%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n021.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 Aug 31 18:19:05 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   35 (  10 unt;   0 def)
%            Number of atoms       :   80 (  43 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   82 (  37   ~;  20   |;  18   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   37 (  26   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f158,plain,
    $false,
    inference(avatar_sat_refutation,[],[f150,f151,f157]) ).

fof(f157,plain,
    ~ spl4_4,
    inference(avatar_contradiction_clause,[],[f156]) ).

fof(f156,plain,
    ( $false
    | ~ spl4_4 ),
    inference(resolution,[],[f149,f120]) ).

fof(f120,plain,
    ~ sQ3_eqProxy(member_of(sK2),sK2),
    inference(equality_proxy_replacement,[],[f105,f115]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( sQ3_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ3_eqProxy])]) ).

fof(f105,plain,
    member_of(sK2) != sK2,
    inference(definition_unfolding,[],[f95,f93]) ).

fof(f93,plain,
    sK1 = sK2,
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( member_of(sK1) != sK2
    & ! [X2] :
        ( singleton(X2) != sK1
        | ~ member(X2,universal_class) )
    & sK1 = sK2 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f72,f73]) ).

fof(f73,plain,
    ( ? [X0,X1] :
        ( member_of(X0) != X1
        & ! [X2] :
            ( singleton(X2) != X0
            | ~ member(X2,universal_class) )
        & X0 = X1 )
   => ( member_of(sK1) != sK2
      & ! [X2] :
          ( singleton(X2) != sK1
          | ~ member(X2,universal_class) )
      & sK1 = sK2 ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ? [X0,X1] :
      ( member_of(X0) != X1
      & ! [X2] :
          ( singleton(X2) != X0
          | ~ member(X2,universal_class) )
      & X0 = X1 ),
    inference(rectify,[],[f60]) ).

fof(f60,plain,
    ? [X1,X0] :
      ( member_of(X1) != X0
      & ! [X2] :
          ( singleton(X2) != X1
          | ~ member(X2,universal_class) )
      & X0 = X1 ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ? [X1,X0] :
      ( member_of(X1) != X0
      & ! [X2] :
          ( singleton(X2) != X1
          | ~ member(X2,universal_class) )
      & X0 = X1 ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,plain,
    ~ ! [X1,X0] :
        ( ( ~ ? [X2] :
                ( singleton(X2) = X1
                & member(X2,universal_class) )
          & X0 = X1 )
       => member_of(X1) = X0 ),
    inference(rectify,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ! [X2,X0] :
        ( ( ~ ? [X1] :
                ( singleton(X1) = X0
                & member(X1,universal_class) )
          & X0 = X2 )
       => member_of(X0) = X2 ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ! [X2,X0] :
      ( ( ~ ? [X1] :
              ( singleton(X1) = X0
              & member(X1,universal_class) )
        & X0 = X2 )
     => member_of(X0) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_when_not_a_singleton) ).

fof(f95,plain,
    member_of(sK1) != sK2,
    inference(cnf_transformation,[],[f74]) ).

fof(f149,plain,
    ( sQ3_eqProxy(member_of(sK2),sK2)
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f147,plain,
    ( spl4_4
  <=> sQ3_eqProxy(member_of(sK2),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f151,plain,
    spl4_3,
    inference(avatar_split_clause,[],[f125,f143]) ).

fof(f143,plain,
    ( spl4_3
  <=> member(member_of(sK2),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f125,plain,
    member(member_of(sK2),universal_class),
    inference(resolution,[],[f120,f117]) ).

fof(f117,plain,
    ! [X0] :
      ( sQ3_eqProxy(member_of(X0),X0)
      | member(member_of(X0),universal_class) ),
    inference(equality_proxy_replacement,[],[f88,f115]) ).

fof(f88,plain,
    ! [X0] :
      ( member_of(X0) = X0
      | member(member_of(X0),universal_class) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0] :
      ( member_of(X0) = X0
      | member(member_of(X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_universal_self) ).

fof(f150,plain,
    ( ~ spl4_3
    | spl4_4 ),
    inference(avatar_split_clause,[],[f138,f147,f143]) ).

fof(f138,plain,
    ( sQ3_eqProxy(member_of(sK2),sK2)
    | ~ member(member_of(sK2),universal_class) ),
    inference(resolution,[],[f121,f122]) ).

fof(f122,plain,
    ! [X0] :
      ( sQ3_eqProxy(unordered_pair(member_of(X0),member_of(X0)),X0)
      | sQ3_eqProxy(member_of(X0),X0) ),
    inference(equality_proxy_replacement,[],[f110,f115,f115]) ).

fof(f110,plain,
    ! [X0] :
      ( unordered_pair(member_of(X0),member_of(X0)) = X0
      | member_of(X0) = X0 ),
    inference(definition_unfolding,[],[f101,f99]) ).

fof(f99,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f101,plain,
    ! [X0] :
      ( singleton(member_of(X0)) = X0
      | member_of(X0) = X0 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,axiom,
    ! [X0] :
      ( singleton(member_of(X0)) = X0
      | member_of(X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_self) ).

fof(f121,plain,
    ! [X2] :
      ( ~ sQ3_eqProxy(unordered_pair(X2,X2),sK2)
      | ~ member(X2,universal_class) ),
    inference(equality_proxy_replacement,[],[f106,f115]) ).

fof(f106,plain,
    ! [X2] :
      ( unordered_pair(X2,X2) != sK2
      | ~ member(X2,universal_class) ),
    inference(definition_unfolding,[],[f94,f99,f93]) ).

fof(f94,plain,
    ! [X2] :
      ( singleton(X2) != sK1
      | ~ member(X2,universal_class) ),
    inference(cnf_transformation,[],[f74]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.07/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 13:09:41 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.20/0.49  % (13811)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.49  % (13803)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.49  % (13793)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.50  % (13796)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.50  % (13803)First to succeed.
% 0.20/0.50  % (13795)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.50  % (13803)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (13803)------------------------------
% 0.20/0.50  % (13803)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (13803)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (13803)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (13803)Memory used [KB]: 6012
% 0.20/0.50  % (13803)Time elapsed: 0.116 s
% 0.20/0.50  % (13803)Instructions burned: 3 (million)
% 0.20/0.50  % (13803)------------------------------
% 0.20/0.50  % (13803)------------------------------
% 0.20/0.50  % (13783)Success in time 0.164 s
%------------------------------------------------------------------------------