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

View Problem - Process Solution

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

% Computer : n014.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 16:13:32 EDT 2022

% Result   : Theorem 1.25s 0.52s
% Output   : Refutation 1.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   47 (  11 unt;   0 def)
%            Number of atoms       :  170 (  35 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  187 (  64   ~;  57   |;  49   &)
%                                         (   1 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  124 (  93   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f700,plain,
    $false,
    inference(avatar_sat_refutation,[],[f552,f699]) ).

fof(f699,plain,
    spl15_16,
    inference(avatar_split_clause,[],[f698,f520]) ).

fof(f520,plain,
    ( spl15_16
  <=> ! [X2,X3] : ~ path(X2,X3,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).

fof(f698,plain,
    ! [X0,X1] : ~ path(X0,X1,sK6),
    inference(subsumption_resolution,[],[f697,f176]) ).

fof(f176,plain,
    sF13 != sF14,
    inference(definition_folding,[],[f146,f175,f174]) ).

fof(f174,plain,
    number_of_in(sequential_pairs,sK6) = sF13,
    introduced(function_definition,[]) ).

fof(f175,plain,
    number_of_in(triangles,sK6) = sF14,
    introduced(function_definition,[]) ).

fof(f146,plain,
    number_of_in(sequential_pairs,sK6) != number_of_in(triangles,sK6),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ( complete
    & ! [X3,X4] :
        ( ~ sequential(X3,X4)
        | ~ on_path(X4,sK6)
        | ~ on_path(X3,sK6)
        | triangle(X3,X4,sK9(X3,X4)) )
    & number_of_in(sequential_pairs,sK6) != number_of_in(triangles,sK6)
    & path(sK7,sK8,sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f90,f92,f91]) ).

fof(f91,plain,
    ( ? [X0,X1,X2] :
        ( ! [X3,X4] :
            ( ~ sequential(X3,X4)
            | ~ on_path(X4,X0)
            | ~ on_path(X3,X0)
            | ? [X5] : triangle(X3,X4,X5) )
        & number_of_in(triangles,X0) != number_of_in(sequential_pairs,X0)
        & path(X1,X2,X0) )
   => ( ! [X4,X3] :
          ( ~ sequential(X3,X4)
          | ~ on_path(X4,sK6)
          | ~ on_path(X3,sK6)
          | ? [X5] : triangle(X3,X4,X5) )
      & number_of_in(sequential_pairs,sK6) != number_of_in(triangles,sK6)
      & path(sK7,sK8,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ! [X3,X4] :
      ( ? [X5] : triangle(X3,X4,X5)
     => triangle(X3,X4,sK9(X3,X4)) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ( complete
    & ? [X0,X1,X2] :
        ( ! [X3,X4] :
            ( ~ sequential(X3,X4)
            | ~ on_path(X4,X0)
            | ~ on_path(X3,X0)
            | ? [X5] : triangle(X3,X4,X5) )
        & number_of_in(triangles,X0) != number_of_in(sequential_pairs,X0)
        & path(X1,X2,X0) ) ),
    inference(rectify,[],[f60]) ).

fof(f60,plain,
    ( complete
    & ? [X2,X1,X0] :
        ( ! [X3,X4] :
            ( ~ sequential(X3,X4)
            | ~ on_path(X4,X2)
            | ~ on_path(X3,X2)
            | ? [X5] : triangle(X3,X4,X5) )
        & number_of_in(triangles,X2) != number_of_in(sequential_pairs,X2)
        & path(X1,X0,X2) ) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ( ? [X1,X0,X2] :
        ( number_of_in(triangles,X2) != number_of_in(sequential_pairs,X2)
        & path(X1,X0,X2)
        & ! [X4,X3] :
            ( ? [X5] : triangle(X3,X4,X5)
            | ~ on_path(X3,X2)
            | ~ on_path(X4,X2)
            | ~ sequential(X3,X4) ) )
    & complete ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ~ ( complete
     => ! [X1,X0,X2] :
          ( ( path(X1,X0,X2)
            & ! [X4,X3] :
                ( ( on_path(X3,X2)
                  & on_path(X4,X2)
                  & sequential(X3,X4) )
               => ? [X5] : triangle(X3,X4,X5) ) )
         => number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) ) ),
    inference(rectify,[],[f20]) ).

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

fof(f19,conjecture,
    ( complete
   => ! [X2,X1,X3] :
        ( ( path(X1,X2,X3)
          & ! [X6,X7] :
              ( ( on_path(X7,X3)
                & sequential(X6,X7)
                & on_path(X6,X3) )
             => ? [X8] : triangle(X6,X7,X8) ) )
       => 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(f697,plain,
    ! [X0,X1] :
      ( ~ path(X0,X1,sK6)
      | sF13 = sF14 ),
    inference(forward_demodulation,[],[f696,f174]) ).

fof(f696,plain,
    ! [X0,X1] :
      ( number_of_in(sequential_pairs,sK6) = sF14
      | ~ path(X0,X1,sK6) ),
    inference(forward_demodulation,[],[f695,f175]) ).

fof(f695,plain,
    ! [X0,X1] :
      ( number_of_in(sequential_pairs,sK6) = number_of_in(triangles,sK6)
      | ~ path(X0,X1,sK6) ),
    inference(subsumption_resolution,[],[f694,f296]) ).

fof(f296,plain,
    on_path(sK0(sK6),sK6),
    inference(subsumption_resolution,[],[f295,f176]) ).

fof(f295,plain,
    ( on_path(sK0(sK6),sK6)
    | sF13 = sF14 ),
    inference(forward_demodulation,[],[f294,f174]) ).

fof(f294,plain,
    ( on_path(sK0(sK6),sK6)
    | number_of_in(sequential_pairs,sK6) = sF14 ),
    inference(forward_demodulation,[],[f290,f175]) ).

fof(f290,plain,
    ( number_of_in(sequential_pairs,sK6) = number_of_in(triangles,sK6)
    | on_path(sK0(sK6),sK6) ),
    inference(resolution,[],[f109,f145]) ).

fof(f145,plain,
    path(sK7,sK8,sK6),
    inference(cnf_transformation,[],[f93]) ).

fof(f109,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X0,X2)
      | number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2)
      | on_path(sK0(X2),X2) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ( sequential(sK1(X2),sK0(X2))
        & on_path(sK0(X2),X2)
        & ! [X5] : ~ triangle(sK1(X2),sK0(X2),X5)
        & on_path(sK1(X2),X2) )
      | ~ path(X1,X0,X2)
      | number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f65,f66]) ).

fof(f66,plain,
    ! [X2] :
      ( ? [X3,X4] :
          ( sequential(X4,X3)
          & on_path(X3,X2)
          & ! [X5] : ~ triangle(X4,X3,X5)
          & on_path(X4,X2) )
     => ( sequential(sK1(X2),sK0(X2))
        & on_path(sK0(X2),X2)
        & ! [X5] : ~ triangle(sK1(X2),sK0(X2),X5)
        & on_path(sK1(X2),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4] :
          ( sequential(X4,X3)
          & on_path(X3,X2)
          & ! [X5] : ~ triangle(X4,X3,X5)
          & on_path(X4,X2) )
      | ~ path(X1,X0,X2)
      | number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) ),
    inference(rectify,[],[f41]) ).

fof(f41,plain,
    ! [X2,X0,X1] :
      ( ? [X4,X3] :
          ( sequential(X3,X4)
          & on_path(X4,X1)
          & ! [X5] : ~ triangle(X3,X4,X5)
          & on_path(X3,X1) )
      | ~ path(X0,X2,X1)
      | number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ! [X0,X2,X1] :
      ( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & on_path(X3,X1)
          & sequential(X3,X4)
          & on_path(X4,X1) )
      | ~ path(X0,X2,X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3,X4] :
            ( ( on_path(X3,X1)
              & sequential(X3,X4)
              & on_path(X4,X1) )
           => ? [X5] : triangle(X3,X4,X5) )
        & path(X0,X2,X1) )
     => number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1) ),
    inference(rectify,[],[f16]) ).

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

fof(f694,plain,
    ! [X0,X1] :
      ( ~ path(X0,X1,sK6)
      | number_of_in(sequential_pairs,sK6) = number_of_in(triangles,sK6)
      | ~ on_path(sK0(sK6),sK6) ),
    inference(resolution,[],[f310,f285]) ).

fof(f285,plain,
    on_path(sK1(sK6),sK6),
    inference(subsumption_resolution,[],[f284,f176]) ).

fof(f284,plain,
    ( sF13 = sF14
    | on_path(sK1(sK6),sK6) ),
    inference(forward_demodulation,[],[f283,f174]) ).

fof(f283,plain,
    ( on_path(sK1(sK6),sK6)
    | number_of_in(sequential_pairs,sK6) = sF14 ),
    inference(forward_demodulation,[],[f280,f175]) ).

fof(f280,plain,
    ( on_path(sK1(sK6),sK6)
    | number_of_in(sequential_pairs,sK6) = number_of_in(triangles,sK6) ),
    inference(resolution,[],[f107,f145]) ).

fof(f107,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X0,X2)
      | on_path(sK1(X2),X2)
      | number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f310,plain,
    ! [X6,X4,X5] :
      ( ~ on_path(sK1(X4),sK6)
      | ~ path(X5,X6,X4)
      | number_of_in(triangles,X4) = number_of_in(sequential_pairs,X4)
      | ~ on_path(sK0(X4),sK6) ),
    inference(subsumption_resolution,[],[f309,f110]) ).

fof(f110,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X0,X2)
      | number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2)
      | sequential(sK1(X2),sK0(X2)) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f309,plain,
    ! [X6,X4,X5] :
      ( ~ on_path(sK0(X4),sK6)
      | number_of_in(triangles,X4) = number_of_in(sequential_pairs,X4)
      | ~ path(X5,X6,X4)
      | ~ sequential(sK1(X4),sK0(X4))
      | ~ on_path(sK1(X4),sK6) ),
    inference(resolution,[],[f108,f147]) ).

fof(f147,plain,
    ! [X3,X4] :
      ( triangle(X3,X4,sK9(X3,X4))
      | ~ on_path(X4,sK6)
      | ~ sequential(X3,X4)
      | ~ on_path(X3,sK6) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f108,plain,
    ! [X2,X0,X1,X5] :
      ( ~ triangle(sK1(X2),sK0(X2),X5)
      | number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2)
      | ~ path(X1,X0,X2) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f552,plain,
    ~ spl15_16,
    inference(avatar_contradiction_clause,[],[f551]) ).

fof(f551,plain,
    ( $false
    | ~ spl15_16 ),
    inference(resolution,[],[f521,f145]) ).

fof(f521,plain,
    ( ! [X2,X3] : ~ path(X2,X3,sK6)
    | ~ spl15_16 ),
    inference(avatar_component_clause,[],[f520]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n014.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon Aug 29 22:01:48 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  % (26440)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.48  % (26433)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51  % (26425)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51  % (26440)First to succeed.
% 0.20/0.51  % (26441)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51  % (26442)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.51  % (26430)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52  % (26424)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)
% 0.20/0.52  % (26426)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.25/0.52  % (26440)Refutation found. Thanks to Tanya!
% 1.25/0.52  % SZS status Theorem for theBenchmark
% 1.25/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.25/0.52  % (26440)------------------------------
% 1.25/0.52  % (26440)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.52  % (26440)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.52  % (26440)Termination reason: Refutation
% 1.25/0.52  
% 1.25/0.52  % (26440)Memory used [KB]: 6140
% 1.25/0.52  % (26440)Time elapsed: 0.091 s
% 1.25/0.52  % (26440)Instructions burned: 36 (million)
% 1.25/0.52  % (26440)------------------------------
% 1.25/0.52  % (26440)------------------------------
% 1.25/0.52  % (26420)Success in time 0.163 s
%------------------------------------------------------------------------------