TSTP Solution File: SET882+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET882+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 : n009.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 09:08:57 EDT 2024

% Result   : Theorem 0.60s 0.76s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   26 (   6 unt;   0 def)
%            Number of atoms       :   97 (  57 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  122 (  51   ~;  42   |;  22   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   48 (  41   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f44,plain,
    $false,
    inference(subsumption_resolution,[],[f40,f19]) ).

fof(f19,plain,
    sK0 != sK1,
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ( singleton(sK0) != set_difference(unordered_pair(sK0,sK1),singleton(sK1))
    & sK0 != sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11]) ).

fof(f11,plain,
    ( ? [X0,X1] :
        ( singleton(X0) != set_difference(unordered_pair(X0,X1),singleton(X1))
        & X0 != X1 )
   => ( singleton(sK0) != set_difference(unordered_pair(sK0,sK1),singleton(sK1))
      & sK0 != sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ? [X0,X1] :
      ( singleton(X0) != set_difference(unordered_pair(X0,X1),singleton(X1))
      & X0 != X1 ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( X0 != X1
       => singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( X0 != X1
     => singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.TTCOwzS0B4/Vampire---4.8_24439',t23_zfmisc_1) ).

fof(f40,plain,
    sK0 = sK1,
    inference(resolution,[],[f39,f33]) ).

fof(f33,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f22]) ).

fof(f22,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK2(X0,X1) != X0
            | ~ in(sK2(X0,X1),X1) )
          & ( sK2(X0,X1) = X0
            | in(sK2(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f14,f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK2(X0,X1) != X0
          | ~ in(sK2(X0,X1),X1) )
        & ( sK2(X0,X1) = X0
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,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,[],[f13]) ).

fof(f13,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/sandbox/tmp/tmp.TTCOwzS0B4/Vampire---4.8_24439',d1_tarski) ).

fof(f39,plain,
    in(sK0,singleton(sK1)),
    inference(subsumption_resolution,[],[f38,f32]) ).

fof(f32,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f31]) ).

fof(f31,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f23]) ).

fof(f23,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f38,plain,
    ( ~ in(sK1,singleton(sK1))
    | in(sK0,singleton(sK1)) ),
    inference(trivial_inequality_removal,[],[f37]) ).

fof(f37,plain,
    ( singleton(sK0) != singleton(sK0)
    | ~ in(sK1,singleton(sK1))
    | in(sK0,singleton(sK1)) ),
    inference(superposition,[],[f20,f28]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( singleton(X0) = set_difference(unordered_pair(X0,X1),X2)
      | ~ in(X1,X2)
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( singleton(X0) = set_difference(unordered_pair(X0,X1),X2)
        | ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | singleton(X0) != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ( singleton(X0) = set_difference(unordered_pair(X0,X1),X2)
        | ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | singleton(X0) != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( singleton(X0) = set_difference(unordered_pair(X0,X1),X2)
    <=> ( ( X0 = X1
          | in(X1,X2) )
        & ~ in(X0,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.TTCOwzS0B4/Vampire---4.8_24439',l39_zfmisc_1) ).

fof(f20,plain,
    singleton(sK0) != set_difference(unordered_pair(sK0,sK1),singleton(sK1)),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15  % 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 : n009.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 17:03:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.21/0.37  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.TTCOwzS0B4/Vampire---4.8_24439
% 0.60/0.76  % (24837)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  % (24837)Refutation not found, incomplete strategy% (24837)------------------------------
% 0.60/0.76  % (24837)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (24837)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76  
% 0.60/0.76  % (24837)Memory used [KB]: 970
% 0.60/0.76  % (24837)Time elapsed: 0.002 s
% 0.60/0.76  % (24837)Instructions burned: 2 (million)
% 0.60/0.76  % (24830)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  % (24832)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  % (24834)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  % (24837)------------------------------
% 0.60/0.76  % (24837)------------------------------
% 0.60/0.76  % (24835)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  % (24831)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  % (24833)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  % (24836)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  % (24834)Refutation not found, incomplete strategy% (24834)------------------------------
% 0.60/0.76  % (24834)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (24834)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76  
% 0.60/0.76  % (24834)Memory used [KB]: 972
% 0.60/0.76  % (24834)Time elapsed: 0.003 s
% 0.60/0.76  % (24834)Instructions burned: 3 (million)
% 0.60/0.76  % (24830)Refutation not found, incomplete strategy% (24830)------------------------------
% 0.60/0.76  % (24830)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (24835)First to succeed.
% 0.60/0.76  % (24830)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76  
% 0.60/0.76  % (24830)Memory used [KB]: 972
% 0.60/0.76  % (24830)Time elapsed: 0.003 s
% 0.60/0.76  % (24830)Instructions burned: 3 (million)
% 0.60/0.76  % (24834)------------------------------
% 0.60/0.76  % (24834)------------------------------
% 0.60/0.76  % (24836)Also succeeded, but the first one will report.
% 0.60/0.76  % (24830)------------------------------
% 0.60/0.76  % (24830)------------------------------
% 0.60/0.76  % (24835)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24689"
% 0.60/0.76  % (24839)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)
% 0.60/0.76  % (24831)Also succeeded, but the first one will report.
% 0.60/0.76  % (24833)Also succeeded, but the first one will report.
% 0.60/0.76  % (24835)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  % (24835)------------------------------
% 0.60/0.76  % (24835)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (24835)Termination reason: Refutation
% 0.60/0.76  
% 0.60/0.76  % (24835)Memory used [KB]: 979
% 0.60/0.76  % (24835)Time elapsed: 0.004 s
% 0.60/0.76  % (24835)Instructions burned: 4 (million)
% 0.60/0.76  % (24689)Success in time 0.387 s
% 0.60/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------