TSTP Solution File: GRA010+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n018.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 : Fri Sep  1 14:56:23 EDT 2023

% Result   : Theorem 0.13s 0.35s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   34 (   5 unt;   0 def)
%            Number of atoms       :  162 (  33 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  202 (  74   ~;  69   |;  43   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   9 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   2 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  143 (; 118   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f337,plain,
    $false,
    inference(trivial_inequality_removal,[],[f335]) ).

fof(f335,plain,
    number_of_in(sequential_pairs,sK5) != number_of_in(sequential_pairs,sK5),
    inference(superposition,[],[f106,f333]) ).

fof(f333,plain,
    number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5),
    inference(resolution,[],[f328,f104]) ).

fof(f104,plain,
    path(sK6,sK7,sK5),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ( number_of_in(sequential_pairs,sK5) != number_of_in(triangles,sK5)
    & ! [X3,X4] :
        ( triangle(X3,X4,sK8(X3,X4))
        | ~ sequential(X3,X4)
        | ~ on_path(X4,sK5)
        | ~ on_path(X3,sK5) )
    & path(sK6,sK7,sK5)
    & complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f37,f69,f68]) ).

fof(f68,plain,
    ( ? [X0,X1,X2] :
        ( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
        & ! [X3,X4] :
            ( ? [X5] : triangle(X3,X4,X5)
            | ~ sequential(X3,X4)
            | ~ on_path(X4,X0)
            | ~ on_path(X3,X0) )
        & path(X1,X2,X0) )
   => ( number_of_in(sequential_pairs,sK5) != number_of_in(triangles,sK5)
      & ! [X4,X3] :
          ( ? [X5] : triangle(X3,X4,X5)
          | ~ sequential(X3,X4)
          | ~ on_path(X4,sK5)
          | ~ on_path(X3,sK5) )
      & path(sK6,sK7,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X3,X4] :
      ( ? [X5] : triangle(X3,X4,X5)
     => triangle(X3,X4,sK8(X3,X4)) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ( ? [X0,X1,X2] :
        ( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
        & ! [X3,X4] :
            ( ? [X5] : triangle(X3,X4,X5)
            | ~ sequential(X3,X4)
            | ~ on_path(X4,X0)
            | ~ on_path(X3,X0) )
        & path(X1,X2,X0) )
    & complete ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ( ? [X0,X1,X2] :
        ( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
        & ! [X3,X4] :
            ( ? [X5] : triangle(X3,X4,X5)
            | ~ sequential(X3,X4)
            | ~ on_path(X4,X0)
            | ~ on_path(X3,X0) )
        & path(X1,X2,X0) )
    & complete ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ( complete
     => ! [X0,X1,X2] :
          ( ( ! [X3,X4] :
                ( ( sequential(X3,X4)
                  & on_path(X4,X0)
                  & on_path(X3,X0) )
               => ? [X5] : triangle(X3,X4,X5) )
            & path(X1,X2,X0) )
         => number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ( complete
     => ! [X3,X1,X2] :
          ( ( ! [X6,X7] :
                ( ( 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) ) ),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ( complete
   => ! [X3,X1,X2] :
        ( ( ! [X6,X7] :
              ( ( 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/tmp/tmp.eE3d6aH07R/Vampire---4.8_7378',complete_means_sequential_pairs_and_triangles) ).

fof(f328,plain,
    ! [X0,X1] :
      ( ~ path(X0,X1,sK5)
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
    inference(resolution,[],[f319,f104]) ).

fof(f319,plain,
    ! [X2,X3,X0,X1] :
      ( ~ path(X2,X3,sK5)
      | ~ path(X0,X1,sK5)
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
    inference(resolution,[],[f305,f104]) ).

fof(f305,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ path(X4,X5,sK5)
      | ~ path(X2,X3,sK5)
      | ~ path(X0,X1,sK5)
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
    inference(resolution,[],[f304,f104]) ).

fof(f304,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ path(X6,X7,sK5)
      | ~ path(X4,X5,sK5)
      | ~ path(X2,X3,sK5)
      | ~ path(X0,X1,sK5)
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
    inference(duplicate_literal_removal,[],[f303]) ).

fof(f303,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
      | ~ path(X0,X1,sK5)
      | ~ path(X2,X3,sK5)
      | ~ path(X4,X5,sK5)
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
      | ~ path(X6,X7,sK5) ),
    inference(resolution,[],[f302,f148]) ).

fof(f148,plain,
    ! [X2,X0,X1] :
      ( sequential(sK13(X0),sK14(X0))
      | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ( ! [X5] : ~ triangle(sK13(X0),sK14(X0),X5)
        & sequential(sK13(X0),sK14(X0))
        & on_path(sK14(X0),X0)
        & on_path(sK13(X0),X0) )
      | ~ path(X1,X2,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f51,f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
     => ( ! [X5] : ~ triangle(sK13(X0),sK14(X0),X5)
        & sequential(sK13(X0),sK14(X0))
        & on_path(sK14(X0),X0)
        & on_path(sK13(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3,X4] :
            ( ( sequential(X3,X4)
              & on_path(X4,X0)
              & on_path(X3,X0) )
           => ? [X5] : triangle(X3,X4,X5) )
        & path(X1,X2,X0) )
     => number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X3,X1,X2] :
      ( ( ! [X6,X7] :
            ( ( 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/tmp/tmp.eE3d6aH07R/Vampire---4.8_7378',sequential_pairs_and_triangles) ).

fof(f302,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ sequential(sK13(sK5),sK14(sK5))
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
      | ~ path(X0,X1,sK5)
      | ~ path(X2,X3,sK5)
      | ~ path(X4,X5,sK5) ),
    inference(duplicate_literal_removal,[],[f301]) ).

fof(f301,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ sequential(sK13(sK5),sK14(sK5))
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
      | ~ path(X0,X1,sK5)
      | ~ path(X2,X3,sK5)
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
      | ~ path(X4,X5,sK5) ),
    inference(resolution,[],[f300,f146]) ).

fof(f146,plain,
    ! [X2,X0,X1] :
      ( on_path(sK13(X0),X0)
      | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f300,plain,
    ! [X2,X3,X0,X1] :
      ( ~ on_path(sK13(sK5),sK5)
      | ~ sequential(sK13(sK5),sK14(sK5))
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
      | ~ path(X0,X1,sK5)
      | ~ path(X2,X3,sK5) ),
    inference(duplicate_literal_removal,[],[f299]) ).

fof(f299,plain,
    ! [X2,X3,X0,X1] :
      ( ~ path(X0,X1,sK5)
      | ~ sequential(sK13(sK5),sK14(sK5))
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
      | ~ on_path(sK13(sK5),sK5)
      | number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
      | ~ path(X2,X3,sK5) ),
    inference(resolution,[],[f298,f147]) ).

fof(f147,plain,
    ! [X2,X0,X1] :
      ( on_path(sK14(X0),X0)
      | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f298,plain,
    ! [X2,X0,X1] :
      ( ~ on_path(sK14(X0),sK5)
      | ~ path(X1,X2,X0)
      | ~ sequential(sK13(X0),sK14(X0))
      | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ~ on_path(sK13(X0),sK5) ),
    inference(resolution,[],[f149,f105]) ).

fof(f105,plain,
    ! [X3,X4] :
      ( triangle(X3,X4,sK8(X3,X4))
      | ~ sequential(X3,X4)
      | ~ on_path(X4,sK5)
      | ~ on_path(X3,sK5) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f149,plain,
    ! [X2,X0,X1,X5] :
      ( ~ triangle(sK13(X0),sK14(X0),X5)
      | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f106,plain,
    number_of_in(sequential_pairs,sK5) != number_of_in(triangles,sK5),
    inference(cnf_transformation,[],[f70]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem    : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.04/0.10  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.08/0.29  % Computer : n018.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit   : 300
% 0.08/0.29  % WCLimit    : 300
% 0.08/0.29  % DateTime   : Wed Aug 30 16:16:49 EDT 2023
% 0.08/0.29  % CPUTime    : 
% 0.13/0.33  % (8626)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.33  % (8737)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 Vampire---4 for (497ds/0Mi)
% 0.13/0.33  % (8734)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.13/0.33  % (8732)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.13/0.33  % (8731)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.13/0.33  % (8736)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 Vampire---4 for (522ds/0Mi)
% 0.13/0.33  % (8733)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 Vampire---4 for (569ds/0Mi)
% 0.13/0.33  % (8735)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 Vampire---4 for (531ds/0Mi)
% 0.13/0.34  TRYING [1]
% 0.13/0.34  TRYING [1]
% 0.13/0.34  TRYING [2]
% 0.13/0.34  TRYING [2]
% 0.13/0.34  TRYING [3]
% 0.13/0.34  % (8736)First to succeed.
% 0.13/0.34  TRYING [3]
% 0.13/0.35  % (8736)Refutation found. Thanks to Tanya!
% 0.13/0.35  % SZS status Theorem for Vampire---4
% 0.13/0.35  % SZS output start Proof for Vampire---4
% See solution above
% 0.13/0.35  % (8736)------------------------------
% 0.13/0.35  % (8736)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.13/0.35  % (8736)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.13/0.35  % (8736)Termination reason: Refutation
% 0.13/0.35  
% 0.13/0.35  % (8736)Memory used [KB]: 1279
% 0.13/0.35  % (8736)Time elapsed: 0.014 s
% 0.13/0.35  % (8736)------------------------------
% 0.13/0.35  % (8736)------------------------------
% 0.13/0.35  % (8626)Success in time 0.049 s
% 0.13/0.35  % Vampire---4.8 exiting
%------------------------------------------------------------------------------