%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GRA002+4 : 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 : n024.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 0.21s 0.49s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   43 (  12 unt;   0 def)
%            Number of atoms       :  130 (  24 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  137 (  50   ~;  36   |;  30   &)
%                                         (   5 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-3 aty)
%            Number of variables   :   92 (  82   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f162,plain,
    $false,
    inference(avatar_sat_refutation,[],[f125,f142,f161]) ).

fof(f161,plain,
    ~ spl8_2,
    inference(avatar_contradiction_clause,[],[f160]) ).

fof(f160,plain,
    ( $false
    | ~ spl8_2 ),
    inference(subsumption_resolution,[],[f159,f157]) ).

fof(f157,plain,
    ( less_or_equal(number_of_in(sequential_pairs,sK5),number_of_in(triangles,graph))
    | ~ spl8_2 ),
    inference(superposition,[],[f82,f156]) ).

fof(f156,plain,
    ( number_of_in(triangles,sK5) = number_of_in(sequential_pairs,sK5)
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f111,f124]) ).

fof(f124,plain,
    ( ! [X2,X0,X1] :
        ( ~ shortest_path(X1,X2,X0)
        | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) )
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f123]) ).

fof(f123,plain,
    ( spl8_2
  <=> ! [X2,X0,X1] :
        ( ~ shortest_path(X1,X2,X0)
        | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f111,plain,
    shortest_path(sK7,sK6,sK5),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( ~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph))
    & shortest_path(sK7,sK6,sK5)
    & complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f46,f73]) ).

fof(f73,plain,
    ( ? [X0,X1,X2] :
        ( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
        & shortest_path(X2,X1,X0) )
   => ( ~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph))
      & shortest_path(sK7,sK6,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ( ? [X0,X1,X2] :
        ( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
        & shortest_path(X2,X1,X0) )
    & complete ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ ( complete
     => ! [X2,X0,X1] :
          ( shortest_path(X2,X1,X0)
         => less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ( complete
     => ! [X3,X2,X1] :
          ( shortest_path(X1,X2,X3)
         => less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ( complete
   => ! [X3,X2,X1] :
        ( shortest_path(X1,X2,X3)
       => less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).

fof(f82,plain,
    ! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X10,X11] : less_or_equal(number_of_in(X10,X11),number_of_in(X10,graph)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).

fof(f159,plain,
    ~ less_or_equal(number_of_in(sequential_pairs,sK5),number_of_in(triangles,graph)),
    inference(backward_demodulation,[],[f112,f158]) ).

fof(f158,plain,
    number_of_in(sequential_pairs,sK5) = minus(length_of(sK5),n1),
    inference(unit_resulting_resolution,[],[f155,f108]) ).

fof(f108,plain,
    ! [X2,X0,X1] :
      ( ~ path(X2,X1,X0)
      | minus(length_of(X0),n1) = number_of_in(sequential_pairs,X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ~ path(X2,X1,X0)
      | minus(length_of(X0),n1) = number_of_in(sequential_pairs,X0) ),
    inference(rectify,[],[f43]) ).

fof(f43,plain,
    ! [X2,X1,X0] :
      ( ~ path(X0,X1,X2)
      | number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0,X2] :
      ( path(X0,X1,X2)
     => number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X1,X2,X3] :
      ( path(X1,X2,X3)
     => number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).

fof(f155,plain,
    path(sK7,sK6,sK5),
    inference(unit_resulting_resolution,[],[f111,f79]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X2,X1,X0)
      | path(X2,X1,X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ( shortest_path(X2,X1,X0)
        | ~ path(X2,X1,X0)
        | ( path(X2,X1,sK0(X0,X1,X2))
          & ~ less_or_equal(length_of(X0),length_of(sK0(X0,X1,X2))) )
        | X1 = X2 )
      & ( ( path(X2,X1,X0)
          & ! [X4] :
              ( ~ path(X2,X1,X4)
              | less_or_equal(length_of(X0),length_of(X4)) )
          & X1 != X2 )
        | ~ shortest_path(X2,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f53,f54]) ).

fof(f54,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( path(X2,X1,X3)
          & ~ less_or_equal(length_of(X0),length_of(X3)) )
     => ( path(X2,X1,sK0(X0,X1,X2))
        & ~ less_or_equal(length_of(X0),length_of(sK0(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ( shortest_path(X2,X1,X0)
        | ~ path(X2,X1,X0)
        | ? [X3] :
            ( path(X2,X1,X3)
            & ~ less_or_equal(length_of(X0),length_of(X3)) )
        | X1 = X2 )
      & ( ( path(X2,X1,X0)
          & ! [X4] :
              ( ~ path(X2,X1,X4)
              | less_or_equal(length_of(X0),length_of(X4)) )
          & X1 != X2 )
        | ~ shortest_path(X2,X1,X0) ) ),
    inference(rectify,[],[f52]) ).

fof(f52,plain,
    ! [X1,X2,X0] :
      ( ( shortest_path(X0,X2,X1)
        | ~ path(X0,X2,X1)
        | ? [X3] :
            ( path(X0,X2,X3)
            & ~ less_or_equal(length_of(X1),length_of(X3)) )
        | X0 = X2 )
      & ( ( path(X0,X2,X1)
          & ! [X3] :
              ( ~ path(X0,X2,X3)
              | less_or_equal(length_of(X1),length_of(X3)) )
          & X0 != X2 )
        | ~ shortest_path(X0,X2,X1) ) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X1,X2,X0] :
      ( ( shortest_path(X0,X2,X1)
        | ~ path(X0,X2,X1)
        | ? [X3] :
            ( path(X0,X2,X3)
            & ~ less_or_equal(length_of(X1),length_of(X3)) )
        | X0 = X2 )
      & ( ( path(X0,X2,X1)
          & ! [X3] :
              ( ~ path(X0,X2,X3)
              | less_or_equal(length_of(X1),length_of(X3)) )
          & X0 != X2 )
        | ~ shortest_path(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X1,X2,X0] :
      ( shortest_path(X0,X2,X1)
    <=> ( path(X0,X2,X1)
        & ! [X3] :
            ( ~ path(X0,X2,X3)
            | less_or_equal(length_of(X1),length_of(X3)) )
        & X0 != X2 ) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( path(X0,X2,X1)
        & X0 != X2
        & ! [X3] :
            ( path(X0,X2,X3)
           => less_or_equal(length_of(X1),length_of(X3)) ) )
    <=> shortest_path(X0,X2,X1) ),
    inference(rectify,[],[f11]) ).

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

fof(f112,plain,
    ~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph)),
    inference(cnf_transformation,[],[f74]) ).

fof(f142,plain,
    spl8_1,
    inference(avatar_split_clause,[],[f110,f119]) ).

fof(f119,plain,
    ( spl8_1
  <=> complete ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f110,plain,
    complete,
    inference(cnf_transformation,[],[f74]) ).

fof(f125,plain,
    ( ~ spl8_1
    | spl8_2 ),
    inference(avatar_split_clause,[],[f90,f123,f119]) ).

fof(f90,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X1,X2,X0)
      | ~ complete
      | number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ( ! [X0,X1,X2] :
        ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0)
        | ~ shortest_path(X1,X2,X0) )
    | ~ complete ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ( complete
   => ! [X1,X2,X0] :
        ( shortest_path(X1,X2,X0)
       => number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ( complete
   => ! [X3,X1,X2] :
        ( shortest_path(X1,X2,X3)
       => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 29 22:02:34 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  % (22095)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)
% 0.21/0.48  % (22103)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)
% 0.21/0.49  % (22095)First to succeed.
% 0.21/0.49  % (22095)Refutation found. Thanks to Tanya!
% 0.21/0.49  % SZS status Theorem for theBenchmark
% 0.21/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49  % (22095)------------------------------
% 0.21/0.49  % (22095)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49  % (22095)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49  % (22095)Termination reason: Refutation
% 0.21/0.49  
% 0.21/0.49  % (22095)Memory used [KB]: 6012
% 0.21/0.49  % (22095)Time elapsed: 0.076 s
% 0.21/0.49  % (22095)Instructions burned: 5 (million)
% 0.21/0.49  % (22095)------------------------------
% 0.21/0.49  % (22095)------------------------------
% 0.21/0.49  % (22081)Success in time 0.137 s
%------------------------------------------------------------------------------