TSTP Solution File: SET814+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET814+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 : n017.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 : Wed May  1 03:49:04 EDT 2024

% Result   : Theorem 0.62s 0.79s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   40 (   9 unt;   0 def)
%            Number of atoms       :  150 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  169 (  59   ~;  48   |;  46   &)
%                                         (   7 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   76 (  62   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f102,plain,
    $false,
    inference(subsumption_resolution,[],[f97,f81]) ).

fof(f81,plain,
    member(sK1(sum(sK0),sK0),sK2(sK1(sum(sK0),sK0),sK0)),
    inference(unit_resulting_resolution,[],[f62,f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( member(X0,sK2(X0,X1))
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ( member(X0,sK2(X0,X1))
          & member(sK2(X0,X1),X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f38,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X0,X3)
          & member(X3,X1) )
     => ( member(X0,sK2(X0,X1))
        & member(sK2(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ? [X3] :
            ( member(X0,X3)
            & member(X3,X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(rectify,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ? [X2] :
            ( member(X0,X2)
            & member(X2,X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(nnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( member(X0,sum(X1))
    <=> ? [X2] :
          ( member(X0,X2)
          & member(X2,X1) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X2,X0] :
      ( member(X2,sum(X0))
    <=> ? [X4] :
          ( member(X2,X4)
          & member(X4,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.e9KEIANluZ/Vampire---4.8_4643',sum) ).

fof(f62,plain,
    member(sK1(sum(sK0),sK0),sum(sK0)),
    inference(unit_resulting_resolution,[],[f47,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK1(X0,X1),X1)
          & member(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f34,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.e9KEIANluZ/Vampire---4.8_4643',subset) ).

fof(f47,plain,
    ~ subset(sum(sK0),sK0),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ( ~ subset(sum(sK0),sK0)
    & member(sK0,on) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f26,f31]) ).

fof(f31,plain,
    ( ? [X0] :
        ( ~ subset(sum(X0),X0)
        & member(X0,on) )
   => ( ~ subset(sum(sK0),sK0)
      & member(sK0,on) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0] :
      ( ~ subset(sum(X0),X0)
      & member(X0,on) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,negated_conjecture,
    ~ ! [X0] :
        ( member(X0,on)
       => subset(sum(X0),X0) ),
    inference(negated_conjecture,[],[f21]) ).

fof(f21,conjecture,
    ! [X0] :
      ( member(X0,on)
     => subset(sum(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.e9KEIANluZ/Vampire---4.8_4643',thV14) ).

fof(f97,plain,
    ~ member(sK1(sum(sK0),sK0),sK2(sK1(sum(sK0),sK0),sK0)),
    inference(unit_resulting_resolution,[],[f63,f84,f49]) ).

fof(f49,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f84,plain,
    subset(sK2(sK1(sum(sK0),sK0),sK0),sK0),
    inference(unit_resulting_resolution,[],[f76,f46,f57]) ).

fof(f57,plain,
    ! [X2,X0] :
      ( subset(X2,X0)
      | ~ member(X2,X0)
      | ~ member(X0,on) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ( member(X0,on)
        | ( ~ subset(sK3(X0),X0)
          & member(sK3(X0),X0) )
        | ~ strict_well_order(member_predicate,X0)
        | ~ set(X0) )
      & ( ( ! [X2] :
              ( subset(X2,X0)
              | ~ member(X2,X0) )
          & strict_well_order(member_predicate,X0)
          & set(X0) )
        | ~ member(X0,on) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f43,f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & member(X1,X0) )
     => ( ~ subset(sK3(X0),X0)
        & member(sK3(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0] :
      ( ( member(X0,on)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & member(X1,X0) )
        | ~ strict_well_order(member_predicate,X0)
        | ~ set(X0) )
      & ( ( ! [X2] :
              ( subset(X2,X0)
              | ~ member(X2,X0) )
          & strict_well_order(member_predicate,X0)
          & set(X0) )
        | ~ member(X0,on) ) ),
    inference(rectify,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ( member(X0,on)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & member(X1,X0) )
        | ~ strict_well_order(member_predicate,X0)
        | ~ set(X0) )
      & ( ( ! [X1] :
              ( subset(X1,X0)
              | ~ member(X1,X0) )
          & strict_well_order(member_predicate,X0)
          & set(X0) )
        | ~ member(X0,on) ) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( member(X0,on)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & member(X1,X0) )
        | ~ strict_well_order(member_predicate,X0)
        | ~ set(X0) )
      & ( ( ! [X1] :
              ( subset(X1,X0)
              | ~ member(X1,X0) )
          & strict_well_order(member_predicate,X0)
          & set(X0) )
        | ~ member(X0,on) ) ),
    inference(nnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0] :
      ( member(X0,on)
    <=> ( ! [X1] :
            ( subset(X1,X0)
            | ~ member(X1,X0) )
        & strict_well_order(member_predicate,X0)
        & set(X0) ) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0] :
      ( member(X0,on)
    <=> ( ! [X1] :
            ( member(X1,X0)
           => subset(X1,X0) )
        & strict_well_order(member_predicate,X0)
        & set(X0) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( member(X0,on)
    <=> ( ! [X2] :
            ( member(X2,X0)
           => subset(X2,X0) )
        & strict_well_order(member_predicate,X0)
        & set(X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.e9KEIANluZ/Vampire---4.8_4643',ordinal_number) ).

fof(f46,plain,
    member(sK0,on),
    inference(cnf_transformation,[],[f32]) ).

fof(f76,plain,
    member(sK2(sK1(sum(sK0),sK0),sK0),sK0),
    inference(unit_resulting_resolution,[],[f62,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X1)
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f63,plain,
    ~ member(sK1(sum(sK0),sK0),sK0),
    inference(unit_resulting_resolution,[],[f47,f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ member(sK1(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.11  % 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
% 0.11/0.32  % Computer : n017.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Apr 30 16:48:19 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  This is a FOF_THM_RFO_SEQ problem
% 0.11/0.32  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.e9KEIANluZ/Vampire---4.8_4643
% 0.62/0.78  % (4759)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)
% 0.62/0.78  % (4758)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)
% 0.62/0.78  % (4763)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)
% 0.62/0.78  % (4760)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.78  % (4761)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)
% 0.62/0.78  % (4764)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)
% 0.62/0.78  % (4762)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)
% 0.62/0.78  % (4765)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)
% 0.62/0.79  % (4761)First to succeed.
% 0.62/0.79  % (4761)Refutation found. Thanks to Tanya!
% 0.62/0.79  % SZS status Theorem for Vampire---4
% 0.62/0.79  % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.79  % (4761)------------------------------
% 0.62/0.79  % (4761)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.79  % (4761)Termination reason: Refutation
% 0.62/0.79  
% 0.62/0.79  % (4761)Memory used [KB]: 1068
% 0.62/0.79  % (4761)Time elapsed: 0.005 s
% 0.62/0.79  % (4761)Instructions burned: 5 (million)
% 0.62/0.79  % (4761)------------------------------
% 0.62/0.79  % (4761)------------------------------
% 0.62/0.79  % (4756)Success in time 0.46 s
% 0.62/0.79  % Vampire---4.8 exiting
%------------------------------------------------------------------------------