%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU123+2 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n013.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 09:20:20 EDT 2024

% Result   : Theorem 0.60s 0.76s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   29 (   7 unt;   0 def)
%            Number of atoms       :   76 (  17 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   80 (  33   ~;  22   |;  15   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   48 (  40   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f128,plain,
    $false,
    inference(subsumption_resolution,[],[f124,f123]) ).

fof(f123,plain,
    ! [X0] : ~ in(X0,sK1),
    inference(subsumption_resolution,[],[f122,f104]) ).

fof(f104,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f84]) ).

fof(f84,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK4(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f53,f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK4(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.n8xE8Juh2l/Vampire---4.8_25670',d1_xboole_0) ).

fof(f122,plain,
    ! [X0] :
      ( ~ in(X0,sK1)
      | in(X0,empty_set) ),
    inference(resolution,[],[f71,f76]) ).

fof(f76,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK3(X0,X1),X1)
          & in(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f47,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK3(X0,X1),X1)
        & in(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.n8xE8Juh2l/Vampire---4.8_25670',d3_tarski) ).

fof(f71,plain,
    subset(sK1,empty_set),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ( empty_set != sK1
    & subset(sK1,empty_set) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f32,f42]) ).

fof(f42,plain,
    ( ? [X0] :
        ( empty_set != X0
        & subset(X0,empty_set) )
   => ( empty_set != sK1
      & subset(sK1,empty_set) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ? [X0] :
      ( empty_set != X0
      & subset(X0,empty_set) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X0] :
        ( subset(X0,empty_set)
       => empty_set = X0 ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X0] :
      ( subset(X0,empty_set)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/tmp/tmp.n8xE8Juh2l/Vampire---4.8_25670',t3_xboole_1) ).

fof(f124,plain,
    in(sK4(sK1),sK1),
    inference(resolution,[],[f109,f112]) ).

fof(f112,plain,
    ! [X0] :
      ( sQ8_eqProxy(empty_set,X0)
      | in(sK4(X0),X0) ),
    inference(equality_proxy_replacement,[],[f85,f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( sQ8_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ8_eqProxy])]) ).

fof(f85,plain,
    ! [X0] :
      ( empty_set = X0
      | in(sK4(X0),X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f109,plain,
    ~ sQ8_eqProxy(empty_set,sK1),
    inference(equality_proxy_replacement,[],[f72,f108]) ).

fof(f72,plain,
    empty_set != sK1,
    inference(cnf_transformation,[],[f43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU123+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14  % 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
% 0.14/0.35  % Computer : n013.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
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 11:19:04 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.n8xE8Juh2l/Vampire---4.8_25670
% 0.60/0.76  % (26002)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)
% 0.60/0.76  % (25997)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.76  % (25995)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)
% 0.60/0.76  % (26002)First to succeed.
% 0.60/0.76  % (25996)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)
% 0.60/0.76  % (25998)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)
% 0.60/0.76  % (26000)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)
% 0.60/0.76  % (25999)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)
% 0.60/0.76  % (26001)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)
% 0.60/0.76  % (26002)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25833"
% 0.60/0.76  % (26002)Refutation found. Thanks to Tanya!
% 0.60/0.76  % SZS status Theorem for Vampire---4
% 0.60/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.76  % (26002)------------------------------
% 0.60/0.76  % (26002)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (26002)Termination reason: Refutation
% 0.60/0.76  
% 0.60/0.76  % (26002)Memory used [KB]: 1051
% 0.60/0.76  % (26002)Time elapsed: 0.002 s
% 0.60/0.76  % (26002)Instructions burned: 4 (million)
% 0.60/0.76  % (25833)Success in time 0.396 s
% 0.60/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------