TSTP Solution File: SET921+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET921+1 : TPTP v8.2.0. 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n026.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 : Tue May 21 03:13:56 EDT 2024

% Result   : Theorem 0.73s 0.93s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   52 (   3 unt;   0 def)
%            Number of atoms       :  230 (  62 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  288 ( 110   ~; 117   |;  49   &)
%                                         (   8 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   94 (  75   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f68,plain,
    $false,
    inference(avatar_sat_refutation,[],[f52,f53,f61,f67]) ).

fof(f67,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f66]) ).

fof(f66,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f64,f38]) ).

fof(f38,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f37]) ).

fof(f37,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f27]) ).

fof(f27,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK3(X0,X1) != X0
            | ~ in(sK3(X0,X1),X1) )
          & ( sK3(X0,X1) = X0
            | in(sK3(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f15,f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK3(X0,X1) != X0
          | ~ in(sK3(X0,X1),X1) )
        & ( sK3(X0,X1) = X0
          | in(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,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,[],[f14]) ).

fof(f14,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,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f64,plain,
    ( ~ in(sK0,singleton(sK0))
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(resolution,[],[f62,f41]) ).

fof(f41,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_difference(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f32]) ).

fof(f32,plain,
    ! [X2,X0,X1,X4] :
      ( ~ in(X4,X1)
      | ~ in(X4,X2)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ( ( in(sK4(X0,X1,X2),X1)
            | ~ in(sK4(X0,X1,X2),X0)
            | ~ in(sK4(X0,X1,X2),X2) )
          & ( ( ~ in(sK4(X0,X1,X2),X1)
              & in(sK4(X0,X1,X2),X0) )
            | in(sK4(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( ~ in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f20,f21]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( ~ in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( in(sK4(X0,X1,X2),X1)
          | ~ in(sK4(X0,X1,X2),X0)
          | ~ in(sK4(X0,X1,X2),X2) )
        & ( ( ~ in(sK4(X0,X1,X2),X1)
            & in(sK4(X0,X1,X2),X0) )
          | in(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( ~ in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( set_difference(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f62,plain,
    ( in(sK0,set_difference(sK1,singleton(sK0)))
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(forward_demodulation,[],[f46,f51]) ).

fof(f51,plain,
    ( sK0 = sK2
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f49]) ).

fof(f49,plain,
    ( spl5_2
  <=> sK0 = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f46,plain,
    ( in(sK0,set_difference(sK1,singleton(sK2)))
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f45]) ).

fof(f45,plain,
    ( spl5_1
  <=> in(sK0,set_difference(sK1,singleton(sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

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

fof(f60,plain,
    ( $false
    | spl5_1
    | spl5_2 ),
    inference(subsumption_resolution,[],[f58,f50]) ).

fof(f50,plain,
    ( sK0 != sK2
    | spl5_2 ),
    inference(avatar_component_clause,[],[f49]) ).

fof(f58,plain,
    ( sK0 = sK2
    | spl5_1 ),
    inference(resolution,[],[f57,f39]) ).

fof(f39,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f26]) ).

fof(f26,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f57,plain,
    ( in(sK0,singleton(sK2))
    | spl5_1 ),
    inference(subsumption_resolution,[],[f56,f54]) ).

fof(f54,plain,
    in(sK0,sK1),
    inference(subsumption_resolution,[],[f23,f42]) ).

fof(f42,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_difference(X0,X1))
      | in(X4,X0) ),
    inference(equality_resolution,[],[f31]) ).

fof(f31,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f23,plain,
    ( in(sK0,sK1)
    | in(sK0,set_difference(sK1,singleton(sK2))) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ( ( sK0 = sK2
      | ~ in(sK0,sK1)
      | ~ in(sK0,set_difference(sK1,singleton(sK2))) )
    & ( ( sK0 != sK2
        & in(sK0,sK1) )
      | in(sK0,set_difference(sK1,singleton(sK2))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).

fof(f12,plain,
    ( ? [X0,X1,X2] :
        ( ( X0 = X2
          | ~ in(X0,X1)
          | ~ in(X0,set_difference(X1,singleton(X2))) )
        & ( ( X0 != X2
            & in(X0,X1) )
          | in(X0,set_difference(X1,singleton(X2))) ) )
   => ( ( sK0 = sK2
        | ~ in(sK0,sK1)
        | ~ in(sK0,set_difference(sK1,singleton(sK2))) )
      & ( ( sK0 != sK2
          & in(sK0,sK1) )
        | in(sK0,set_difference(sK1,singleton(sK2))) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0,X1,X2] :
      ( ( X0 = X2
        | ~ in(X0,X1)
        | ~ in(X0,set_difference(X1,singleton(X2))) )
      & ( ( X0 != X2
          & in(X0,X1) )
        | in(X0,set_difference(X1,singleton(X2))) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ? [X0,X1,X2] :
      ( ( X0 = X2
        | ~ in(X0,X1)
        | ~ in(X0,set_difference(X1,singleton(X2))) )
      & ( ( X0 != X2
          & in(X0,X1) )
        | in(X0,set_difference(X1,singleton(X2))) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ? [X0,X1,X2] :
      ( in(X0,set_difference(X1,singleton(X2)))
    <~> ( X0 != X2
        & in(X0,X1) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( in(X0,set_difference(X1,singleton(X2)))
      <=> ( X0 != X2
          & in(X0,X1) ) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ! [X0,X1,X2] :
      ( in(X0,set_difference(X1,singleton(X2)))
    <=> ( X0 != X2
        & in(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).

fof(f56,plain,
    ( in(sK0,singleton(sK2))
    | ~ in(sK0,sK1)
    | spl5_1 ),
    inference(resolution,[],[f47,f40]) ).

fof(f40,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_difference(X0,X1))
      | in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | in(X4,X1)
      | ~ in(X4,X0)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f47,plain,
    ( ~ in(sK0,set_difference(sK1,singleton(sK2)))
    | spl5_1 ),
    inference(avatar_component_clause,[],[f45]) ).

fof(f53,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f24,f49,f45]) ).

fof(f24,plain,
    ( sK0 != sK2
    | in(sK0,set_difference(sK1,singleton(sK2))) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f52,plain,
    ( ~ spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f43,f49,f45]) ).

fof(f43,plain,
    ( sK0 = sK2
    | ~ in(sK0,set_difference(sK1,singleton(sK2))) ),
    inference(subsumption_resolution,[],[f25,f42]) ).

fof(f25,plain,
    ( sK0 = sK2
    | ~ in(sK0,sK1)
    | ~ in(sK0,set_difference(sK1,singleton(sK2))) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET921+1 : TPTP v8.2.0. Released v3.2.0.
% 0.13/0.14  % 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
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 12:51:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  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/benchmark/theBenchmark.p
% 0.73/0.92  % (8807)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 theBenchmark for (2994ds/34Mi)
% 0.73/0.92  % (8809)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2994ds/78Mi)
% 0.73/0.92  % (8810)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2994ds/33Mi)
% 0.73/0.92  % (8808)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 theBenchmark for (2994ds/51Mi)
% 0.73/0.92  % (8811)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 theBenchmark for (2994ds/34Mi)
% 0.73/0.92  % (8812)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2994ds/45Mi)
% 0.73/0.92  % (8813)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 theBenchmark for (2994ds/83Mi)
% 0.73/0.93  % (8814)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2994ds/56Mi)
% 0.73/0.93  % (8811)Refutation not found, incomplete strategy% (8811)------------------------------
% 0.73/0.93  % (8811)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.73/0.93  % (8811)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.93  
% 0.73/0.93  % (8811)Memory used [KB]: 975
% 0.73/0.93  % (8811)Time elapsed: 0.003 s
% 0.73/0.93  % (8811)Instructions burned: 3 (million)
% 0.73/0.93  % (8814)Refutation not found, incomplete strategy% (8814)------------------------------
% 0.73/0.93  % (8814)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.73/0.93  % (8814)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.93  
% 0.73/0.93  % (8814)Memory used [KB]: 972
% 0.73/0.93  % (8814)Time elapsed: 0.003 s
% 0.73/0.93  % (8814)Instructions burned: 3 (million)
% 0.73/0.93  % (8812)First to succeed.
% 0.73/0.93  % (8811)------------------------------
% 0.73/0.93  % (8811)------------------------------
% 0.73/0.93  % (8814)------------------------------
% 0.73/0.93  % (8814)------------------------------
% 0.73/0.93  % (8808)Also succeeded, but the first one will report.
% 0.73/0.93  % (8809)Also succeeded, but the first one will report.
% 0.73/0.93  % (8810)Also succeeded, but the first one will report.
% 0.73/0.93  % (8812)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8806"
% 0.73/0.93  % (8813)Also succeeded, but the first one will report.
% 0.73/0.93  % (8812)Refutation found. Thanks to Tanya!
% 0.73/0.93  % SZS status Theorem for theBenchmark
% 0.73/0.93  % SZS output start Proof for theBenchmark
% See solution above
% 0.73/0.93  % (8812)------------------------------
% 0.73/0.93  % (8812)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.73/0.93  % (8812)Termination reason: Refutation
% 0.73/0.93  
% 0.73/0.93  % (8812)Memory used [KB]: 990
% 0.73/0.93  % (8812)Time elapsed: 0.004 s
% 0.73/0.93  % (8812)Instructions burned: 5 (million)
% 0.73/0.93  % (8806)Success in time 0.561 s
% 0.73/0.93  % Vampire---4.8 exiting
%------------------------------------------------------------------------------