TSTP Solution File: SET975+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/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 : Sun May  5 09:09:14 EDT 2024

% Result   : Theorem 0.57s 0.77s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   46 (   3 unt;   0 def)
%            Number of atoms       :  164 (  50 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  193 (  75   ~;  79   |;  29   &)
%                                         (   7 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   76 (  57   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f62,plain,
    $false,
    inference(avatar_sat_refutation,[],[f46,f48,f54,f61]) ).

fof(f61,plain,
    ( ~ spl5_1
    | spl5_2 ),
    inference(avatar_contradiction_clause,[],[f60]) ).

fof(f60,plain,
    ( $false
    | ~ spl5_1
    | spl5_2 ),
    inference(subsumption_resolution,[],[f58,f45]) ).

fof(f45,plain,
    ( sK0 != sK2
    | spl5_2 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f43,plain,
    ( spl5_2
  <=> sK0 = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f58,plain,
    ( sK0 = sK2
    | ~ spl5_1 ),
    inference(resolution,[],[f55,f36]) ).

fof(f36,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f27]) ).

fof(f27,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK4(X0,X1) != X0
            | ~ in(sK4(X0,X1),X1) )
          & ( sK4(X0,X1) = X0
            | in(sK4(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f18,f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK4(X0,X1) != X0
          | ~ in(sK4(X0,X1),X1) )
        & ( sK4(X0,X1) = X0
          | in(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.W2Hd9vTW7I/Vampire---4.8_20088',d1_tarski) ).

fof(f55,plain,
    ( in(sK0,singleton(sK2))
    | ~ spl5_1 ),
    inference(resolution,[],[f40,f31]) ).

fof(f31,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.W2Hd9vTW7I/Vampire---4.8_20088',l55_zfmisc_1) ).

fof(f40,plain,
    ( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3))
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f39,plain,
    ( spl5_1
  <=> in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f54,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f53]) ).

fof(f53,plain,
    ( $false
    | spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f52,f35]) ).

fof(f35,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f34]) ).

fof(f34,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f28]) ).

fof(f28,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f52,plain,
    ( ~ in(sK0,singleton(sK0))
    | spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f51,f47]) ).

fof(f47,plain,
    in(sK1,sK3),
    inference(subsumption_resolution,[],[f24,f32]) ).

fof(f32,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X1,X3) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f24,plain,
    ( in(sK1,sK3)
    | in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( ( ~ in(sK1,sK3)
      | sK0 != sK2
      | ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
    & ( ( in(sK1,sK3)
        & sK0 = sK2 )
      | in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f15]) ).

fof(f15,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ in(X1,X3)
          | X0 != X2
          | ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
        & ( ( in(X1,X3)
            & X0 = X2 )
          | in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) )
   => ( ( ~ in(sK1,sK3)
        | sK0 != sK2
        | ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
      & ( ( in(sK1,sK3)
          & sK0 = sK2 )
        | in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ in(X1,X3)
        | X0 != X2
        | ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
      & ( ( in(X1,X3)
          & X0 = X2 )
        | in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ in(X1,X3)
        | X0 != X2
        | ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
      & ( ( in(X1,X3)
          & X0 = X2 )
        | in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ? [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
    <~> ( in(X1,X3)
        & X0 = X2 ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
      <=> ( in(X1,X3)
          & X0 = X2 ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
    <=> ( in(X1,X3)
        & X0 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.W2Hd9vTW7I/Vampire---4.8_20088',t128_zfmisc_1) ).

fof(f51,plain,
    ( ~ in(sK1,sK3)
    | ~ in(sK0,singleton(sK0))
    | spl5_1
    | ~ spl5_2 ),
    inference(resolution,[],[f49,f33]) ).

fof(f33,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | ~ in(X1,X3)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f49,plain,
    ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),sK3))
    | spl5_1
    | ~ spl5_2 ),
    inference(forward_demodulation,[],[f41,f44]) ).

fof(f44,plain,
    ( sK0 = sK2
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f41,plain,
    ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3))
    | spl5_1 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f48,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f23,f43,f39]) ).

fof(f23,plain,
    ( sK0 = sK2
    | in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f46,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f37,f43,f39]) ).

fof(f37,plain,
    ( sK0 != sK2
    | ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
    inference(subsumption_resolution,[],[f25,f32]) ).

fof(f25,plain,
    ( ~ in(sK1,sK3)
    | sK0 != sK2
    | ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
    inference(cnf_transformation,[],[f16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14  % Problem    : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Fri May  3 16:41:23 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.W2Hd9vTW7I/Vampire---4.8_20088
% 0.57/0.76  % (20288)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)
% 0.57/0.76  % (20289)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)
% 0.57/0.77  % (20289)Refutation not found, incomplete strategy% (20289)------------------------------
% 0.57/0.77  % (20289)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.77  % (20289)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.77  
% 0.57/0.77  % (20289)Memory used [KB]: 971
% 0.57/0.77  % (20289)Time elapsed: 0.002 s
% 0.57/0.77  % (20289)Instructions burned: 3 (million)
% 0.57/0.77  % (20282)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)
% 0.57/0.77  % (20283)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)
% 0.57/0.77  % (20284)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.77  % (20285)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)
% 0.57/0.77  % (20289)------------------------------
% 0.57/0.77  % (20289)------------------------------
% 0.57/0.77  % (20286)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)
% 0.57/0.77  % (20287)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)
% 0.57/0.77  % (20286)Refutation not found, incomplete strategy% (20286)------------------------------
% 0.57/0.77  % (20286)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.77  % (20286)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.77  
% 0.57/0.77  % (20286)Memory used [KB]: 974
% 0.57/0.77  % (20286)Time elapsed: 0.003 s
% 0.57/0.77  % (20286)Instructions burned: 3 (million)
% 0.57/0.77  % (20287)First to succeed.
% 0.57/0.77  % (20286)------------------------------
% 0.57/0.77  % (20286)------------------------------
% 0.57/0.77  % (20282)Refutation not found, incomplete strategy% (20282)------------------------------
% 0.57/0.77  % (20282)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.77  % (20282)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.77  
% 0.57/0.77  % (20282)Memory used [KB]: 977
% 0.57/0.77  % (20282)Time elapsed: 0.004 s
% 0.57/0.77  % (20282)Instructions burned: 4 (million)
% 0.57/0.77  % (20292)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)
% 0.57/0.77  % (20282)------------------------------
% 0.57/0.77  % (20282)------------------------------
% 0.57/0.77  % (20287)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20264"
% 0.57/0.77  % (20287)Refutation found. Thanks to Tanya!
% 0.57/0.77  % SZS status Theorem for Vampire---4
% 0.57/0.77  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.77  % (20287)------------------------------
% 0.57/0.77  % (20287)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.77  % (20287)Termination reason: Refutation
% 0.57/0.77  
% 0.57/0.77  % (20287)Memory used [KB]: 990
% 0.57/0.77  % (20287)Time elapsed: 0.004 s
% 0.57/0.77  % (20287)Instructions burned: 4 (million)
% 0.57/0.77  % (20264)Success in time 0.393 s
% 0.57/0.77  % Vampire---4.8 exiting
%------------------------------------------------------------------------------