TSTP Solution File: SET696+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET696+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 : n012.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 15:45:15 EDT 2023

% Result   : Theorem 0.21s 0.42s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   55 (  10 unt;   0 def)
%            Number of atoms       :  143 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  147 (  59   ~;  46   |;  26   &)
%                                         (   9 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   81 (;  74   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f120,plain,
    $false,
    inference(avatar_sat_refutation,[],[f104,f113,f119]) ).

fof(f119,plain,
    spl7_1,
    inference(avatar_contradiction_clause,[],[f118]) ).

fof(f118,plain,
    ( $false
    | spl7_1 ),
    inference(subsumption_resolution,[],[f117,f106]) ).

fof(f106,plain,
    ( member(sK2(sF6,empty_set),sF6)
    | spl7_1 ),
    inference(resolution,[],[f99,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/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',subset) ).

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

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

fof(f117,plain,
    ( ~ member(sK2(sF6,empty_set),sF6)
    | spl7_1 ),
    inference(resolution,[],[f116,f94]) ).

fof(f94,plain,
    ! [X0] :
      ( member(X0,sK0)
      | ~ member(X0,sF6) ),
    inference(superposition,[],[f81,f87]) ).

fof(f87,plain,
    intersection(sF5,sK0) = sF6,
    introduced(function_definition,[]) ).

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

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

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

fof(f23,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
    <=> ( member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',intersection) ).

fof(f116,plain,
    ( ~ member(sK2(sF6,empty_set),sK0)
    | spl7_1 ),
    inference(resolution,[],[f115,f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ~ member(X0,sF5)
      | ~ member(X0,sK0) ),
    inference(superposition,[],[f78,f86]) ).

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

fof(f78,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,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,[],[f50]) ).

fof(f50,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,[],[f22]) ).

fof(f22,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/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',difference) ).

fof(f115,plain,
    ( member(sK2(sF6,empty_set),sF5)
    | spl7_1 ),
    inference(resolution,[],[f106,f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ member(X0,sF6)
      | member(X0,sF5) ),
    inference(superposition,[],[f80,f87]) ).

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

fof(f113,plain,
    spl7_2,
    inference(avatar_contradiction_clause,[],[f112]) ).

fof(f112,plain,
    ( $false
    | spl7_2 ),
    inference(subsumption_resolution,[],[f111,f56]) ).

fof(f56,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',empty_set) ).

fof(f111,plain,
    ( member(sK2(empty_set,sF6),empty_set)
    | spl7_2 ),
    inference(resolution,[],[f103,f59]) ).

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

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

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

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

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

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

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

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

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

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

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

fof(f12,conjecture,
    ! [X0,X3] :
      ( subset(X0,X3)
     => equal_set(intersection(difference(X3,X0),X0),empty_set) ),
    file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',thI28) ).

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/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',equal_set) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35  % Computer : n012.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sat Aug 26 09:09:40 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.35  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891
% 0.15/0.36  % (29999)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (30004)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)
% 0.21/0.42  % (30006)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)
% 0.21/0.42  % (30002)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)
% 0.21/0.42  % (30005)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.42  % (30003)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)
% 0.21/0.42  % (30001)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)
% 0.21/0.42  % (30005)First to succeed.
% 0.21/0.42  % (30003)Refutation not found, incomplete strategy% (30003)------------------------------
% 0.21/0.42  % (30003)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42  % (30003)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42  % (30003)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42  
% 0.21/0.42  % (30003)Memory used [KB]: 9978
% 0.21/0.42  % (30003)Time elapsed: 0.005 s
% 0.21/0.42  % (30003)------------------------------
% 0.21/0.42  % (30003)------------------------------
% 0.21/0.42  % (30004)Also succeeded, but the first one will report.
% 0.21/0.42  % (30006)Also succeeded, but the first one will report.
% 0.21/0.42  % (30005)Refutation found. Thanks to Tanya!
% 0.21/0.42  % SZS status Theorem for Vampire---4
% 0.21/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.42  % (30005)------------------------------
% 0.21/0.42  % (30005)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42  % (30005)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42  % (30005)Termination reason: Refutation
% 0.21/0.42  
% 0.21/0.42  % (30005)Memory used [KB]: 5500
% 0.21/0.42  % (30005)Time elapsed: 0.006 s
% 0.21/0.42  % (30005)------------------------------
% 0.21/0.42  % (30005)------------------------------
% 0.21/0.42  % (29999)Success in time 0.065 s
% 0.21/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------