TSTP Solution File: GRA002+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---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_sat --cores 0 -t %d %s

% Computer : n013.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      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   45 (  12 unt;   0 def)
%            Number of atoms       :  136 (  25 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  144 (  53   ~;  38   |;  32   &)
%                                         (   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   :   98 (  85   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f294,plain,
    $false,
    inference(avatar_sat_refutation,[],[f227,f252,f293]) ).

fof(f293,plain,
    ~ spl37_2,
    inference(avatar_contradiction_clause,[],[f292]) ).

fof(f292,plain,
    ( $false
    | ~ spl37_2 ),
    inference(subsumption_resolution,[],[f291,f284]) ).

fof(f284,plain,
    ( less_or_equal(number_of_in(sequential_pairs,sK3),number_of_in(triangles,graph))
    | ~ spl37_2 ),
    inference(superposition,[],[f143,f283]) ).

fof(f283,plain,
    ( number_of_in(sequential_pairs,sK3) = number_of_in(triangles,sK3)
    | ~ spl37_2 ),
    inference(resolution,[],[f226,f127]) ).

fof(f127,plain,
    shortest_path(sK5,sK4,sK3),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ( shortest_path(sK5,sK4,sK3)
    & ~ less_or_equal(minus(length_of(sK3),n1),number_of_in(triangles,graph))
    & complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f78,f79]) ).

fof(f79,plain,
    ( ? [X0,X1,X2] :
        ( shortest_path(X2,X1,X0)
        & ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) )
   => ( shortest_path(sK5,sK4,sK3)
      & ~ less_or_equal(minus(length_of(sK3),n1),number_of_in(triangles,graph)) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ( ? [X0,X1,X2] :
        ( shortest_path(X2,X1,X0)
        & ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) )
    & complete ),
    inference(rectify,[],[f62]) ).

fof(f62,plain,
    ( ? [X0,X2,X1] :
        ( shortest_path(X1,X2,X0)
        & ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) )
    & complete ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ( complete
     => ! [X0,X1,X2] :
          ( shortest_path(X1,X2,X0)
         => less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ( complete
     => ! [X3,X1,X2] :
          ( 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,X1,X2] :
        ( shortest_path(X1,X2,X3)
       => less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).

fof(f226,plain,
    ( ! [X2,X0,X1] :
        ( ~ shortest_path(X1,X2,X0)
        | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
    | ~ spl37_2 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f225,plain,
    ( spl37_2
  <=> ! [X2,X0,X1] :
        ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
        | ~ shortest_path(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl37_2])]) ).

fof(f143,plain,
    ! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,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/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).

fof(f291,plain,
    ~ less_or_equal(number_of_in(sequential_pairs,sK3),number_of_in(triangles,graph)),
    inference(backward_demodulation,[],[f126,f290]) ).

fof(f290,plain,
    number_of_in(sequential_pairs,sK3) = minus(length_of(sK3),n1),
    inference(resolution,[],[f124,f256]) ).

fof(f256,plain,
    path(sK5,sK4,sK3),
    inference(resolution,[],[f106,f127]) ).

fof(f106,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X0,X1,X2)
      | path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ( shortest_path(X0,X1,X2)
        | ~ path(X0,X1,X2)
        | ( ~ less_or_equal(length_of(X2),length_of(sK0(X0,X1,X2)))
          & path(X0,X1,sK0(X0,X1,X2)) )
        | X0 = X1 )
      & ( ( path(X0,X1,X2)
          & ! [X4] :
              ( less_or_equal(length_of(X2),length_of(X4))
              | ~ path(X0,X1,X4) )
          & X0 != X1 )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f66,f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ less_or_equal(length_of(X2),length_of(X3))
          & path(X0,X1,X3) )
     => ( ~ less_or_equal(length_of(X2),length_of(sK0(X0,X1,X2)))
        & path(X0,X1,sK0(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ( shortest_path(X0,X1,X2)
        | ~ path(X0,X1,X2)
        | ? [X3] :
            ( ~ less_or_equal(length_of(X2),length_of(X3))
            & path(X0,X1,X3) )
        | X0 = X1 )
      & ( ( path(X0,X1,X2)
          & ! [X4] :
              ( less_or_equal(length_of(X2),length_of(X4))
              | ~ path(X0,X1,X4) )
          & X0 != X1 )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(rectify,[],[f65]) ).

fof(f65,plain,
    ! [X0,X2,X1] :
      ( ( shortest_path(X0,X2,X1)
        | ~ path(X0,X2,X1)
        | ? [X3] :
            ( ~ less_or_equal(length_of(X1),length_of(X3))
            & path(X0,X2,X3) )
        | X0 = X2 )
      & ( ( path(X0,X2,X1)
          & ! [X3] :
              ( less_or_equal(length_of(X1),length_of(X3))
              | ~ path(X0,X2,X3) )
          & X0 != X2 )
        | ~ shortest_path(X0,X2,X1) ) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ! [X0,X2,X1] :
      ( ( shortest_path(X0,X2,X1)
        | ~ path(X0,X2,X1)
        | ? [X3] :
            ( ~ less_or_equal(length_of(X1),length_of(X3))
            & path(X0,X2,X3) )
        | X0 = X2 )
      & ( ( path(X0,X2,X1)
          & ! [X3] :
              ( less_or_equal(length_of(X1),length_of(X3))
              | ~ path(X0,X2,X3) )
          & X0 != X2 )
        | ~ shortest_path(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X2,X1] :
      ( shortest_path(X0,X2,X1)
    <=> ( path(X0,X2,X1)
        & ! [X3] :
            ( less_or_equal(length_of(X1),length_of(X3))
            | ~ path(X0,X2,X3) )
        & X0 != X2 ) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X1,X0,X2] :
      ( shortest_path(X0,X2,X1)
    <=> ( ! [X3] :
            ( path(X0,X2,X3)
           => less_or_equal(length_of(X1),length_of(X3)) )
        & X0 != X2
        & path(X0,X2,X1) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X9,X2] :
      ( ( ! [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/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).

fof(f124,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | number_of_in(sequential_pairs,X0) = minus(length_of(X0),n1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ~ path(X1,X2,X0)
      | number_of_in(sequential_pairs,X0) = minus(length_of(X0),n1) ),
    inference(rectify,[],[f49]) ).

fof(f49,plain,
    ! [X0,X2,X1] :
      ( ~ path(X2,X1,X0)
      | number_of_in(sequential_pairs,X0) = minus(length_of(X0),n1) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X1,X2,X0] :
      ( path(X2,X1,X0)
     => number_of_in(sequential_pairs,X0) = minus(length_of(X0),n1) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3,X2,X1] :
      ( path(X1,X2,X3)
     => number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).

fof(f126,plain,
    ~ less_or_equal(minus(length_of(sK3),n1),number_of_in(triangles,graph)),
    inference(cnf_transformation,[],[f80]) ).

fof(f252,plain,
    spl37_1,
    inference(avatar_split_clause,[],[f125,f221]) ).

fof(f221,plain,
    ( spl37_1
  <=> complete ),
    introduced(avatar_definition,[new_symbols(naming,[spl37_1])]) ).

fof(f125,plain,
    complete,
    inference(cnf_transformation,[],[f80]) ).

fof(f227,plain,
    ( ~ spl37_1
    | spl37_2 ),
    inference(avatar_split_clause,[],[f121,f225,f221]) ).

fof(f121,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ~ complete
      | ~ shortest_path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ( ~ complete
    | ! [X0,X1,X2] :
        ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
        | ~ shortest_path(X1,X2,X0) ) ),
    inference(rectify,[],[f50]) ).

fof(f50,plain,
    ( ~ complete
    | ! [X2,X0,X1] :
        ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ( complete
   => ! [X1,X0,X2] :
        ( shortest_path(X0,X1,X2)
       => number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ( complete
   => ! [X1,X2,X3] :
        ( shortest_path(X1,X2,X3)
       => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.12  % 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 : n013.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 21:57:02 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.47  % (12706)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.48  % (12698)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.48  % (12706)First to succeed.
% 0.19/0.48  % (12714)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.48  % (12698)Instruction limit reached!
% 0.19/0.48  % (12698)------------------------------
% 0.19/0.48  % (12698)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (12698)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (12698)Termination reason: Unknown
% 0.19/0.48  % (12698)Termination phase: Naming
% 0.19/0.48  
% 0.19/0.48  % (12698)Memory used [KB]: 895
% 0.19/0.48  % (12698)Time elapsed: 0.003 s
% 0.19/0.48  % (12698)Instructions burned: 2 (million)
% 0.19/0.48  % (12698)------------------------------
% 0.19/0.48  % (12698)------------------------------
% 0.19/0.49  % (12693)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.49  % (12706)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  % (12706)------------------------------
% 0.19/0.49  % (12706)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (12706)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (12706)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (12706)Memory used [KB]: 5628
% 0.19/0.49  % (12706)Time elapsed: 0.095 s
% 0.19/0.49  % (12706)Instructions burned: 8 (million)
% 0.19/0.49  % (12706)------------------------------
% 0.19/0.49  % (12706)------------------------------
% 0.19/0.49  % (12684)Success in time 0.144 s
%------------------------------------------------------------------------------