%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU090+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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n023.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 09:20:12 EDT 2024

% Result   : Theorem 0.57s 0.76s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   29 (  11 unt;   1 typ;   0 def)
%            Number of atoms       :  148 (   2 equ)
%            Maximal formula atoms :   10 (   5 avg)
%            Number of connectives :   85 (  32   ~;  19   |;  29   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   67 (  67 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   5 prp; 0-4 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   49 (  36   !;  12   ?;  10   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_19,type,
    sQ7_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f130,plain,
    $false,
    inference(subsumption_resolution,[],[f129,f95]) ).

tff(f95,plain,
    finite(sK0),
    inference(cnf_transformation,[],[f88]) ).

tff(f88,plain,
    ( ~ finite(cartesian_product4(sK0,sK1,sK2,sK3))
    & finite(sK3)
    & finite(sK2)
    & finite(sK1)
    & finite(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f73,f87]) ).

tff(f87,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ finite(cartesian_product4(X0,X1,X2,X3))
        & finite(X3)
        & finite(X2)
        & finite(X1)
        & finite(X0) )
   => ( ~ finite(cartesian_product4(sK0,sK1,sK2,sK3))
      & finite(sK3)
      & finite(sK2)
      & finite(sK1)
      & finite(sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f73,plain,
    ? [X0,X1,X2,X3] :
      ( ~ finite(cartesian_product4(X0,X1,X2,X3))
      & finite(X3)
      & finite(X2)
      & finite(X1)
      & finite(X0) ),
    inference(flattening,[],[f72]) ).

tff(f72,plain,
    ? [X0,X1,X2,X3] :
      ( ~ finite(cartesian_product4(X0,X1,X2,X3))
      & finite(X3)
      & finite(X2)
      & finite(X1)
      & finite(X0) ),
    inference(ennf_transformation,[],[f57]) ).

tff(f57,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( finite(X3)
          & finite(X2)
          & finite(X1)
          & finite(X0) )
       => finite(cartesian_product4(X0,X1,X2,X3)) ),
    inference(negated_conjecture,[],[f56]) ).

tff(f56,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( finite(X3)
        & finite(X2)
        & finite(X1)
        & finite(X0) )
     => finite(cartesian_product4(X0,X1,X2,X3)) ),
    file('/export/starexec/sandbox/tmp/tmp.uhEuZdrm6p/Vampire---4.8_10685',t21_finset_1) ).

tff(f129,plain,
    ~ finite(sK0),
    inference(subsumption_resolution,[],[f128,f96]) ).

tff(f96,plain,
    finite(sK1),
    inference(cnf_transformation,[],[f88]) ).

tff(f128,plain,
    ( ~ finite(sK1)
    | ~ finite(sK0) ),
    inference(subsumption_resolution,[],[f127,f97]) ).

tff(f97,plain,
    finite(sK2),
    inference(cnf_transformation,[],[f88]) ).

tff(f127,plain,
    ( ~ finite(sK2)
    | ~ finite(sK1)
    | ~ finite(sK0) ),
    inference(resolution,[],[f102,f123]) ).

tff(f123,plain,
    ~ finite(cartesian_product3(sK0,sK1,sK2)),
    inference(subsumption_resolution,[],[f122,f98]) ).

tff(f98,plain,
    finite(sK3),
    inference(cnf_transformation,[],[f88]) ).

tff(f122,plain,
    ( ~ finite(sK3)
    | ~ finite(cartesian_product3(sK0,sK1,sK2)) ),
    inference(resolution,[],[f103,f116]) ).

tff(f116,plain,
    ~ finite(cartesian_product2(cartesian_product3(sK0,sK1,sK2),sK3)),
    inference(definition_unfolding,[],[f99,f101]) ).

tff(f101,plain,
    ! [X2: $i,X3: $i,X0: $i,X1: $i] : ( cartesian_product4(X0,X1,X2,X3) = cartesian_product2(cartesian_product3(X0,X1,X2),X3) ),
    inference(cnf_transformation,[],[f14]) ).

tff(f14,axiom,
    ! [X0,X1,X2,X3] : ( cartesian_product4(X0,X1,X2,X3) = cartesian_product2(cartesian_product3(X0,X1,X2),X3) ),
    file('/export/starexec/sandbox/tmp/tmp.uhEuZdrm6p/Vampire---4.8_10685',d4_zfmisc_1) ).

tff(f99,plain,
    ~ finite(cartesian_product4(sK0,sK1,sK2,sK3)),
    inference(cnf_transformation,[],[f88]) ).

tff(f103,plain,
    ! [X0: $i,X1: $i] :
      ( finite(cartesian_product2(X0,X1))
      | ~ finite(X1)
      | ~ finite(X0) ),
    inference(cnf_transformation,[],[f79]) ).

tff(f79,plain,
    ! [X0,X1] :
      ( finite(cartesian_product2(X0,X1))
      | ~ finite(X1)
      | ~ finite(X0) ),
    inference(flattening,[],[f78]) ).

tff(f78,plain,
    ! [X0,X1] :
      ( finite(cartesian_product2(X0,X1))
      | ~ finite(X1)
      | ~ finite(X0) ),
    inference(ennf_transformation,[],[f53]) ).

tff(f53,axiom,
    ! [X0,X1] :
      ( ( finite(X1)
        & finite(X0) )
     => finite(cartesian_product2(X0,X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.uhEuZdrm6p/Vampire---4.8_10685',t19_finset_1) ).

tff(f102,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( finite(cartesian_product3(X0,X1,X2))
      | ~ finite(X2)
      | ~ finite(X1)
      | ~ finite(X0) ),
    inference(cnf_transformation,[],[f77]) ).

tff(f77,plain,
    ! [X0,X1,X2] :
      ( finite(cartesian_product3(X0,X1,X2))
      | ~ finite(X2)
      | ~ finite(X1)
      | ~ finite(X0) ),
    inference(flattening,[],[f76]) ).

tff(f76,plain,
    ! [X0,X1,X2] :
      ( finite(cartesian_product3(X0,X1,X2))
      | ~ finite(X2)
      | ~ finite(X1)
      | ~ finite(X0) ),
    inference(ennf_transformation,[],[f55]) ).

tff(f55,axiom,
    ! [X0,X1,X2] :
      ( ( finite(X2)
        & finite(X1)
        & finite(X0) )
     => finite(cartesian_product3(X0,X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.uhEuZdrm6p/Vampire---4.8_10685',t20_finset_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SEU090+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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n023.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
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 11:26:08 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.uhEuZdrm6p/Vampire---4.8_10685
% 0.57/0.76  % (10941)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)
% 0.57/0.76  % (10947)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  % (10941)First to succeed.
% 0.57/0.76  % (10943)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.76  % (10942)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)
% 0.57/0.76  % (10944)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)
% 0.57/0.76  % (10945)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)
% 0.57/0.76  % (10946)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)
% 0.57/0.76  % (10941)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10937"
% 0.57/0.76  % (10946)Also succeeded, but the first one will report.
% 0.57/0.76  % (10945)Refutation not found, incomplete strategy% (10945)------------------------------
% 0.57/0.76  % (10945)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76  % (10941)Refutation found. Thanks to Tanya!
% 0.57/0.76  % SZS status Theorem for Vampire---4
% 0.57/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.76  % (10941)------------------------------
% 0.57/0.76  % (10941)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76  % (10941)Termination reason: Refutation
% 0.57/0.76  
% 0.57/0.76  % (10941)Memory used [KB]: 1058
% 0.57/0.76  % (10941)Time elapsed: 0.003 s
% 0.57/0.76  % (10941)Instructions burned: 4 (million)
% 0.57/0.76  % (10937)Success in time 0.383 s
% 0.57/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------