TSTP Solution File: SEU341+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -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 : Wed May  1 03:52:05 EDT 2024

% Result   : Theorem 0.59s 0.75s
% Output   : Refutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   51 (  10 unt;   0 def)
%            Number of atoms       :  234 (  12 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  296 ( 113   ~;  94   |;  63   &)
%                                         (   5 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   3 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   81 (  66   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f212,plain,
    $false,
    inference(avatar_sat_refutation,[],[f147,f174,f211]) ).

fof(f211,plain,
    ~ spl8_4,
    inference(avatar_contradiction_clause,[],[f210]) ).

fof(f210,plain,
    ( $false
    | ~ spl8_4 ),
    inference(subsumption_resolution,[],[f207,f90]) ).

fof(f90,plain,
    in(sK2,sK1),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ( ~ point_neighbourhood(sK1,sK0,sK2)
    & in(sK2,sK1)
    & open_subset(sK1,sK0)
    & element(sK2,the_carrier(sK0))
    & element(sK1,powerset(the_carrier(sK0)))
    & top_str(sK0)
    & topological_space(sK0)
    & ~ empty_carrier(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f48,f71,f70,f69]) ).

fof(f69,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ point_neighbourhood(X1,X0,X2)
                & in(X2,X1)
                & open_subset(X1,X0)
                & element(X2,the_carrier(X0)) )
            & element(X1,powerset(the_carrier(X0))) )
        & top_str(X0)
        & topological_space(X0)
        & ~ empty_carrier(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ point_neighbourhood(X1,sK0,X2)
              & in(X2,X1)
              & open_subset(X1,sK0)
              & element(X2,the_carrier(sK0)) )
          & element(X1,powerset(the_carrier(sK0))) )
      & top_str(sK0)
      & topological_space(sK0)
      & ~ empty_carrier(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ point_neighbourhood(X1,sK0,X2)
            & in(X2,X1)
            & open_subset(X1,sK0)
            & element(X2,the_carrier(sK0)) )
        & element(X1,powerset(the_carrier(sK0))) )
   => ( ? [X2] :
          ( ~ point_neighbourhood(sK1,sK0,X2)
          & in(X2,sK1)
          & open_subset(sK1,sK0)
          & element(X2,the_carrier(sK0)) )
      & element(sK1,powerset(the_carrier(sK0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ( ? [X2] :
        ( ~ point_neighbourhood(sK1,sK0,X2)
        & in(X2,sK1)
        & open_subset(sK1,sK0)
        & element(X2,the_carrier(sK0)) )
   => ( ~ point_neighbourhood(sK1,sK0,sK2)
      & in(sK2,sK1)
      & open_subset(sK1,sK0)
      & element(sK2,the_carrier(sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ point_neighbourhood(X1,X0,X2)
              & in(X2,X1)
              & open_subset(X1,X0)
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & top_str(X0)
      & topological_space(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ point_neighbourhood(X1,X0,X2)
              & in(X2,X1)
              & open_subset(X1,X0)
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & top_str(X0)
      & topological_space(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,negated_conjecture,
    ~ ! [X0] :
        ( ( top_str(X0)
          & topological_space(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,powerset(the_carrier(X0)))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => ( ( in(X2,X1)
                    & open_subset(X1,X0) )
                 => point_neighbourhood(X1,X0,X2) ) ) ) ),
    inference(negated_conjecture,[],[f41]) ).

fof(f41,conjecture,
    ! [X0] :
      ( ( top_str(X0)
        & topological_space(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( ( in(X2,X1)
                  & open_subset(X1,X0) )
               => point_neighbourhood(X1,X0,X2) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.whrUVUYhei/Vampire---4.8_26072',t5_connsp_2) ).

fof(f207,plain,
    ( ~ in(sK2,sK1)
    | ~ spl8_4 ),
    inference(resolution,[],[f206,f91]) ).

fof(f91,plain,
    ~ point_neighbourhood(sK1,sK0,sK2),
    inference(cnf_transformation,[],[f72]) ).

fof(f206,plain,
    ( ! [X0] :
        ( point_neighbourhood(sK1,sK0,X0)
        | ~ in(X0,sK1) )
    | ~ spl8_4 ),
    inference(subsumption_resolution,[],[f204,f129]) ).

fof(f129,plain,
    ! [X0] :
      ( element(X0,the_carrier(sK0))
      | ~ in(X0,sK1) ),
    inference(resolution,[],[f87,f94]) ).

fof(f94,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X2))
      | element(X0,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.whrUVUYhei/Vampire---4.8_26072',t4_subset) ).

fof(f87,plain,
    element(sK1,powerset(the_carrier(sK0))),
    inference(cnf_transformation,[],[f72]) ).

fof(f204,plain,
    ( ! [X0] :
        ( ~ in(X0,sK1)
        | point_neighbourhood(sK1,sK0,X0)
        | ~ element(X0,the_carrier(sK0)) )
    | ~ spl8_4 ),
    inference(superposition,[],[f137,f146]) ).

fof(f146,plain,
    ( sK1 = interior(sK0,sK1)
    | ~ spl8_4 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f144,plain,
    ( spl8_4
  <=> sK1 = interior(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

fof(f137,plain,
    ! [X0] :
      ( ~ in(X0,interior(sK0,sK1))
      | point_neighbourhood(sK1,sK0,X0)
      | ~ element(X0,the_carrier(sK0)) ),
    inference(subsumption_resolution,[],[f136,f84]) ).

fof(f84,plain,
    ~ empty_carrier(sK0),
    inference(cnf_transformation,[],[f72]) ).

fof(f136,plain,
    ! [X0] :
      ( ~ in(X0,interior(sK0,sK1))
      | point_neighbourhood(sK1,sK0,X0)
      | ~ element(X0,the_carrier(sK0))
      | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f135,f85]) ).

fof(f85,plain,
    topological_space(sK0),
    inference(cnf_transformation,[],[f72]) ).

fof(f135,plain,
    ! [X0] :
      ( ~ in(X0,interior(sK0,sK1))
      | point_neighbourhood(sK1,sK0,X0)
      | ~ element(X0,the_carrier(sK0))
      | ~ topological_space(sK0)
      | empty_carrier(sK0) ),
    inference(subsumption_resolution,[],[f126,f86]) ).

fof(f86,plain,
    top_str(sK0),
    inference(cnf_transformation,[],[f72]) ).

fof(f126,plain,
    ! [X0] :
      ( ~ in(X0,interior(sK0,sK1))
      | point_neighbourhood(sK1,sK0,X0)
      | ~ element(X0,the_carrier(sK0))
      | ~ top_str(sK0)
      | ~ topological_space(sK0)
      | empty_carrier(sK0) ),
    inference(resolution,[],[f87,f112]) ).

fof(f112,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,powerset(the_carrier(X0)))
      | ~ in(X1,interior(X0,X2))
      | point_neighbourhood(X2,X0,X1)
      | ~ element(X1,the_carrier(X0))
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( point_neighbourhood(X2,X0,X1)
                  | ~ in(X1,interior(X0,X2)) )
                & ( in(X1,interior(X0,X2))
                  | ~ point_neighbourhood(X2,X0,X1) ) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( point_neighbourhood(X2,X0,X1)
              <=> in(X1,interior(X0,X2)) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( point_neighbourhood(X2,X0,X1)
              <=> in(X1,interior(X0,X2)) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] :
      ( ( top_str(X0)
        & topological_space(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,powerset(the_carrier(X0)))
             => ( point_neighbourhood(X2,X0,X1)
              <=> in(X1,interior(X0,X2)) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.whrUVUYhei/Vampire---4.8_26072',d1_connsp_2) ).

fof(f174,plain,
    ~ spl8_3,
    inference(avatar_contradiction_clause,[],[f173]) ).

fof(f173,plain,
    ( $false
    | ~ spl8_3 ),
    inference(subsumption_resolution,[],[f172,f86]) ).

fof(f172,plain,
    ( ~ top_str(sK0)
    | ~ spl8_3 ),
    inference(subsumption_resolution,[],[f166,f85]) ).

fof(f166,plain,
    ( ~ topological_space(sK0)
    | ~ top_str(sK0)
    | ~ spl8_3 ),
    inference(resolution,[],[f142,f87]) ).

fof(f142,plain,
    ( ! [X0,X1] :
        ( ~ element(X0,powerset(the_carrier(X1)))
        | ~ topological_space(X1)
        | ~ top_str(X1) )
    | ~ spl8_3 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f141,plain,
    ( spl8_3
  <=> ! [X0,X1] :
        ( ~ element(X0,powerset(the_carrier(X1)))
        | ~ topological_space(X1)
        | ~ top_str(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

fof(f147,plain,
    ( spl8_3
    | spl8_4 ),
    inference(avatar_split_clause,[],[f139,f144,f141]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( sK1 = interior(sK0,sK1)
      | ~ element(X0,powerset(the_carrier(X1)))
      | ~ top_str(X1)
      | ~ topological_space(X1) ),
    inference(subsumption_resolution,[],[f138,f86]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( sK1 = interior(sK0,sK1)
      | ~ element(X0,powerset(the_carrier(X1)))
      | ~ top_str(sK0)
      | ~ top_str(X1)
      | ~ topological_space(X1) ),
    inference(subsumption_resolution,[],[f127,f89]) ).

fof(f89,plain,
    open_subset(sK1,sK0),
    inference(cnf_transformation,[],[f72]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( ~ open_subset(sK1,sK0)
      | sK1 = interior(sK0,sK1)
      | ~ element(X0,powerset(the_carrier(X1)))
      | ~ top_str(sK0)
      | ~ top_str(X1)
      | ~ topological_space(X1) ),
    inference(resolution,[],[f87,f102]) ).

fof(f102,plain,
    ! [X2,X3,X0,X1] :
      ( ~ element(X3,powerset(the_carrier(X1)))
      | ~ open_subset(X3,X1)
      | interior(X1,X3) = X3
      | ~ element(X2,powerset(the_carrier(X0)))
      | ~ top_str(X1)
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( open_subset(X2,X0)
                      | interior(X0,X2) != X2 )
                    & ( interior(X1,X3) = X3
                      | ~ open_subset(X3,X1) ) )
                  | ~ element(X3,powerset(the_carrier(X1))) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ top_str(X1) )
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( open_subset(X2,X0)
                      | interior(X0,X2) != X2 )
                    & ( interior(X1,X3) = X3
                      | ~ open_subset(X3,X1) ) )
                  | ~ element(X3,powerset(the_carrier(X1))) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ top_str(X1) )
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,axiom,
    ! [X0] :
      ( ( top_str(X0)
        & topological_space(X0) )
     => ! [X1] :
          ( top_str(X1)
         => ! [X2] :
              ( element(X2,powerset(the_carrier(X0)))
             => ! [X3] :
                  ( element(X3,powerset(the_carrier(X1)))
                 => ( ( interior(X0,X2) = X2
                     => open_subset(X2,X0) )
                    & ( open_subset(X3,X1)
                     => interior(X1,X3) = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.whrUVUYhei/Vampire---4.8_26072',t55_tops_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13  % Problem    : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36  % Computer : n018.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 16:24:28 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.whrUVUYhei/Vampire---4.8_26072
% 0.59/0.75  % (26420)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.59/0.75  % (26413)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.59/0.75  % (26415)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.59/0.75  % (26416)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.59/0.75  % (26417)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.59/0.75  % (26418)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.59/0.75  % (26420)Refutation not found, incomplete strategy% (26420)------------------------------
% 0.59/0.75  % (26420)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.59/0.75  % (26420)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.75  
% 0.59/0.75  % (26420)Memory used [KB]: 1050
% 0.59/0.75  % (26420)Time elapsed: 0.002 s
% 0.59/0.75  % (26420)Instructions burned: 3 (million)
% 0.59/0.75  % (26420)------------------------------
% 0.59/0.75  % (26420)------------------------------
% 0.59/0.75  % (26419)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.59/0.75  % (26414)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.59/0.75  % (26422)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.59/0.75  % (26418)First to succeed.
% 0.59/0.75  % (26418)Refutation found. Thanks to Tanya!
% 0.59/0.75  % SZS status Theorem for Vampire---4
% 0.59/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.59/0.75  % (26418)------------------------------
% 0.59/0.75  % (26418)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.59/0.75  % (26418)Termination reason: Refutation
% 0.59/0.75  
% 0.59/0.75  % (26418)Memory used [KB]: 1081
% 0.59/0.75  % (26418)Time elapsed: 0.006 s
% 0.59/0.75  % (26418)Instructions burned: 7 (million)
% 0.59/0.75  % (26418)------------------------------
% 0.59/0.75  % (26418)------------------------------
% 0.59/0.75  % (26326)Success in time 0.38 s
% 0.59/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------