TSTP Solution File: ITP116^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP116^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 22:23:04 EDT 2024

% Result   : Theorem 41.91s 23.57s
% Output   : Refutation 42.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  463
% Syntax   : Number of formulae    :  862 ( 274 unt;  66 typ;   0 def)
%            Number of atoms       : 2475 ( 530 equ;   2 cnn)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives : 9959 (  34   ~;   3   |; 190   &;9038   @)
%                                         (   0 <=>; 694  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  490 ( 490   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   69 (  65 usr;   8 con; 0-5 aty)
%            Number of variables   : 2373 ( 241   ^2063   !;   6   ?;2373   :)
%                                         (  63  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(real_type,type,
    real: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(int_type,type,
    int: $tType ).

thf(n_type,type,
    n: $tType ).

thf(real_V2090557954_space_type,type,
    real_V2090557954_space: 
      !>[TA: $tType] : $o ).

thf(ordere890947078_space_type,type,
    ordere890947078_space: 
      !>[TA: $tType] : $o ).

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

thf(plus_type,type,
    plus: 
      !>[TA: $tType] : $o ).

thf(zero_type,type,
    zero: 
      !>[TA: $tType] : $o ).

thf(minus_type,type,
    minus: 
      !>[TA: $tType] : $o ).

thf(ring_char_0_type,type,
    ring_char_0: 
      !>[TA: $tType] : $o ).

thf(group_add_type,type,
    group_add: 
      !>[TA: $tType] : $o ).

thf(lattice_type,type,
    lattice: 
      !>[TA: $tType] : $o ).

thf(finite_finite_type,type,
    finite_finite: 
      !>[TA: $tType] : $o ).

thf(monoid_add_type,type,
    monoid_add: 
      !>[TA: $tType] : $o ).

thf(countable_type,type,
    countable: 
      !>[TA: $tType] : $o ).

thf(ab_group_add_type,type,
    ab_group_add: 
      !>[TA: $tType] : $o ).

thf(semigroup_add_type,type,
    semigroup_add: 
      !>[TA: $tType] : $o ).

thf(comm_monoid_add_type,type,
    comm_monoid_add: 
      !>[TA: $tType] : $o ).

thf(ab_semigroup_add_type,type,
    ab_semigroup_add: 
      !>[TA: $tType] : $o ).

thf(comm_monoid_diff_type,type,
    comm_monoid_diff: 
      !>[TA: $tType] : $o ).

thf(semilattice_inf_type,type,
    semilattice_inf: 
      !>[TA: $tType] : $o ).

thf(cancel_semigroup_add_type,type,
    cancel_semigroup_add: 
      !>[TA: $tType] : $o ).

thf(ordered_ab_group_add_type,type,
    ordered_ab_group_add: 
      !>[TA: $tType] : $o ).

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

thf(cancel1352612707id_add_type,type,
    cancel1352612707id_add: 
      !>[TA: $tType] : $o ).

thf(topolo1314133330id_add_type,type,
    topolo1314133330id_add: 
      !>[TA: $tType] : $o ).

thf(cancel146912293up_add_type,type,
    cancel146912293up_add: 
      !>[TA: $tType] : $o ).

thf(linord219039673up_add_type,type,
    linord219039673up_add: 
      !>[TA: $tType] : $o ).

thf(real_V1076094709vector_type,type,
    real_V1076094709vector: 
      !>[TA: $tType] : $o ).

thf(euclid925273238_space_type,type,
    euclid925273238_space: 
      !>[TA: $tType] : $o ).

thf(ordere779506340up_add_type,type,
    ordere779506340up_add: 
      !>[TA: $tType] : $o ).

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

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

thf(canoni770627133id_add_type,type,
    canoni770627133id_add: 
      !>[TA: $tType] : $o ).

thf(real_V55928688vector_type,type,
    real_V55928688vector: 
      !>[TA: $tType] : $o ).

thf(ordere236663937imp_le_type,type,
    ordere236663937imp_le: 
      !>[TA: $tType] : $o ).

thf(elemen1026692323pology_type,type,
    elemen1026692323pology: 
      !>[TA: $tType] : $o ).

thf(ordere516151231imp_le_type,type,
    ordere516151231imp_le: 
      !>[TA: $tType] : $o ).

thf(borel_is_borel_type,type,
    borel_is_borel: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( sigma_measure @ TB ) > $o ) ).

thf(borel_1404511681_borel_type,type,
    borel_1404511681_borel: 
      !>[TA: $tType] : ( sigma_measure @ TA ) ).

thf(complete_completion_type,type,
    complete_completion: 
      !>[TA: $tType] : ( ( sigma_measure @ TA ) > ( sigma_measure @ TA ) ) ).

thf(complete_main_part_type,type,
    complete_main_part: 
      !>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ TA ) > ( set @ TA ) ) ).

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

thf(plus_plus_type,type,
    plus_plus: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(zero_zero_type,type,
    zero_zero: 
      !>[TA: $tType] : TA ).

thf(if_type,type,
    if: 
      !>[TA: $tType] : ( $o > TA > TA > TA ) ).

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

thf(lebesgue_lborel_type,type,
    lebesgue_lborel: 
      !>[TA: $tType] : ( sigma_measure @ TA ) ).

thf(minkow1937162798nt_vec_type,type,
    minkow1937162798nt_vec: 
      !>[TA: $tType,TB: $tType] : ( ( finite_Cartesian_vec @ int @ TB ) > ( finite_Cartesian_vec @ TA @ TB ) ) ).

thf(ord_Least_type,type,
    ord_Least: 
      !>[TA: $tType] : ( ( TA > $o ) > TA ) ).

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

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

thf(image_type,type,
    image: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).

thf(vimage_type,type,
    vimage: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TA ) > ( set @ TB ) ) ).

thf(sigma_measurable_type,type,
    sigma_measurable: 
      !>[TA: $tType,TB: $tType] : ( ( sigma_measure @ TB ) > ( sigma_measure @ TA ) > ( set @ ( TB > TA ) ) ) ).

thf(sigma_restrict_space_type,type,
    sigma_restrict_space: 
      !>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ TA ) > ( sigma_measure @ TA ) ) ).

thf(sigma_sets_type,type,
    sigma_sets: 
      !>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ ( set @ TA ) ) ) ).

thf(sigma_space_type,type,
    sigma_space: 
      !>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ TA ) ) ).

thf(sigma_vimage_algebra_type,type,
    sigma_vimage_algebra: 
      !>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > ( sigma_measure @ TA ) > ( sigma_measure @ TB ) ) ).

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

thf(r_type,type,
    r: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).

thf(s_type,type,
    s: set @ ( finite_Cartesian_vec @ real @ n ) ).

thf(t_type,type,
    t: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).

thf(t2_type,type,
    t2: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).

thf(a_type,type,
    a: finite_Cartesian_vec @ int @ n ).

thf(286,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: sigma_measure @ TA,D: sigma_measure @ TA] :
      ( ( A = B )
     => ( ( ( sigma_sets @ TA @ C )
          = ( sigma_sets @ TA @ D ) )
       => ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ C @ A ) )
          = ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_restrict__space__sets__cong) ).

thf(1036,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: sigma_measure @ TA,D: sigma_measure @ TA] :
      ( ( A = B )
     => ( ( ( sigma_sets @ TA @ C )
          = ( sigma_sets @ TA @ D ) )
       => ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ C @ A ) )
          = ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(122,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordere516151231imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_75) ).

thf(629,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordere516151231imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(282,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( euclid925273238_space @ TB )
     => ! [A: set @ TB,B: TB > TA,C: TB > TA,D: sigma_measure @ TA] :
          ( ! [E: TB] :
              ( ( member @ TB @ E @ A )
             => ( ( B @ E )
                = ( C @ E ) ) )
         => ( ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ D ) )
            = ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_measurable__lebesgue__cong) ).

thf(1024,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( euclid925273238_space @ TB )
     => ! [A: set @ TB,B: TB > TA,C: TB > TA,D: sigma_measure @ TA] :
          ( ! [E: TB] :
              ( ( member @ TB @ E @ A )
             => ( ( B @ E )
                = ( C @ E ) ) )
         => ( ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ D ) )
            = ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(51,axiom,
    cancel1352612707id_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_16) ).

thf(479,plain,
    cancel1352612707id_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(121,axiom,
    topolo2117631714pology @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Olinorder__topology_52) ).

thf(628,plain,
    topolo2117631714pology @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(232,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
      = ( ( member @ TA @ A @ B )
        & ( C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Int__Collect) ).

thf(893,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
      ( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
      = ( ( member @ TA @ A @ B )
        & ( C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(303,axiom,
    ! [TA: $tType,A: sigma_measure @ TA] : ( member @ ( set @ TA ) @ ( sigma_space @ TA @ A ) @ ( sigma_sets @ TA @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_sets_Otop) ).

thf(1083,plain,
    ! [TA: $tType,A: sigma_measure @ TA] : ( member @ ( set @ TA ) @ ( sigma_space @ TA @ A ) @ ( sigma_sets @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(249,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ B ) ) )
     => ( member @ ( set @ TA ) @ ( complete_main_part @ TA @ B @ A ) @ ( sigma_sets @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_main__part__sets) ).

thf(941,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ B ) ) )
     => ( member @ ( set @ TA ) @ ( complete_main_part @ TA @ B @ A ) @ ( sigma_sets @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(346,axiom,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > TA,C: sigma_measure @ TA] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ ( sigma_space @ TB @ A ) )
         => ( member @ TA @ ( B @ D ) @ ( sigma_space @ TA @ C ) ) )
     => ( ! [D: set @ TA] :
            ( ( member @ ( set @ TA ) @ D @ ( sigma_sets @ TA @ C ) )
           => ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ B @ D ) @ ( sigma_space @ TB @ A ) ) @ ( sigma_sets @ TB @ A ) ) )
       => ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_measurableI) ).

thf(1179,plain,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > TA,C: sigma_measure @ TA] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ ( sigma_space @ TB @ A ) )
         => ( member @ TA @ ( B @ D ) @ ( sigma_space @ TA @ C ) ) )
     => ( ! [D: set @ TA] :
            ( ( member @ ( set @ TA ) @ D @ ( sigma_sets @ TA @ C ) )
           => ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ B @ D ) @ ( sigma_space @ TB @ A ) ) @ ( sigma_sets @ TB @ A ) ) )
       => ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(180,axiom,
    real_V2090557954_space @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_2) ).

thf(777,plain,
    real_V2090557954_space @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(342,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(1168,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(175,axiom,
    ! [TA: $tType] :
      ( ( monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_add_Oright__neutral) ).

thf(760,plain,
    ! [TA: $tType] :
      ( ( monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(365,axiom,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_add__diff__cancel__right_H) ).

thf(1237,plain,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(212,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_235_subset__antisym) ).

thf(846,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)],[212]) ).

thf(351,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordere890947078_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space) ).

thf(1200,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordere890947078_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(355,axiom,
    topological_t2_space @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Ot2__space_58) ).

thf(1211,plain,
    topological_t2_space @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(98,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( image @ TA @ TA
        @ ^ [B: TA] : B
        @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_image__ident) ).

thf(582,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( image @ TA @ TA
        @ ^ [B: TA] : B
        @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(275,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_243_Int__subset__iff) ).

thf(1005,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)],[275]) ).

thf(162,axiom,
    ! [TA: $tType] :
      ( ( monoid_add @ TA )
     => ( monoid_add @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Omonoid__add_34) ).

thf(730,plain,
    ! [TA: $tType] :
      ( ( monoid_add @ TA )
     => ( monoid_add @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(298,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_diff__add__eq__diff__diff__swap) ).

thf(1068,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(270,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA,B: sigma_measure @ TB] :
          ( member @ ( TB > TA )
          @ ^ [C: TB] : A
          @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_borel__measurable__const) ).

thf(994,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA,B: sigma_measure @ TB] :
          ( member @ ( TB > TA )
          @ ^ [C: TB] : A
          @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(166,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_193_DiffD1) ).

thf(741,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)],[166]) ).

thf(36,axiom,
    ab_semigroup_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_20) ).

thf(449,plain,
    ab_semigroup_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(288,axiom,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
          = ( minus_minus @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_add__diff__cancel__right) ).

thf(1041,plain,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
          = ( minus_minus @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(11,axiom,
    comm_monoid_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocomm__monoid__add) ).

thf(408,plain,
    comm_monoid_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(264,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_double__add__le__zero__iff__single__add__le__zero) ).

thf(977,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(225,axiom,
    lattice @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Olattice_67) ).

thf(878,plain,
    lattice @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(67,axiom,
    ! [A: nat] :
      ( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_minus__nat_Odiff__0) ).

thf(511,plain,
    ! [A: nat] :
      ( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(113,axiom,
    ordere779506340up_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add) ).

thf(614,plain,
    ordere779506340up_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(142,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA] :
      ( ( ( sigma_sets @ TA @ A )
        = ( sigma_sets @ TA @ B ) )
     => ( member @ ( TA > TA )
        @ ^ [C: TA] : C
        @ ( sigma_measurable @ TA @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_measurable__ident__sets) ).

thf(677,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA] :
      ( ( ( sigma_sets @ TA @ A )
        = ( sigma_sets @ TA @ B ) )
     => ( member @ ( TA > TA )
        @ ^ [C: TA] : C
        @ ( sigma_measurable @ TA @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(77,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_inf__left__commute) ).

thf(533,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(83,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
          = ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_inf_Oassoc) ).

thf(550,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
          = ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(62,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_diff__zero) ).

thf(500,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(340,axiom,
    ! [TA: $tType] :
      ( ( semigroup_add @ TA )
     => ( semigroup_add @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Osemigroup__add_32) ).

thf(1164,plain,
    ! [TA: $tType] :
      ( ( semigroup_add @ TA )
     => ( semigroup_add @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(47,axiom,
    ordere779506340up_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_13) ).

thf(472,plain,
    ordere779506340up_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(364,axiom,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( A = B )
            & ( C = D ) )
         => ( ( plus_plus @ TA @ A @ C )
            = ( plus_plus @ TA @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__mono__thms__linordered__semiring_I4_J) ).

thf(1233,plain,
    ! [TA: $tType] :
      ( ( ordere779506340up_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( A = B )
            & ( C = D ) )
         => ( ( plus_plus @ TA @ A @ C )
            = ( plus_plus @ TA @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(197,axiom,
    cancel146912293up_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_55) ).

thf(814,plain,
    cancel146912293up_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(374,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: TA > $o] :
      ( ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
              & ( B @ C ) ) )
        @ ( sigma_sets @ TA @ A ) )
     => ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
              & ~ ( B @ C ) ) )
        @ ( sigma_sets @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_sets_Osets__Collect__neg) ).

thf(1260,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: TA > $o] :
      ( ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
              & ( B @ C ) ) )
        @ ( sigma_sets @ TA @ A ) )
     => ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [C: TA] :
              ( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
              & ~ ( B @ C ) ) )
        @ ( sigma_sets @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(251,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: sigma_measure @ TA,C: sigma_measure @ TB] :
      ( ( member @ TA @ A @ ( sigma_space @ TA @ B ) )
     => ( member @ ( TB > TA )
        @ ^ [D: TB] : A
        @ ( sigma_measurable @ TB @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_measurable__const) ).

thf(945,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: sigma_measure @ TA,C: sigma_measure @ TB] :
      ( ( member @ TA @ A @ ( sigma_space @ TA @ B ) )
     => ( member @ ( TB > TA )
        @ ^ [D: TB] : A
        @ ( sigma_measurable @ TB @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(296,axiom,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: set @ TA] : ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_sets__lebesgue__on__refl) ).

thf(1063,plain,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: set @ TA] : ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(139,axiom,
    ordere236663937imp_le @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_50) ).

thf(670,plain,
    ordere236663937imp_le @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(169,axiom,
    semigroup_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Osemigroup__add_64) ).

thf(747,plain,
    semigroup_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(240,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__le__same__cancel2) ).

thf(913,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(323,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ( collect @ TB
        @ ^ [D: TB] :
            ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
            & ( C @ D ) ) )
      = ( image @ TA @ TB @ A
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( member @ TA @ D @ B )
              & ( C @ ( A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Compr__image__eq) ).

thf(1127,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ( collect @ TB
        @ ^ [D: TB] :
            ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
            & ( C @ D ) ) )
      = ( image @ TA @ TB @ A
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( member @ TA @ D @ B )
              & ( C @ ( A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(154,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
      ( ( member @ TA @ A @ B )
     => ( ( C
          = ( D @ A ) )
       => ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_rev__image__eqI) ).

thf(709,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
      ( ( member @ TA @ A @ B )
     => ( ( C
          = ( D @ A ) )
       => ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(20,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_diff__0__right) ).

thf(417,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(29,axiom,
    ! [A: nat] :
      ( ( minus_minus @ nat @ A @ A )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_diff__self__eq__0) ).

thf(436,plain,
    ! [A: nat] :
      ( ( minus_minus @ nat @ A @ A )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(376,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o] :
      ( ( vimage @ TA @ TB @ A @ ( collect @ TB @ B ) )
      = ( collect @ TA
        @ ^ [C: TA] : ( B @ ( A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_vimage__Collect__eq) ).

thf(1265,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o] :
      ( ( vimage @ TA @ TB @ A @ ( collect @ TB @ B ) )
      = ( collect @ TA
        @ ^ [C: TA] : ( B @ ( A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(131,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
     => ( member @ TA @ ( B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_vimageE) ).

thf(651,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
     => ( member @ TA @ ( B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(309,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_comm__monoid__add__class_Oadd__0) ).

thf(1095,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(7,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).

thf(404,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(64,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ A @ A )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_diff__self) ).

thf(504,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ A @ A )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(398,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(1323,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(171,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_189_DiffI) ).

thf(751,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)],[171]) ).

thf(349,axiom,
    ! [TA: $tType] :
      ( ( plus @ TA )
     => ! [A: TA,B: set @ TA,C: TA,D: set @ TA] :
          ( ( member @ TA @ A @ B )
         => ( ( member @ TA @ C @ D )
           => ( member @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_set__plus__intro) ).

thf(1191,plain,
    ! [TA: $tType] :
      ( ( plus @ TA )
     => ! [A: TA,B: set @ TA,C: TA,D: set @ TA] :
          ( ( member @ TA @ A @ B )
         => ( ( member @ TA @ C @ D )
           => ( member @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(325,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: set @ TB,B: TB > TA] :
          ( ( member @ ( TB > TA )
            @ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ A ) @ ( B @ C ) @ ( zero_zero @ TA ) )
            @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
         => ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_borel__measurable__if__D) ).

thf(1132,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: set @ TB,B: TB > TA] :
          ( ( member @ ( TB > TA )
            @ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ A ) @ ( B @ C ) @ ( zero_zero @ TA ) )
            @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
         => ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(293,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TA )
        & ( lattice @ TA )
        & ( topolo2117631714pology @ TA ) )
     => ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
         => ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
           => ( member @ ( TB > TA )
              @ ^ [D: TB] : ( inf_inf @ TA @ ( C @ D ) @ ( A @ D ) )
              @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_borel__measurable__inf) ).

thf(1055,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TA )
        & ( lattice @ TA )
        & ( topolo2117631714pology @ TA ) )
     => ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
         => ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
           => ( member @ ( TB > TA )
              @ ^ [D: TB] : ( inf_inf @ TA @ ( C @ D ) @ ( A @ D ) )
              @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(159,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( zero_zero @ TA )
            = ( plus_plus @ TA @ A @ B ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_zero__eq__add__iff__both__eq__0) ).

thf(724,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( zero_zero @ TA )
            = ( plus_plus @ TA @ A @ B ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(87,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
          = ( inf_inf @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_inf__right__idem) ).

thf(559,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
          = ( inf_inf @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(305,axiom,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: TA > $o] :
          ( ( member @ ( set @ TA )
            @ ( collect @ TA
              @ ^ [B: TA] :
                  ( ( member @ TA @ B @ ( sigma_space @ TA @ ( borel_1404511681_borel @ TA ) ) )
                  & ( A @ B ) ) )
            @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
         => ( member @ ( set @ TA )
            @ ( collect @ TA
              @ ^ [B: TA] :
                  ( ( member @ TA @ B @ ( sigma_space @ TA @ ( lebesgue_lborel @ TA ) ) )
                  & ( A @ B ) ) )
            @ ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_lborelD__Collect) ).

thf(1087,plain,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: TA > $o] :
          ( ( member @ ( set @ TA )
            @ ( collect @ TA
              @ ^ [B: TA] :
                  ( ( member @ TA @ B @ ( sigma_space @ TA @ ( borel_1404511681_borel @ TA ) ) )
                  & ( A @ B ) ) )
            @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
         => ( member @ ( set @ TA )
            @ ( collect @ TA
              @ ^ [B: TA] :
                  ( ( member @ TA @ B @ ( sigma_space @ TA @ ( lebesgue_lborel @ TA ) ) )
                  & ( A @ B ) ) )
            @ ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(22,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
     => ( A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_inf1D1) ).

thf(421,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
     => ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(261,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( countable @ TB )
        & ( finite_finite @ TA ) )
     => ( countable @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_94) ).

thf(969,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( countable @ TB )
        & ( finite_finite @ TA ) )
     => ( countable @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(179,axiom,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: sigma_measure @ TB,C: sigma_measure @ TA,D: sigma_measure @ TA,E: TB > TA,F: TB > TA] :
      ( ( A = B )
     => ( ( C = D )
       => ( ! [G: TB] :
              ( ( member @ TB @ G @ ( sigma_space @ TB @ A ) )
             => ( ( E @ G )
                = ( F @ G ) ) )
         => ( ( member @ ( TB > TA ) @ E @ ( sigma_measurable @ TB @ TA @ A @ C ) )
            = ( member @ ( TB > TA ) @ F @ ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_measurable__cong__simp) ).

thf(770,plain,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: sigma_measure @ TB,C: sigma_measure @ TA,D: sigma_measure @ TA,E: TB > TA,F: TB > TA] :
      ( ( A = B )
     => ( ( C = D )
       => ( ! [G: TB] :
              ( ( member @ TB @ G @ ( sigma_space @ TB @ A ) )
             => ( ( E @ G )
                = ( F @ G ) ) )
         => ( ( member @ ( TB > TA ) @ E @ ( sigma_measurable @ TB @ TA @ A @ C ) )
            = ( member @ ( TB > TA ) @ F @ ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(317,axiom,
    ab_group_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__group__add_65) ).

thf(1115,plain,
    ab_group_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(35,axiom,
    minus @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ominus_26) ).

thf(448,plain,
    minus @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(311,axiom,
    group_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add_68) ).

thf(1100,plain,
    group_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(227,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
          = ( A = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_add__right__cancel) ).

thf(881,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
          = ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(19,axiom,
    lattice @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Lattices_Olattice_6) ).

thf(416,plain,
    lattice @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(58,axiom,
    linord219039673up_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Olinordered__ab__group__add) ).

thf(492,plain,
    linord219039673up_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(118,axiom,
    countable @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Countable_Ocountable_23) ).

thf(623,plain,
    countable @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(129,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(646,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(68,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( minus @ TB )
     => ( ( minus_minus @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_fun__diff__def) ).

thf(514,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( minus @ TB )
     => ( ( minus_minus @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(334,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_24_IntD1) ).

thf(1151,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)],[334]) ).

thf(260,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_28_Int__commute) ).

thf(966,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)],[260]) ).

thf(200,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( countable @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Countable_Ocountable_33) ).

thf(821,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( countable @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(52,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_inf_Oleft__commute) ).

thf(480,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(287,axiom,
    ordere890947078_space @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1) ).

thf(1040,plain,
    ordere890947078_space @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(315,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_diff__add__cancel) ).

thf(1109,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(327,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TB )
        & ( finite_finite @ TA ) )
     => ( elemen1026692323pology @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Elementary__Topology_Osecond__countable__topology_76) ).

thf(1136,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TB )
        & ( finite_finite @ TA ) )
     => ( elemen1026692323pology @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(207,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( vimage @ TA @ TA
        @ ^ [B: TA] : B
        @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_vimage__ident) ).

thf(834,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( vimage @ TA @ TA
        @ ^ [B: TA] : B
        @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(177,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_25_IntD2) ).

thf(766,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)],[177]) ).

thf(146,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordere236663937imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_77) ).

thf(687,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordere236663937imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(255,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V55928688vector @ TB )
        & ( finite_finite @ TA ) )
     => ( topolo1314133330id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Limits_Otopological__monoid__add_84) ).

thf(956,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V55928688vector @ TB )
        & ( finite_finite @ TA ) )
     => ( topolo1314133330id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(219,axiom,
    finite_finite @ n,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).

thf(866,plain,
    finite_finite @ n,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(39,axiom,
    plus @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oplus_28) ).

thf(453,plain,
    plus @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(135,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_171_Diff__Int2) ).

thf(660,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)],[135]) ).

thf(272,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TA )
        & ( real_V55928688vector @ TA ) )
     => ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
         => ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
           => ( member @ ( TB > TA )
              @ ^ [D: TB] : ( minus_minus @ TA @ ( A @ D ) @ ( C @ D ) )
              @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_borel__measurable__diff) ).

thf(998,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TA )
        & ( real_V55928688vector @ TA ) )
     => ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
         => ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
           => ( member @ ( TB > TA )
              @ ^ [D: TB] : ( minus_minus @ TA @ ( A @ D ) @ ( C @ D ) )
              @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(14,axiom,
    ab_group_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__group__add) ).

thf(411,plain,
    ab_group_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(26,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
      ( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
      = ( image @ TA @ TC
        @ ^ [D: TA] : ( A @ ( B @ D ) )
        @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_image__image) ).

thf(428,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
      ( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
      = ( image @ TA @ TC
        @ ^ [D: TA] : ( A @ ( B @ D ) )
        @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(65,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( semilattice_inf @ TB )
     => ( ( inf_inf @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_inf__fun__def) ).

thf(507,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( semilattice_inf @ TB )
     => ( ( inf_inf @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(357,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: sigma_measure @ TA,C: sigma_measure @ TB,D: set @ TB] :
      ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ C ) )
     => ( ( member @ ( set @ TB ) @ D @ ( sigma_sets @ TB @ C ) )
       => ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ A @ D ) @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_measurable__sets) ).

thf(1215,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: sigma_measure @ TA,C: sigma_measure @ TB,D: set @ TB] :
      ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ C ) )
     => ( ( member @ ( set @ TB ) @ D @ ( sigma_sets @ TB @ C ) )
       => ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ A @ D ) @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(124,axiom,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > TA,C: TB > TA,D: sigma_measure @ TA] :
      ( ! [E: TB] :
          ( ( member @ TB @ E @ ( sigma_space @ TB @ A ) )
         => ( ( B @ E )
            = ( C @ E ) ) )
     => ( ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ A @ D ) )
        = ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_measurable__cong) ).

thf(634,plain,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > TA,C: TB > TA,D: sigma_measure @ TA] :
      ( ! [E: TB] :
          ( ( member @ TB @ E @ ( sigma_space @ TB @ A ) )
         => ( ( B @ E )
            = ( C @ E ) ) )
     => ( ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ A @ D ) )
        = ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(313,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: sigma_measure @ TA] : ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_sets__vimage__algebra__space) ).

thf(1104,plain,
    ! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: sigma_measure @ TA] : ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(367,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
          = ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_add__le__same__cancel1) ).

thf(1242,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
          = ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(213,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
      = ( member @ TA @ ( B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_vimage__eq) ).

thf(849,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
      = ( member @ TA @ ( B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(300,axiom,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > $o,C: TB > TA,D: TB > TA,E: sigma_measure @ TA] :
      ( ( member @ ( set @ TB )
        @ ( collect @ TB
          @ ^ [F: TB] :
              ( ( member @ TB @ F @ ( sigma_space @ TB @ A ) )
              & ( B @ F ) ) )
        @ ( sigma_sets @ TB @ A ) )
     => ( ( member @ ( TB > TA )
          @ ^ [F: TB] : ( if @ TA @ ( B @ F ) @ ( C @ F ) @ ( D @ F ) )
          @ ( sigma_measurable @ TB @ TA @ A @ E ) )
        = ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ A @ ( collect @ TB @ B ) ) @ E ) )
          & ( member @ ( TB > TA ) @ D
            @ ( sigma_measurable @ TB @ TA
              @ ( sigma_restrict_space @ TB @ A
                @ ( collect @ TB
                  @ ^ [F: TB] :
                      ~ ( B @ F ) ) )
              @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_measurable__If__restrict__space__iff) ).

thf(1074,plain,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > $o,C: TB > TA,D: TB > TA,E: sigma_measure @ TA] :
      ( ( member @ ( set @ TB )
        @ ( collect @ TB
          @ ^ [F: TB] :
              ( ( member @ TB @ F @ ( sigma_space @ TB @ A ) )
              & ( B @ F ) ) )
        @ ( sigma_sets @ TB @ A ) )
     => ( ( member @ ( TB > TA )
          @ ^ [F: TB] : ( if @ TA @ ( B @ F ) @ ( C @ F ) @ ( D @ F ) )
          @ ( sigma_measurable @ TB @ TA @ A @ E ) )
        = ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ A @ ( collect @ TB @ B ) ) @ E ) )
          & ( member @ ( TB > TA ) @ D
            @ ( sigma_measurable @ TB @ TA
              @ ( sigma_restrict_space @ TB @ A
                @ ( collect @ TB
                  @ ^ [F: TB] :
                      ~ ( B @ F ) ) )
              @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(38,axiom,
    cancel_semigroup_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_18) ).

thf(452,plain,
    cancel_semigroup_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(243,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_zero__le__double__add__iff__zero__le__single__add) ).

thf(920,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(30,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ A @ A )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_cancel__comm__monoid__add__class_Odiff__cancel) ).

thf(439,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ A @ A )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(75,axiom,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
          = ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_inf__sup__aci_I2_J) ).

thf(529,plain,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
          = ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(188,axiom,
    ! [TA: $tType] :
      ( ( minus_minus @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( collect @ TA
            @ ^ [C: TA] :
                ( ( member @ TA @ C @ A )
                & ~ ( member @ TA @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_set__diff__eq) ).

thf(793,plain,
    ! [TA: $tType] :
      ( ( minus_minus @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( collect @ TA
            @ ^ [C: TA] :
                ( ( member @ TA @ C @ A )
                & ~ ( member @ TA @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(391,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: sigma_measure @ TA,C: sigma_measure @ TB,D: TB > $o] :
      ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ C ) )
     => ( ( member @ ( set @ TB )
          @ ( collect @ TB
            @ ^ [E: TB] :
                ( ( member @ TB @ E @ ( sigma_space @ TB @ C ) )
                & ( D @ E ) ) )
          @ ( sigma_sets @ TB @ C ) )
       => ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ ( sigma_space @ TA @ B ) )
                & ( D @ ( A @ E ) ) ) )
          @ ( sigma_sets @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_measurable__sets__Collect) ).

thf(1306,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: sigma_measure @ TA,C: sigma_measure @ TB,D: TB > $o] :
      ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ C ) )
     => ( ( member @ ( set @ TB )
          @ ( collect @ TB
            @ ^ [E: TB] :
                ( ( member @ TB @ E @ ( sigma_space @ TB @ C ) )
                & ( D @ E ) ) )
          @ ( sigma_sets @ TB @ C ) )
       => ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ ( sigma_space @ TA @ B ) )
                & ( D @ ( A @ E ) ) ) )
          @ ( sigma_sets @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(335,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_234_subsetI) ).

thf(1153,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)],[335]) ).

thf(194,axiom,
    member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).

thf(810,plain,
    member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(393,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_187_Diff__idemp) ).

thf(1311,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)],[393]) ).

thf(294,axiom,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ( ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) )
        = ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_sets__lborel) ).

thf(1057,plain,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ( ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) )
        = ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(239,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_diff @ TA )
     => ! [A: TA,B: TA] :
          ( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_diff__add__zero) ).

thf(910,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_diff @ TA )
     => ! [A: TA,B: TA] :
          ( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(360,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( lattice @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_97) ).

thf(1223,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( lattice @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(307,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( ( countable @ TA )
        & ( elemen1026692323pology @ TB ) )
     => ! [A: TC > TA > TB,B: sigma_measure @ TC] :
          ( ! [C: TA] :
              ( member @ ( TC > TB )
              @ ^ [D: TC] : ( A @ D @ C )
              @ ( sigma_measurable @ TC @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
         => ( member @ ( TC > TA > TB ) @ A @ ( sigma_measurable @ TC @ ( TA > TB ) @ B @ ( borel_1404511681_borel @ ( TA > TB ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_measurable__coordinatewise__then__product) ).

thf(1091,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( ( countable @ TA )
        & ( elemen1026692323pology @ TB ) )
     => ! [A: TC > TA > TB,B: sigma_measure @ TC] :
          ( ! [C: TA] :
              ( member @ ( TC > TB )
              @ ^ [D: TC] : ( A @ D @ C )
              @ ( sigma_measurable @ TC @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
         => ( member @ ( TC > TA > TB ) @ A @ ( sigma_measurable @ TC @ ( TA > TB ) @ B @ ( borel_1404511681_borel @ ( TA > TB ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(202,axiom,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: set @ TA,B: TA] :
          ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) )
         => ( member @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_lebesgue__sets__translation) ).

thf(825,plain,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: set @ TA,B: TA] :
          ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) )
         => ( member @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(181,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = A )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_add__cancel__left__right) ).

thf(778,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = A )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(372,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_172_Diff__Diff__Int) ).

thf(1255,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)],[372]) ).

thf(321,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( cancel_semigroup_add @ TB )
        & ( finite_finite @ TA ) )
     => ( cancel_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_88) ).

thf(1123,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( cancel_semigroup_add @ TB )
        & ( finite_finite @ TA ) )
     => ( cancel_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(344,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_18_IntI) ).

thf(1174,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)],[344]) ).

thf(24,axiom,
    ordere236663937imp_le @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_10) ).

thf(424,plain,
    ordere236663937imp_le @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(10,axiom,
    topolo2117631714pology @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Topological__Spaces_Olinorder__topology) ).

thf(407,plain,
    topolo2117631714pology @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(186,axiom,
    ! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_29) ).

thf(788,plain,
    ! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(198,axiom,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: set @ TA] :
          ( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ A ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_space__lebesgue__on) ).

thf(815,plain,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: set @ TA] :
          ( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ A ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(358,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_23_IntE) ).

thf(1217,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)],[358]) ).

thf(105,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
     => ( B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_inf1D2) ).

thf(598,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
     => ( B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(241,axiom,
    ! [TA: $tType] : ( minus @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ominus_37) ).

thf(916,plain,
    ! [TA: $tType] : ( minus @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(90,axiom,
    ordere516151231imp_le @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_8) ).

thf(566,plain,
    ordere516151231imp_le @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(284,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TA )
        & ( ring_char_0 @ TB ) )
     => ! [A: finite_Cartesian_vec @ int @ TA,B: finite_Cartesian_vec @ int @ TA] :
          ( ( ( minkow1937162798nt_vec @ TA @ TB @ A )
            = ( minkow1937162798nt_vec @ TA @ TB @ B ) )
          = ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_of__int__vec__eq__iff) ).

thf(1032,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TA )
        & ( ring_char_0 @ TB ) )
     => ! [A: finite_Cartesian_vec @ int @ TA,B: finite_Cartesian_vec @ int @ TA] :
          ( ( ( minkow1937162798nt_vec @ TA @ TB @ A )
            = ( minkow1937162798nt_vec @ TA @ TB @ B ) )
          = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(120,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
          = ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_inf__assoc) ).

thf(625,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
          = ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(226,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA > TB,B: sigma_measure @ TB,C: set @ TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ ( borel_1404511681_borel @ TA ) @ B ) )
         => ( ( member @ ( set @ TB ) @ C @ ( sigma_sets @ TB @ B ) )
           => ( member @ ( set @ TA ) @ ( vimage @ TA @ TB @ A @ C ) @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_measurable__sets__borel) ).

thf(879,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA > TB,B: sigma_measure @ TB,C: set @ TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ ( borel_1404511681_borel @ TA ) @ B ) )
         => ( ( member @ ( set @ TB ) @ C @ ( sigma_sets @ TB @ B ) )
           => ( member @ ( set @ TA ) @ ( vimage @ TA @ TB @ A @ C ) @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(214,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: set @ TB] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ B @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_measurable__restrict__space1) ).

thf(852,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: set @ TB] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ B @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(137,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_add__eq__0__iff__both__eq__0) ).

thf(665,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            & ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(230,axiom,
    topolo1314133330id_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Limits_Otopological__monoid__add_56) ).

thf(889,plain,
    topolo1314133330id_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(337,axiom,
    ordere516151231imp_le @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_48) ).

thf(1159,plain,
    ordere516151231imp_le @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(59,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: sigma_measure @ TB] :
      ( ( sigma_space @ TA @ ( sigma_vimage_algebra @ TA @ TB @ A @ B @ C ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_space__vimage__algebra) ).

thf(493,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: sigma_measure @ TB] :
      ( ( sigma_space @ TA @ ( sigma_vimage_algebra @ TA @ TB @ A @ B @ C ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(144,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: TA > TB,B: set @ TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ ( borel_1404511681_borel @ TB ) ) )
         => ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( borel_1404511681_borel @ TB ) ) )
           => ( member @ ( set @ TA )
              @ ( collect @ TA
                @ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) )
              @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_lebesgue__measurable__vimage__borel) ).

thf(682,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: TA > TB,B: set @ TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ ( borel_1404511681_borel @ TB ) ) )
         => ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( borel_1404511681_borel @ TB ) ) )
           => ( member @ ( set @ TA )
              @ ( collect @ TA
                @ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) )
              @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(386,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
          = ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add_Oleft__cancel) ).

thf(1291,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
          = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(210,axiom,
    ordere779506340up_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_53) ).

thf(842,plain,
    ordere779506340up_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(263,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_sets_OInt__space__eq2) ).

thf(974,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(314,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA,C: set @ TA] :
      ( ( ( sigma_sets @ TA @ A )
        = ( sigma_sets @ TA @ B ) )
     => ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ C ) )
        = ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_sets__restrict__space__cong) ).

thf(1106,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA,C: set @ TA] :
      ( ( ( sigma_sets @ TA @ A )
        = ( sigma_sets @ TA @ B ) )
     => ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ C ) )
        = ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(72,axiom,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ( ( inf_inf @ TA )
        = ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_inf__sup__aci_I1_J) ).

thf(522,plain,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ( ( inf_inf @ TA )
        = ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(204,axiom,
    euclid925273238_space @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space) ).

thf(830,plain,
    euclid925273238_space @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(96,axiom,
    zero @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_27) ).

thf(578,plain,
    zero @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(306,axiom,
    ! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).

thf(1089,plain,
    ! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(279,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( minus @ TB )
        & ( finite_finite @ TA ) )
     => ( minus @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_100) ).

thf(1017,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( minus @ TB )
        & ( finite_finite @ TA ) )
     => ( minus @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(114,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( countable @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Finite__Set_Ofinite___Countable_Ocountable) ).

thf(615,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( countable @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(320,axiom,
    ( t
    = ( ^ [A: finite_Cartesian_vec @ int @ n] :
          ( image @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
          @ ^ [B: finite_Cartesian_vec @ real @ n] : ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
          @ ( t2 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_T_H__def) ).

thf(1121,plain,
    ( t
    = ( ^ [A: finite_Cartesian_vec @ int @ n] :
          ( image @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
          @ ^ [B: finite_Cartesian_vec @ real @ n] : ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
          @ ( t2 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(362,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
      ( ( A
        = ( B @ C ) )
     => ( ( member @ TA @ C @ D )
       => ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_image__eqI) ).

thf(1227,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
      ( ( A
        = ( B @ C ) )
     => ( ( member @ TA @ C @ D )
       => ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(328,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( plus @ TB )
        & ( finite_finite @ TA ) )
     => ( plus @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oplus_102) ).

thf(1138,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( plus @ TB )
        & ( finite_finite @ TA ) )
     => ( plus @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(103,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( countable @ TB )
        & ( elemen1026692323pology @ TA ) )
     => ( elemen1026692323pology @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Elementary__Topology_Osecond__countable__topology) ).

thf(593,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( countable @ TB )
        & ( elemen1026692323pology @ TA ) )
     => ( elemen1026692323pology @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(221,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
          = ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_add__left__cancel) ).

thf(869,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
          = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(61,axiom,
    topological_t2_space @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Topological__Spaces_Ot2__space) ).

thf(499,plain,
    topological_t2_space @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(216,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: sigma_measure @ TB] :
          ( ( sigma_measurable @ TB @ TA @ A @ ( lebesgue_lborel @ TA ) )
          = ( sigma_measurable @ TB @ TA @ A @ ( borel_1404511681_borel @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_measurable__lborel1) ).

thf(857,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: sigma_measure @ TB] :
          ( ( sigma_measurable @ TB @ TA @ A @ ( lebesgue_lborel @ TA ) )
          = ( sigma_measurable @ TB @ TA @ A @ ( borel_1404511681_borel @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(223,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( topolo503727757_space @ TB )
        & ( finite_finite @ TA ) )
     => ( topolo503727757_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_79) ).

thf(874,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( topolo503727757_space @ TB )
        & ( finite_finite @ TA ) )
     => ( topolo503727757_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(330,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ( plus_plus @ TA @ A @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_double__zero) ).

thf(1143,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ( plus_plus @ TA @ A @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(265,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordere779506340up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_80) ).

thf(980,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordere779506340up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(6,axiom,
    countable @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Countable_Ocountable_5) ).

thf(403,plain,
    countable @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(183,axiom,
    minus @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ominus_70) ).

thf(783,plain,
    minus @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(21,axiom,
    topolo503727757_space @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_40) ).

thf(420,plain,
    topolo503727757_space @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(319,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_space__restrict__space2) ).

thf(1118,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(228,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( complete_main_part @ TA @ B @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_main__part) ).

thf(884,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( complete_main_part @ TA @ B @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(338,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_sets_Ocompl__sets) ).

thf(1160,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(56,axiom,
    semilattice_inf @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_43) ).

thf(488,plain,
    semilattice_inf @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(247,axiom,
    ! [TA: $tType] :
      ( ( plus @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( member @ TA @ A @ ( plus_plus @ ( set @ TA ) @ B @ C ) )
         => ~ ! [D: TA,E: TA] :
                ( ( A
                  = ( plus_plus @ TA @ D @ E ) )
               => ( ( member @ TA @ D @ B )
                 => ~ ( member @ TA @ E @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_set__plus__elim) ).

thf(933,plain,
    ! [TA: $tType] :
      ( ( plus @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( member @ TA @ A @ ( plus_plus @ ( set @ TA ) @ B @ C ) )
         => ~ ! [D: TA,E: TA] :
                ( ( A
                  = ( plus_plus @ TA @ D @ E ) )
               => ( ( member @ TA @ D @ B )
                 => ~ ( member @ TA @ E @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(79,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( minus_minus @ TA @ A @ B )
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_eq__iff__diff__eq__0) ).

thf(537,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( minus_minus @ TA @ A @ B )
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(50,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( ( ord_less_eq @ TA @ A @ B )
            & ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_inf_Obounded__iff) ).

thf(476,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( ( ord_less_eq @ TA @ A @ B )
            & ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(57,axiom,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
          = ( inf_inf @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_inf__sup__aci_I4_J) ).

thf(489,plain,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
          = ( inf_inf @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(102,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( ( ord_less_eq @ TA @ A @ B )
            & ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_le__inf__iff) ).

thf(590,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( ( ord_less_eq @ TA @ A @ B )
            & ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(82,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
          = ( inf_inf @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_inf__left__idem) ).

thf(547,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
          = ( inf_inf @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(85,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( finite_finite @ TA ) )
     => ( finite_finite @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).

thf(554,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( finite_finite @ TA ) )
     => ( finite_finite @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(172,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
      ( ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
              & ( B @ D ) ) )
        @ ( sigma_sets @ TA @ A ) )
     => ( ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ A ) )
       => ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( ( C @ D )
                 => ( B @ D ) ) ) )
          @ ( sigma_sets @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_sets_Osets__Collect__imp) ).

thf(753,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
      ( ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
              & ( B @ D ) ) )
        @ ( sigma_sets @ TA @ A ) )
     => ( ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ A ) )
       => ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( ( C @ D )
                 => ( B @ D ) ) ) )
          @ ( sigma_sets @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(208,axiom,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ( zero @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ozero_38) ).

thf(837,plain,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ( zero @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(267,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB,D: set @ TB] :
      ( ! [E: TA] :
          ( ( member @ TA @ E @ A )
         => ( ( B @ E )
            = ( C @ E ) ) )
     => ( ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ B @ D ) @ A )
        = ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ C @ D ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_vimage__inter__cong) ).

thf(985,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB,D: set @ TB] :
      ( ! [E: TA] :
          ( ( member @ TA @ E @ A )
         => ( ( B @ E )
            = ( C @ E ) ) )
     => ( ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ B @ D ) @ A )
        = ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ C @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(151,axiom,
    ! [TA: $tType,A: sigma_measure @ TA] :
      ( ( sigma_space @ TA @ ( complete_completion @ TA @ A ) )
      = ( sigma_space @ TA @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_space__completion) ).

thf(701,plain,
    ! [TA: $tType,A: sigma_measure @ TA] :
      ( ( sigma_space @ TA @ ( complete_completion @ TA @ A ) )
      = ( sigma_space @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(388,axiom,
    ! [TA: $tType] :
      ( ( real_V1076094709vector @ TA )
     => ! [A: set @ TA,B: TA,C: set @ TA] :
          ( ! [D: TA] :
              ( ( member @ TA @ D @ A )
              = ( member @ TA @ ( plus_plus @ TA @ B @ D ) @ C ) )
         => ( C
            = ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_affine__parallel__expl__aux) ).

thf(1297,plain,
    ! [TA: $tType] :
      ( ( real_V1076094709vector @ TA )
     => ! [A: set @ TA,B: TA,C: set @ TA] :
          ( ! [D: TA] :
              ( ( member @ TA @ D @ A )
              = ( member @ TA @ ( plus_plus @ TA @ B @ D ) @ C ) )
         => ( C
            = ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(165,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: set @ TB,B: set @ TB,C: TB > TA] :
          ( ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
         => ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
           => ( ( ord_less_eq @ ( set @ TB ) @ A @ B )
             => ( ( member @ ( TB > TA )
                  @ ^ [D: TB] : ( if @ TA @ ( member @ TB @ D @ A ) @ ( C @ D ) @ ( zero_zero @ TA ) )
                  @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
                = ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_borel__measurable__if__lebesgue__on) ).

thf(738,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: set @ TB,B: set @ TB,C: TB > TA] :
          ( ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
         => ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
           => ( ( ord_less_eq @ ( set @ TB ) @ A @ B )
             => ( ( member @ ( TB > TA )
                  @ ^ [D: TB] : ( if @ TA @ ( member @ TB @ D @ A ) @ ( C @ D ) @ ( zero_zero @ TA ) )
                  @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
                = ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(363,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: nat > TA > $o,C: set @ nat] :
      ( ! [D: nat] :
          ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ ( sigma_space @ TA @ A ) )
                & ( B @ D @ E ) ) )
          @ ( sigma_sets @ TA @ A ) )
     => ( member @ ( set @ TA )
        @ ( inf_inf @ ( set @ TA )
          @ ( vimage @ TA @ nat
            @ ^ [D: TA] :
                ( ord_Least @ nat
                @ ^ [E: nat] : ( B @ E @ D ) )
            @ C )
          @ ( sigma_space @ TA @ A ) )
        @ ( sigma_sets @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_sets__Least) ).

thf(1231,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: nat > TA > $o,C: set @ nat] :
      ( ! [D: nat] :
          ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ ( sigma_space @ TA @ A ) )
                & ( B @ D @ E ) ) )
          @ ( sigma_sets @ TA @ A ) )
     => ( member @ ( set @ TA )
        @ ( inf_inf @ ( set @ TA )
          @ ( vimage @ TA @ nat
            @ ^ [D: TA] :
                ( ord_Least @ nat
                @ ^ [E: nat] : ( B @ E @ D ) )
            @ C )
          @ ( sigma_space @ TA @ A ) )
        @ ( sigma_sets @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(295,axiom,
    ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
      ( ! [D: TA] :
          ( ( A @ ( B @ D ) )
          = ( C @ D ) )
     => ( ( vimage @ TA @ TB @ B @ ( collect @ TB @ A ) )
        = ( collect @ TA @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_vimage__Collect) ).

thf(1060,plain,
    ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
      ( ! [D: TA] :
          ( ( A @ ( B @ D ) )
          = ( C @ D ) )
     => ( ( vimage @ TA @ TB @ B @ ( collect @ TB @ A ) )
        = ( collect @ TA @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(158,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_26_Int__assoc) ).

thf(721,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)],[158]) ).

thf(93,axiom,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_zero__reorient) ).

thf(569,plain,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(63,axiom,
    countable @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Countable_Ocountable_44) ).

thf(503,plain,
    countable @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(396,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordered_ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_87) ).

thf(1318,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( ordered_ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(352,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: sigma_measure @ TB,C: sigma_measure @ TC,D: TC > TA,E: sigma_measure @ TA] :
      ( ( member @ ( TB > TC ) @ A @ ( sigma_measurable @ TB @ TC @ B @ C ) )
     => ( ( member @ ( TC > TA ) @ D @ ( sigma_measurable @ TC @ TA @ C @ E ) )
       => ( member @ ( TB > TA )
          @ ^ [F: TB] : ( D @ ( A @ F ) )
          @ ( sigma_measurable @ TB @ TA @ B @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_measurable__compose) ).

thf(1202,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: sigma_measure @ TB,C: sigma_measure @ TC,D: TC > TA,E: sigma_measure @ TA] :
      ( ( member @ ( TB > TC ) @ A @ ( sigma_measurable @ TB @ TC @ B @ C ) )
     => ( ( member @ ( TC > TA ) @ D @ ( sigma_measurable @ TC @ TA @ C @ E ) )
       => ( member @ ( TB > TA )
          @ ^ [F: TB] : ( D @ ( A @ F ) )
          @ ( sigma_measurable @ TB @ TA @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(248,axiom,
    ! [TA: $tType] :
      ( ( minus_minus @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( collect @ TA
            @ ( minus_minus @ ( TA > $o )
              @ ^ [C: TA] : ( member @ TA @ C @ A )
              @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_minus__set__def) ).

thf(938,plain,
    ! [TA: $tType] :
      ( ( minus_minus @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( collect @ TA
            @ ( minus_minus @ ( TA > $o )
              @ ^ [C: TA] : ( member @ TA @ C @ A )
              @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(285,axiom,
    comm_monoid_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocomm__monoid__add_63) ).

thf(1035,plain,
    comm_monoid_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(299,axiom,
    ! [TA: $tType] :
      ( ( real_V1076094709vector @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) )
          = ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_subset__translation__eq) ).

thf(1071,plain,
    ! [TA: $tType] :
      ( ( real_V1076094709vector @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) )
          = ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(254,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( inf_inf @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_sets_OInt__space__eq1) ).

thf(953,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( inf_inf @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(100,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( type @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Finite__Set_Ofinite___HOL_Otype) ).

thf(586,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( type @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(157,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( image @ TA @ TA
            @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
            @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
          = ( inf_inf @ ( set @ TA )
            @ ( image @ TA @ TA
              @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
              @ B )
            @ ( image @ TA @ TA
              @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
              @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_translation__subtract__Int) ).

thf(718,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( image @ TA @ TA
            @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
            @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
          = ( inf_inf @ ( set @ TA )
            @ ( image @ TA @ TA
              @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
              @ B )
            @ ( image @ TA @ TA
              @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
              @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(245,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_19_Int__iff) ).

thf(926,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)],[245]) ).

thf(348,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ C ) )
         => ( ( plus_plus @ TA @ D @ A )
            = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_group__cancel_Oadd2) ).

thf(1187,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ C ) )
         => ( ( plus_plus @ TA @ D @ A )
            = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(141,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_170_Int__Diff) ).

thf(674,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)],[141]) ).

thf(237,axiom,
    topolo503727757_space @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_51) ).

thf(906,plain,
    topolo503727757_space @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(15,axiom,
    cancel146912293up_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).

thf(412,plain,
    cancel146912293up_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(25,axiom,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_inf__sup__aci_I3_J) ).

thf(425,plain,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(331,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TB > TC > TA,B: sigma_measure @ TB,C: TC] :
          ( ( member @ ( TB > TC > TA ) @ A @ ( sigma_measurable @ TB @ ( TC > TA ) @ B @ ( borel_1404511681_borel @ ( TC > TA ) ) ) )
         => ( member @ ( TB > TA )
            @ ^ [D: TB] : ( A @ D @ C )
            @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_measurable__product__then__coordinatewise) ).

thf(1146,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TB > TC > TA,B: sigma_measure @ TB,C: TC] :
          ( ( member @ ( TB > TC > TA ) @ A @ ( sigma_measurable @ TB @ ( TC > TA ) @ B @ ( borel_1404511681_borel @ ( TC > TA ) ) ) )
         => ( member @ ( TB > TA )
            @ ^ [D: TB] : ( A @ D @ C )
            @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(379,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = B )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__cancel__left__left) ).

thf(1273,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = B )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(168,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( cancel1352612707id_add @ TB )
        & ( finite_finite @ TA ) )
     => ( cancel1352612707id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_85) ).

thf(745,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( cancel1352612707id_add @ TB )
        & ( finite_finite @ TA ) )
     => ( cancel1352612707id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(147,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
      ( ( A = B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ B )
           => ( ( C @ E )
              = ( D @ E ) ) )
       => ( ( image @ TA @ TB @ C @ A )
          = ( image @ TA @ TB @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_image__cong) ).

thf(689,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
      ( ( A = B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ B )
           => ( ( C @ E )
              = ( D @ E ) ) )
       => ( ( image @ TA @ TB @ C @ A )
          = ( image @ TA @ TB @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(107,axiom,
    ! [A: nat] :
      ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_diff__0__eq__0) ).

thf(601,plain,
    ! [A: nat] :
      ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(370,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( semilattice_inf @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__inf_89) ).

thf(1251,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ordere890947078_space @ TB )
        & ( finite_finite @ TA ) )
     => ( semilattice_inf @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(116,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( countable @ TA ) )
     => ( countable @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Countable_Ocountable) ).

thf(618,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( countable @ TA ) )
     => ( countable @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(23,axiom,
    ring_char_0 @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Oring__char__0) ).

thf(423,plain,
    ring_char_0 @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(5,axiom,
    group_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).

thf(402,plain,
    group_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(163,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( minus_minus @ TA @ A @ B )
            = C )
          = ( A
            = ( plus_plus @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_diff__eq__eq) ).

thf(732,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( minus_minus @ TA @ A @ B )
            = C )
          = ( A
            = ( plus_plus @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(167,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: $o] :
      ( member @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
            & B ) )
      @ ( sigma_sets @ TA @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_sets_Osets__Collect__const) ).

thf(743,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: $o] :
      ( member @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
            & B ) )
      @ ( sigma_sets @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(97,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_diff__ge__0__iff__ge) ).

thf(579,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(256,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_173_Diff__Int__distrib) ).

thf(958,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)],[256]) ).

thf(16,axiom,
    ab_semigroup_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add) ).

thf(413,plain,
    ab_semigroup_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(88,axiom,
    zero @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).

thf(562,plain,
    zero @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(236,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: sigma_measure @ TC,C: sigma_measure @ TA,D: TB > TC,E: sigma_measure @ TB] :
      ( ( member @ ( TC > TA ) @ A @ ( sigma_measurable @ TC @ TA @ B @ C ) )
     => ( ( member @ ( TB > TC ) @ D @ ( sigma_measurable @ TB @ TC @ E @ B ) )
       => ( member @ ( TB > TA )
          @ ^ [F: TB] : ( A @ ( D @ F ) )
          @ ( sigma_measurable @ TB @ TA @ E @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_measurable__compose__rev) ).

thf(904,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: sigma_measure @ TC,C: sigma_measure @ TA,D: TB > TC,E: sigma_measure @ TB] :
      ( ( member @ ( TC > TA ) @ A @ ( sigma_measurable @ TC @ TA @ B @ C ) )
     => ( ( member @ ( TB > TC ) @ D @ ( sigma_measurable @ TB @ TC @ E @ B ) )
       => ( member @ ( TB > TA )
          @ ^ [F: TB] : ( A @ ( D @ F ) )
          @ ( sigma_measurable @ TB @ TA @ E @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(211,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: set @ TA] :
          ( ( image @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_image__add__0) ).

thf(843,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: set @ TA] :
          ( ( image @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(322,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
      ( ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
              & ( B @ D ) ) )
        @ ( sigma_sets @ TA @ A ) )
     => ( ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ A ) )
       => ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( C @ D )
                & ( B @ D ) ) )
          @ ( sigma_sets @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_sets_Osets__Collect__conj) ).

thf(1125,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
      ( ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
              & ( B @ D ) ) )
        @ ( sigma_sets @ TA @ A ) )
     => ( ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ A ) )
       => ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( C @ D )
                & ( B @ D ) ) )
          @ ( sigma_sets @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(126,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
       => ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_sets_ODiff) ).

thf(641,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
       => ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(32,axiom,
    lattice @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_46) ).

thf(445,plain,
    lattice @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(94,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_inf__idem) ).

thf(572,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(378,axiom,
    ( t2
    = ( ^ [A: finite_Cartesian_vec @ int @ n] : ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( r @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_T__def) ).

thf(1271,plain,
    ( t2
    = ( ^ [A: finite_Cartesian_vec @ int @ n] : ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( r @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(155,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA] :
      ( ( ( sigma_sets @ TA @ A )
        = ( sigma_sets @ TA @ B ) )
     => ( ( sigma_space @ TA @ A )
        = ( sigma_space @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_sets__eq__imp__space__eq) ).

thf(713,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA] :
      ( ( ( sigma_sets @ TA @ A )
        = ( sigma_sets @ TA @ B ) )
     => ( ( sigma_space @ TA @ A )
        = ( sigma_space @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(45,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
          = ( inf_inf @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_inf_Oright__idem) ).

thf(466,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
          = ( inf_inf @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(192,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Int__absorb) ).

thf(804,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( inf_inf @ ( set @ TA ) @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(252,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
      ( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
      = ( inf_inf @ ( set @ TA ) @ B @ ( sigma_space @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_space__restrict__space) ).

thf(947,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
      ( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
      = ( inf_inf @ ( set @ TA ) @ B @ ( sigma_space @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(80,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).

thf(540,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(111,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( semilattice_inf @ TA )
     => ( semilattice_inf @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).

thf(611,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( semilattice_inf @ TA )
     => ( semilattice_inf @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(185,axiom,
    monoid_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__add_66) ).

thf(787,plain,
    monoid_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(373,axiom,
    ! [TA: $tType] :
      ( ( plus @ TA )
     => ! [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 ) @ ( plus_plus @ ( set @ TA ) @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_set__plus__mono2) ).

thf(1258,plain,
    ! [TA: $tType] :
      ( ( plus @ TA )
     => ! [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 ) @ ( plus_plus @ ( set @ TA ) @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(152,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
      ( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
      = ( ? [D: TA] :
            ( ( member @ TA @ D @ C )
            & ( A
              = ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_image__iff) ).

thf(704,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
      ( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
      = ( ? [D: TA] :
            ( ( member @ TA @ D @ C )
            & ( A
              = ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(108,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
          = ( inf_inf @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_inf_Oleft__idem) ).

thf(604,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
          = ( inf_inf @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(9,axiom,
    cancel1352612707id_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).

thf(406,plain,
    cancel1352612707id_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(205,axiom,
    ! [A: finite_Cartesian_vec @ int @ n] :
      ( ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
     => ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
        @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
          @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
            @ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
            @ ( t2 @ A ) )
          @ ( sigma_space @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
        @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).

thf(831,plain,
    ! [A: finite_Cartesian_vec @ int @ n] :
      ( ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
     => ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
        @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
          @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
            @ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
            @ ( t2 @ A ) )
          @ ( sigma_space @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
        @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(383,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
      ( ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
              & ( B @ D ) ) )
        @ ( sigma_sets @ TA @ A ) )
     => ( ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ A ) )
       => ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( ( C @ D )
                  | ( B @ D ) ) ) )
          @ ( sigma_sets @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_sets_Osets__Collect__disj) ).

thf(1282,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
      ( ( member @ ( set @ TA )
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
              & ( B @ D ) ) )
        @ ( sigma_sets @ TA @ A ) )
     => ( ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ A ) )
       => ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
                & ( ( C @ D )
                  | ( B @ D ) ) ) )
          @ ( sigma_sets @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(184,axiom,
    ! [TA: $tType] :
      ( ( inf_inf @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( collect @ TA
            @ ( inf_inf @ ( TA > $o )
              @ ^ [C: TA] : ( member @ TA @ C @ A )
              @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_inf__set__def) ).

thf(784,plain,
    ! [TA: $tType] :
      ( ( inf_inf @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( collect @ TA
            @ ( inf_inf @ ( TA > $o )
              @ ^ [C: TA] : ( member @ TA @ C @ A )
              @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(277,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
      ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
      = ( image @ ( set @ TA ) @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ B ) @ ( sigma_sets @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_sets__restrict__space) ).

thf(1011,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
      ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
      = ( image @ ( set @ TA ) @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ B ) @ ( sigma_sets @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(91,axiom,
    topolo1314133330id_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Limits_Otopological__monoid__add_15) ).

thf(567,plain,
    topolo1314133330id_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(130,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V2090557954_space @ TB )
        & ( finite_finite @ TA ) )
     => ( real_V2090557954_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space) ).

thf(649,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V2090557954_space @ TB )
        & ( finite_finite @ TA ) )
     => ( real_V2090557954_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(218,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_174_Diff__Int__distrib2) ).

thf(863,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)],[218]) ).

thf(268,axiom,
    linord219039673up_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add_54) ).

thf(990,plain,
    linord219039673up_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(271,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V55928688vector @ TB )
        & ( finite_finite @ TA ) )
     => ( real_V55928688vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_78) ).

thf(996,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V55928688vector @ TB )
        & ( finite_finite @ TA ) )
     => ( real_V55928688vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(231,axiom,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
          = ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_diff__diff__add) ).

thf(890,plain,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
          = ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(195,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TB] :
          ( member @ ( ( TB > TA ) > TA )
          @ ^ [B: TB > TA] : ( B @ A )
          @ ( sigma_measurable @ ( TB > TA ) @ TA @ ( borel_1404511681_borel @ ( TB > TA ) ) @ ( borel_1404511681_borel @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_measurable__product__coordinates) ).

thf(811,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TB] :
          ( member @ ( ( TB > TA ) > TA )
          @ ^ [B: TB > TA] : ( B @ A )
          @ ( sigma_measurable @ ( TB > TA ) @ TA @ ( borel_1404511681_borel @ ( TB > TA ) ) @ ( borel_1404511681_borel @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(302,axiom,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ( ( sigma_space @ TA @ ( lebesgue_lborel @ TA ) )
        = ( sigma_space @ TA @ ( borel_1404511681_borel @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_space__lborel) ).

thf(1080,plain,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ( ( sigma_space @ TA @ ( lebesgue_lborel @ TA ) )
        = ( sigma_space @ TA @ ( borel_1404511681_borel @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(123,axiom,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA,C: set @ TB,D: TB > TA] :
      ( ( ( sigma_sets @ TA @ A )
        = ( sigma_sets @ TA @ B ) )
     => ( ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ C @ D @ A ) )
        = ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ C @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_sets__vimage__algebra__cong) ).

thf(631,plain,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA,C: set @ TB,D: TB > TA] :
      ( ( ( sigma_sets @ TA @ A )
        = ( sigma_sets @ TA @ B ) )
     => ( ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ C @ D @ A ) )
        = ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ C @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(174,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TB )
        & ( finite_finite @ TA ) )
     => ( euclid925273238_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Euclidean__Space_Oeuclidean__space_81) ).

thf(758,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TB )
        & ( finite_finite @ TA ) )
     => ( euclid925273238_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(53,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( semilattice_inf @ TB )
     => ( ( inf_inf @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_inf__apply) ).

thf(483,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( semilattice_inf @ TB )
     => ( ( inf_inf @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(283,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TB > TA,B: sigma_measure @ TB] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
          = ( ! [C: set @ TA] :
                ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
               => ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ C ) @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_in__borel__measurable__borel) ).

thf(1029,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TB > TA,B: sigma_measure @ TB] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
          = ( ! [C: set @ TA] :
                ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
               => ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ C ) @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(138,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ring_char_0 @ TB )
        & ( finite_finite @ TA ) )
     => ( ring_char_0 @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_99) ).

thf(668,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ring_char_0 @ TB )
        & ( finite_finite @ TA ) )
     => ( ring_char_0 @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(43,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(462,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( topolo503727757_space @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(316,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( collect @ TA
        @ ^ [C: TA] :
            ( ( A @ C )
            & ( B @ C ) ) )
      = ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Collect__conj__eq) ).

thf(1112,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( collect @ TA
        @ ^ [C: TA] :
            ( ( A @ C )
            & ( B @ C ) ) )
      = ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(190,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( zero @ TB )
        & ( finite_finite @ TA ) )
     => ( zero @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_101) ).

thf(799,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( zero @ TB )
        & ( finite_finite @ TA ) )
     => ( zero @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(339,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
       => ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_sets_OInt) ).

thf(1162,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
       => ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(150,axiom,
    semilattice_inf @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osemilattice__inf_61) ).

thf(700,plain,
    semilattice_inf @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(70,axiom,
    monoid_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add_24) ).

thf(520,plain,
    monoid_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(333,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: $o] :
      ( member @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
            & B ) )
      @ ( sigma_sets @ TA @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_sets_Osets__Collect_I5_J) ).

thf(1149,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: $o] :
      ( member @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
            & B ) )
      @ ( sigma_sets @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(259,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( cancel146912293up_add @ TB )
        & ( finite_finite @ TA ) )
     => ( cancel146912293up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_83) ).

thf(964,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( cancel146912293up_add @ TB )
        & ( finite_finite @ TA ) )
     => ( cancel146912293up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(250,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_measurable__completion) ).

thf(943,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(281,axiom,
    ! [TA: $tType] :
      ( ( plus @ TA )
     => ( plus @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Oplus_39) ).

thf(1022,plain,
    ! [TA: $tType] :
      ( ( plus @ TA )
     => ( plus @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(1,conjecture,
    ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
    @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
      @ ^ [A: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ A @ ( minkow1937162798nt_vec @ n @ real @ a ) )
      @ ( t2 @ a ) )
    @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
      @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
        @ ^ [A: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ A @ ( minkow1937162798nt_vec @ n @ real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(399,plain,
    ~ ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
      @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
        @ ^ [A: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ A @ ( minkow1937162798nt_vec @ n @ real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(89,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_diff @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_zero__diff) ).

thf(563,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_diff @ TA )
     => ! [A: TA] :
          ( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(273,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
      ( ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) )
     => ( ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) )
       => ( ( sigma_restrict_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) @ C )
          = ( sigma_restrict_space @ TA @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_restrict__restrict__space) ).

thf(1000,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
      ( ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) )
     => ( ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) )
       => ( ( sigma_restrict_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) @ C )
          = ( sigma_restrict_space @ TA @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(27,axiom,
    ! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
      ( ( A @ B )
     => ( ( C @ B )
       => ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_inf1I) ).

thf(431,plain,
    ! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
      ( ( A @ B )
     => ( ( C @ B )
       => ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(132,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TB )
     => ( ( borel_is_borel @ TA @ TB )
        = ( ^ [A: TA > TB,B: sigma_measure @ TA] : ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_is__borel__def) ).

thf(653,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TB )
     => ( ( borel_is_borel @ TA @ TB )
        = ( ^ [A: TA > TB,B: sigma_measure @ TA] : ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(134,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ab_group_add @ TB )
        & ( finite_finite @ TA ) )
     => ( ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_93) ).

thf(658,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ab_group_add @ TB )
        & ( finite_finite @ TA ) )
     => ( ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(71,axiom,
    semilattice_inf @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__inf_19) ).

thf(521,plain,
    semilattice_inf @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(343,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_194_DiffE) ).

thf(1171,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)],[343]) ).

thf(178,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( comm_monoid_add @ TB )
        & ( finite_finite @ TA ) )
     => ( comm_monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_91) ).

thf(768,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( comm_monoid_add @ TB )
        & ( finite_finite @ TA ) )
     => ( comm_monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(203,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( euclid925273238_space @ TB )
     => ! [A: sigma_measure @ TA] :
          ( ( sigma_measurable @ TB @ TA @ ( lebesgue_lborel @ TB ) @ A )
          = ( sigma_measurable @ TB @ TA @ ( borel_1404511681_borel @ TB ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_measurable__lborel2) ).

thf(827,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( euclid925273238_space @ TB )
     => ! [A: sigma_measure @ TA] :
          ( ( sigma_measurable @ TB @ TA @ ( lebesgue_lborel @ TB ) @ A )
          = ( sigma_measurable @ TB @ TA @ ( borel_1404511681_borel @ TB ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(289,axiom,
    ring_char_0 @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0_69) ).

thf(1044,plain,
    ring_char_0 @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(368,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_29_Int__left__absorb) ).

thf(1245,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)],[368]) ).

thf(345,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: set @ TA,C: set @ TA] :
      ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ ( sigma_restrict_space @ TA @ A @ B ) @ C ) )
      = ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_sets__restrict__restrict__space) ).

thf(1176,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: set @ TA,C: set @ TA] :
      ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ ( sigma_restrict_space @ TA @ A @ B ) @ C ) )
      = ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(110,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( minus_minus @ TA @ A @ B )
            = ( minus_minus @ TA @ C @ D ) )
         => ( ( A = B )
            = ( C = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_diff__eq__diff__eq) ).

thf(608,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( ( minus_minus @ TA @ A @ B )
            = ( minus_minus @ TA @ C @ D ) )
         => ( ( A = B )
            = ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(48,axiom,
    topolo2117631714pology @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Olinorder__topology_12) ).

thf(473,plain,
    topolo2117631714pology @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(341,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB > TA,E: set @ TB] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( ( member @ ( TB > TA ) @ D @ ( sigma_measurable @ TB @ TA @ B @ C ) )
       => ( ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ E @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) )
         => ( member @ ( TB > TA )
            @ ^ [F: TB] : ( if @ TA @ ( member @ TB @ F @ E ) @ ( A @ F ) @ ( D @ F ) )
            @ ( sigma_measurable @ TB @ TA @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_measurable__If__set) ).

thf(1166,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB > TA,E: set @ TB] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( ( member @ ( TB > TA ) @ D @ ( sigma_measurable @ TB @ TA @ B @ C ) )
       => ( ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ E @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) )
         => ( member @ ( TB > TA )
            @ ^ [F: TB] : ( if @ TA @ ( member @ TB @ F @ E ) @ ( A @ F ) @ ( D @ F ) )
            @ ( sigma_measurable @ TB @ TA @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(354,axiom,
    ! [TA: $tType] :
      ( ( inf_inf @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( collect @ TA
            @ ^ [C: TA] :
                ( ( member @ TA @ C @ A )
                & ( member @ TA @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Int__def) ).

thf(1208,plain,
    ! [TA: $tType] :
      ( ( inf_inf @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( collect @ TA
            @ ^ [C: TA] :
                ( ( member @ TA @ C @ A )
                & ( member @ TA @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(143,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
      ( ( member @ TA @ A @ B )
     => ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_imageI) ).

thf(680,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
      ( ( member @ TA @ A @ B )
     => ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(136,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
     => ( member @ TA @ ( B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_vimageD) ).

thf(663,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
     => ( member @ TA @ ( B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(381,axiom,
    ! [TA: $tType] :
      ( ( monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_add_Oleft__neutral) ).

thf(1277,plain,
    ! [TA: $tType] :
      ( ( monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(115,axiom,
    ordered_ab_group_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__group__add) ).

thf(617,plain,
    ordered_ab_group_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(84,axiom,
    topological_t2_space @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Ot2__space_42) ).

thf(553,plain,
    topological_t2_space @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(291,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ A ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_add__cancel__right__left) ).

thf(1049,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ A ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(326,axiom,
    ! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).

thf(1134,plain,
    ! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(55,axiom,
    cancel146912293up_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_14) ).

thf(487,plain,
    cancel146912293up_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(41,axiom,
    semigroup_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_22) ).

thf(458,plain,
    semigroup_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(201,axiom,
    ! [TA: $tType] : ( lattice @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_36) ).

thf(823,plain,
    ! [TA: $tType] : ( lattice @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(73,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
     => ~ ( ( A @ C )
         => ~ ( B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_inf1E) ).

thf(525,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
     => ~ ( ( A @ C )
         => ~ ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(274,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB > TA,E: TB > $o] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( ( member @ ( TB > TA ) @ D @ ( sigma_measurable @ TB @ TA @ B @ C ) )
       => ( ( member @ ( set @ TB )
            @ ( collect @ TB
              @ ^ [F: TB] :
                  ( ( member @ TB @ F @ ( sigma_space @ TB @ B ) )
                  & ( E @ F ) ) )
            @ ( sigma_sets @ TB @ B ) )
         => ( member @ ( TB > TA )
            @ ^ [F: TB] : ( if @ TA @ ( E @ F ) @ ( A @ F ) @ ( D @ F ) )
            @ ( sigma_measurable @ TB @ TA @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_measurable__If) ).

thf(1003,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB > TA,E: TB > $o] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( ( member @ ( TB > TA ) @ D @ ( sigma_measurable @ TB @ TA @ B @ C ) )
       => ( ( member @ ( set @ TB )
            @ ( collect @ TB
              @ ^ [F: TB] :
                  ( ( member @ TB @ F @ ( sigma_space @ TB @ B ) )
                  & ( E @ F ) ) )
            @ ( sigma_sets @ TB @ B ) )
         => ( member @ ( TB > TA )
            @ ^ [F: TB] : ( if @ TA @ ( E @ F ) @ ( A @ F ) @ ( D @ F ) )
            @ ( sigma_measurable @ TB @ TA @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(222,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( ( member @ TB @ D @ ( sigma_space @ TB @ B ) )
       => ( member @ TA @ ( A @ D ) @ ( sigma_space @ TA @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_measurable__space) ).

thf(872,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB] :
      ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
     => ( ( member @ TB @ D @ ( sigma_space @ TB @ B ) )
       => ( member @ TA @ ( A @ D ) @ ( sigma_space @ TA @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(336,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_add__diff__cancel) ).

thf(1156,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(229,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_sets__completionI__sets) ).

thf(887,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(12,axiom,
    minus @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ominus_7) ).

thf(409,plain,
    minus @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(310,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( real_V55928688vector @ TA )
     => ! [A: TB > TA,B: sigma_measure @ TB,C: TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
         => ( member @ ( TB > TA )
            @ ^ [D: TB] : ( plus_plus @ TA @ C @ ( A @ D ) )
            @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_borel__measurable__const__add) ).

thf(1098,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( real_V55928688vector @ TA )
     => ! [A: TB > TA,B: sigma_measure @ TB,C: TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
         => ( member @ ( TB > TA )
            @ ^ [D: TB] : ( plus_plus @ TA @ C @ ( A @ D ) )
            @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(361,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: TB > TA,B: set @ TB] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
         => ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
           => ( member @ ( TB > TA )
              @ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ B ) @ ( A @ C ) @ ( zero_zero @ TA ) )
              @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_borel__measurable__if__I) ).

thf(1225,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: TB > TA,B: set @ TB] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
         => ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
           => ( member @ ( TB > TA )
              @ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ B ) @ ( A @ C ) @ ( zero_zero @ TA ) )
              @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(153,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: set @ TA] :
      ( ( member @ TA @ ( A @ B ) @ C )
     => ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_vimageI2) ).

thf(707,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: set @ TA] :
      ( ( member @ TA @ ( A @ B ) @ C )
     => ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(17,axiom,
    semilattice_inf @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Lattices_Osemilattice__inf_4) ).

thf(414,plain,
    semilattice_inf @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(262,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B )
            = ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) )
         => ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_translation__invert) ).

thf(971,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B )
            = ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) )
         => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(389,axiom,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
          = ( ord_less_eq @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_add__le__cancel__right) ).

thf(1300,plain,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
          = ( ord_less_eq @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(99,axiom,
    semigroup_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add) ).

thf(585,plain,
    semigroup_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(375,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: TA,C: set @ TA] :
          ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ C ) )
          = ( image @ TA @ TA @ ( plus_plus @ TA @ ( plus_plus @ TA @ B @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_translation__assoc) ).

thf(1262,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: TA,C: set @ TA] :
          ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ C ) )
          = ( image @ TA @ TA @ ( plus_plus @ TA @ ( plus_plus @ TA @ B @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(304,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( group_add @ TB )
        & ( finite_finite @ TA ) )
     => ( group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_98) ).

thf(1085,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( group_add @ TB )
        & ( finite_finite @ TA ) )
     => ( group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(324,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V2090557954_space @ TB )
        & ( finite_finite @ TA ) )
     => ( topological_t2_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Ot2__space_86) ).

thf(1130,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V2090557954_space @ TB )
        & ( finite_finite @ TA ) )
     => ( topological_t2_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(127,axiom,
    plus @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oplus_72) ).

thf(643,plain,
    plus @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(359,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
          = ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_diff__diff__eq2) ).

thf(1220,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
          = ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(238,axiom,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: TA > $o] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) ) )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ B @ A ) ) )
        = ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
                & ( member @ TA @ D @ A )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_sets__Collect__restrict__space__iff) ).

thf(907,plain,
    ! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: TA > $o] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) ) )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ B @ A ) ) )
        = ( member @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
                & ( member @ TA @ D @ A )
                & ( C @ D ) ) )
          @ ( sigma_sets @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(133,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TB )
        & ( topological_t2_space @ TB ) )
     => ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
         => ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
           => ( member @ ( set @ TA )
              @ ( collect @ TA
                @ ^ [D: TA] :
                    ( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
                    & ( ( A @ D )
                      = ( C @ D ) ) ) )
              @ ( sigma_sets @ TA @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_measurable__equality__set) ).

thf(656,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TB )
        & ( topological_t2_space @ TB ) )
     => ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
         => ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
           => ( member @ ( set @ TA )
              @ ( collect @ TA
                @ ^ [D: TA] :
                    ( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
                    & ( ( A @ D )
                      = ( C @ D ) ) ) )
              @ ( sigma_sets @ TA @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(112,axiom,
    finite_finite @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_45) ).

thf(613,plain,
    finite_finite @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(384,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = C )
         => ( A
            = ( minus_minus @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_add__implies__diff) ).

thf(1284,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = C )
         => ( A
            = ( minus_minus @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(106,axiom,
    ordere236663937imp_le @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(600,plain,
    ordere236663937imp_le @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(292,axiom,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
          = ( minus_minus @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_add__diff__cancel__left) ).

thf(1052,plain,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
          = ( minus_minus @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(160,axiom,
    cancel1352612707id_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_57) ).

thf(727,plain,
    cancel1352612707id_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(329,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( plus_plus @ TA @ A @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_double__zero__sym) ).

thf(1140,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( plus_plus @ TA @ A @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(276,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
         => ( C @ D ) )
     => ! [D: TA] :
          ( ( member @ TA @ D @ B )
         => ( C @ ( A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_ball__imageD) ).

thf(1008,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
         => ( C @ D ) )
     => ! [D: TA] :
          ( ( member @ TA @ D @ B )
         => ( C @ ( A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(33,axiom,
    topolo1314133330id_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Limits_Otopological__monoid__add) ).

thf(446,plain,
    topolo1314133330id_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(104,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(595,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)],[104]) ).

thf(224,axiom,
    ! [TA: $tType,A: sigma_measure @ TA] :
      ( member @ ( TA > TA )
      @ ^ [B: TA] : B
      @ ( sigma_measurable @ TA @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_measurable__id) ).

thf(876,plain,
    ! [TA: $tType,A: sigma_measure @ TA] :
      ( member @ ( TA > TA )
      @ ^ [B: TA] : B
      @ ( sigma_measurable @ TA @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(366,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ( ab_semigroup_add @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Oab__semigroup__add_30) ).

thf(1240,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ( ab_semigroup_add @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(269,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_add_Ogroup__left__neutral) ).

thf(991,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(86,axiom,
    ! [A: nat,B: nat] :
      ( ( ( minus_minus @ nat @ A @ B )
        = ( zero_zero @ nat ) )
     => ( ( ( minus_minus @ nat @ B @ A )
          = ( zero_zero @ nat ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_diffs0__imp__equal) ).

thf(556,plain,
    ! [A: nat,B: nat] :
      ( ( ( minus_minus @ nat @ A @ B )
        = ( zero_zero @ nat ) )
     => ( ( ( minus_minus @ nat @ B @ A )
          = ( zero_zero @ nat ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(140,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ A @ B ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_eq__add__iff) ).

thf(671,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ A @ B ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(235,axiom,
    elemen1026692323pology @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Elementary__Topology_Osecond__countable__topology_49) ).

thf(903,plain,
    elemen1026692323pology @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(395,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TA )
        & ( topolo1314133330id_add @ TA ) )
     => ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
         => ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
           => ( member @ ( TB > TA )
              @ ^ [D: TB] : ( plus_plus @ TA @ ( A @ D ) @ ( C @ D ) )
              @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_borel__measurable__add) ).

thf(1316,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TA )
        & ( topolo1314133330id_add @ TA ) )
     => ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
         => ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
           => ( member @ ( TB > TA )
              @ ^ [D: TB] : ( plus_plus @ TA @ ( A @ D ) @ ( C @ D ) )
              @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(37,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TA )
     => ( lattice @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).

thf(450,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TA )
     => ( lattice @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(380,axiom,
    ordered_ab_group_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add_59) ).

thf(1276,plain,
    ordered_ab_group_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(312,axiom,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ A @ B ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add__cancel__right__right) ).

thf(1101,plain,
    ! [TA: $tType] :
      ( ( cancel1352612707id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( plus_plus @ TA @ A @ B ) )
          = ( B
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(4,axiom,
    topolo503727757_space @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Topological__Spaces_Otopological__space_3) ).

thf(401,plain,
    topolo503727757_space @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(182,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( monoid_add @ TB )
        & ( finite_finite @ TA ) )
     => ( monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_95) ).

thf(781,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( monoid_add @ TB )
        & ( finite_finite @ TA ) )
     => ( monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(101,axiom,
    ! [TA: $tType] : ( lattice @ ( sigma_measure @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sigma__Algebra_Omeasure___Lattices_Olattice_74) ).

thf(588,plain,
    ! [TA: $tType] : ( lattice @ ( sigma_measure @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(371,axiom,
    ! [A: finite_Cartesian_vec @ int @ n] :
      ( member @ ( ( finite_Cartesian_vec @ real @ n ) > ( finite_Cartesian_vec @ real @ n ) )
      @ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
      @ ( sigma_measurable @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062_092_060And_062a_O_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_092_060in_062_Alebesgue_A_092_060rightarrow_062_092_060_094sub_062M_Alebesgue_092_060close_062) ).

thf(1253,plain,
    ! [A: finite_Cartesian_vec @ int @ n] :
      ( member @ ( ( finite_Cartesian_vec @ real @ n ) > ( finite_Cartesian_vec @ real @ n ) )
      @ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
      @ ( sigma_measurable @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(149,axiom,
    cancel_semigroup_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__semigroup__add_60) ).

thf(699,plain,
    cancel_semigroup_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(257,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ab_semigroup_add @ TB )
        & ( finite_finite @ TA ) )
     => ( ab_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_90) ).

thf(961,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ab_semigroup_add @ TB )
        & ( finite_finite @ TA ) )
     => ( ab_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(196,axiom,
    zero @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_71) ).

thf(813,plain,
    zero @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(258,axiom,
    real_V55928688vector @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector) ).

thf(963,plain,
    real_V55928688vector @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(69,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_inf_Oidem) ).

thf(517,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(233,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ( ( plus_plus @ TA )
        = ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add_Ocommute) ).

thf(896,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ( ( plus_plus @ TA )
        = ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(170,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
          = ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_add__diff__eq) ).

thf(748,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
          = ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(92,axiom,
    comm_monoid_diff @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).

thf(568,plain,
    comm_monoid_diff @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(387,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
          = ( inf_inf @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_translation__Int) ).

thf(1294,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
          = ( inf_inf @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(246,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ C ) )
         => ( ( plus_plus @ TA @ A @ D )
            = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_group__cancel_Oadd1) ).

thf(929,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ C ) )
         => ( ( plus_plus @ TA @ A @ D )
            = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(392,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add_Ocomm__neutral) ).

thf(1308,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(350,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TB,C: TB > TA,D: TB > TA,E: sigma_measure @ TA,F: sigma_measure @ TA] :
      ( ( A = B )
     => ( ! [G: TB] :
            ( ( member @ TB @ G @ B )
           => ( ( C @ G )
              = ( D @ G ) ) )
       => ( ( ( sigma_sets @ TA @ E )
            = ( sigma_sets @ TA @ F ) )
         => ( ( sigma_vimage_algebra @ TB @ TA @ A @ C @ E )
            = ( sigma_vimage_algebra @ TB @ TA @ B @ D @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_vimage__algebra__cong) ).

thf(1193,plain,
    ! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TB,C: TB > TA,D: TB > TA,E: sigma_measure @ TA,F: sigma_measure @ TA] :
      ( ( A = B )
     => ( ! [G: TB] :
            ( ( member @ TB @ G @ B )
           => ( ( C @ G )
              = ( D @ G ) ) )
       => ( ( ( sigma_sets @ TA @ E )
            = ( sigma_sets @ TA @ F ) )
         => ( ( sigma_vimage_algebra @ TB @ TA @ A @ C @ E )
            = ( sigma_vimage_algebra @ TB @ TA @ B @ D @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(301,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( inf_inf @ ( TA > $o )
        @ ^ [C: TA] : ( member @ TA @ C @ A )
        @ ^ [C: TA] : ( member @ TA @ C @ B ) )
      = ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_inf__Int__eq) ).

thf(1077,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( inf_inf @ ( TA > $o )
        @ ^ [C: TA] : ( member @ TA @ C @ A )
        @ ^ [C: TA] : ( member @ TA @ C @ B ) )
      = ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(356,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
      ( ( vimage @ TB @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
      = ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_vimage__Int) ).

thf(1212,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
      ( ( vimage @ TB @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
      = ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(176,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: set @ TB,B: TB > TA] :
          ( ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
         => ( ( member @ ( TB > TA )
              @ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ A ) @ ( B @ C ) @ ( zero_zero @ TA ) )
              @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
            = ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_borel__measurable__if) ).

thf(763,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: set @ TB,B: TB > TA] :
          ( ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
         => ( ( member @ ( TB > TA )
              @ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ A ) @ ( B @ C ) @ ( zero_zero @ TA ) )
              @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
            = ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(234,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
      ( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
     => ~ ! [D: TA] :
            ( ( A
              = ( B @ D ) )
           => ~ ( member @ TA @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_imageE) ).

thf(899,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
      ( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
     => ~ ! [D: TA] :
            ( ( A
              = ( B @ D ) )
           => ~ ( member @ TA @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(145,axiom,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: sigma_measure @ TB,C: sigma_measure @ TA,D: sigma_measure @ TA] :
      ( ( ( sigma_sets @ TB @ A )
        = ( sigma_sets @ TB @ B ) )
     => ( ( ( sigma_sets @ TA @ C )
          = ( sigma_sets @ TA @ D ) )
       => ( ( sigma_measurable @ TB @ TA @ A @ C )
          = ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_measurable__cong__sets) ).

thf(684,plain,
    ! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: sigma_measure @ TB,C: sigma_measure @ TA,D: sigma_measure @ TA] :
      ( ( ( sigma_sets @ TB @ A )
        = ( sigma_sets @ TB @ B ) )
     => ( ( ( sigma_sets @ TA @ C )
          = ( sigma_sets @ TA @ D ) )
       => ( ( sigma_measurable @ TB @ TA @ A @ C )
          = ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(78,axiom,
    topolo2117631714pology @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Olinorder__topology_41) ).

thf(536,plain,
    topolo2117631714pology @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(290,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ C ) )
         => ( ( minus_minus @ TA @ A @ D )
            = ( plus_plus @ TA @ B @ ( minus_minus @ TA @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_group__cancel_Osub1) ).

thf(1045,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( plus_plus @ TA @ B @ C ) )
         => ( ( minus_minus @ TA @ A @ D )
            = ( plus_plus @ TA @ B @ ( minus_minus @ TA @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(156,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TB )
        & ( topolo2117631714pology @ TB ) )
     => ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
         => ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
           => ( member @ ( set @ TA )
              @ ( collect @ TA
                @ ^ [D: TA] :
                    ( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
                    & ( ( A @ D )
                     != ( C @ D ) ) ) )
              @ ( sigma_sets @ TA @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_borel__measurable__neq) ).

thf(716,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TB )
        & ( topolo2117631714pology @ TB ) )
     => ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
         => ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
           => ( member @ ( set @ TA )
              @ ( collect @ TA
                @ ^ [D: TA] :
                    ( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
                    & ( ( A @ D )
                     != ( C @ D ) ) ) )
              @ ( sigma_sets @ TA @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(28,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).

thf(433,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(66,axiom,
    elemen1026692323pology @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Elementary__Topology_Osecond__countable__topology_9) ).

thf(510,plain,
    elemen1026692323pology @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(318,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_192_DiffD2) ).

thf(1116,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)],[318]) ).

thf(117,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_le__zero__eq) ).

thf(620,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(34,axiom,
    canoni770627133id_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).

thf(447,plain,
    canoni770627133id_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(382,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( semigroup_add @ TB )
        & ( finite_finite @ TA ) )
     => ( semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_92) ).

thf(1280,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( semigroup_add @ TB )
        & ( finite_finite @ TA ) )
     => ( semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(253,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
         => ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add__left__imp__eq) ).

thf(950,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ A @ C ) )
         => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(199,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_30_Int__left__commute) ).

thf(818,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)],[199]) ).

thf(8,axiom,
    cancel_semigroup_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__semigroup__add) ).

thf(405,plain,
    cancel_semigroup_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(332,axiom,
    real_V1076094709vector @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector) ).

thf(1148,plain,
    real_V1076094709vector @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(220,axiom,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: set @ TA] :
          ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
         => ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_lborelD) ).

thf(867,plain,
    ! [TA: $tType] :
      ( ( euclid925273238_space @ TA )
     => ! [A: set @ TA] :
          ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
         => ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(164,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
         => ( A = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__right__imp__eq) ).

thf(735,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
         => ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(206,axiom,
    ab_semigroup_add @ real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__semigroup__add_62) ).

thf(833,plain,
    ab_semigroup_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(13,axiom,
    monoid_add @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__add) ).

thf(410,plain,
    monoid_add @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(215,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_le__add__same__cancel1) ).

thf(854,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(390,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add_Oleft__commute) ).

thf(1303,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(369,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( image @ TA @ TA
            @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
            @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
          = ( minus_minus @ ( set @ TA )
            @ ( image @ TA @ TA
              @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
              @ B )
            @ ( image @ TA @ TA
              @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
              @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_translation__subtract__diff) ).

thf(1248,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( image @ TA @ TA
            @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
            @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
          = ( minus_minus @ ( set @ TA )
            @ ( image @ TA @ TA
              @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
              @ B )
            @ ( image @ TA @ TA
              @ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
              @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(187,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( vimage @ TA @ TB )
      = ( ^ [A: TA > TB,B: set @ TB] :
            ( collect @ TA
            @ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_vimage__def) ).

thf(790,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( vimage @ TA @ TB )
      = ( ^ [A: TA > TB,B: set @ TB] :
            ( collect @ TA
            @ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(394,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( finite_finite @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_35) ).

thf(1314,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( finite_finite @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(193,axiom,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
          = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_add__diff__cancel__left_H) ).

thf(807,plain,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
          = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(49,axiom,
    ! [TA: $tType] : ( semilattice_inf @ ( sigma_measure @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sigma__Algebra_Omeasure___Lattices_Osemilattice__inf_73) ).

thf(474,plain,
    ! [TA: $tType] : ( semilattice_inf @ ( sigma_measure @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(148,axiom,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_le__add__same__cancel2) ).

thf(696,plain,
    ! [TA: $tType] :
      ( ( ordere516151231imp_le @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(189,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A
            = ( minus_minus @ TA @ B @ C ) )
          = ( ( plus_plus @ TA @ A @ C )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_eq__diff__eq) ).

thf(796,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A
            = ( minus_minus @ TA @ B @ C ) )
          = ( ( plus_plus @ TA @ A @ C )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(18,axiom,
    ordere516151231imp_le @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).

thf(415,plain,
    ordere516151231imp_le @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(242,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( finite_finite @ TA ) )
     => ( finite_finite @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_96) ).

thf(918,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( finite_finite @ TA ) )
     => ( finite_finite @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(191,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_188_Diff__iff) ).

thf(801,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)],[191]) ).

thf(385,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ? [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
          & ( C @ D ) )
     => ? [D: TA] :
          ( ( member @ TA @ D @ B )
          & ( C @ ( A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_bex__imageD) ).

thf(1288,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ? [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
          & ( C @ D ) )
     => ? [D: TA] :
          ( ( member @ TA @ D @ B )
          & ( C @ ( A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(3,axiom,
    plus @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oplus) ).

thf(400,plain,
    plus @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(76,axiom,
    minus @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ominus_47) ).

thf(532,plain,
    minus @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(297,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
      ( ( vimage @ TB @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
      = ( minus_minus @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_vimage__Diff) ).

thf(1065,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
      ( ( vimage @ TB @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
      = ( minus_minus @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(161,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ( comm_monoid_add @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ocomm__monoid__add_31) ).

thf(728,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ( comm_monoid_add @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(44,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( minus @ TA )
     => ( minus @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ominus) ).

thf(464,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( minus @ TA )
     => ( minus @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(217,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: TB > TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
          = ( ! [B: set @ TA] :
                ( ( member @ ( set @ TA ) @ B @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
               => ( member @ ( set @ TB )
                  @ ( collect @ TB
                    @ ^ [C: TB] : ( member @ TA @ ( A @ C ) @ B ) )
                  @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_borel__measurable__lebesgue__preimage__borel) ).

thf(860,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: TB > TA] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
          = ( ! [B: set @ TA] :
                ( ( member @ ( set @ TA ) @ B @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
               => ( member @ ( set @ TB )
                  @ ( collect @ TB
                    @ ^ [C: TB] : ( member @ TA @ ( A @ C ) @ B ) )
                  @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(280,axiom,
    ! [TA: $tType] :
      ( ( semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add_Oassoc) ).

thf(1019,plain,
    ! [TA: $tType] :
      ( ( semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
          = ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(74,axiom,
    comm_monoid_add @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add_21) ).

thf(528,plain,
    comm_monoid_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(128,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TB )
        & ( topolo2117631714pology @ TB ) )
     => ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
         => ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
           => ( member @ ( set @ TA )
              @ ( collect @ TA
                @ ^ [D: TA] :
                    ( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
                    & ( ( A @ D )
                      = ( C @ D ) ) ) )
              @ ( sigma_sets @ TA @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_borel__measurable__eq) ).

thf(644,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( elemen1026692323pology @ TB )
        & ( topolo2117631714pology @ TB ) )
     => ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
          ( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
         => ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
           => ( member @ ( set @ TA )
              @ ( collect @ TA
                @ ^ [D: TA] :
                    ( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
                    & ( ( A @ D )
                      = ( C @ D ) ) ) )
              @ ( sigma_sets @ TA @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(42,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ( ( inf_inf @ TA )
        = ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_inf__commute) ).

thf(459,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ( ( inf_inf @ TA )
        = ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(266,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
          = ( minus_minus @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_translation__diff) ).

thf(982,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: set @ TA,C: set @ TA] :
          ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
          = ( minus_minus @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(31,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ( ( inf_inf @ TA )
        = ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_inf_Ocommute) ).

thf(442,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ( ( inf_inf @ TA )
        = ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(109,axiom,
    lattice @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_25) ).

thf(607,plain,
    lattice @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(308,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: sigma_measure @ TA,C: TB > TA,D: set @ TB] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ C @ A ) @ D ) @ ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ D @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_in__vimage__algebra) ).

thf(1093,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: sigma_measure @ TA,C: TB > TA,D: set @ TB] :
      ( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
     => ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ C @ A ) @ D ) @ ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ D @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(119,axiom,
    topolo503727757_space @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Otopological__space_11) ).

thf(624,plain,
    topolo503727757_space @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(209,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TB,B: sigma_measure @ TB,C: TA,D: sigma_measure @ TA,E: TB > TA] :
      ( ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ A @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) )
     => ( ( member @ TA @ C @ ( sigma_space @ TA @ D ) )
       => ( ( member @ ( TB > TA ) @ E @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ B @ A ) @ D ) )
          = ( member @ ( TB > TA )
            @ ^ [F: TB] : ( if @ TA @ ( member @ TB @ F @ A ) @ ( E @ F ) @ C )
            @ ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_measurable__restrict__space__iff) ).

thf(839,plain,
    ! [TA: $tType,TB: $tType,A: set @ TB,B: sigma_measure @ TB,C: TA,D: sigma_measure @ TA,E: TB > TA] :
      ( ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ A @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) )
     => ( ( member @ TA @ C @ ( sigma_space @ TA @ D ) )
       => ( ( member @ ( TB > TA ) @ E @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ B @ A ) @ D ) )
          = ( member @ ( TB > TA )
            @ ^ [F: TB] : ( if @ TA @ ( member @ TB @ F @ A ) @ ( E @ F ) @ C )
            @ ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(377,axiom,
    ! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
      ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
      = ( sigma_sets @ TA
        @ ( sigma_vimage_algebra @ TA @ TA @ ( inf_inf @ ( set @ TA ) @ B @ ( sigma_space @ TA @ A ) )
          @ ^ [C: TA] : C
          @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_restrict__space__eq__vimage__algebra_H) ).

thf(1268,plain,
    ! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
      ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
      = ( sigma_sets @ TA
        @ ( sigma_vimage_algebra @ TA @ TA @ ( inf_inf @ ( set @ TA ) @ B @ ( sigma_space @ TA @ A ) )
          @ ^ [C: TA] : C
          @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(95,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( minus @ TB )
     => ( ( minus_minus @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_minus__apply) ).

thf(575,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( minus @ TB )
     => ( ( minus_minus @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(54,axiom,
    topological_t2_space @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Ot2__space_17) ).

thf(486,plain,
    topological_t2_space @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(397,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: TB > TA,B: set @ TB] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
          = ( ! [C: set @ TA] :
                ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
               => ( member @ ( set @ TB )
                  @ ( collect @ TB
                    @ ^ [D: TB] :
                        ( ( member @ TB @ D @ B )
                        & ( member @ TA @ ( A @ D ) @ C ) ) )
                  @ ( sigma_sets @ TB @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_borel__measurable__vimage__borel) ).

thf(1320,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( euclid925273238_space @ TA )
        & ( euclid925273238_space @ TB ) )
     => ! [A: TB > TA,B: set @ TB] :
          ( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
          = ( ! [C: set @ TA] :
                ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
               => ( member @ ( set @ TB )
                  @ ( collect @ TB
                    @ ^ [D: TB] :
                        ( ( member @ TB @ D @ B )
                        & ( member @ TA @ ( A @ D ) @ C ) ) )
                  @ ( sigma_sets @ TB @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(46,axiom,
    ! [A: nat > $o] :
      ( ( A @ ( zero_zero @ nat ) )
     => ( ( ord_Least @ nat @ A )
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Least__eq__0) ).

thf(469,plain,
    ! [A: nat > $o] :
      ( ( A @ ( zero_zero @ nat ) )
     => ( ( ord_Least @ nat @ A )
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(244,axiom,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
          = ( ord_less_eq @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_add__le__cancel__left) ).

thf(923,plain,
    ! [TA: $tType] :
      ( ( ordere236663937imp_le @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
          = ( ord_less_eq @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(347,axiom,
    ! [A: finite_Cartesian_vec @ int @ n] :
      ( ( t @ A )
      = ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
        @ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
        @ ( t2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_T_H__altdef) ).

thf(1184,plain,
    ! [A: finite_Cartesian_vec @ int @ n] :
      ( ( t @ A )
      = ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
        @ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
        @ ( t2 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(81,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( inf_inf @ TA @ B @ C ) )
         => ( ( inf_inf @ TA @ A @ D )
            = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_boolean__algebra__cancel_Oinf1) ).

thf(543,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( inf_inf @ TA @ B @ C ) )
         => ( ( inf_inf @ TA @ A @ D )
            = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(125,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V1076094709vector @ TB )
        & ( finite_finite @ TA ) )
     => ( real_V1076094709vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__vector_82) ).

thf(639,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( real_V1076094709vector @ TB )
        & ( finite_finite @ TA ) )
     => ( real_V1076094709vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(173,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
          = ( A = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add_Oright__cancel) ).

thf(755,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ A @ B )
            = ( plus_plus @ TA @ C @ B ) )
          = ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(353,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TA] :
      ( ( ( A @ B )
        = C )
     => ( ( member @ TA @ C @ D )
       => ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_vimageI) ).

thf(1204,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TA] :
      ( ( ( A @ B )
        = C )
     => ( ( member @ TA @ C @ D )
       => ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(278,axiom,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
          = ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_diff__add__eq) ).

thf(1014,plain,
    ! [TA: $tType] :
      ( ( ab_group_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
          = ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(60,axiom,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
          = ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_diff__right__commute) ).

thf(496,plain,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
          = ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(40,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( inf_inf @ TA @ B @ C ) )
         => ( ( inf_inf @ TA @ D @ A )
            = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_boolean__algebra__cancel_Oinf2) ).

thf(454,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A
            = ( inf_inf @ TA @ B @ C ) )
         => ( ( inf_inf @ TA @ D @ A )
            = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(1326,plain,
    $false,
    inference(e,[status(thm)],[1036,629,1024,479,628,893,1083,941,1179,777,1168,760,1237,846,1200,1211,582,1005,730,1068,994,741,449,1041,408,977,878,511,614,677,533,550,500,1164,472,1233,814,1260,945,1063,670,747,913,1127,709,417,436,1265,651,1095,404,504,1323,751,1191,1132,1055,724,559,1087,421,969,770,1115,448,1100,881,416,492,623,646,514,1151,966,821,480,1040,1109,1136,834,766,687,956,866,453,660,998,411,428,507,1215,634,1104,1242,849,1074,452,920,439,529,793,1306,1153,810,1311,1057,910,1223,1091,825,778,1255,1123,1174,424,407,788,815,1217,598,916,566,1032,625,879,852,665,889,1159,493,682,1291,842,974,1106,522,830,578,1089,1017,615,1121,1227,1138,593,869,499,857,874,1143,980,403,783,420,1118,884,1160,488,933,537,476,489,590,547,554,753,837,985,701,1297,738,1231,1060,721,569,503,1318,1202,938,1035,1071,953,586,718,926,1187,674,906,412,425,1146,1273,745,689,601,1251,618,423,402,732,743,579,958,413,562,904,843,1125,641,445,572,1271,713,466,804,947,540,611,787,1258,704,604,406,831,1282,784,1011,567,649,863,990,996,890,811,1080,631,758,483,1029,668,462,1112,799,1162,700,520,1149,964,943,1022,399,563,1000,431,653,658,521,1171,768,827,1044,1245,1176,608,473,1166,1208,680,663,1277,617,553,1049,1134,487,458,823,525,1003,872,1156,887,409,1098,1225,707,414,971,1300,585,1262,1085,1130,643,1220,907,656,613,1284,600,1052,727,1140,1008,446,595,876,1240,991,556,671,903,1316,450,1276,1101,401,781,588,1253,699,961,813,963,517,896,748,568,1294,929,1308,1193,1077,1212,763,899,684,536,1045,716,433,510,1116,620,447,1280,950,818,405,1148,867,735,833,410,854,1303,1248,790,1314,807,474,696,796,415,918,801,1288,400,532,1065,728,464,860,1019,528,644,459,982,442,607,1093,624,839,1268,575,486,1320,469,923,1184,543,639,755,1204,1014,496,454]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ITP116^2 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.14  % Command  : run_Leo-III %s %d
% 0.12/0.34  % Computer : n002.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat May 18 17:06:09 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 1.01/1.01  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.08/1.43  % [INFO] 	 Parsing done (415ms). 
% 2.08/1.45  % [INFO] 	 Running in sequential loop mode. 
% 3.50/1.82  % [INFO] 	 eprover registered as external prover. 
% 3.50/1.83  % [INFO] 	 cvc4 registered as external prover. 
% 3.50/1.83  % [INFO] 	 Scanning for conjecture ... 
% 3.88/2.01  % [INFO] 	 Found a conjecture (or negated_conjecture) and 397 axioms. Running axiom selection ... 
% 4.41/2.20  % [INFO] 	 Axiom selection finished. Selected 396 axioms (removed 1 axioms). 
% 5.84/2.55  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 5.84/2.58  % [INFO] 	 Type checking passed. 
% 5.84/2.59  % [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 ... 
% 41.91/23.56  % External prover 'e' found a proof!
% 41.91/23.56  % [INFO] 	 Killing All external provers ... 
% 41.91/23.56  % Time passed: 23059ms (effective reasoning time: 22109ms)
% 41.91/23.56  % 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)>
% 41.91/23.57  % Axioms used in derivation (396): fact_11_vimage__eq, fact_250_add__le__same__cancel1, tcon_Nat_Onat___Lattices_Olattice_25, tcon_fun___Groups_Ominus, fact_150_vimage__algebra__cong, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_53, fact_23_IntE, fact_126_image__image, fact_130_rev__image__eqI, fact_57_measurableI, fact_26_Int__assoc, fact_31_Collect__conj__eq, fact_220_diff__zero, tfree_0, fact_229_zero__reorient, fact_221_cancel__comm__monoid__add__class_Odiff__cancel, tcon_Real_Oreal___Groups_Ocancel__semigroup__add_60, fact_167_sets_ODiff, tcon_Int_Oint___Groups_Oplus, fact_101_inf__Int__eq, fact_88_sets__eq__imp__space__eq, fact_76_inf_Oassoc, tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_79, tcon_Real_Oreal___Groups_Omonoid__add_66, fact_39_add_Ocommute, tcon_fun___Finite__Set_Ofinite, fact_166_measurable__lborel2, fact_145_add__diff__eq, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, tcon_Real_Oreal___Groups_Olinordered__ab__group__add_54, fact_89_measurable__cong__simp, fact_159_borel__measurable__neq, fact_185_restrict__restrict__space, fact_69_inf_Oidem, tcon_Set_Oset___Lattices_Osemilattice__inf_29, fact_139_measurable__restrict__space1, tcon_Real_Oreal___Groups_Ozero_71, tcon_Sigma__Algebra_Omeasure___Lattices_Olattice_74, fact_148_group__cancel_Osub1, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_16, fact_202_measurable__product__coordinates, fact_96_sets_Osets__Collect__conj, tcon_Int_Oint___Groups_Ozero, tcon_HOL_Obool___Countable_Ocountable_44, fact_65_inf_Oright__idem, fact_125_Compr__image__eq, fact_30_Int__left__commute, fact_242_inf_Obounded__iff, fact_142_diff__add__eq__diff__diff__swap, fact_184_restrict__space__eq__vimage__algebra_H, fact_32_Int__Collect, fact_224_eq__add__iff, fact_35_vimage__inter__cong, tcon_HOL_Obool___Lattices_Osemilattice__inf_43, fact_176_sets__restrict__space, fact_10_vimageI, tcon_Finite__Cartesian__Product_Ovec___Limits_Otopological__monoid__add_84, tcon_Int_Oint___Nat_Oring__char__0, tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_96, fact_18_IntI, tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_98, fact_99_measurable__const, fact_25_IntD2, tcon_Nat_Onat___Groups_Oab__semigroup__add_20, fact_83_inf__sup__aci_I4_J, fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_8_vimage__ident, tcon_Int_Oint___Groups_Oordered__ab__group__add, fact_192_DiffD2, fact_171_Diff__Int2, fact_155_space__restrict__space, fact_244_set__plus__mono2, fact_151_borel__measurable__const__add, fact_226_comm__monoid__add__class_Oadd__0, fact_152_borel__measurable__add, tcon_Real_Oreal___Topological__Spaces_Ot2__space_58, fact_51_ab__semigroup__add__class_Oadd__ac_I1_J, fact_181_lebesgue__measurable__vimage__borel, tcon_Int_Oint___Groups_Oab__group__add, fact_144_diff__diff__eq2, fact_9_vimage__Collect__eq, tcon_Set_Oset___Groups_Osemigroup__add_32, tcon_Real_Oreal___Groups_Oab__semigroup__add_62, fact_63_inf__apply, fact_215_add__eq__0__iff__both__eq__0, tcon_Int_Oint___Limits_Otopological__monoid__add, tcon_Real_Oreal___Nat_Oring__char__0_69, tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_97, fact_52_vimage__Collect, tcon_fun___Topological__Spaces_Otopological__space, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_50, fact_86_measurable__id, fact_79_inf__fun__def, fact_141_diff__diff__add, fact_14_add__right__cancel, fact_233_borel__measurable__if__lebesgue__on, fact_61_measurable__sets__Collect, tcon_Real_Oreal___Groups_Ogroup__add_68, fact_210_double__zero__sym, fact_134_image__iff, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_75, fact_19_Int__iff, fact_157_sets__Collect__restrict__space__iff, tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__inf_89, fact_71_inf__left__commute, tcon_Set_Oset___Groups_Oab__semigroup__add_30, fact_85_measurable__compose, fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_72_inf_Oleft__commute, fact_92_measurable__ident__sets, fact_131_ball__imageD, fact_80_inf__sup__aci_I1_J, tcon_HOL_Obool___Topological__Spaces_Olinorder__topology_41, fact_117_space__vimage__algebra, fact_201_measurable__coordinatewise__then__product, tcon_Nat_Onat___Elementary__Topology_Osecond__countable__topology_9, fact_189_DiffI, tcon_Real_Oreal___Groups_Ocomm__monoid__add_63, tcon_Int_Oint___Groups_Ominus_7, tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_99, fact_161_measurable__If__restrict__space__iff, fact_158_borel__measurable__eq, tcon_Int_Oint___Groups_Ocancel__semigroup__add, fact_98_sets_Osets__Collect__const, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_88, tcon_Int_Oint___Groups_Omonoid__add, fact_234_subsetI, fact_100_T_H__def, fact_188_Diff__iff, fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, tcon_HOL_Obool___Topological__Spaces_Ot2__space_42, fact_191_minus__set__def, fact_77_boolean__algebra__cancel_Oinf2, fact_118_main__part, tcon_HOL_Obool___Finite__Set_Ofinite_45, tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_101, tcon_Int_Oint___Groups_Osemigroup__add, fact_12_set__plus__intro, fact_49_group__cancel_Oadd1, tcon_Set_Oset___Groups_Oplus_39, tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Ot2__space_86, fact_46_Collect__mem__eq, tcon_Sigma__Algebra_Omeasure___Lattices_Osemilattice__inf_73, tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1, tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector, tcon_Int_Oint___Groups_Oab__semigroup__add, fact_120_inf1E, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_83, fact_41_add_Oleft__cancel, tcon_Set_Oset___Groups_Ominus_37, fact_251_diff__ge__0__iff__ge, tcon_Real_Oreal___Limits_Otopological__monoid__add_56, fact_27_Int__absorb, tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__vector_82, fact_94_sets_Osets__Collect__imp, tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_90, subcl_Finite__Set_Ofinite___Countable_Ocountable, fact_174_Diff__Int__distrib2, fact_135_imageI, fact_207_add_Oleft__neutral, fact_200_measurable__product__then__coordinatewise, help_If_1_1_T, fact_146_eq__diff__eq, fact_252_subset__translation__eq, fact_74_inf_Ocommute, tcon_fun___Countable_Ocountable, fact_113_add__diff__cancel__left_H, fact_253_diffs0__imp__equal, tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_100, fact_6_sets__completionI__sets, fact_196_translation__subtract__diff, fact_128_diff__right__commute, fact_216_zero__eq__add__iff__both__eq__0, fact_137_sets__restrict__space__cong, tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_57, fact_214_add__cancel__right__right, fact_68_inf__idem, fact_82_inf__sup__aci_I3_J, tcon_Nat_Onat___Topological__Spaces_Ot2__space_17, tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le, tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, fact_140_add__implies__diff, fact_93_sets_Osets__Collect_I5_J, tcon_Real_Oreal___Topological__Spaces_Otopological__space_51, tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space, fact_124_fun__diff__def, fact_204_translation__assoc, fact_110_image__ident, fact_55_sets_OInt__space__eq1, fact_208_add_Oright__neutral, fact_67_inf_Oleft__idem, tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_94, fact_13_add__left__cancel, fact_132_image__cong, fact_119_space__restrict__space2, fact_235_subset__antisym, tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector, fact_194_DiffE, fact_105_in__vimage__algebra, fact_199_translation__Int, tcon_Real_Oreal___Groups_Oab__group__add_65, tcon_fun___Lattices_Osemilattice__inf, fact_16_vimageD, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_91, fact_28_Int__commute, fact_122_inf1D2, fact_219_zero__diff, fact_20_space__completion, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_10, tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_93, tcon_Finite__Cartesian__Product_Ovec___Groups_Oplus_102, fact_87_measurable__cong__sets, fact_45_mem__Collect__eq, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_80, fact_123_borel__measurable__diff, tcon_Set_Oset___Groups_Ocomm__monoid__add_31, fact_37_add__left__imp__eq, fact_104_sets__Least, fact_205_affine__parallel__expl__aux, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_77, fact_97_sets_Osets__Collect__disj, tcon_Set_Oset___Groups_Omonoid__add_34, fact_165_measurable__lborel1, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add, fact_198_translation__diff, fact_53_vimageI2, fact_168_sets_Ocompl__sets, tcon_Int_Oint___Countable_Ocountable_5, fact_187_Diff__idemp, fact_248_le__add__same__cancel1, fact_36_add__right__imp__eq, fact_90_measurable__space, tcon_Real_Oreal___Groups_Ominus_70, fact_228_add_Ogroup__left__neutral, fact_24_IntD1, fact_239_add__le__cancel__right, tcon_Nat_Onat___Countable_Ocountable_23, fact_60_measurable__If__set, tcon_Nat_Onat___Groups_Osemigroup__add_22, fact_136_borel__measurable__const, fact_42_add_Oassoc, tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add, tcon_Real_Oreal___Topological__Spaces_Olinorder__topology_52, fact_164_space__lborel, fact_149_sets__vimage__algebra__cong, tcon_Int_Oint___Groups_Ocomm__monoid__add, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_85, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_13, fact_50_add__mono__thms__linordered__semiring_I4_J, fact_180_lebesgue__sets__translation, fact_38_add_Oleft__commute, fact_179_lborelD__Collect, fact_121_inf1D1, fact_84_measurable__compose__rev, tcon_Int_Oint___Groups_Ogroup__add, tcon_Real_Oreal___Lattices_Osemilattice__inf_61, fact_47_Collect__cong, fact_66_inf__left__idem, fact_209_double__zero, tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space, fact_169_sets__lborel, help_If_3_1_T, fact_4_T_H__altdef, fact_178_measurable__lebesgue__cong, help_If_2_1_T, fact_58_sets_Otop, fact_217_diff__self, tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_55, fact_81_inf__sup__aci_I2_J, fact_156_measurable__sets__borel, fact_243_Int__subset__iff, fact_1_of__int__vec__eq__iff, fact_95_sets_Osets__Collect__neg, fact_211_add__cancel__left__left, fact_154_sets__restrict__restrict__space, tcon_Real_Oreal___Groups_Oplus_72, fact_91_measurable__cong, tcon_Real_Oreal___Groups_Oordered__ab__group__add_59, tcon_Nat_Onat___Topological__Spaces_Otopological__space_11, fact_183_borel__measurable__vimage__borel, tcon_Int_Oint___Groups_Olinordered__ab__group__add, fact_230_borel__measurable__if__D, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_206_borel__measurable__if, fact_160_measurable__equality__set, fact_114_add__diff__cancel__left, fact_106_in__borel__measurable__borel, tcon_Int_Oint___Topological__Spaces_Otopological__space_3, fact_163_sets__lebesgue__on__refl, tcon_Nat_Onat___Groups_Oplus_28, fact_43_set__plus__elim, fact_33_Int__def, tcon_HOL_Obool___Topological__Spaces_Otopological__space_40, fact_75_inf__assoc, fact_177_lborelD, fact_237_diff__self__eq__0, fact_231_borel__measurable__if__I, tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_92, tcon_Int_Oint___Topological__Spaces_Olinorder__topology, fact_246_double__add__le__zero__iff__single__add__le__zero, fact_109_inf1I, tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_95, fact_62_measurable__If, fact_143_diff__add__eq, fact_195_sets__vimage__algebra__space, fact_190_set__diff__eq, tcon_Set_Oset___Lattices_Olattice_36, fact_44_group__cancel_Oadd2, tcon_Int_Oint___Lattices_Olattice_6, fact_172_Diff__Diff__Int, subcl_Finite__Set_Ofinite___HOL_Otype, fact_111_add__diff__cancel__right_H, fact_193_DiffD1, tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_78, fact_213_add__cancel__right__left, fact_182_borel__measurable__lebesgue__preimage__borel, fact_7__092_060open_062_092_060And_062a_O_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_092_060in_062_Alebesgue_A_092_060rightarrow_062_092_060_094sub_062M_Alebesgue_092_060close_062, fact_40_add_Oright__cancel, fact_102_main__part__sets, fact_129_diff__eq__diff__eq, tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space, tcon_HOL_Obool___Lattices_Olattice_46, fact_70_inf__set__def, fact_54_sets_OInt__space__eq2, fact_15_vimage__def, fact_222_image__add__0, fact_138_restrict__space__sets__cong, fact_133_bex__imageD, fact_115_diff__add__cancel, fact_56_measurable__sets, fact_241_le__inf__iff, fact_107_image__eqI, fact_127_imageE, fact_78_boolean__algebra__cancel_Oinf1, tcon_Set_Oset___Countable_Ocountable_33, fact_147_diff__eq__eq, tcon_Nat_Onat___Lattices_Osemilattice__inf_19, tcon_Nat_Onat___Groups_Omonoid__add_24, fact_21_vimage__Int, fact_153_borel__measurable__inf, tcon_fun___Elementary__Topology_Osecond__countable__topology, fact_223_diff__add__zero, fact_170_Int__Diff, fact_245_zero__le__double__add__iff__zero__le__single__add, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_48, fact_249_add__le__same__cancel2, tcon_Nat_Onat___Topological__Spaces_Olinorder__topology_12, fact_227_add_Ocomm__neutral, tcon_Nat_Onat___Groups_Ocomm__monoid__add_21, fact_240_add__le__cancel__left, fact_186_is__borel__def, fact_238_le__zero__eq, fact_64_inf__right__idem, fact_0_assms_I1_J, fact_247_le__add__same__cancel2, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_8, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_29_Int__left__absorb, tcon_Finite__Cartesian__Product_Ovec___Euclidean__Space_Oeuclidean__space_81, fact_232_Least__eq__0, fact_116_add__diff__cancel, fact_236_diff__0__eq__0, fact_34_measurable__completion, fact_212_add__cancel__left__right, tcon_Real_Oreal___Elementary__Topology_Osecond__countable__topology_49, tcon_Nat_Onat___Groups_Ocancel__semigroup__add_18, tcon_Finite__Cartesian__Product_Ovec___Elementary__Topology_Osecond__countable__topology_76, fact_162_space__lebesgue__on, tcon_Int_Oint___Lattices_Osemilattice__inf_4, fact_103_measurable__restrict__space__iff, fact_218_diff__0__right, fact_108_minus__apply, fact_197_translation__subtract__Int, tcon_Nat_Onat___Limits_Otopological__monoid__add_15, fact_173_Diff__Int__distrib, fact_112_add__diff__cancel__right, tcon_Real_Oreal___Lattices_Olattice_67, tcon_Int_Oint___Topological__Spaces_Ot2__space, fact_22_T__def, tcon_Set_Oset___Finite__Set_Ofinite_35, fact_73_inf__commute, fact_17_vimageE, tcon_Set_Oset___Groups_Ozero_38, fact_59_sets_OInt, tcon_Real_Oreal___Groups_Osemigroup__add_64, tcon_Nat_Onat___Groups_Ominus_26, fact_225_eq__iff__diff__eq__0, fact_254_minus__nat_Odiff__0, fact_203_translation__invert, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_14, tcon_HOL_Obool___Groups_Ominus_47, tcon_Nat_Onat___Groups_Ozero_27, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_87, tcon_fun___Lattices_Olattice, fact_175_vimage__Diff, tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_2
% 41.91/23.57  % No. of inferences in proof: 796
% 41.91/23.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23059 ms resp. 22109 ms w/o parsing
% 42.79/23.74  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 42.79/23.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------