TSTP Solution File: SET351+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET351+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n007.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 09:05:45 EDT 2024

% Result   : Theorem 0.55s 0.75s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   55 (   9 unt;   0 def)
%            Number of atoms       :  144 (   7 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  143 (  54   ~;  54   |;  21   &)
%                                         (   9 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   80 (  70   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f108,plain,
    $false,
    inference(avatar_sat_refutation,[],[f66,f78,f107]) ).

fof(f107,plain,
    spl3_2,
    inference(avatar_contradiction_clause,[],[f106]) ).

fof(f106,plain,
    ( $false
    | spl3_2 ),
    inference(subsumption_resolution,[],[f103,f83]) ).

fof(f83,plain,
    ( member(sK2(sK0,sum(singleton(sK0))),sK0)
    | spl3_2 ),
    inference(resolution,[],[f65,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f32,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,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,[],[f31]) ).

fof(f31,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,[],[f22]) ).

fof(f22,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/sandbox2/tmp/tmp.zjWIqHb0Xi/Vampire---4.8_12529',subset) ).

fof(f65,plain,
    ( ~ subset(sK0,sum(singleton(sK0)))
    | spl3_2 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f63,plain,
    ( spl3_2
  <=> subset(sK0,sum(singleton(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f103,plain,
    ( ~ member(sK2(sK0,sum(singleton(sK0))),sK0)
    | spl3_2 ),
    inference(resolution,[],[f102,f52]) ).

fof(f52,plain,
    ! [X1] : member(X1,singleton(X1)),
    inference(equality_resolution,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( member(X0,singleton(X1))
        | X0 != X1 )
      & ( X0 = X1
        | ~ member(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
    <=> X0 = X1 ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X2,X0] :
      ( member(X2,singleton(X0))
    <=> X0 = X2 ),
    file('/export/starexec/sandbox2/tmp/tmp.zjWIqHb0Xi/Vampire---4.8_12529',singleton) ).

fof(f102,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton(sK0))
        | ~ member(sK2(sK0,sum(singleton(sK0))),X0) )
    | spl3_2 ),
    inference(resolution,[],[f75,f65]) ).

fof(f75,plain,
    ! [X2,X0,X1] :
      ( subset(X0,sum(X1))
      | ~ member(X2,X1)
      | ~ member(sK2(X0,sum(X1)),X2) ),
    inference(resolution,[],[f43,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( member(X0,sum(X1))
      | ~ member(X0,X2)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ( member(X0,sK1(X0,X1))
          & member(sK1(X0,X1),X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X0,X3)
          & member(X3,X1) )
     => ( member(X0,sK1(X0,X1))
        & member(sK1(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,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,[],[f26]) ).

fof(f26,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,[],[f15]) ).

fof(f15,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/sandbox2/tmp/tmp.zjWIqHb0Xi/Vampire---4.8_12529',sum) ).

fof(f78,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f77]) ).

fof(f77,plain,
    ( $false
    | spl3_1 ),
    inference(subsumption_resolution,[],[f76,f61]) ).

fof(f61,plain,
    ( ~ subset(sum(singleton(sK0)),sK0)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f59,plain,
    ( spl3_1
  <=> subset(sum(singleton(sK0)),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f76,plain,
    ( subset(sum(singleton(sK0)),sK0)
    | spl3_1 ),
    inference(resolution,[],[f73,f48]) ).

fof(f73,plain,
    ( member(sK2(sum(singleton(sK0)),sK0),sK0)
    | spl3_1 ),
    inference(subsumption_resolution,[],[f72,f67]) ).

fof(f67,plain,
    ( member(sK2(sum(singleton(sK0)),sK0),sum(singleton(sK0)))
    | spl3_1 ),
    inference(resolution,[],[f61,f47]) ).

fof(f72,plain,
    ( member(sK2(sum(singleton(sK0)),sK0),sK0)
    | ~ member(sK2(sum(singleton(sK0)),sK0),sum(singleton(sK0)))
    | spl3_1 ),
    inference(superposition,[],[f42,f69]) ).

fof(f69,plain,
    ( sK0 = sK1(sK2(sum(singleton(sK0)),sK0),singleton(sK0))
    | spl3_1 ),
    inference(resolution,[],[f68,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f68,plain,
    ( member(sK1(sK2(sum(singleton(sK0)),sK0),singleton(sK0)),singleton(sK0))
    | spl3_1 ),
    inference(resolution,[],[f67,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ member(X0,sum(X1))
      | member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( member(X0,sK1(X0,X1))
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f66,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f57,f63,f59]) ).

fof(f57,plain,
    ( ~ subset(sK0,sum(singleton(sK0)))
    | ~ subset(sum(singleton(sK0)),sK0) ),
    inference(resolution,[],[f38,f37]) ).

fof(f37,plain,
    ~ equal_set(sum(singleton(sK0)),sK0),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ~ equal_set(sum(singleton(sK0)),sK0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f23]) ).

fof(f23,plain,
    ( ? [X0] : ~ equal_set(sum(singleton(X0)),X0)
   => ~ equal_set(sum(singleton(sK0)),sK0) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ? [X0] : ~ equal_set(sum(singleton(X0)),X0),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : equal_set(sum(singleton(X0)),X0),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0] : equal_set(sum(singleton(X0)),X0),
    file('/export/starexec/sandbox2/tmp/tmp.zjWIqHb0Xi/Vampire---4.8_12529',thI39) ).

fof(f38,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( equal_set(X0,X1)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.zjWIqHb0Xi/Vampire---4.8_12529',equal_set) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET351+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n007.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 16:59:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.zjWIqHb0Xi/Vampire---4.8_12529
% 0.55/0.74  % (12919)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)
% 0.55/0.74  % (12910)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)
% 0.55/0.74  % (12919)Refutation not found, incomplete strategy% (12919)------------------------------
% 0.55/0.74  % (12919)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (12919)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (12919)Memory used [KB]: 979
% 0.55/0.74  % (12919)Time elapsed: 0.002 s
% 0.55/0.74  % (12919)Instructions burned: 2 (million)
% 0.55/0.74  % (12913)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.74  % (12916)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)
% 0.55/0.74  % (12911)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)
% 0.55/0.74  % (12915)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)
% 0.55/0.74  % (12919)------------------------------
% 0.55/0.74  % (12919)------------------------------
% 0.55/0.74  % (12917)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)
% 0.55/0.74  % (12918)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)
% 0.55/0.74  % (12910)Refutation not found, incomplete strategy% (12910)------------------------------
% 0.55/0.74  % (12910)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (12910)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (12910)Memory used [KB]: 960
% 0.55/0.74  % (12910)Time elapsed: 0.003 s
% 0.55/0.74  % (12910)Instructions burned: 2 (million)
% 0.55/0.75  % (12910)------------------------------
% 0.55/0.75  % (12910)------------------------------
% 0.55/0.75  % (12917)Refutation not found, incomplete strategy% (12917)------------------------------
% 0.55/0.75  % (12917)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.75  % (12917)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.75  
% 0.55/0.75  % (12917)Memory used [KB]: 965
% 0.55/0.75  % (12917)Time elapsed: 0.003 s
% 0.55/0.75  % (12917)Instructions burned: 2 (million)
% 0.55/0.75  % (12916)Refutation not found, incomplete strategy% (12916)------------------------------
% 0.55/0.75  % (12916)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.75  % (12916)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.75  
% 0.55/0.75  % (12916)Memory used [KB]: 1036
% 0.55/0.75  % (12916)Time elapsed: 0.003 s
% 0.55/0.75  % (12916)Instructions burned: 3 (million)
% 0.55/0.75  % (12917)------------------------------
% 0.55/0.75  % (12917)------------------------------
% 0.55/0.75  % (12916)------------------------------
% 0.55/0.75  % (12916)------------------------------
% 0.55/0.75  % (12922)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)
% 0.55/0.75  % (12918)Also succeeded, but the first one will report.
% 0.55/0.75  % (12913)First to succeed.
% 0.55/0.75  % (12913)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-12742"
% 0.55/0.75  % (12913)Refutation found. Thanks to Tanya!
% 0.55/0.75  % SZS status Theorem for Vampire---4
% 0.55/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.75  % (12913)------------------------------
% 0.55/0.75  % (12913)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.75  % (12913)Termination reason: Refutation
% 0.55/0.75  
% 0.55/0.75  % (12913)Memory used [KB]: 1075
% 0.55/0.75  % (12913)Time elapsed: 0.006 s
% 0.55/0.75  % (12913)Instructions burned: 7 (million)
% 0.55/0.75  % (12742)Success in time 0.382 s
% 0.55/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------