TSTP Solution File: ITP115^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP115^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Mon May 20 22:23:03 EDT 2024

% Result   : Theorem 26.99s 13.00s
% Output   : Refutation 27.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  217
% Syntax   : Number of formulae    :  402 ( 156 unt;  34 typ;   0 def)
%            Number of atoms       : 1572 ( 360 equ;   2 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives : 4997 ( 132   ~;   8   |; 120   &;4423   @)
%                                         (   0 <=>; 314  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   61 (  61   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   36 (  33 usr;   7 con; 0-4 aty)
%            Number of variables   : 1160 (  36   ^1056   !;  40   ?;1160   :)
%                                         (  28  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(b_type,type,
    b: $tType ).

thf(a_type,type,
    a: $tType ).

thf(topolo2117631714pology_type,type,
    topolo2117631714pology: 
      !>[TA: $tType] : $o ).

thf(comple1035589618norder_type,type,
    comple1035589618norder: 
      !>[TA: $tType] : $o ).

thf(topological_t0_space_type,type,
    topological_t0_space: 
      !>[TA: $tType] : $o ).

thf(topological_t1_space_type,type,
    topological_t1_space: 
      !>[TA: $tType] : $o ).

thf(topological_t2_space_type,type,
    topological_t2_space: 
      !>[TA: $tType] : $o ).

thf(bounded_lattice_bot_type,type,
    bounded_lattice_bot: 
      !>[TA: $tType] : $o ).

thf(topolo890362671_space_type,type,
    topolo890362671_space: 
      !>[TA: $tType] : $o ).

thf(topolo47006728_space_type,type,
    topolo47006728_space: 
      !>[TA: $tType] : $o ).

thf(topolo2133971006pology_type,type,
    topolo2133971006pology: 
      !>[TA: $tType] : $o ).

thf(topolo503727757_space_type,type,
    topolo503727757_space: 
      !>[TA: $tType] : $o ).

thf(topolo2135403230pology_type,type,
    topolo2135403230pology: 
      !>[TA: $tType] : $o ).

thf(minus_minus_type,type,
    minus_minus: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(inf_inf_type,type,
    inf_inf: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(lower_582600101lsc_at_type,type,
    lower_582600101lsc_at: 
      !>[TA: $tType,TB: $tType] : ( TB > ( TB > TA ) > $o ) ).

thf(bot_bot_type,type,
    bot_bot: 
      !>[TA: $tType] : TA ).

thf(ord_less_eq_type,type,
    ord_less_eq: 
      !>[TA: $tType] : ( TA > TA > $o ) ).

thf(top_top_type,type,
    top_top: 
      !>[TA: $tType] : TA ).

thf(collect_type,type,
    collect: 
      !>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).

thf(insert_type,type,
    insert: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).

thf(is_empty_type,type,
    is_empty: 
      !>[TA: $tType] : ( ( set @ TA ) > $o ) ).

thf(is_singleton_type,type,
    is_singleton: 
      !>[TA: $tType] : ( ( set @ TA ) > $o ) ).

thf(remove_type,type,
    remove: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).

thf(the_elem_type,type,
    the_elem: 
      !>[TA: $tType] : ( ( set @ TA ) > TA ) ).

thf(topolo1751647064n_open_type,type,
    topolo1751647064n_open: 
      !>[TA: $tType] : ( ( set @ TA ) > $o ) ).

thf(topolo507301023within_type,type,
    topolo507301023within: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > ( filter @ TA ) ) ).

thf(topolo406746546ounded_type,type,
    topolo406746546ounded: 
      !>[TA: $tType] : ( ( set @ TA ) > $o ) ).

thf(member_type,type,
    member: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).

thf(a2_type,type,
    a2: b ).

thf(f_type,type,
    f: a > b ).

thf(thesis_type,type,
    thesis: $o ).

thf(x0_type,type,
    x0: a ).

thf(184,axiom,
    ! [A: set @ b,B: set @ b] :
      ( ( ( topolo1751647064n_open @ b @ A )
        & ( topolo1751647064n_open @ b @ B )
        & ( member @ b @ ( f @ x0 ) @ A )
        & ( member @ b @ a2 @ B )
        & ( ( inf_inf @ ( set @ b ) @ A @ B )
          = ( bot_bot @ ( set @ b ) ) ) )
     => thesis ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(715,plain,
    ! [A: set @ b,B: set @ b] :
      ( ( ( topolo1751647064n_open @ b @ A )
        & ( topolo1751647064n_open @ b @ B )
        & ( member @ b @ ( f @ x0 ) @ A )
        & ( member @ b @ a2 @ B )
        & ( ( inf_inf @ ( set @ b ) @ A @ B )
          = ( bot_bot @ ( set @ b ) ) ) )
     => thesis ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(112,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Diff__insert__absorb) ).

thf(479,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(108,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
      = ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_empty__Diff) ).

thf(468,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
      = ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(21,axiom,
    ! [TA: $tType] :
      ( ( is_singleton @ TA )
      = ( ^ [A: set @ TA] :
          ? [B: TA] :
            ( A
            = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_is__singleton__def) ).

thf(234,plain,
    ! [TA: $tType] :
      ( ( is_singleton @ TA )
      = ( ^ [A: set @ TA] :
          ? [B: TA] :
            ( A
            = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(67,axiom,
    topological_t2_space @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Ot2__space_32) ).

thf(352,plain,
    topological_t2_space @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(145,axiom,
    ! [TA: $tType] :
      ( ( topological_t0_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
          = ( ? [C: set @ TA] :
                ( ( topolo1751647064n_open @ TA @ C )
                & ( ( member @ TA @ A @ C )
                 != ( member @ TA @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_separation__t0) ).

thf(582,plain,
    ! [TA: $tType] :
      ( ( topological_t0_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
          = ( ? [C: set @ TA] :
                ( ( topolo1751647064n_open @ TA @ C )
                & ( ( member @ TA @ A @ C )
                 != ( member @ TA @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(38,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( member @ TA @ A @ B )
       => ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
          = ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
      & ( ~ ( member @ TA @ A @ B )
       => ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
          = ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insert__Diff__if) ).

thf(276,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( member @ TA @ A @ B )
       => ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
          = ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
      & ( ~ ( member @ TA @ A @ B )
       => ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
          = ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(51,axiom,
    ! [TA: $tType] :
      ( ( is_singleton @ TA )
      = ( ^ [A: set @ TA] :
            ( A
            = ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_is__singleton__the__elem) ).

thf(308,plain,
    ! [TA: $tType] :
      ( ( is_singleton @ TA )
      = ( ^ [A: set @ TA] :
            ( A
            = ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(101,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
      = ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Diff__Int__distrib2) ).

thf(449,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
      = ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(155,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_singleton__inject) ).

thf(614,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(173,axiom,
    ! [TA: $tType] :
      ( ( topological_t1_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ? [C: set @ TA] :
              ( ( topolo1751647064n_open @ TA @ C )
              & ( member @ TA @ A @ C )
              & ~ ( member @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_t1__space) ).

thf(677,plain,
    ! [TA: $tType] :
      ( ( topological_t1_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ? [C: set @ TA] :
              ( ( topolo1751647064n_open @ TA @ C )
              & ( member @ TA @ A @ C )
              & ~ ( member @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(9,axiom,
    ! [TA: $tType] :
      ( ( topolo2117631714pology @ TA )
     => ( topolo503727757_space @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Otopological__space) ).

thf(202,plain,
    ! [TA: $tType] :
      ( ( topolo2117631714pology @ TA )
     => ( topolo503727757_space @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(150,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ A )
      = ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Diff__cancel) ).

thf(597,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ A )
      = ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(1,conjecture,
    thesis,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(2,negated_conjecture,
    ~ thesis,
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(185,plain,
    ~ thesis,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(89,axiom,
    ! [TA: $tType,A: TA] :
      ( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_the__elem__eq) ).

thf(417,plain,
    ! [TA: $tType,A: TA] :
      ( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(48,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_double__diff) ).

thf(301,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(31,axiom,
    ! [TA: $tType] :
      ( ( topological_t1_space @ TA )
     => ! [A: set @ TA,B: TA] :
          ( ( topolo1751647064n_open @ TA @ A )
         => ( topolo1751647064n_open @ TA @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_open__delete) ).

thf(257,plain,
    ! [TA: $tType] :
      ( ( topological_t1_space @ TA )
     => ! [A: set @ TA,B: TA] :
          ( ( topolo1751647064n_open @ TA @ A )
         => ( topolo1751647064n_open @ TA @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(147,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ A )
           => ( ( C @ E )
             => ( D @ E ) ) )
       => ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_Int__Collect__mono) ).

thf(587,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ A )
           => ( ( C @ E )
             => ( D @ E ) ) )
       => ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(179,axiom,
    ! [TA: $tType] :
      ( ( bot_bot @ ( TA > $o ) )
      = ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_bot__empty__eq) ).

thf(702,plain,
    ! [TA: $tType] :
      ( ( bot_bot @ ( TA > $o ) )
      = ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(64,axiom,
    ! [TA: $tType] :
      ( ( topolo47006728_space @ TA )
     => ! [A: set @ TA,B: set @ TA] :
          ( ( topolo406746546ounded @ TA @ A )
         => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
           => ( topolo406746546ounded @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_totally__bounded__subset) ).

thf(344,plain,
    ! [TA: $tType] :
      ( ( topolo47006728_space @ TA )
     => ! [A: set @ TA,B: set @ TA] :
          ( ( topolo406746546ounded @ TA @ A )
         => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
           => ( topolo406746546ounded @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(7,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA] :
          ( ( ( topolo507301023within @ TA @ A @ ( top_top @ ( set @ TA ) ) )
            = ( bot_bot @ ( filter @ TA ) ) )
          = ( topolo1751647064n_open @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_at__eq__bot__iff) ).

thf(196,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA] :
          ( ( ( topolo507301023within @ TA @ A @ ( top_top @ ( set @ TA ) ) )
            = ( bot_bot @ ( filter @ TA ) ) )
          = ( topolo1751647064n_open @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(133,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ B @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Int__absorb1) ).

thf(542,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ B @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(105,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
      = ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Diff__Int__distrib) ).

thf(460,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
      = ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(163,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
      = ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Diff__Int2) ).

thf(638,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
      = ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(153,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_Int__absorb2) ).

thf(606,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(33,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( TA > $o ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Collect__empty__eq__bot) ).

thf(261,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( TA > $o ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(15,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_subset__trans) ).

thf(216,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(148,axiom,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ~ ( member @ TA @ B @ A )
        & ( ( inf_inf @ ( set @ TA ) @ A @ C )
          = ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_disjoint__insert_I1_J) ).

thf(591,plain,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ~ ( member @ TA @ B @ A )
        & ( ( inf_inf @ ( set @ TA ) @ A @ C )
          = ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(54,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Diff__insert0) ).

thf(321,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(158,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
     => ( ( minus_minus @ ( set @ TA ) @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Diff__triv) ).

thf(623,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
     => ( ( minus_minus @ ( set @ TA ) @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(114,axiom,
    ! [TA: $tType] :
      ( ( topological_t2_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
          = ( ? [C: set @ TA,D: set @ TA] :
                ( ( topolo1751647064n_open @ TA @ C )
                & ( topolo1751647064n_open @ TA @ D )
                & ( member @ TA @ A @ C )
                & ( member @ TA @ B @ D )
                & ( ( inf_inf @ ( set @ TA ) @ C @ D )
                  = ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_separation__t2) ).

thf(485,plain,
    ! [TA: $tType] :
      ( ( topological_t2_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
          = ( ? [C: set @ TA,D: set @ TA] :
                ( ( topolo1751647064n_open @ TA @ C )
                & ( topolo1751647064n_open @ TA @ D )
                & ( member @ TA @ A @ C )
                & ( member @ TA @ B @ D )
                & ( ( inf_inf @ ( set @ TA ) @ C @ D )
                  = ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(142,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ~ ( member @ TA @ A @ C )
        & ( ( inf_inf @ ( set @ TA ) @ B @ C )
          = ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_insert__disjoint_I1_J) ).

thf(574,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ~ ( member @ TA @ A @ C )
        & ( ( inf_inf @ ( set @ TA ) @ B @ C )
          = ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(68,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
      = ( ( A = B )
        | ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_insert__iff) ).

thf(353,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
      = ( ( A = B )
        | ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(82,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_in__mono) ).

thf(397,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(17,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( minus_minus @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Diff__eq__empty__iff) ).

thf(221,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( minus_minus @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(44,axiom,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_subset__refl) ).

thf(293,plain,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(168,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_empty__iff) ).

thf(660,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(11,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_subset__antisym) ).

thf(206,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(102,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: set @ TA,B: set @ TA] :
          ( ( topolo1751647064n_open @ TA @ A )
         => ( ( topolo1751647064n_open @ TA @ B )
           => ( topolo1751647064n_open @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_open__Int) ).

thf(452,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: set @ TA,B: set @ TA] :
          ( ( topolo1751647064n_open @ TA @ A )
         => ( ( topolo1751647064n_open @ TA @ B )
           => ( topolo1751647064n_open @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(28,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
      ( ( ! [D: TA] :
            ( ( member @ TA @ D @ ( insert @ TA @ A @ B ) )
           => ( C @ D ) ) )
      = ( ( C @ A )
        & ! [D: TA] :
            ( ( member @ TA @ D @ B )
           => ( C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ball__insert) ).

thf(248,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
      ( ( ! [D: TA] :
            ( ( member @ TA @ D @ ( insert @ TA @ A @ B ) )
           => ( C @ D ) ) )
      = ( ( C @ A )
        & ! [D: TA] :
            ( ( member @ TA @ D @ B )
           => ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(76,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( insert @ TA @ B @ C ) )
      = ( ( B = A )
        & ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_singleton__insert__inj__eq) ).

thf(380,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( insert @ TA @ B @ C ) )
      = ( ( B = A )
        & ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(123,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ C ) )
      = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_insert__inter__insert) ).

thf(512,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ C ) )
      = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(36,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_set__eq__subset) ).

thf(270,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(130,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
      = ( ( member @ TA @ A @ B )
        & ~ ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Diff__iff) ).

thf(534,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
      = ( ( member @ TA @ A @ B )
        & ~ ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(60,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ~ ! [C: set @ TA] :
            ( ( B
              = ( insert @ TA @ A @ C ) )
           => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Set_Oset__insert) ).

thf(334,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ~ ! [C: set @ TA] :
            ( ( B
              = ( insert @ TA @ A @ C ) )
           => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(66,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).

thf(349,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(137,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
     => ~ ( ( member @ TA @ A @ B )
         => ~ ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_IntE) ).

thf(561,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
     => ~ ( ( member @ TA @ A @ B )
         => ~ ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(46,axiom,
    topological_t1_space @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Ot1__space_33) ).

thf(297,plain,
    topological_t1_space @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(176,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_equals0I) ).

thf(693,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(96,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
        & ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Int__subset__iff) ).

thf(435,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
        & ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(126,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Int__absorb) ).

thf(522,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(117,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
      = ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Diff__disjoint) ).

thf(493,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
      = ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(182,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
       => ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Int__mono) ).

thf(710,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
       => ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(55,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ( insert @ TA @ A @ B )
        = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( A = C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_singleton__insert__inj__eq_H) ).

thf(324,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ( insert @ TA @ A @ B )
        = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( A = C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(41,axiom,
    ! [TA: $tType] :
      ( ( comple1035589618norder @ TA )
     => ( bounded_lattice_bot @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Complete__Lattices_Ocomplete__linorder___Lattices_Obounded__lattice__bot) ).

thf(285,plain,
    ! [TA: $tType] :
      ( ( comple1035589618norder @ TA )
     => ( bounded_lattice_bot @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(18,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( insert @ TA @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_insert__absorb) ).

thf(224,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( insert @ TA @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(125,axiom,
    ! [TA: $tType] :
      ( ( is_empty @ TA )
      = ( ^ [A: set @ TA] :
            ( A
            = ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Set_Ois__empty__def) ).

thf(519,plain,
    ! [TA: $tType] :
      ( ( is_empty @ TA )
      = ( ^ [A: set @ TA] :
            ( A
            = ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(85,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
      = ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Int__assoc) ).

thf(403,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
      = ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(4,axiom,
    ! [TA: $tType] :
      ( ( topolo2133971006pology @ TA )
     => ( ( topolo507301023within @ TA )
        = ( ^ [A: TA,B: set @ TA] : ( bot_bot @ ( filter @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_at__discrete) ).

thf(188,plain,
    ! [TA: $tType] :
      ( ( topolo2133971006pology @ TA )
     => ( ( topolo507301023within @ TA )
        = ( ^ [A: TA,B: set @ TA] : ( bot_bot @ ( filter @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(79,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ C @ D )
       => ( ( ( insert @ TA @ A @ B )
            = ( insert @ TA @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set @ TA] :
                  ( ( B
                    = ( insert @ TA @ C @ E ) )
                  & ~ ( member @ TA @ C @ E )
                  & ( D
                    = ( insert @ TA @ A @ E ) )
                  & ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_insert__eq__iff) ).

thf(388,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ C @ D )
       => ( ( ( insert @ TA @ A @ B )
            = ( insert @ TA @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set @ TA] :
                  ( ( B
                    = ( insert @ TA @ C @ E ) )
                  & ~ ( member @ TA @ C @ E )
                  & ( D
                    = ( insert @ TA @ A @ E ) )
                  & ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(69,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).

thf(356,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(90,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_subset__eq) ).

thf(420,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(109,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ? [B: TA] : ( member @ TA @ B @ A ) )
      = ( A
       != ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_ex__in__conv) ).

thf(471,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ? [B: TA] : ( member @ TA @ B @ A ) )
      = ( A
       != ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(115,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
      = ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Int__Diff) ).

thf(488,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
      = ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(62,axiom,
    ! [TA: $tType] :
      ( ( topolo2117631714pology @ TA )
     => ( topological_t0_space @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot0__space) ).

thf(339,plain,
    ! [TA: $tType] :
      ( ( topolo2117631714pology @ TA )
     => ( topological_t0_space @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(131,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_insert__Diff) ).

thf(537,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(111,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: set @ TA] :
          ( ! [B: TA] :
              ( ( member @ TA @ B @ A )
             => ? [C: set @ TA] :
                  ( ( topolo1751647064n_open @ TA @ C )
                  & ( member @ TA @ B @ C )
                  & ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) )
         => ( topolo1751647064n_open @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_topological__space__class_OopenI) ).

thf(476,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: set @ TA] :
          ( ! [B: TA] :
              ( ( member @ TA @ B @ A )
             => ? [C: set @ TA] :
                  ( ( topolo1751647064n_open @ TA @ C )
                  & ( member @ TA @ B @ C )
                  & ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) )
         => ( topolo1751647064n_open @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(13,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_insert__mono) ).

thf(212,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(124,axiom,
    ! [A: set @ b] :
      ( ( ( topolo1751647064n_open @ b @ A )
        & ( member @ b @ ( f @ x0 ) @ A ) )
     => ? [B: set @ a] :
          ( ( topolo1751647064n_open @ a @ B )
          & ( member @ a @ x0 @ B )
          & ! [C: a] :
              ( ( member @ a @ C @ B )
             => ( ( ord_less_eq @ b @ ( f @ C ) @ ( f @ x0 ) )
               => ( member @ b @ ( f @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060forall_062S_O_Aopen_AS_A_092_060and_062_Af_Ax0_A_092_060in_062_AS_A_092_060longrightarrow_062_A_I_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062x_H_092_060in_062T_O_Af_Ax_H_A_092_060le_062_Af_Ax0_A_092_060longrightarrow_062_Af_Ax_H_A_092_060in_062_AS_J_J_092_060close_062) ).

thf(515,plain,
    ! [A: set @ b] :
      ( ( ( topolo1751647064n_open @ b @ A )
        & ( member @ b @ ( f @ x0 ) @ A ) )
     => ? [B: set @ a] :
          ( ( topolo1751647064n_open @ a @ B )
          & ( member @ a @ x0 @ B )
          & ! [C: a] :
              ( ( member @ a @ C @ B )
             => ( ( ord_less_eq @ b @ ( f @ C ) @ ( f @ x0 ) )
               => ( member @ b @ ( f @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(104,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( collect @ TA @ A ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_empty__Collect__eq) ).

thf(457,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( collect @ TA @ A ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(22,axiom,
    ! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_is__singletonI) ).

thf(237,plain,
    ! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(26,axiom,
    ! [TA: $tType] :
      ( ( topolo2117631714pology @ TA )
     => ( topological_t2_space @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot2__space) ).

thf(244,plain,
    ! [TA: $tType] :
      ( ( topolo2117631714pology @ TA )
     => ( topological_t2_space @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(52,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
      = ( minus_minus @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Diff__idemp) ).

thf(311,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
      = ( minus_minus @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(136,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_singletonD) ).

thf(558,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(172,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_singleton__iff) ).

thf(674,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(169,axiom,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_singletonI) ).

thf(662,plain,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(47,axiom,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
      = ( ( ( member @ TA @ B @ A )
         => ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) )
        & ( ~ ( member @ TA @ B @ A )
         => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_subset__insert__iff) ).

thf(298,plain,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
      = ( ( ( member @ TA @ B @ A )
         => ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) )
        & ( ~ ( member @ TA @ B @ A )
         => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(88,axiom,
    ! [TA: $tType] :
      ( ( topolo2135403230pology @ TA )
     => ! [A: TA] :
        ? [B: nat > ( set @ TA )] :
          ( ! [C: nat] :
              ( ( member @ TA @ A @ ( B @ C ) )
              & ( topolo1751647064n_open @ TA @ ( B @ C ) ) )
          & ! [C: set @ TA] :
              ( ( ( topolo1751647064n_open @ TA @ C )
                & ( member @ TA @ A @ C ) )
             => ? [D: nat] : ( ord_less_eq @ ( set @ TA ) @ ( B @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_first__countable__basis) ).

thf(412,plain,
    ! [TA: $tType] :
      ( ( topolo2135403230pology @ TA )
     => ! [A: TA] :
        ? [B: nat > ( set @ TA )] :
          ( ! [C: nat] :
              ( ( member @ TA @ A @ ( B @ C ) )
              & ( topolo1751647064n_open @ TA @ ( B @ C ) ) )
          & ! [C: set @ TA] :
              ( ( ( topolo1751647064n_open @ TA @ C )
                & ( member @ TA @ A @ C ) )
             => ? [D: nat] : ( ord_less_eq @ ( set @ TA ) @ ( B @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(92,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Int__greatest) ).

thf(425,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(94,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C ) )
      = ( ~ ( member @ TA @ A @ C )
        & ( ( bot_bot @ ( set @ TA ) )
          = ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_insert__disjoint_I2_J) ).

thf(430,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C ) )
      = ( ~ ( member @ TA @ A @ C )
        & ( ( bot_bot @ ( set @ TA ) )
          = ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(34,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( is_singleton @ TA @ A )
     => ~ ! [B: TA] :
            ( A
           != ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_is__singletonE) ).

thf(264,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( is_singleton @ TA @ A )
     => ~ ! [B: TA] :
            ( A
           != ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(99,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ~ ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_disjoint__iff) ).

thf(444,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ~ ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(91,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
     => ( member @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_DiffD1) ).

thf(423,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
     => ( member @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(5,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA] :
          ( ( topolo507301023within @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
          = ( bot_bot @ ( filter @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_at__within__empty) ).

thf(191,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA] :
          ( ( topolo507301023within @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
          = ( bot_bot @ ( filter @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(143,axiom,
    ! [TA: $tType] :
      ( ( topolo2133971006pology @ TA )
     => ! [A: set @ TA] : ( topolo1751647064n_open @ TA @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_open__discrete) ).

thf(577,plain,
    ! [TA: $tType] :
      ( ( topolo2133971006pology @ TA )
     => ! [A: set @ TA] : ( topolo1751647064n_open @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(144,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ! [D: TA] :
                ( ( member @ TA @ D @ B )
               => ( C != D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_disjoint__iff__not__equal) ).

thf(579,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ! [D: TA] :
                ( ( member @ TA @ D @ B )
               => ( C != D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(134,axiom,
    ! [TA: $tType] :
      ( ( topological_t2_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ? [C: set @ TA,D: set @ TA] :
              ( ( topolo1751647064n_open @ TA @ C )
              & ( topolo1751647064n_open @ TA @ D )
              & ( member @ TA @ A @ C )
              & ( member @ TA @ B @ D )
              & ( ( inf_inf @ ( set @ TA ) @ C @ D )
                = ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_hausdorff) ).

thf(545,plain,
    ! [TA: $tType] :
      ( ( topological_t2_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ? [C: set @ TA,D: set @ TA] :
              ( ( topolo1751647064n_open @ TA @ C )
              & ( topolo1751647064n_open @ TA @ D )
              & ( member @ TA @ A @ C )
              & ( member @ TA @ B @ D )
              & ( ( inf_inf @ ( set @ TA ) @ C @ D )
                = ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(32,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( topolo503727757_space @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).

thf(259,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( topolo503727757_space @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(39,axiom,
    topological_t0_space @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Ot0__space_34) ).

thf(281,plain,
    topological_t0_space @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(10,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_subset__insertI2) ).

thf(204,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(164,axiom,
    ! [TA: $tType] :
      ( ( bounded_lattice_bot @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
          = ( bot_bot @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_inf__bot__left) ).

thf(641,plain,
    ! [TA: $tType] :
      ( ( bounded_lattice_bot @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
          = ( bot_bot @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(80,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
      = ( ( member @ TA @ A @ C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_insert__subset) ).

thf(391,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
      = ( ( member @ TA @ A @ C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(119,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Int__empty__right) ).

thf(498,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(107,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( topolo1751647064n_open @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_open__empty) ).

thf(466,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( topolo1751647064n_open @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(132,axiom,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_UNIV__I) ).

thf(540,plain,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(86,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
        = ( inf_inf @ ( set @ TA ) @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Int__insert__left__if0) ).

thf(406,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
        = ( inf_inf @ ( set @ TA ) @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(20,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ? [C: set @ TA] :
          ( ( B
            = ( insert @ TA @ A @ C ) )
          & ~ ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_mk__disjoint__insert) ).

thf(230,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ? [C: set @ TA] :
          ( ( B
            = ( insert @ TA @ A @ C ) )
          & ~ ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(139,axiom,
    comple1035589618norder @ b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).

thf(567,plain,
    comple1035589618norder @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(122,axiom,
    ! [TA: $tType] :
      ( ( bounded_lattice_bot @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
          = ( bot_bot @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_inf__bot__right) ).

thf(509,plain,
    ! [TA: $tType] :
      ( ( bounded_lattice_bot @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
          = ( bot_bot @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(160,axiom,
    topolo2117631714pology @ b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_1) ).

thf(631,plain,
    topolo2117631714pology @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(72,axiom,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
      = ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Diff__insert) ).

thf(367,plain,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
      = ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(154,axiom,
    ! [TA: $tType] :
      ( ( topological_t0_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ? [C: set @ TA] :
              ( ( topolo1751647064n_open @ TA @ C )
              & ( ( member @ TA @ A @ C )
               != ( member @ TA @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_t0__space) ).

thf(609,plain,
    ! [TA: $tType] :
      ( ( topological_t0_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ? [C: set @ TA] :
              ( ( topolo1751647064n_open @ TA @ C )
              & ( ( member @ TA @ A @ C )
               != ( member @ TA @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(149,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_subsetI) ).

thf(594,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(159,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( member @ TA @ A @ B )
       => ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
          = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) )
      & ( ~ ( member @ TA @ A @ B )
       => ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
          = ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Int__insert__right) ).

thf(626,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( member @ TA @ A @ B )
       => ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
          = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) )
      & ( ~ ( member @ TA @ A @ B )
       => ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
          = ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(57,axiom,
    topolo503727757_space @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_29) ).

thf(330,plain,
    topolo503727757_space @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(24,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_subset__insertI) ).

thf(240,plain,
    ! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(29,axiom,
    ! [TA: $tType] :
      ( ( bot_bot @ ( set @ TA ) )
      = ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_bot__set__def) ).

thf(251,plain,
    ! [TA: $tType] :
      ( ( bot_bot @ ( set @ TA ) )
      = ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(83,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Int__lower2) ).

thf(399,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(35,axiom,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
      = ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Diff__insert2) ).

thf(267,plain,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
      = ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(97,axiom,
    ( ~ ! [A: set @ b] :
          ( ( ( topolo1751647064n_open @ b @ A )
            & ( member @ b @ ( f @ x0 ) @ A ) )
         => ? [B: set @ a] :
              ( ( topolo1751647064n_open @ a @ B )
              & ( member @ a @ x0 @ B )
              & ! [C: a] :
                  ( ( member @ a @ C @ B )
                 => ( ( ord_less_eq @ b @ ( f @ C ) @ ( f @ x0 ) )
                   => ( member @ b @ ( f @ C ) @ A ) ) ) ) )
   => ~ ( lower_582600101lsc_at @ a @ b @ x0 @ f ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_calculation) ).

thf(438,plain,
    ( ~ ! [A: set @ b] :
          ( ( ( topolo1751647064n_open @ b @ A )
            & ( member @ b @ ( f @ x0 ) @ A ) )
         => ? [B: set @ a] :
              ( ( topolo1751647064n_open @ a @ B )
              & ( member @ a @ x0 @ B )
              & ! [C: a] :
                  ( ( member @ a @ C @ B )
                 => ( ( ord_less_eq @ b @ ( f @ C ) @ ( f @ x0 ) )
                   => ( member @ b @ ( f @ C ) @ A ) ) ) ) )
   => ~ ( lower_582600101lsc_at @ a @ b @ x0 @ f ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(167,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
     => ~ ( member @ TA @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_DiffD2) ).

thf(658,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
     => ~ ( member @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(81,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_Collect__mono) ).

thf(394,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(50,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
       => ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_Diff__mono) ).

thf(306,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
       => ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(129,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ! [B: TA] :
            ~ ( member @ TA @ B @ A ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_all__not__in__conv) ).

thf(531,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ! [B: TA] :
            ~ ( member @ TA @ B @ A ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(12,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ A @ C )
       => ( ( ( insert @ TA @ A @ B )
            = ( insert @ TA @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_insert__ident) ).

thf(209,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ A @ C )
       => ( ( ( insert @ TA @ A @ B )
            = ( insert @ TA @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(156,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
      = ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Int__empty__left) ).

thf(617,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
      = ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(6,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: set @ TA,B: set @ TA,C: TA] :
          ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ( ord_less_eq @ ( filter @ TA ) @ ( topolo507301023within @ TA @ C @ A ) @ ( topolo507301023within @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_at__le) ).

thf(194,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: set @ TA,B: set @ TA,C: TA] :
          ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ( ord_less_eq @ ( filter @ TA ) @ ( topolo507301023within @ TA @ C @ A ) @ ( topolo507301023within @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(127,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Collect__empty__eq) ).

thf(525,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(183,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
      = ( ( member @ TA @ A @ C )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_member__remove) ).

thf(712,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
      = ( ( member @ TA @ A @ C )
        & ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(45,axiom,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Diff__single__insert) ).

thf(295,plain,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(181,axiom,
    ! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
      ( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
        = ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_doubleton__eq__iff) ).

thf(707,plain,
    ! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
      ( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
        = ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(56,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA,D: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ C @ D ) ) )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ D ) )
        & ~ ( member @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_subset__Diff__insert) ).

thf(327,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA,D: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ C @ D ) ) )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ D ) )
        & ~ ( member @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(87,axiom,
    ! [TA: $tType] :
      ( ( topological_t1_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
          = ( ? [C: set @ TA] :
                ( ( topolo1751647064n_open @ TA @ C )
                & ( member @ TA @ A @ C )
                & ~ ( member @ TA @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_separation__t1) ).

thf(409,plain,
    ! [TA: $tType] :
      ( ( topological_t1_space @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
          = ( ? [C: set @ TA] :
                ( ( topolo1751647064n_open @ TA @ C )
                & ( member @ TA @ A @ C )
                & ~ ( member @ TA @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(180,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_subsetD) ).

thf(705,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(40,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA,D: set @ TA] :
          ( ( member @ TA @ A @ B )
         => ( ( topolo1751647064n_open @ TA @ B )
           => ( ( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
                = ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ D @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
             => ( ( topolo507301023within @ TA @ A @ C )
                = ( topolo507301023within @ TA @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_at__within__nhd) ).

thf(282,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA,D: set @ TA] :
          ( ( member @ TA @ A @ B )
         => ( ( topolo1751647064n_open @ TA @ B )
           => ( ( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
                = ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ D @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
             => ( ( topolo507301023within @ TA @ A @ C )
                = ( topolo507301023within @ TA @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(8,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        | ( A
          = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subset__singletonD) ).

thf(199,plain,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        | ( A
          = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(58,axiom,
    bounded_lattice_bot @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__bot_31) ).

thf(331,plain,
    bounded_lattice_bot @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(106,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( ( topolo1751647064n_open @ TA )
        = ( ^ [A: set @ TA] :
            ! [B: TA] :
              ( ( member @ TA @ B @ A )
             => ? [C: set @ TA] :
                  ( ( topolo1751647064n_open @ TA @ C )
                  & ( member @ TA @ B @ C )
                  & ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_open__subopen) ).

thf(463,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( ( topolo1751647064n_open @ TA )
        = ( ^ [A: set @ TA] :
            ! [B: TA] :
              ( ( member @ TA @ B @ A )
             => ? [C: set @ TA] :
                  ( ( topolo1751647064n_open @ TA @ C )
                  & ( member @ TA @ B @ C )
                  & ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(61,axiom,
    topolo2133971006pology @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology_30) ).

thf(338,plain,
    topolo2133971006pology @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(70,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_equalityD2) ).

thf(359,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(146,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
     => ( member @ TA @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_IntD2) ).

thf(585,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
     => ( member @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(73,axiom,
    ! [TA: $tType] :
      ( ( remove @ TA )
      = ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_remove__def) ).

thf(370,plain,
    ! [TA: $tType] :
      ( ( remove @ TA )
      = ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(166,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ A @ C )
       => ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_DiffI) ).

thf(656,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ A @ C )
       => ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(151,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
      = ( ( member @ TA @ A @ B )
        & ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Int__iff) ).

thf(600,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
      = ( ( member @ TA @ A @ B )
        & ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(78,axiom,
    ! [TA: $tType] :
      ( ( topolo2135403230pology @ TA )
     => ( topolo503727757_space @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Ofirst__countable__topology___Topological__Spaces_Otopological__space) ).

thf(386,plain,
    ! [TA: $tType] :
      ( ( topolo2135403230pology @ TA )
     => ( topolo503727757_space @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(53,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_equalityE) ).

thf(314,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(141,axiom,
    ( a2
   != ( f @ x0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).

thf(571,plain,
    ( a2
   != ( f @ x0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(113,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
        = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Int__insert__left__if1) ).

thf(482,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
        = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(171,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Diff__empty) ).

thf(671,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(175,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ~ ( member @ TA @ C @ B ) )
     => ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Int__emptyI) ).

thf(688,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ~ ( member @ TA @ C @ B ) )
     => ( ( inf_inf @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(16,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        | ( A
          = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subset__singleton__iff) ).

thf(218,plain,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        | ( A
          = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(71,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_equalityD1) ).

thf(363,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(135,axiom,
    ! [TA: $tType] :
      ( ( topolo47006728_space @ TA )
     => ( topolo406746546ounded @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_totally__bounded__empty) ).

thf(556,plain,
    ! [TA: $tType] :
      ( ( topolo47006728_space @ TA )
     => ( topolo406746546ounded @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(178,axiom,
    ! [TA: $tType] :
      ( ( inf_inf @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Int__commute) ).

thf(699,plain,
    ! [TA: $tType] :
      ( ( inf_inf @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(49,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
       => ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_insert__subsetI) ).

thf(304,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
       => ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(3,axiom,
    ! [TA: $tType] : ( bounded_lattice_bot @ ( filter @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Filter_Ofilter___Lattices_Obounded__lattice__bot_45) ).

thf(186,plain,
    ! [TA: $tType] : ( bounded_lattice_bot @ ( filter @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(161,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Int__insert__right__if1) ).

thf(632,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(84,axiom,
    ! [TA: $tType] :
      ( ( topolo890362671_space @ TA )
     => ! [A: TA] :
          ~ ( topolo1751647064n_open @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_not__open__singleton) ).

thf(401,plain,
    ! [TA: $tType] :
      ( ( topolo890362671_space @ TA )
     => ! [A: TA] :
          ~ ( topolo1751647064n_open @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(140,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
      = ( inf_inf @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Int__left__absorb) ).

thf(568,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
      = ( inf_inf @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(27,axiom,
    ! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__bot_19) ).

thf(246,plain,
    ! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(95,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_subset__emptyI) ).

thf(433,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(77,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Collect__mono__iff) ).

thf(383,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(174,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( A
        = ( bot_bot @ ( set @ TA ) ) )
     => ~ ( member @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_equals0D) ).

thf(684,plain,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( A
        = ( bot_bot @ ( set @ TA ) ) )
     => ~ ( member @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(65,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).

thf(346,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(43,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
        = ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_insert__Diff1) ).

thf(290,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
        = ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(75,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_insertI1) ).

thf(378,plain,
    ! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(14,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_insertI2) ).

thf(214,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(42,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_subset__insert) ).

thf(287,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(157,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Int__insert__right__if0) ).

thf(620,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(100,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( member @ TA @ A @ C )
       => ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_IntI) ).

thf(447,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( member @ TA @ A @ C )
       => ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(37,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
      = ( insert @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_insert__Diff__single) ).

thf(273,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
      = ( insert @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(74,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ~ ( member @ TA @ A @ B )
       => ( A = C ) )
     => ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_insertCI) ).

thf(373,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ~ ( member @ TA @ A @ B )
       => ( A = C ) )
     => ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(152,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ B )
     != ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_insert__not__empty) ).

thf(603,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ B )
     != ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(138,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
      = ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Int__Diff__disjoint) ).

thf(564,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
      = ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(63,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
     => ( ( A != B )
       => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_insertE) ).

thf(341,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
     => ( ( A != B )
       => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(121,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
     => ~ ( ( member @ TA @ A @ B )
         => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_DiffE) ).

thf(506,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
     => ~ ( ( member @ TA @ A @ B )
         => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(110,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_emptyE) ).

thf(474,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(170,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( A
       != ( bot_bot @ ( set @ TA ) ) )
     => ( ! [B: TA,C: TA] :
            ( ( member @ TA @ B @ A )
           => ( ( member @ TA @ C @ A )
             => ( B = C ) ) )
       => ( is_singleton @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_is__singletonI_H) ).

thf(664,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( A
       != ( bot_bot @ ( set @ TA ) ) )
     => ( ! [B: TA,C: TA] :
            ( ( member @ TA @ B @ A )
           => ( ( member @ TA @ C @ A )
             => ( B = C ) ) )
       => ( is_singleton @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(162,axiom,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) )
      = ( ~ ( member @ TA @ B @ A )
        & ( ( bot_bot @ ( set @ TA ) )
          = ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_disjoint__insert_I2_J) ).

thf(635,plain,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) )
      = ( ~ ( member @ TA @ B @ A )
        & ( ( bot_bot @ ( set @ TA ) )
          = ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(177,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
      = ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Int__left__commute) ).

thf(696,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
      = ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(23,axiom,
    topolo2135403230pology @ a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_2) ).

thf(239,plain,
    topolo2135403230pology @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(25,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Diff__subset) ).

thf(242,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(59,axiom,
    ! [TA: $tType] :
      ( ( topolo2117631714pology @ TA )
     => ( topological_t1_space @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot1__space) ).

thf(332,plain,
    ! [TA: $tType] :
      ( ( topolo2117631714pology @ TA )
     => ( topological_t1_space @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(93,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_subset__iff) ).

thf(427,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(128,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
      = ( inf_inf @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Diff__Diff__Int) ).

thf(528,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
      = ( inf_inf @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(165,axiom,
    ( ( ( f @ x0 )
     != a2 )
   => ? [A: set @ b,B: set @ b] :
        ( ( topolo1751647064n_open @ b @ A )
        & ( topolo1751647064n_open @ b @ B )
        & ( member @ b @ ( f @ x0 ) @ A )
        & ( member @ b @ a2 @ B )
        & ( ( inf_inf @ ( set @ b ) @ A @ B )
          = ( bot_bot @ ( set @ b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).

thf(644,plain,
    ( ( ( f @ x0 )
     != a2 )
   => ? [A: set @ b,B: set @ b] :
        ( ( topolo1751647064n_open @ b @ A )
        & ( topolo1751647064n_open @ b @ B )
        & ( member @ b @ ( f @ x0 ) @ A )
        & ( member @ b @ a2 @ B )
        & ( ( inf_inf @ ( set @ b ) @ A @ B )
          = ( bot_bot @ ( set @ b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(98,axiom,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_empty__subsetI) ).

thf(442,plain,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(120,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( member @ TA @ A @ B )
       => ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
          = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) )
      & ( ~ ( member @ TA @ A @ B )
       => ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
          = ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Int__insert__left) ).

thf(501,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( member @ TA @ A @ B )
       => ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
          = ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) )
      & ( ~ ( member @ TA @ A @ B )
       => ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
          = ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(116,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
     => ( member @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_IntD1) ).

thf(491,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
     => ( member @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(30,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
      = ( insert @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_insert__absorb2) ).

thf(254,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
      = ( insert @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(19,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
      = ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insert__commute) ).

thf(227,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
      = ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(118,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Int__lower1) ).

thf(496,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(103,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subset__empty) ).

thf(454,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(719,plain,
    $false,
    inference(e,[status(thm)],[715,479,468,234,352,582,276,308,449,614,677,202,597,185,417,301,257,587,702,344,196,542,460,638,606,261,216,591,321,623,485,574,353,397,221,293,660,206,452,248,380,512,270,534,334,349,561,297,693,435,522,493,710,324,285,224,519,403,188,388,356,420,471,488,339,537,476,212,515,457,237,244,311,558,674,662,298,412,425,430,264,444,423,191,577,579,545,259,281,204,641,391,498,466,540,406,230,567,509,631,367,609,594,626,330,240,251,399,267,438,658,394,306,531,209,617,194,525,712,295,707,327,409,705,282,199,331,463,338,359,585,370,656,600,386,314,571,482,671,688,218,363,556,699,304,186,632,401,568,246,433,383,684,346,290,378,214,287,620,447,273,373,603,564,341,506,474,664,635,696,239,242,332,427,528,644,442,501,491,254,227,496,454]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : ITP115^2 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat May 18 17:00:24 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.98/1.01  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.13/1.41  % [INFO] 	 Parsing done (394ms). 
% 2.13/1.42  % [INFO] 	 Running in sequential loop mode. 
% 3.41/1.80  % [INFO] 	 eprover registered as external prover. 
% 3.41/1.80  % [INFO] 	 cvc4 registered as external prover. 
% 3.41/1.81  % [INFO] 	 Scanning for conjecture ... 
% 3.66/1.95  % [INFO] 	 Found a conjecture (or negated_conjecture) and 357 axioms. Running axiom selection ... 
% 4.27/2.09  % [INFO] 	 Axiom selection finished. Selected 182 axioms (removed 175 axioms). 
% 4.95/2.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.95/2.39  % [INFO] 	 Type checking passed. 
% 5.16/2.39  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 26.99/13.00  % External prover 'e' found a proof!
% 26.99/13.00  % [INFO] 	 Killing All external provers ... 
% 26.99/13.00  % Time passed: 12483ms (effective reasoning time: 11569ms)
% 26.99/13.00  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 26.99/13.00  % Axioms used in derivation (182): fact_4_inf__bot__left, tcon_Set_Oset___Lattices_Obounded__lattice__bot_19, subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot2__space, tcon_HOL_Obool___Topological__Spaces_Ot2__space_32, fact_217_Diff__mono, fact_97_is__singletonI, fact_200_Diff__eq__empty__iff, subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot1__space, fact_240_equalityD2, tfree_0, fact_41_Int__left__absorb, subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Otopological__space, fact_85_Int__insert__left__if1, fact_233_member__remove, fact_72_insert__disjoint_I2_J, fact_140_insert__Diff, fact_146_is__singletonE, fact_204_insert__mono, fact_95_disjoint__insert_I1_J, fact_194_empty__subsetI, fact_71_insert__disjoint_I1_J, fact_87_Int__insert__right__if0, fact_188_open__delete, fact_201_subset__insertI2, fact_225_subset__insert__iff, fact_202_subset__insertI, fact_239_equalityD1, fact_107_insert__eq__iff, fact_65_totally__bounded__empty, fact_155_Diff__Int2, fact_219_subset__singletonD, fact_214_topological__space__class_OopenI, fact_59_Int__empty__left, fact_109_insert__commute, fact_158_Diff__Int__distrib2, fact_157_Diff__Int__distrib, fact_79_Diff__iff, fact_212_first__countable__basis, tcon_fun___Topological__Spaces_Otopological__space, fact_224_Diff__single__insert, fact_106_insert__absorb, fact_186_not__open__singleton, fact_154_Int__Diff, fact_232_subset__antisym, fact_195_subset__empty, fact_229_remove__def, fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062, fact_58_Int__empty__right, fact_103_insertI2, fact_93_insert__Diff1, fact_152_Int__insert__left, fact_23_ex__in__conv, tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology_30, fact_92_Diff__insert0, fact_94_disjoint__insert_I2_J, fact_98_DiffE, fact_6_hausdorff, fact_43_Int__absorb, fact_80_Diff__idemp, fact_46_Collect__mem__eq, fact_22_bot__set__def, fact_218_totally__bounded__subset, fact_248_at__discrete, fact_235_in__mono, fact_244_subset__trans, fact_76_insert__iff, fact_42_Int__commute, fact_54_separation__t0, fact_57_disjoint__iff__not__equal, fact_247_at__le, fact_138_Diff__insert__absorb, fact_189_Int__Diff__disjoint, fact_16_all__not__in__conv, fact_49_IntD2, fact_88_Int__insert__right__if1, fact_2_open__Int, fact_53_separation__t1, fact_111_mk__disjoint__insert, fact_63_calculation, fact_83_singletonI, fact_86_insert__inter__insert, fact_207_Int__absorb2, fact_208_Int__absorb1, fact_149_doubleton__eq__iff, fact_150_insert__not__empty, fact_151_singleton__inject, fact_199_singleton__insert__inj__eq_H, fact_234_at__within__empty, fact_243_Collect__mono, fact_17_empty__iff, fact_66_Collect__empty__eq__bot, fact_50_IntD1, subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot0__space, fact_51_IntE, fact_108_insert__Diff__if, fact_237_equalityE, fact_196_insert__subset, fact_40_Int__left__commute, tfree_2, fact_45_mem__Collect__eq, fact_56_t0__space, tcon_HOL_Obool___Topological__Spaces_Ot1__space_33, fact_190_is__singleton__the__elem, fact_5_inf__bot__right, fact_67_bot__empty__eq, fact_61_Int__emptyI, fact_209_Int__lower2, fact_141_Diff__insert, fact_187_Diff__triv, subcl_Topological__Spaces_Ofirst__countable__topology___Topological__Spaces_Otopological__space, fact_221_subset__Diff__insert, fact_210_Int__lower1, fact_55_t1__space, fact_26_emptyE, fact_9_Int__iff, fact_105_insert__ident, fact_47_Collect__cong, fact_24_equals0I, fact_191_ball__insert, fact_231_subsetI, fact_14_empty__Collect__eq, fact_206_Int__greatest, fact_211_Int__mono, fact_15_Collect__empty__eq, fact_147_singletonD, fact_78_DiffI, fact_197_Int__subset__iff, fact_44_Int__assoc, fact_25_equals0D, fact_148_singleton__iff, fact_84_Int__insert__left__if0, fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062, fact_156_Diff__Diff__Int, fact_236_subsetD, fact_75_insertCI, fact_102_insertI1, tfree_1, fact_69_is__singletonI_H, fact_213_open__subopen, fact_241_subset__iff, fact_230_at__within__nhd, fact_216_Diff__subset, fact_100_DiffD2, fact_7_separation__t2, fact_242_subset__refl, fact_215_double__diff, fact_145_is__singleton__def, fact_249_insert__subsetI, tcon_HOL_Obool___Topological__Spaces_Ot0__space_34, fact_101_insertE, fact_153_Int__insert__right, fact_89_Diff__empty, fact_8_IntI, tcon_HOL_Obool___Lattices_Obounded__lattice__bot_31, fact_198_singleton__insert__inj__eq, fact_139_Diff__insert2, fact_104_Set_Oset__insert, fact_77_insert__absorb2, fact_3_open__empty, fact_205_Int__Collect__mono, fact_254_UNIV__I, fact_91_Diff__cancel, fact_99_DiffD1, fact_96_insert__Diff__single, fact_60_disjoint__iff, conj_0, fact_245_set__eq__subset, fact_192_the__elem__eq, subcl_Complete__Lattices_Ocomplete__linorder___Lattices_Obounded__lattice__bot, fact_220_subset__singleton__iff, fact_52_open__discrete, fact_64_Set_Ois__empty__def, fact_70_Diff__disjoint, tcon_HOL_Obool___Topological__Spaces_Otopological__space_29, fact_251_at__eq__bot__iff, fact_21__092_060open_062_092_060forall_062S_O_Aopen_AS_A_092_060and_062_Af_Ax0_A_092_060in_062_AS_A_092_060longrightarrow_062_A_I_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062x_H_092_060in_062T_O_Af_Ax_H_A_092_060le_062_Af_Ax0_A_092_060longrightarrow_062_Af_Ax_H_A_092_060in_062_AS_J_J_092_060close_062, tcon_Filter_Ofilter___Lattices_Obounded__lattice__bot_45, fact_250_subset__emptyI, fact_238_subset__eq, fact_203_subset__insert, fact_246_Collect__mono__iff, fact_90_empty__Diff
% 26.99/13.00  % No. of inferences in proof: 368
% 26.99/13.00  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12483 ms resp. 11569 ms w/o parsing
% 27.85/13.12  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.85/13.12  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------