TSTP Solution File: GRA010+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GRA010+2 : 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 : n025.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 16:13:21 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   38 (   4 unt;   0 def)
%            Number of atoms       :  130 (  19 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  136 (  44   ~;  48   |;  27   &)
%                                         (   4 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   6 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   70 (  53   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f494,plain,
    $false,
    inference(avatar_sat_refutation,[],[f187,f201,f211,f232,f493]) ).

fof(f493,plain,
    ( ~ spl13_6
    | spl13_7
    | ~ spl13_10
    | ~ spl13_12 ),
    inference(avatar_contradiction_clause,[],[f492]) ).

fof(f492,plain,
    ( $false
    | ~ spl13_6
    | spl13_7
    | ~ spl13_10
    | ~ spl13_12 ),
    inference(subsumption_resolution,[],[f491,f182]) ).

fof(f182,plain,
    ( on_path(sK11(sK5),sK5)
    | ~ spl13_6 ),
    inference(avatar_component_clause,[],[f180]) ).

fof(f180,plain,
    ( spl13_6
  <=> on_path(sK11(sK5),sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

fof(f491,plain,
    ( ~ on_path(sK11(sK5),sK5)
    | spl13_7
    | ~ spl13_10
    | ~ spl13_12 ),
    inference(subsumption_resolution,[],[f490,f210]) ).

fof(f210,plain,
    ( on_path(sK12(sK5),sK5)
    | ~ spl13_12 ),
    inference(avatar_component_clause,[],[f208]) ).

fof(f208,plain,
    ( spl13_12
  <=> on_path(sK12(sK5),sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).

fof(f490,plain,
    ( ~ on_path(sK12(sK5),sK5)
    | ~ on_path(sK11(sK5),sK5)
    | spl13_7
    | ~ spl13_10 ),
    inference(subsumption_resolution,[],[f471,f200]) ).

fof(f200,plain,
    ( sequential(sK11(sK5),sK12(sK5))
    | ~ spl13_10 ),
    inference(avatar_component_clause,[],[f198]) ).

fof(f198,plain,
    ( spl13_10
  <=> sequential(sK11(sK5),sK12(sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).

fof(f471,plain,
    ( ~ sequential(sK11(sK5),sK12(sK5))
    | ~ on_path(sK11(sK5),sK5)
    | ~ on_path(sK12(sK5),sK5)
    | spl13_7 ),
    inference(resolution,[],[f408,f98]) ).

fof(f98,plain,
    ! [X3,X4] :
      ( triangle(X3,X4,sK8(X3,X4))
      | ~ on_path(X4,sK5)
      | ~ sequential(X3,X4)
      | ~ on_path(X3,sK5) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ( complete
    & ? [X1,X0,X2] :
        ( path(X2,X0,X1)
        & number_of_in(triangles,X1) != number_of_in(sequential_pairs,X1)
        & ! [X3,X4] :
            ( ~ on_path(X4,X1)
            | ? [X5] : triangle(X3,X4,X5)
            | ~ sequential(X3,X4)
            | ~ on_path(X3,X1) ) ) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ( ? [X2,X0,X1] :
        ( number_of_in(triangles,X1) != number_of_in(sequential_pairs,X1)
        & ! [X3,X4] :
            ( ? [X5] : triangle(X3,X4,X5)
            | ~ sequential(X3,X4)
            | ~ on_path(X4,X1)
            | ~ on_path(X3,X1) )
        & path(X2,X0,X1) )
    & complete ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ ( complete
     => ! [X2,X0,X1] :
          ( ( ! [X3,X4] :
                ( ( sequential(X3,X4)
                  & on_path(X4,X1)
                  & on_path(X3,X1) )
               => ? [X5] : triangle(X3,X4,X5) )
            & path(X2,X0,X1) )
         => number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ( complete
     => ! [X2,X3,X1] :
          ( ( ! [X6,X7] :
                ( ( on_path(X7,X3)
                  & on_path(X6,X3)
                  & sequential(X6,X7) )
               => ? [X8] : triangle(X6,X7,X8) )
            & path(X1,X2,X3) )
         => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ( complete
   => ! [X2,X3,X1] :
        ( ( ! [X6,X7] :
              ( ( on_path(X7,X3)
                & on_path(X6,X3)
                & sequential(X6,X7) )
             => ? [X8] : triangle(X6,X7,X8) )
          & path(X1,X2,X3) )
       => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).

fof(f408,plain,
    ( ! [X0] : ~ triangle(sK11(sK5),sK12(sK5),X0)
    | spl13_7 ),
    inference(unit_resulting_resolution,[],[f100,f185,f124]) ).

fof(f124,plain,
    ! [X2,X0,X1,X5] :
      ( ~ triangle(sK11(X2),sK12(X2),X5)
      | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
      | ~ path(X1,X0,X2) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ? [X4,X3] :
          ( on_path(X4,X2)
          & ! [X5] : ~ triangle(X4,X3,X5)
          & on_path(X3,X2)
          & sequential(X4,X3) )
      | ~ path(X1,X0,X2)
      | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
      | ~ path(X1,X0,X2)
      | ? [X4,X3] :
          ( ! [X5] : ~ triangle(X4,X3,X5)
          & sequential(X4,X3)
          & on_path(X4,X2)
          & on_path(X3,X2) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( ( path(X1,X0,X2)
        & ! [X4,X3] :
            ( ( sequential(X4,X3)
              & on_path(X4,X2)
              & on_path(X3,X2) )
           => ? [X5] : triangle(X4,X3,X5) ) )
     => number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X2,X1,X3] :
      ( ( ! [X7,X6] :
            ( ( sequential(X6,X7)
              & on_path(X7,X3)
              & on_path(X6,X3) )
           => ? [X8] : triangle(X6,X7,X8) )
        & path(X1,X2,X3) )
     => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).

fof(f185,plain,
    ( number_of_in(sequential_pairs,sK5) != number_of_in(triangles,sK5)
    | spl13_7 ),
    inference(avatar_component_clause,[],[f184]) ).

fof(f184,plain,
    ( spl13_7
  <=> number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).

fof(f100,plain,
    path(sK7,sK6,sK5),
    inference(cnf_transformation,[],[f48]) ).

fof(f232,plain,
    ~ spl13_7,
    inference(avatar_split_clause,[],[f99,f184]) ).

fof(f99,plain,
    number_of_in(sequential_pairs,sK5) != number_of_in(triangles,sK5),
    inference(cnf_transformation,[],[f48]) ).

fof(f211,plain,
    ( spl13_7
    | spl13_12 ),
    inference(avatar_split_clause,[],[f164,f208,f184]) ).

fof(f164,plain,
    ( on_path(sK12(sK5),sK5)
    | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
    inference(resolution,[],[f100,f123]) ).

fof(f123,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X0,X2)
      | on_path(sK12(X2),X2)
      | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f201,plain,
    ( spl13_10
    | spl13_7 ),
    inference(avatar_split_clause,[],[f163,f184,f198]) ).

fof(f163,plain,
    ( number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
    | sequential(sK11(sK5),sK12(sK5)) ),
    inference(resolution,[],[f100,f122]) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X0,X2)
      | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
      | sequential(sK11(X2),sK12(X2)) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f187,plain,
    ( spl13_6
    | spl13_7 ),
    inference(avatar_split_clause,[],[f165,f184,f180]) ).

fof(f165,plain,
    ( number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
    | on_path(sK11(sK5),sK5) ),
    inference(resolution,[],[f100,f125]) ).

fof(f125,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X0,X2)
      | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
      | on_path(sK11(X2),X2) ),
    inference(cnf_transformation,[],[f44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GRA010+2 : 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
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon Aug 29 22:09:59 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.40  % (24231)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)
% 0.19/0.41  % (24223)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.44  % (24231)First to succeed.
% 0.19/0.45  % (24231)Refutation found. Thanks to Tanya!
% 0.19/0.45  % SZS status Theorem for theBenchmark
% 0.19/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.45  % (24231)------------------------------
% 0.19/0.45  % (24231)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.45  % (24231)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.45  % (24231)Termination reason: Refutation
% 0.19/0.45  
% 0.19/0.45  % (24231)Memory used [KB]: 6396
% 0.19/0.45  % (24231)Time elapsed: 0.050 s
% 0.19/0.45  % (24231)Instructions burned: 19 (million)
% 0.19/0.45  % (24231)------------------------------
% 0.19/0.45  % (24231)------------------------------
% 0.19/0.45  % (24216)Success in time 0.107 s
%------------------------------------------------------------------------------