TSTP Solution File: SET012+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n004.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 : Thu Aug 31 15:34:04 EDT 2023

% Result   : Theorem 0.22s 0.42s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   73 (   6 unt;   0 def)
%            Number of atoms       :  185 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  187 (  75   ~;  74   |;  20   &)
%                                         (  11 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   74 (;  67   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f193,plain,
    $false,
    inference(avatar_sat_refutation,[],[f104,f135,f153,f157,f183,f188,f192]) ).

fof(f192,plain,
    ( spl7_2
    | ~ spl7_6 ),
    inference(avatar_contradiction_clause,[],[f191]) ).

fof(f191,plain,
    ( $false
    | spl7_2
    | ~ spl7_6 ),
    inference(subsumption_resolution,[],[f190,f108]) ).

fof(f108,plain,
    ( member(sK2(sK0,sF6),sK0)
    | spl7_2 ),
    inference(resolution,[],[f103,f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,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])],[f33,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,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,[],[f32]) ).

fof(f32,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,[],[f28]) ).

fof(f28,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.Sq1OxZmUtJ/Vampire---4.8_27306',subset) ).

fof(f103,plain,
    ( ~ subset(sK0,sF6)
    | spl7_2 ),
    inference(avatar_component_clause,[],[f101]) ).

fof(f101,plain,
    ( spl7_2
  <=> subset(sK0,sF6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f190,plain,
    ( ~ member(sK2(sK0,sF6),sK0)
    | ~ spl7_6 ),
    inference(resolution,[],[f182,f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ member(X0,sF5)
      | ~ member(X0,sK0) ),
    inference(superposition,[],[f81,f86]) ).

fof(f86,plain,
    difference(sK1,sK0) = sF5,
    introduced(function_definition,[]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.Sq1OxZmUtJ/Vampire---4.8_27306',difference) ).

fof(f182,plain,
    ( member(sK2(sK0,sF6),sF5)
    | ~ spl7_6 ),
    inference(avatar_component_clause,[],[f180]) ).

fof(f180,plain,
    ( spl7_6
  <=> member(sK2(sK0,sF6),sF5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).

fof(f188,plain,
    ( spl7_2
    | spl7_5 ),
    inference(avatar_contradiction_clause,[],[f187]) ).

fof(f187,plain,
    ( $false
    | spl7_2
    | spl7_5 ),
    inference(subsumption_resolution,[],[f184,f108]) ).

fof(f184,plain,
    ( ~ member(sK2(sK0,sF6),sK0)
    | spl7_5 ),
    inference(resolution,[],[f178,f109]) ).

fof(f109,plain,
    ! [X0] :
      ( member(X0,sK1)
      | ~ member(X0,sK0) ),
    inference(resolution,[],[f58,f54]) ).

fof(f54,plain,
    subset(sK0,sK1),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( ~ equal_set(difference(sK1,difference(sK1,sK0)),sK0)
    & subset(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f25,f30]) ).

fof(f30,plain,
    ( ? [X0,X1] :
        ( ~ equal_set(difference(X1,difference(X1,X0)),X0)
        & subset(X0,X1) )
   => ( ~ equal_set(difference(sK1,difference(sK1,sK0)),sK0)
      & subset(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0,X1] :
      ( ~ equal_set(difference(X1,difference(X1,X0)),X0)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => equal_set(difference(X1,difference(X1,X0)),X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X3] :
        ( subset(X0,X3)
       => equal_set(difference(X3,difference(X3,X0)),X0) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0,X3] :
      ( subset(X0,X3)
     => equal_set(difference(X3,difference(X3,X0)),X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.Sq1OxZmUtJ/Vampire---4.8_27306',thI23) ).

fof(f58,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ member(X3,X0)
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f178,plain,
    ( ~ member(sK2(sK0,sF6),sK1)
    | spl7_5 ),
    inference(avatar_component_clause,[],[f176]) ).

fof(f176,plain,
    ( spl7_5
  <=> member(sK2(sK0,sF6),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).

fof(f183,plain,
    ( ~ spl7_5
    | spl7_6
    | spl7_2 ),
    inference(avatar_split_clause,[],[f126,f101,f180,f176]) ).

fof(f126,plain,
    ( member(sK2(sK0,sF6),sF5)
    | ~ member(sK2(sK0,sF6),sK1)
    | spl7_2 ),
    inference(resolution,[],[f124,f107]) ).

fof(f107,plain,
    ( ~ member(sK2(sK0,sF6),sF6)
    | spl7_2 ),
    inference(resolution,[],[f103,f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f124,plain,
    ! [X1] :
      ( member(X1,sF6)
      | member(X1,sF5)
      | ~ member(X1,sK1) ),
    inference(superposition,[],[f82,f87]) ).

fof(f87,plain,
    difference(sK1,sF5) = sF6,
    introduced(function_definition,[]) ).

fof(f82,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f157,plain,
    ( spl7_1
    | ~ spl7_4 ),
    inference(avatar_contradiction_clause,[],[f156]) ).

fof(f156,plain,
    ( $false
    | spl7_1
    | ~ spl7_4 ),
    inference(subsumption_resolution,[],[f154,f106]) ).

fof(f106,plain,
    ( member(sK2(sF6,sK0),sF6)
    | spl7_1 ),
    inference(resolution,[],[f99,f59]) ).

fof(f99,plain,
    ( ~ subset(sF6,sK0)
    | spl7_1 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f97,plain,
    ( spl7_1
  <=> subset(sF6,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f154,plain,
    ( ~ member(sK2(sF6,sK0),sF6)
    | ~ spl7_4 ),
    inference(resolution,[],[f134,f94]) ).

fof(f94,plain,
    ! [X1] :
      ( ~ member(X1,sF5)
      | ~ member(X1,sF6) ),
    inference(superposition,[],[f81,f87]) ).

fof(f134,plain,
    ( member(sK2(sF6,sK0),sF5)
    | ~ spl7_4 ),
    inference(avatar_component_clause,[],[f132]) ).

fof(f132,plain,
    ( spl7_4
  <=> member(sK2(sF6,sK0),sF5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).

fof(f153,plain,
    ( spl7_1
    | spl7_3 ),
    inference(avatar_contradiction_clause,[],[f152]) ).

fof(f152,plain,
    ( $false
    | spl7_1
    | spl7_3 ),
    inference(subsumption_resolution,[],[f150,f106]) ).

fof(f150,plain,
    ( ~ member(sK2(sF6,sK0),sF6)
    | spl7_3 ),
    inference(resolution,[],[f130,f92]) ).

fof(f92,plain,
    ! [X1] :
      ( member(X1,sK1)
      | ~ member(X1,sF6) ),
    inference(superposition,[],[f80,f87]) ).

fof(f80,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f130,plain,
    ( ~ member(sK2(sF6,sK0),sK1)
    | spl7_3 ),
    inference(avatar_component_clause,[],[f128]) ).

fof(f128,plain,
    ( spl7_3
  <=> member(sK2(sF6,sK0),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).

fof(f135,plain,
    ( ~ spl7_3
    | spl7_4
    | spl7_1 ),
    inference(avatar_split_clause,[],[f125,f97,f132,f128]) ).

fof(f125,plain,
    ( member(sK2(sF6,sK0),sF5)
    | ~ member(sK2(sF6,sK0),sK1)
    | spl7_1 ),
    inference(resolution,[],[f123,f105]) ).

fof(f105,plain,
    ( ~ member(sK2(sF6,sK0),sK0)
    | spl7_1 ),
    inference(resolution,[],[f99,f60]) ).

fof(f123,plain,
    ! [X0] :
      ( member(X0,sK0)
      | member(X0,sF5)
      | ~ member(X0,sK1) ),
    inference(superposition,[],[f82,f86]) ).

fof(f104,plain,
    ( ~ spl7_1
    | ~ spl7_2 ),
    inference(avatar_split_clause,[],[f95,f101,f97]) ).

fof(f95,plain,
    ( ~ subset(sK0,sF6)
    | ~ subset(sF6,sK0) ),
    inference(resolution,[],[f57,f88]) ).

fof(f88,plain,
    ~ equal_set(sF6,sK0),
    inference(definition_folding,[],[f55,f87,f86]) ).

fof(f55,plain,
    ~ equal_set(difference(sK1,difference(sK1,sK0)),sK0),
    inference(cnf_transformation,[],[f31]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,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.Sq1OxZmUtJ/Vampire---4.8_27306',equal_set) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.35  % Computer : n004.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit   : 300
% 0.16/0.35  % WCLimit    : 300
% 0.16/0.35  % DateTime   : Sat Aug 26 08:45:38 EDT 2023
% 0.20/0.35  % CPUTime    : 
% 0.20/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.20/0.35  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.Sq1OxZmUtJ/Vampire---4.8_27306
% 0.20/0.35  % (27706)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.39  % (27733)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.41  % (27722)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.41  % (27724)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.41  % (27728)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.41  % (27731)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.22/0.41  % (27738)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.41  % (27737)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.42  % (27731)Refutation not found, incomplete strategy% (27731)------------------------------
% 0.22/0.42  % (27731)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.42  % (27731)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.42  % (27731)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.42  
% 0.22/0.42  % (27731)Memory used [KB]: 9978
% 0.22/0.42  % (27731)Time elapsed: 0.005 s
% 0.22/0.42  % (27731)------------------------------
% 0.22/0.42  % (27731)------------------------------
% 0.22/0.42  % (27737)First to succeed.
% 0.22/0.42  % (27737)Refutation found. Thanks to Tanya!
% 0.22/0.42  % SZS status Theorem for Vampire---4
% 0.22/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.42  % (27737)------------------------------
% 0.22/0.42  % (27737)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.42  % (27737)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.42  % (27737)Termination reason: Refutation
% 0.22/0.42  
% 0.22/0.42  % (27737)Memory used [KB]: 5500
% 0.22/0.42  % (27737)Time elapsed: 0.009 s
% 0.22/0.42  % (27737)------------------------------
% 0.22/0.42  % (27737)------------------------------
% 0.22/0.42  % (27706)Success in time 0.066 s
% 0.22/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------