TSTP Solution File: SET799+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET799+4 : 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 09:08:32 EDT 2024

% Result   : Theorem 0.57s 0.81s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   39 (   9 unt;   0 def)
%            Number of atoms       :  167 (   0 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  170 (  42   ~;  26   |;  74   &)
%                                         (   6 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-3 aty)
%            Number of variables   :  129 (  96   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f94,plain,
    $false,
    inference(subsumption_resolution,[],[f93,f72]) ).

fof(f72,plain,
    member(sK4,sK2),
    inference(resolution,[],[f51,f58]) ).

fof(f58,plain,
    ! [X2,X3,X0,X1] :
      ( ~ least_upper_bound(X0,X1,X2,X3)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3] :
      ( ( ! [X4] :
            ( apply(X2,X0,X4)
            | ~ upper_bound(X4,X2,X1)
            | ~ member(X4,X3) )
        & upper_bound(X0,X2,X1)
        & member(X0,X1) )
      | ~ least_upper_bound(X0,X1,X2,X3) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3] :
      ( ( ! [X4] :
            ( apply(X2,X0,X4)
            | ~ upper_bound(X4,X2,X1)
            | ~ member(X4,X3) )
        & upper_bound(X0,X2,X1)
        & member(X0,X1) )
      | ~ least_upper_bound(X0,X1,X2,X3) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( least_upper_bound(X0,X1,X2,X3)
     => ( ! [X4] :
            ( ( upper_bound(X4,X2,X1)
              & member(X4,X3) )
           => apply(X2,X0,X4) )
        & upper_bound(X0,X2,X1)
        & member(X0,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] :
      ( least_upper_bound(X0,X1,X2,X3)
    <=> ( ! [X4] :
            ( ( upper_bound(X4,X2,X1)
              & member(X4,X3) )
           => apply(X2,X0,X4) )
        & upper_bound(X0,X2,X1)
        & member(X0,X1) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X2,X5,X3] :
      ( least_upper_bound(X0,X2,X5,X3)
    <=> ( ! [X7] :
            ( ( upper_bound(X7,X5,X2)
              & member(X7,X3) )
           => apply(X5,X0,X7) )
        & upper_bound(X0,X5,X2)
        & member(X0,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.ofwbEFeGOy/Vampire---4.8_21638',least_upper_bound) ).

fof(f51,plain,
    least_upper_bound(sK4,sK2,sK0,sK1),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ( ~ apply(sK0,sK4,sK5)
    & least_upper_bound(sK5,sK3,sK0,sK1)
    & least_upper_bound(sK4,sK2,sK0,sK1)
    & subset(sK2,sK3)
    & subset(sK3,sK1)
    & subset(sK2,sK1)
    & order(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f32,f41,f40,f39]) ).

fof(f39,plain,
    ( ? [X0,X1] :
        ( ? [X2,X3] :
            ( ? [X4,X5] :
                ( ~ apply(X0,X4,X5)
                & least_upper_bound(X5,X3,X0,X1)
                & least_upper_bound(X4,X2,X0,X1) )
            & subset(X2,X3)
            & subset(X3,X1)
            & subset(X2,X1) )
        & order(X0,X1) )
   => ( ? [X3,X2] :
          ( ? [X5,X4] :
              ( ~ apply(sK0,X4,X5)
              & least_upper_bound(X5,X3,sK0,sK1)
              & least_upper_bound(X4,X2,sK0,sK1) )
          & subset(X2,X3)
          & subset(X3,sK1)
          & subset(X2,sK1) )
      & order(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ( ? [X3,X2] :
        ( ? [X5,X4] :
            ( ~ apply(sK0,X4,X5)
            & least_upper_bound(X5,X3,sK0,sK1)
            & least_upper_bound(X4,X2,sK0,sK1) )
        & subset(X2,X3)
        & subset(X3,sK1)
        & subset(X2,sK1) )
   => ( ? [X5,X4] :
          ( ~ apply(sK0,X4,X5)
          & least_upper_bound(X5,sK3,sK0,sK1)
          & least_upper_bound(X4,sK2,sK0,sK1) )
      & subset(sK2,sK3)
      & subset(sK3,sK1)
      & subset(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ( ? [X5,X4] :
        ( ~ apply(sK0,X4,X5)
        & least_upper_bound(X5,sK3,sK0,sK1)
        & least_upper_bound(X4,sK2,sK0,sK1) )
   => ( ~ apply(sK0,sK4,sK5)
      & least_upper_bound(sK5,sK3,sK0,sK1)
      & least_upper_bound(sK4,sK2,sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( ? [X4,X5] :
              ( ~ apply(X0,X4,X5)
              & least_upper_bound(X5,X3,X0,X1)
              & least_upper_bound(X4,X2,X0,X1) )
          & subset(X2,X3)
          & subset(X3,X1)
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( ? [X4,X5] :
              ( ~ apply(X0,X4,X5)
              & least_upper_bound(X5,X3,X0,X1)
              & least_upper_bound(X4,X2,X0,X1) )
          & subset(X2,X3)
          & subset(X3,X1)
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ~ ! [X0,X1] :
        ( order(X0,X1)
       => ! [X2,X3] :
            ( ( subset(X2,X3)
              & subset(X3,X1)
              & subset(X2,X1) )
           => ! [X4,X5] :
                ( ( least_upper_bound(X5,X3,X0,X1)
                  & least_upper_bound(X4,X2,X0,X1) )
               => apply(X0,X4,X5) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,negated_conjecture,
    ~ ! [X5,X3] :
        ( order(X5,X3)
       => ! [X8,X9] :
            ( ( subset(X8,X9)
              & subset(X9,X3)
              & subset(X8,X3) )
           => ! [X10,X11] :
                ( ( least_upper_bound(X11,X9,X5,X3)
                  & least_upper_bound(X10,X8,X5,X3) )
               => apply(X5,X10,X11) ) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f22,conjecture,
    ! [X5,X3] :
      ( order(X5,X3)
     => ! [X8,X9] :
          ( ( subset(X8,X9)
            & subset(X9,X3)
            & subset(X8,X3) )
         => ! [X10,X11] :
              ( ( least_upper_bound(X11,X9,X5,X3)
                & least_upper_bound(X10,X8,X5,X3) )
             => apply(X5,X10,X11) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.ofwbEFeGOy/Vampire---4.8_21638',thIV11) ).

fof(f93,plain,
    ~ member(sK4,sK2),
    inference(resolution,[],[f89,f71]) ).

fof(f71,plain,
    ! [X0] :
      ( member(X0,sK3)
      | ~ member(X0,sK2) ),
    inference(resolution,[],[f50,f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) )
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
     => ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.ofwbEFeGOy/Vampire---4.8_21638',subset) ).

fof(f50,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f42]) ).

fof(f89,plain,
    ~ member(sK4,sK3),
    inference(resolution,[],[f79,f53]) ).

fof(f53,plain,
    ~ apply(sK0,sK4,sK5),
    inference(cnf_transformation,[],[f42]) ).

fof(f79,plain,
    ! [X0] :
      ( apply(sK0,X0,sK5)
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f76,f61]) ).

fof(f61,plain,
    ! [X2,X0,X1,X4] :
      ( ~ upper_bound(X2,X0,X1)
      | ~ member(X4,X1)
      | apply(X0,X4,X2) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( ( upper_bound(X2,X0,X1)
        | ( ~ apply(X0,sK6(X0,X1,X2),X2)
          & member(sK6(X0,X1,X2),X1) ) )
      & ( ! [X4] :
            ( apply(X0,X4,X2)
            | ~ member(X4,X1) )
        | ~ upper_bound(X2,X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f44,f45]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ apply(X0,X3,X2)
          & member(X3,X1) )
     => ( ~ apply(X0,sK6(X0,X1,X2),X2)
        & member(sK6(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ( upper_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X3,X2)
            & member(X3,X1) ) )
      & ( ! [X4] :
            ( apply(X0,X4,X2)
            | ~ member(X4,X1) )
        | ~ upper_bound(X2,X0,X1) ) ),
    inference(rectify,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ( upper_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X3,X2)
            & member(X3,X1) ) )
      & ( ! [X3] :
            ( apply(X0,X3,X2)
            | ~ member(X3,X1) )
        | ~ upper_bound(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( upper_bound(X2,X0,X1)
    <=> ! [X3] :
          ( apply(X0,X3,X2)
          | ~ member(X3,X1) ) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( upper_bound(X2,X0,X1)
    <=> ! [X3] :
          ( member(X3,X1)
         => apply(X0,X3,X2) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X5,X3,X7] :
      ( upper_bound(X7,X5,X3)
    <=> ! [X2] :
          ( member(X2,X3)
         => apply(X5,X2,X7) ) ),
    file('/export/starexec/sandbox/tmp/tmp.ofwbEFeGOy/Vampire---4.8_21638',upper_bound) ).

fof(f76,plain,
    upper_bound(sK5,sK0,sK3),
    inference(resolution,[],[f52,f59]) ).

fof(f59,plain,
    ! [X2,X3,X0,X1] :
      ( ~ least_upper_bound(X0,X1,X2,X3)
      | upper_bound(X0,X2,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f52,plain,
    least_upper_bound(sK5,sK3,sK0,sK1),
    inference(cnf_transformation,[],[f42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET799+4 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % 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
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri May  3 17:02:52 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.34  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.ofwbEFeGOy/Vampire---4.8_21638
% 0.57/0.81  % (21748)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.57/0.81  % (21749)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.57/0.81  % (21746)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 (2995ds/34Mi)
% 0.57/0.81  % (21747)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 (2995ds/51Mi)
% 0.57/0.81  % (21751)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.57/0.81  % (21750)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 (2995ds/34Mi)
% 0.57/0.81  % (21752)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 (2995ds/83Mi)
% 0.57/0.81  % (21753)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 (2995ds/56Mi)
% 0.57/0.81  % (21753)First to succeed.
% 0.57/0.81  % (21751)Also succeeded, but the first one will report.
% 0.57/0.81  % (21752)Also succeeded, but the first one will report.
% 0.57/0.81  % (21748)Also succeeded, but the first one will report.
% 0.57/0.81  % (21753)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21745"
% 0.57/0.81  % (21747)Also succeeded, but the first one will report.
% 0.57/0.81  % (21753)Refutation found. Thanks to Tanya!
% 0.57/0.81  % SZS status Theorem for Vampire---4
% 0.57/0.81  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.82  % (21753)------------------------------
% 0.57/0.82  % (21753)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.82  % (21753)Termination reason: Refutation
% 0.57/0.82  
% 0.57/0.82  % (21753)Memory used [KB]: 1071
% 0.57/0.82  % (21753)Time elapsed: 0.025 s
% 0.57/0.82  % (21753)Instructions burned: 5 (million)
% 0.57/0.82  % (21745)Success in time 0.46 s
% 0.57/0.82  % Vampire---4.8 exiting
%------------------------------------------------------------------------------