TSTP Solution File: SEU165+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU165+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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n031.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 09:20:39 EDT 2024

% Result   : Theorem 0.60s 0.78s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   32 (   5 unt;   0 def)
%            Number of atoms       :  173 (  31 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  218 (  77   ~;  76   |;  55   &)
%                                         (   5 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :  121 (  84   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f535,plain,
    $false,
    inference(subsumption_resolution,[],[f534,f491]) ).

fof(f491,plain,
    in(sK18,sK20),
    inference(subsumption_resolution,[],[f317,f489]) ).

fof(f489,plain,
    ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)),
    inference(subsumption_resolution,[],[f488,f310]) ).

fof(f310,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,X2)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f203]) ).

fof(f203,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,[],[f202]) ).

fof(f202,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,[],[f46]) ).

fof(f46,axiom,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.G1SFEQ73y9/Vampire---4.8_17745',l55_zfmisc_1) ).

fof(f488,plain,
    ( ~ in(sK18,sK20)
    | ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
    inference(subsumption_resolution,[],[f319,f311]) ).

fof(f311,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X3)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f203]) ).

fof(f319,plain,
    ( ~ in(sK19,sK21)
    | ~ in(sK18,sK20)
    | ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
    inference(cnf_transformation,[],[f211]) ).

fof(f211,plain,
    ( ( ~ in(sK19,sK21)
      | ~ in(sK18,sK20)
      | ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) )
    & ( ( in(sK19,sK21)
        & in(sK18,sK20) )
      | in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f209,f210]) ).

fof(f210,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ in(X1,X3)
          | ~ in(X0,X2)
          | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
        & ( ( in(X1,X3)
            & in(X0,X2) )
          | in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) )
   => ( ( ~ in(sK19,sK21)
        | ~ in(sK18,sK20)
        | ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) )
      & ( ( in(sK19,sK21)
          & in(sK18,sK20) )
        | in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f209,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ in(X1,X3)
        | ~ in(X0,X2)
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(flattening,[],[f208]) ).

fof(f208,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ in(X1,X3)
        | ~ in(X0,X2)
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f118,plain,
    ? [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <~> ( in(X1,X3)
        & in(X0,X2) ) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      <=> ( in(X1,X3)
          & in(X0,X2) ) ),
    inference(negated_conjecture,[],[f51]) ).

fof(f51,conjecture,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.G1SFEQ73y9/Vampire---4.8_17745',t106_zfmisc_1) ).

fof(f317,plain,
    ( in(sK18,sK20)
    | in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
    inference(cnf_transformation,[],[f211]) ).

fof(f534,plain,
    ~ in(sK18,sK20),
    inference(subsumption_resolution,[],[f526,f490]) ).

fof(f490,plain,
    in(sK19,sK21),
    inference(subsumption_resolution,[],[f318,f489]) ).

fof(f318,plain,
    ( in(sK19,sK21)
    | in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
    inference(cnf_transformation,[],[f211]) ).

fof(f526,plain,
    ( ~ in(sK19,sK21)
    | ~ in(sK18,sK20) ),
    inference(resolution,[],[f489,f394]) ).

fof(f394,plain,
    ! [X10,X0,X1,X9] :
      ( in(ordered_pair(X9,X10),cartesian_product2(X0,X1))
      | ~ in(X10,X1)
      | ~ in(X9,X0) ),
    inference(equality_resolution,[],[f393]) ).

fof(f393,plain,
    ! [X2,X10,X0,X1,X9] :
      ( in(ordered_pair(X9,X10),X2)
      | ~ in(X10,X1)
      | ~ in(X9,X0)
      | cartesian_product2(X0,X1) != X2 ),
    inference(equality_resolution,[],[f260]) ).

fof(f260,plain,
    ! [X2,X10,X0,X1,X8,X9] :
      ( in(X8,X2)
      | ordered_pair(X9,X10) != X8
      | ~ in(X10,X1)
      | ~ in(X9,X0)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f176]) ).

fof(f176,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != sK5(X0,X1,X2)
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( ( sK5(X0,X1,X2) = ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2))
              & in(sK7(X0,X1,X2),X1)
              & in(sK6(X0,X1,X2),X0) )
            | in(sK5(X0,X1,X2),X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ( ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8
                & in(sK9(X0,X1,X8),X1)
                & in(sK8(X0,X1,X8),X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f172,f175,f174,f173]) ).

fof(f173,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != X3
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(X3,X2) )
          & ( ? [X6,X7] :
                ( ordered_pair(X6,X7) = X3
                & in(X7,X1)
                & in(X6,X0) )
            | in(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( ordered_pair(X4,X5) != sK5(X0,X1,X2)
              | ~ in(X5,X1)
              | ~ in(X4,X0) )
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ordered_pair(X6,X7) = sK5(X0,X1,X2)
              & in(X7,X1)
              & in(X6,X0) )
          | in(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f174,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ordered_pair(X6,X7) = sK5(X0,X1,X2)
          & in(X7,X1)
          & in(X6,X0) )
     => ( sK5(X0,X1,X2) = ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2))
        & in(sK7(X0,X1,X2),X1)
        & in(sK6(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f175,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ordered_pair(X11,X12) = X8
          & in(X12,X1)
          & in(X11,X0) )
     => ( ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8
        & in(sK9(X0,X1,X8),X1)
        & in(sK8(X0,X1,X8),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f172,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X6,X7] :
                  ( ordered_pair(X6,X7) = X3
                  & in(X7,X1)
                  & in(X6,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ? [X11,X12] :
                  ( ordered_pair(X11,X12) = X8
                  & in(X12,X1)
                  & in(X11,X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(rectify,[],[f171]) ).

fof(f171,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) ) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | ~ in(X3,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.G1SFEQ73y9/Vampire---4.8_17745',d2_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.16/0.37  % Computer : n031.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Fri May  3 12:03:02 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  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.G1SFEQ73y9/Vampire---4.8_17745
% 0.60/0.77  % (18148)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)
% 0.60/0.77  % (18141)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)
% 0.60/0.77  % (18142)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)
% 0.60/0.77  % (18143)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.77  % (18145)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)
% 0.60/0.77  % (18146)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)
% 0.60/0.77  % (18144)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)
% 0.60/0.77  % (18147)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)
% 0.60/0.78  % (18145)First to succeed.
% 0.60/0.78  % (18145)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17985"
% 0.60/0.78  % (18145)Refutation found. Thanks to Tanya!
% 0.60/0.78  % SZS status Theorem for Vampire---4
% 0.60/0.78  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.78  % (18145)------------------------------
% 0.60/0.78  % (18145)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.78  % (18145)Termination reason: Refutation
% 0.60/0.78  
% 0.60/0.78  % (18145)Memory used [KB]: 1202
% 0.60/0.78  % (18145)Time elapsed: 0.008 s
% 0.60/0.78  % (18145)Instructions burned: 12 (million)
% 0.60/0.78  % (17985)Success in time 0.395 s
% 0.60/0.78  % Vampire---4.8 exiting
%------------------------------------------------------------------------------