_sat --cores 0 -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 Aug 31 16:13:31 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   76 (  13 unt;   0 def)
%            Number of atoms       :  430 ( 110 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  532 ( 178   ~; 162   |; 163   &)
%                                         (   3 <=>;  20  =>;   0  <=;   6 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :  261 ( 212   !;  49   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f238,plain,
    $false,
    inference(subsumption_resolution,[],[f221,f228]) ).

fof(f228,plain,
    ~ precedes(sK4,sK4,sK5),
    inference(backward_demodulation,[],[f190,f220]) ).

fof(f220,plain,
    sK4 = sK7,
    inference(subsumption_resolution,[],[f219,f151]) ).

fof(f151,plain,
    ! [X2,X1] : ~ shortest_path(X1,X1,X2),
    inference(equality_resolution,[],[f133]) ).

fof(f133,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | ~ shortest_path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( ( ! [X3] :
              ( ~ path(X0,X1,X3)
              | less_or_equal(length_of(X2),length_of(X3)) )
          & path(X0,X1,X2)
          & X0 != X1 )
        | ~ shortest_path(X0,X1,X2) )
      & ( shortest_path(X0,X1,X2)
        | ( path(X0,X1,sK10(X0,X1,X2))
          & ~ less_or_equal(length_of(X2),length_of(sK10(X0,X1,X2))) )
        | ~ path(X0,X1,X2)
        | X0 = X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f86,f87]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( path(X0,X1,X4)
          & ~ less_or_equal(length_of(X2),length_of(X4)) )
     => ( path(X0,X1,sK10(X0,X1,X2))
        & ~ less_or_equal(length_of(X2),length_of(sK10(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ( ( ! [X3] :
              ( ~ path(X0,X1,X3)
              | less_or_equal(length_of(X2),length_of(X3)) )
          & path(X0,X1,X2)
          & X0 != X1 )
        | ~ shortest_path(X0,X1,X2) )
      & ( shortest_path(X0,X1,X2)
        | ? [X4] :
            ( path(X0,X1,X4)
            & ~ less_or_equal(length_of(X2),length_of(X4)) )
        | ~ path(X0,X1,X2)
        | X0 = X1 ) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ! [X1,X2,X0] :
      ( ( ( ! [X3] :
              ( ~ path(X1,X2,X3)
              | less_or_equal(length_of(X0),length_of(X3)) )
          & path(X1,X2,X0)
          & X1 != X2 )
        | ~ shortest_path(X1,X2,X0) )
      & ( shortest_path(X1,X2,X0)
        | ? [X3] :
            ( path(X1,X2,X3)
            & ~ less_or_equal(length_of(X0),length_of(X3)) )
        | ~ path(X1,X2,X0)
        | X1 = X2 ) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X1,X2,X0] :
      ( ( ( ! [X3] :
              ( ~ path(X1,X2,X3)
              | less_or_equal(length_of(X0),length_of(X3)) )
          & path(X1,X2,X0)
          & X1 != X2 )
        | ~ shortest_path(X1,X2,X0) )
      & ( shortest_path(X1,X2,X0)
        | ? [X3] :
            ( path(X1,X2,X3)
            & ~ less_or_equal(length_of(X0),length_of(X3)) )
        | ~ path(X1,X2,X0)
        | X1 = X2 ) ),
    inference(nnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X1,X2,X0] :
      ( ( ! [X3] :
            ( ~ path(X1,X2,X3)
            | less_or_equal(length_of(X0),length_of(X3)) )
        & path(X1,X2,X0)
        & X1 != X2 )
    <=> shortest_path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X2,X1] :
      ( shortest_path(X1,X2,X0)
    <=> ( ! [X3] :
            ( path(X1,X2,X3)
           => less_or_equal(length_of(X0),length_of(X3)) )
        & X1 != X2
        & path(X1,X2,X0) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X9,X1,X2] :
      ( ( path(X1,X2,X9)
        & X1 != X2
        & ! [X3] :
            ( path(X1,X2,X3)
           => less_or_equal(length_of(X9),length_of(X3)) ) )
    <=> shortest_path(X1,X2,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).

fof(f219,plain,
    ( sK4 = sK7
    | shortest_path(sK6,sK6,sK5) ),
    inference(superposition,[],[f127,f214]) ).

fof(f214,plain,
    ( sK6 = sK8
    | sK4 = sK7 ),
    inference(resolution,[],[f176,f184]) ).

fof(f184,plain,
    edge(sK4),
    inference(resolution,[],[f181,f160]) ).

fof(f160,plain,
    path(sK8,sK6,sK5),
    inference(resolution,[],[f134,f127]) ).

fof(f134,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X0,X1,X2)
      | path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f181,plain,
    ! [X4,X5] :
      ( ~ path(X4,X5,sK5)
      | edge(sK4) ),
    inference(resolution,[],[f178,f143]) ).

fof(f143,plain,
    ! [X2,X3,X0,X1] :
      ( ~ on_path(X0,X3)
      | edge(X0)
      | ~ path(X1,X2,X3) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1,X2,X3] :
      ( ~ path(X1,X2,X3)
      | ~ on_path(X0,X3)
      | ( edge(X0)
        & in_path(tail_of(X0),X3)
        & in_path(head_of(X0),X3) ) ),
    inference(rectify,[],[f52]) ).

fof(f52,plain,
    ! [X3,X1,X2,X0] :
      ( ~ path(X1,X2,X0)
      | ~ on_path(X3,X0)
      | ( edge(X3)
        & in_path(tail_of(X3),X0)
        & in_path(head_of(X3),X0) ) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X3,X1,X0,X2] :
      ( ( edge(X3)
        & in_path(tail_of(X3),X0)
        & in_path(head_of(X3),X0) )
      | ~ on_path(X3,X0)
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X3,X1,X0,X2] :
      ( ( on_path(X3,X0)
        & path(X1,X2,X0) )
     => ( edge(X3)
        & in_path(tail_of(X3),X0)
        & in_path(head_of(X3),X0) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X3,X1,X2,X0] :
      ( ( path(X1,X2,X3)
        & on_path(X0,X3) )
     => ( in_path(head_of(X0),X3)
        & in_path(tail_of(X0),X3)
        & edge(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',on_path_properties) ).

fof(f178,plain,
    on_path(sK4,sK5),
    inference(resolution,[],[f168,f160]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ~ path(X0,X1,sK5)
      | on_path(sK4,sK5) ),
    inference(resolution,[],[f140,f126]) ).

fof(f126,plain,
    precedes(sK4,sK7,sK5),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ( shortest_path(sK8,sK6,sK5)
    & precedes(sK4,sK7,sK5)
    & ( ~ edge(sK7)
      | sK6 = sK8
      | sK4 = sK7
      | ~ path(sK8,sK6,sK5)
      | ~ edge(sK4)
      | ~ vertex(sK6)
      | ~ vertex(sK8) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f78,f79]) ).

fof(f79,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( shortest_path(X4,X2,X1)
        & precedes(X0,X3,X1)
        & ( ~ edge(X3)
          | X2 = X4
          | X0 = X3
          | ~ path(X4,X2,X1)
          | ~ edge(X0)
          | ~ vertex(X2)
          | ~ vertex(X4) ) )
   => ( shortest_path(sK8,sK6,sK5)
      & precedes(sK4,sK7,sK5)
      & ( ~ edge(sK7)
        | sK6 = sK8
        | sK4 = sK7
        | ~ path(sK8,sK6,sK5)
        | ~ edge(sK4)
        | ~ vertex(sK6)
        | ~ vertex(sK8) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ? [X0,X1,X2,X3,X4] :
      ( shortest_path(X4,X2,X1)
      & precedes(X0,X3,X1)
      & ( ~ edge(X3)
        | X2 = X4
        | X0 = X3
        | ~ path(X4,X2,X1)
        | ~ edge(X0)
        | ~ vertex(X2)
        | ~ vertex(X4) ) ),
    inference(rectify,[],[f50]) ).

fof(f50,plain,
    ? [X0,X2,X4,X3,X1] :
      ( shortest_path(X1,X4,X2)
      & precedes(X0,X3,X2)
      & ( ~ edge(X3)
        | X1 = X4
        | X0 = X3
        | ~ path(X1,X4,X2)
        | ~ edge(X0)
        | ~ vertex(X4)
        | ~ vertex(X1) ) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ? [X1,X2,X3,X0,X4] :
      ( ( ~ edge(X3)
        | X1 = X4
        | X0 = X3
        | ~ path(X1,X4,X2)
        | ~ edge(X0)
        | ~ vertex(X4)
        | ~ vertex(X1) )
      & precedes(X0,X3,X2)
      & shortest_path(X1,X4,X2) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,plain,
    ~ ! [X1,X2,X3,X0,X4] :
        ( ( precedes(X0,X3,X2)
          & shortest_path(X1,X4,X2) )
       => ( vertex(X1)
          & edge(X3)
          & vertex(X4)
          & X1 != X4
          & path(X1,X4,X2)
          & X0 != X3
          & edge(X0) ) ),
    inference(rectify,[],[f19]) ).

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

fof(f18,conjecture,
    ! [X6,X1,X3,X7,X2] :
      ( ( precedes(X6,X7,X3)
        & shortest_path(X1,X2,X3) )
     => ( X1 != X2
        & edge(X6)
        & X6 != X7
        & path(X1,X2,X3)
        & edge(X7)
        & vertex(X1)
        & vertex(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vertices_and_edges) ).

fof(f140,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X4,X3,X1)
      | on_path(X4,X1)
      | ~ path(X2,X0,X1) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ~ precedes(X4,X3,X1)
          | ( on_path(X4,X1)
            & on_path(X3,X1)
            & ( ! [X5] :
                  ( ~ sequential(X4,X5)
                  | ~ precedes(X5,X3,X1) )
              | ~ sequential(X4,X3) )
            & ( ( sequential(X4,sK11(X1,X3,X4))
                & precedes(sK11(X1,X3,X4),X3,X1) )
              | sequential(X4,X3) ) ) )
      | ~ path(X2,X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f91,f92]) ).

fof(f92,plain,
    ! [X1,X3,X4] :
      ( ? [X6] :
          ( sequential(X4,X6)
          & precedes(X6,X3,X1) )
     => ( sequential(X4,sK11(X1,X3,X4))
        & precedes(sK11(X1,X3,X4),X3,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ~ precedes(X4,X3,X1)
          | ( on_path(X4,X1)
            & on_path(X3,X1)
            & ( ! [X5] :
                  ( ~ sequential(X4,X5)
                  | ~ precedes(X5,X3,X1) )
              | ~ sequential(X4,X3) )
            & ( ? [X6] :
                  ( sequential(X4,X6)
                  & precedes(X6,X3,X1) )
              | sequential(X4,X3) ) ) )
      | ~ path(X2,X0,X1) ),
    inference(rectify,[],[f90]) ).

fof(f90,plain,
    ! [X2,X0,X1] :
      ( ! [X3,X4] :
          ( ~ precedes(X4,X3,X0)
          | ( on_path(X4,X0)
            & on_path(X3,X0)
            & ( ! [X5] :
                  ( ~ sequential(X4,X5)
                  | ~ precedes(X5,X3,X0) )
              | ~ sequential(X4,X3) )
            & ( ? [X5] :
                  ( sequential(X4,X5)
                  & precedes(X5,X3,X0) )
              | sequential(X4,X3) ) ) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f89]) ).

fof(f89,plain,
    ! [X2,X0,X1] :
      ( ! [X3,X4] :
          ( ~ precedes(X4,X3,X0)
          | ( on_path(X4,X0)
            & on_path(X3,X0)
            & ( ! [X5] :
                  ( ~ sequential(X4,X5)
                  | ~ precedes(X5,X3,X0) )
              | ~ sequential(X4,X3) )
            & ( ? [X5] :
                  ( sequential(X4,X5)
                  & precedes(X5,X3,X0) )
              | sequential(X4,X3) ) ) )
      | ~ path(X1,X2,X0) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( ! [X3,X4] :
          ( ~ precedes(X4,X3,X0)
          | ( on_path(X4,X0)
            & on_path(X3,X0)
            & ( sequential(X4,X3)
            <~> ? [X5] :
                  ( sequential(X4,X5)
                  & precedes(X5,X3,X0) ) ) ) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X2,X1,X0] :
      ( path(X1,X2,X0)
     => ! [X3,X4] :
          ( precedes(X4,X3,X0)
         => ( on_path(X4,X0)
            & on_path(X3,X0)
            & ( sequential(X4,X3)
            <~> ? [X5] :
                  ( sequential(X4,X5)
                  & precedes(X5,X3,X0) ) ) ) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X3,X1,X2] :
      ( path(X1,X2,X3)
     => ! [X7,X6] :
          ( precedes(X6,X7,X3)
         => ( on_path(X7,X3)
            & on_path(X6,X3)
            & ( ? [X8] :
                  ( precedes(X8,X7,X3)
                  & sequential(X6,X8) )
            <~> sequential(X6,X7) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_properties) ).

fof(f176,plain,
    ( ~ edge(sK4)
    | sK6 = sK8
    | sK4 = sK7 ),
    inference(resolution,[],[f175,f161]) ).

fof(f161,plain,
    ( ~ edge(sK7)
    | sK4 = sK7
    | sK6 = sK8
    | ~ edge(sK4) ),
    inference(resolution,[],[f160,f153]) ).

fof(f153,plain,
    ( ~ path(sK8,sK6,sK5)
    | sK4 = sK7
    | ~ edge(sK4)
    | ~ edge(sK7)
    | sK6 = sK8 ),
    inference(subsumption_resolution,[],[f152,f100]) ).

fof(f100,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | vertex(X2) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( ~ path(X1,X2,X0)
      | ( edge(sK2(X0,X1,X2))
        & tail_of(sK2(X0,X1,X2)) = X1
        & ( head_of(sK2(X0,X1,X2)) != X2
          | path_cons(sK2(X0,X1,X2),empty) != X0
          | ! [X4] :
              ( path_cons(sK2(X0,X1,X2),X4) != X0
              | ~ path(head_of(sK2(X0,X1,X2)),X2,X4) ) )
        & ( ( head_of(sK2(X0,X1,X2)) = X2
            & path_cons(sK2(X0,X1,X2),empty) = X0 )
          | ( path_cons(sK2(X0,X1,X2),sK3(X0,X1,X2)) = X0
            & path(head_of(sK2(X0,X1,X2)),X2,sK3(X0,X1,X2)) ) )
        & vertex(X1)
        & vertex(X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f66,f68,f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( edge(X3)
          & tail_of(X3) = X1
          & ( head_of(X3) != X2
            | path_cons(X3,empty) != X0
            | ! [X4] :
                ( path_cons(X3,X4) != X0
                | ~ path(head_of(X3),X2,X4) ) )
          & ( ( head_of(X3) = X2
              & path_cons(X3,empty) = X0 )
            | ? [X5] :
                ( path_cons(X3,X5) = X0
                & path(head_of(X3),X2,X5) ) ) )
     => ( edge(sK2(X0,X1,X2))
        & tail_of(sK2(X0,X1,X2)) = X1
        & ( head_of(sK2(X0,X1,X2)) != X2
          | path_cons(sK2(X0,X1,X2),empty) != X0
          | ! [X4] :
              ( path_cons(sK2(X0,X1,X2),X4) != X0
              | ~ path(head_of(sK2(X0,X1,X2)),X2,X4) ) )
        & ( ( head_of(sK2(X0,X1,X2)) = X2
            & path_cons(sK2(X0,X1,X2),empty) = X0 )
          | ? [X5] :
              ( path_cons(sK2(X0,X1,X2),X5) = X0
              & path(head_of(sK2(X0,X1,X2)),X2,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( path_cons(sK2(X0,X1,X2),X5) = X0
          & path(head_of(sK2(X0,X1,X2)),X2,X5) )
     => ( path_cons(sK2(X0,X1,X2),sK3(X0,X1,X2)) = X0
        & path(head_of(sK2(X0,X1,X2)),X2,sK3(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ~ path(X1,X2,X0)
      | ( ? [X3] :
            ( edge(X3)
            & tail_of(X3) = X1
            & ( head_of(X3) != X2
              | path_cons(X3,empty) != X0
              | ! [X4] :
                  ( path_cons(X3,X4) != X0
                  | ~ path(head_of(X3),X2,X4) ) )
            & ( ( head_of(X3) = X2
                & path_cons(X3,empty) = X0 )
              | ? [X5] :
                  ( path_cons(X3,X5) = X0
                  & path(head_of(X3),X2,X5) ) ) )
        & vertex(X1)
        & vertex(X2) ) ),
    inference(rectify,[],[f65]) ).

fof(f65,plain,
    ! [X1,X2,X0] :
      ( ~ path(X2,X0,X1)
      | ( ? [X3] :
            ( edge(X3)
            & tail_of(X3) = X2
            & ( head_of(X3) != X0
              | path_cons(X3,empty) != X1
              | ! [X4] :
                  ( path_cons(X3,X4) != X1
                  | ~ path(head_of(X3),X0,X4) ) )
            & ( ( head_of(X3) = X0
                & path_cons(X3,empty) = X1 )
              | ? [X4] :
                  ( path_cons(X3,X4) = X1
                  & path(head_of(X3),X0,X4) ) ) )
        & vertex(X2)
        & vertex(X0) ) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ! [X1,X2,X0] :
      ( ~ path(X2,X0,X1)
      | ( ? [X3] :
            ( edge(X3)
            & tail_of(X3) = X2
            & ( head_of(X3) != X0
              | path_cons(X3,empty) != X1
              | ! [X4] :
                  ( path_cons(X3,X4) != X1
                  | ~ path(head_of(X3),X0,X4) ) )
            & ( ( head_of(X3) = X0
                & path_cons(X3,empty) = X1 )
              | ? [X4] :
                  ( path_cons(X3,X4) = X1
                  & path(head_of(X3),X0,X4) ) ) )
        & vertex(X2)
        & vertex(X0) ) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X1,X2,X0] :
      ( ~ path(X2,X0,X1)
      | ( ? [X3] :
            ( edge(X3)
            & tail_of(X3) = X2
            & ( ? [X4] :
                  ( path_cons(X3,X4) = X1
                  & path(head_of(X3),X0,X4) )
            <~> ( head_of(X3) = X0
                & path_cons(X3,empty) = X1 ) ) )
        & vertex(X2)
        & vertex(X0) ) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X2,X1,X0] :
      ( path(X2,X0,X1)
     => ( ? [X3] :
            ( edge(X3)
            & tail_of(X3) = X2
            & ( ? [X4] :
                  ( path_cons(X3,X4) = X1
                  & path(head_of(X3),X0,X4) )
            <~> ( head_of(X3) = X0
                & path_cons(X3,empty) = X1 ) ) )
        & vertex(X2)
        & vertex(X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X3,X1] :
      ( path(X1,X2,X3)
     => ( vertex(X2)
        & vertex(X1)
        & ? [X0] :
            ( ( ? [X4] :
                  ( path(head_of(X0),X2,X4)
                  & path_cons(X0,X4) = X3 )
            <~> ( path_cons(X0,empty) = X3
                & head_of(X0) = X2 ) )
            & edge(X0)
            & tail_of(X0) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_properties) ).

fof(f152,plain,
    ( ~ vertex(sK6)
    | sK4 = sK7
    | ~ edge(sK4)
    | ~ path(sK8,sK6,sK5)
    | sK6 = sK8
    | ~ edge(sK7) ),
    inference(subsumption_resolution,[],[f125,f101]) ).

fof(f101,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | vertex(X1) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f125,plain,
    ( ~ path(sK8,sK6,sK5)
    | sK6 = sK8
    | sK4 = sK7
    | ~ edge(sK7)
    | ~ vertex(sK6)
    | ~ edge(sK4)
    | ~ vertex(sK8) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f175,plain,
    edge(sK7),
    inference(resolution,[],[f174,f160]) ).

fof(f174,plain,
    ! [X4,X5] :
      ( ~ path(X4,X5,sK5)
      | edge(sK7) ),
    inference(resolution,[],[f170,f143]) ).

fof(f170,plain,
    on_path(sK7,sK5),
    inference(resolution,[],[f167,f160]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( ~ path(X0,X1,sK5)
      | on_path(sK7,sK5) ),
    inference(resolution,[],[f139,f126]) ).

fof(f139,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X4,X3,X1)
      | on_path(X3,X1)
      | ~ path(X2,X0,X1) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f127,plain,
    shortest_path(sK8,sK6,sK5),
    inference(cnf_transformation,[],[f80]) ).

fof(f190,plain,
    ~ precedes(sK7,sK4,sK5),
    inference(resolution,[],[f171,f126]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( ~ precedes(X1,X0,sK5)
      | ~ precedes(X0,X1,sK5) ),
    inference(resolution,[],[f113,f127]) ).

fof(f113,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ shortest_path(X1,X3,X4)
      | ~ precedes(X2,X0,X4)
      | ~ precedes(X0,X2,X4) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ precedes(X0,X2,X4)
      | ( ~ precedes(X2,X0,X4)
        & ! [X5] :
            ( head_of(X5) != head_of(X2)
            | tail_of(X0) != tail_of(X5) ) )
      | ~ shortest_path(X1,X3,X4) ),
    inference(rectify,[],[f40]) ).

fof(f40,plain,
    ! [X2,X1,X0,X4,X3] :
      ( ~ precedes(X2,X0,X3)
      | ( ~ precedes(X0,X2,X3)
        & ! [X5] :
            ( head_of(X0) != head_of(X5)
            | tail_of(X5) != tail_of(X2) ) )
      | ~ shortest_path(X1,X4,X3) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X3,X0,X4,X1,X2] :
      ( ( ~ precedes(X0,X2,X3)
        & ! [X5] :
            ( head_of(X0) != head_of(X5)
            | tail_of(X5) != tail_of(X2) ) )
      | ~ precedes(X2,X0,X3)
      | ~ shortest_path(X1,X4,X3) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X3,X0,X4,X1,X2] :
      ( ( precedes(X2,X0,X3)
        & shortest_path(X1,X4,X3) )
     => ( ~ ? [X5] :
              ( tail_of(X5) = tail_of(X2)
              & head_of(X0) = head_of(X5) )
        & ~ precedes(X0,X2,X3) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X7,X1,X6,X3,X2] :
      ( ( 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/sandbox2/benchmark/theBenchmark.p',shortest_path_properties) ).

fof(f221,plain,
    precedes(sK4,sK4,sK5),
    inference(backward_demodulation,[],[f126,f220]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n005.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 29 22:00:33 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.47  % (586)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.47  % (594)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.48  % (576)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.48  % (565)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.48  % (586)First to succeed.
% 0.19/0.49  % (586)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (586)------------------------------
% 0.19/0.49  % (586)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (586)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (586)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (586)Memory used [KB]: 1151
% 0.19/0.49  % (586)Time elapsed: 0.070 s
% 0.19/0.49  % (586)Instructions burned: 8 (million)
% 0.19/0.49  % (586)------------------------------
% 0.19/0.49  % (586)------------------------------
% 0.19/0.49  % (564)Success in time 0.149 s
%------------------------------------------------------------------------------