TSTP Solution File: ITP115^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP115^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:03 EDT 2024

% Result   : Theorem 8.56s 3.14s
% Output   : Refutation 8.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  160
% Syntax   : Number of formulae    :  300 ( 152 unt;  22 typ;   0 def)
%            Number of atoms       :  728 ( 316 equ;   6 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 2214 ( 128   ~;   6   |;  94   &;1740   @)
%                                         (   0 <=>; 246  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   34 (  34   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  18 usr;   6 con; 0-2 aty)
%            Number of variables   :  692 (  36   ^ 624   !;  32   ?; 692   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_b_type,type,
    set_b: $tType ).

thf(set_a_type,type,
    set_a: $tType ).

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

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

thf(minus_minus_set_b_type,type,
    minus_minus_set_b: set_b > set_b > set_b ).

thf(inf_inf_set_b_type,type,
    inf_inf_set_b: set_b > set_b > set_b ).

thf(lower_464587817at_a_b_type,type,
    lower_464587817at_a_b: a > ( a > b ) > $o ).

thf(bot_bot_b_o_type,type,
    bot_bot_b_o: b > $o ).

thf(bot_bot_set_b_type,type,
    bot_bot_set_b: set_b ).

thf(ord_less_eq_b_type,type,
    ord_less_eq_b: b > b > $o ).

thf(insert_b_type,type,
    insert_b: b > set_b > set_b ).

thf(is_empty_b_type,type,
    is_empty_b: set_b > $o ).

thf(is_singleton_b_type,type,
    is_singleton_b: set_b > $o ).

thf(the_elem_b_type,type,
    the_elem_b: set_b > b ).

thf(topolo1276428101open_a_type,type,
    topolo1276428101open_a: set_a > $o ).

thf(topolo1276428102open_b_type,type,
    topolo1276428102open_b: set_b > $o ).

thf(member_a_type,type,
    member_a: a > set_a > $o ).

thf(member_b_type,type,
    member_b: b > set_b > $o ).

thf(a2_type,type,
    a2: b ).

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

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

thf(x0_type,type,
    x0: a ).

thf(64,axiom,
    ! [A: b,B: b,C: b > b,D: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: b,F: b] :
              ( ( ord_less_eq_b @ E @ F )
             => ( ord_less_eq_b @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_b @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_ord__le__eq__subst) ).

thf(352,plain,
    ! [A: b,B: b,C: b > b,D: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: b,F: b] :
              ( ( ord_less_eq_b @ E @ F )
             => ( ord_less_eq_b @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_b @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(103,axiom,
    ( inf_inf_set_b
    = ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_inf__commute) ).

thf(503,plain,
    ( inf_inf_set_b
    = ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(56,axiom,
    ! [A: b,B: b,C: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ C )
       => ( ord_less_eq_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_order_Otrans) ).

thf(327,plain,
    ! [A: b,B: b,C: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ C )
       => ( ord_less_eq_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(51,axiom,
    ! [A: b,B: b,C: b,D: b] :
      ( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
        = ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_doubleton__eq__iff) ).

thf(308,plain,
    ! [A: b,B: b,C: b,D: b] :
      ( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
        = ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(106,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ( member_b @ A @ C )
       => ( member_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_IntI) ).

thf(511,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ( member_b @ A @ C )
       => ( member_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(130,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Int__left__commute) ).

thf(597,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(72,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
     => ~ ( ( member_b @ A @ B )
         => ~ ( member_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_IntE) ).

thf(385,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
     => ~ ( ( member_b @ A @ B )
         => ~ ( member_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(102,axiom,
    ! [A: set_b] :
      ( ( ! [B: b] :
            ~ ( member_b @ B @ A ) )
      = ( A = bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_all__not__in__conv) ).

thf(500,plain,
    ! [A: set_b] :
      ( ( ! [B: b] :
            ~ ( member_b @ B @ A ) )
      = ( A = bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(60,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ C ) )
      = ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ ( inf_inf_set_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_Diff__Int__distrib) ).

thf(340,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ C ) )
      = ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ ( inf_inf_set_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(115,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Int__assoc) ).

thf(538,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(77,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_inf__left__commute) ).

thf(404,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(13,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( minus_minus_set_b @ A @ B ) @ C )
      = ( minus_minus_set_b @ ( inf_inf_set_b @ A @ C ) @ ( inf_inf_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Diff__Int__distrib2) ).

thf(185,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( minus_minus_set_b @ A @ B ) @ C )
      = ( minus_minus_set_b @ ( inf_inf_set_b @ A @ C ) @ ( inf_inf_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(137,axiom,
    topolo1276428102open_b @ bot_bot_set_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_open__empty) ).

thf(619,plain,
    topolo1276428102open_b @ bot_bot_set_b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(17,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ~ ( member_b @ A @ C )
       => ( ( ( insert_b @ A @ B )
            = ( insert_b @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_insert__ident) ).

thf(196,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ~ ( member_b @ A @ C )
       => ( ( ( insert_b @ A @ B )
            = ( insert_b @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(121,axiom,
    ! [A: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ A @ B )
        = bot_bot_set_b )
      = ( ! [C: b] :
            ( ( member_b @ C @ A )
           => ! [D: b] :
                ( ( member_b @ D @ B )
               => ( C != D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_disjoint__iff__not__equal) ).

thf(559,plain,
    ! [A: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ A @ B )
        = bot_bot_set_b )
      = ( ! [C: b] :
            ( ( member_b @ C @ A )
           => ! [D: b] :
                ( ( member_b @ D @ B )
               => ( C != D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(83,axiom,
    ! [A: b,B: b] :
      ( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_singletonD) ).

thf(421,plain,
    ! [A: b,B: b] :
      ( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(133,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_inf__sup__aci_I4_J) ).

thf(606,plain,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(45,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
     => ~ ( ( member_b @ A @ B )
         => ( member_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_DiffE) ).

thf(284,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
     => ~ ( ( member_b @ A @ B )
         => ( member_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(26,axiom,
    ! [A: b,B: set_b] :
      ( ( insert_b @ A @ B )
     != bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_insert__not__empty) ).

thf(228,plain,
    ! [A: b,B: set_b] :
      ( ( insert_b @ A @ B )
     != bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(38,axiom,
    ! [A: b,B: b,C: b] :
      ( ( A = B )
     => ( ( ord_less_eq_b @ B @ C )
       => ( ord_less_eq_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ord__eq__le__trans) ).

thf(261,plain,
    ! [A: b,B: b,C: b] :
      ( ( A = B )
     => ( ( ord_less_eq_b @ B @ C )
       => ( ord_less_eq_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(54,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ~ ( member_b @ A @ C )
       => ( member_b @ A @ ( minus_minus_set_b @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_DiffI) ).

thf(321,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ~ ( member_b @ A @ C )
       => ( member_b @ A @ ( minus_minus_set_b @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(97,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Int__left__absorb) ).

thf(485,plain,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(107,axiom,
    ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_singletonI) ).

thf(514,plain,
    ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(90,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ A )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_inf__bot__left) ).

thf(453,plain,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ A )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(85,axiom,
    ! [A: set_b] :
      ( ( ( topolo1276428102open_b @ A )
        & ( member_b @ ( f @ x0 ) @ A ) )
     => ? [B: set_a] :
          ( ( topolo1276428101open_a @ B )
          & ( member_a @ x0 @ B )
          & ! [C: a] :
              ( ( member_a @ C @ B )
             => ( ( ord_less_eq_b @ ( f @ C ) @ ( f @ x0 ) )
               => ( member_b @ ( f @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36__092_060open_062_092_060forall_062S_O_Aopen_AS_A_092_060and_062_Af_Ax0_A_092_060in_062_AS_A_092_060longrightarrow_062_A_I_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062x_H_092_060in_062T_O_Af_Ax_H_A_092_060le_062_Af_Ax0_A_092_060longrightarrow_062_Af_Ax_H_A_092_060in_062_AS_J_J_092_060close_062) ).

thf(428,plain,
    ! [A: set_b] :
      ( ( ( topolo1276428102open_b @ A )
        & ( member_b @ ( f @ x0 ) @ A ) )
     => ? [B: set_a] :
          ( ( topolo1276428101open_a @ B )
          & ( member_a @ x0 @ B )
          & ! [C: a] :
              ( ( member_a @ C @ B )
             => ( ( ord_less_eq_b @ ( f @ C ) @ ( f @ x0 ) )
               => ( member_b @ ( f @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(111,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ ( minus_minus_set_b @ A @ B ) )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_Int__Diff__disjoint) ).

thf(527,plain,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ ( minus_minus_set_b @ A @ B ) )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(20,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( minus_minus_set_b @ B @ ( insert_b @ A @ C ) )
        = ( minus_minus_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Diff__insert0) ).

thf(206,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( minus_minus_set_b @ B @ ( insert_b @ A @ C ) )
        = ( minus_minus_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(33,axiom,
    ! [A: set_b] :
      ( ( minus_minus_set_b @ bot_bot_set_b @ A )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_empty__Diff) ).

thf(248,plain,
    ! [A: set_b] :
      ( ( minus_minus_set_b @ bot_bot_set_b @ A )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(70,axiom,
    ( inf_inf_set_b
    = ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Int__commute) ).

thf(380,plain,
    ( inf_inf_set_b
    = ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(118,axiom,
    ! [A: b,B: b] :
      ( ( A != B )
     => ? [C: set_b] :
          ( ( topolo1276428102open_b @ C )
          & ( member_b @ A @ C )
          & ~ ( member_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_t1__space) ).

thf(546,plain,
    ! [A: b,B: b] :
      ( ( A != B )
     => ? [C: set_b] :
          ( ( topolo1276428102open_b @ C )
          & ( member_b @ A @ C )
          & ~ ( member_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(67,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_inf__sup__aci_I2_J) ).

thf(366,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(58,axiom,
    ! [A: set_b] :
      ( ( minus_minus_set_b @ A @ A )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Diff__cancel) ).

thf(334,plain,
    ! [A: set_b] :
      ( ( minus_minus_set_b @ A @ A )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(63,axiom,
    ! [A: b,B: set_b] :
      ( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
      = ( insert_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_insert__Diff__single) ).

thf(349,plain,
    ! [A: b,B: set_b] :
      ( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
      = ( insert_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(48,axiom,
    ! [A: b,B: b,C: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ C )
       => ( ord_less_eq_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_order__trans) ).

thf(297,plain,
    ! [A: b,B: b,C: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ C )
       => ( ord_less_eq_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(84,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
        = ( inf_inf_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Int__insert__right__if0) ).

thf(424,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
        = ( inf_inf_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(78,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_inf__assoc) ).

thf(407,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(42,axiom,
    ! [A: b,B: b] :
      ( ( ( insert_b @ A @ bot_bot_set_b )
        = ( insert_b @ B @ bot_bot_set_b ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_singleton__inject) ).

thf(275,plain,
    ! [A: b,B: b] :
      ( ( ( insert_b @ A @ bot_bot_set_b )
        = ( insert_b @ B @ bot_bot_set_b ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(94,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_inf__left__idem) ).

thf(467,plain,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(91,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_inf__sup__aci_I3_J) ).

thf(456,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(55,axiom,
    ! [A: set_b,B: b,C: set_b] :
      ( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
      = ( minus_minus_set_b @ ( minus_minus_set_b @ A @ C ) @ ( insert_b @ B @ bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_Diff__insert) ).

thf(324,plain,
    ! [A: set_b,B: b,C: set_b] :
      ( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
      = ( minus_minus_set_b @ ( minus_minus_set_b @ A @ C ) @ ( insert_b @ B @ bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(109,axiom,
    ! [A: set_b,B: b] :
      ( ( A = bot_bot_set_b )
     => ~ ( member_b @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_equals0D) ).

thf(519,plain,
    ! [A: set_b,B: b] :
      ( ( A = bot_bot_set_b )
     => ~ ( member_b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(14,axiom,
    ! [A: set_b] :
      ( ( minus_minus_set_b @ A @ bot_bot_set_b )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Diff__empty) ).

thf(188,plain,
    ! [A: set_b] :
      ( ( minus_minus_set_b @ A @ bot_bot_set_b )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(73,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ A ) )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_Diff__disjoint) ).

thf(388,plain,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ A ) )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(8,axiom,
    ! [A: b] : ( ord_less_eq_b @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_order__refl) ).

thf(169,plain,
    ! [A: b] : ( ord_less_eq_b @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(129,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
        = ( inf_inf_set_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Int__insert__left__if0) ).

thf(593,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
        = ( inf_inf_set_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(3,axiom,
    ! [A: b] :
      ( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_the__elem__eq) ).

thf(141,plain,
    ! [A: b] :
      ( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(36,axiom,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_order__class_Oorder_Oantisym) ).

thf(256,plain,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(98,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_inf_Oassoc) ).

thf(488,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(128,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ bot_bot_set_b )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Int__empty__right) ).

thf(590,plain,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ bot_bot_set_b )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(39,axiom,
    ( ( (=) @ b )
    = ( ^ [A: b,B: b] :
          ( ( ord_less_eq_b @ A @ B )
          & ( ord_less_eq_b @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_eq__iff) ).

thf(266,plain,
    ( ( (=) @ b )
    = ( ^ [A: b,B: b] :
          ( ( ord_less_eq_b @ A @ B )
          & ( ord_less_eq_b @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(65,axiom,
    ( ( (=) @ b )
    = ( ^ [A: b,B: b] :
          ( ( ord_less_eq_b @ B @ A )
          & ( ord_less_eq_b @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_dual__order_Oeq__iff) ).

thf(360,plain,
    ( ( (=) @ b )
    = ( ^ [A: b,B: b] :
          ( ( ord_less_eq_b @ B @ A )
          & ( ord_less_eq_b @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(105,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_empty__iff) ).

thf(508,plain,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(52,axiom,
    ! [A: b,B: b > b,C: b,D: b] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_b @ C @ D )
       => ( ! [E: b,F: b] :
              ( ( ord_less_eq_b @ E @ F )
             => ( ord_less_eq_b @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_b @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_ord__eq__le__subst) ).

thf(311,plain,
    ! [A: b,B: b > b,C: b,D: b] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_b @ C @ D )
       => ( ! [E: b,F: b] :
              ( ( ord_less_eq_b @ E @ F )
             => ( ord_less_eq_b @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_b @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(116,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( ( member_b @ A @ B )
        & ( member_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Int__iff) ).

thf(541,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( ( member_b @ A @ B )
        & ( member_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(112,axiom,
    ( is_empty_b
    = ( ^ [A: set_b] : ( A = bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_Set_Ois__empty__def) ).

thf(530,plain,
    ( is_empty_b
    = ( ^ [A: set_b] : ( A = bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(127,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
        = ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Int__insert__right__if1) ).

thf(586,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
        = ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(61,axiom,
    ! [A: b,B: b,C: set_b] :
      ( ( member_b @ A @ ( insert_b @ B @ C ) )
     => ( ( A != B )
       => ( member_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_insertE) ).

thf(343,plain,
    ! [A: b,B: b,C: set_b] :
      ( ( member_b @ A @ ( insert_b @ B @ C ) )
     => ( ( A != B )
       => ( member_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(29,axiom,
    ( ( (=) @ b )
    = ( ^ [A: b,B: b] :
          ( ( ord_less_eq_b @ A @ B )
          & ( ord_less_eq_b @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_order__class_Oorder_Oeq__iff) ).

thf(237,plain,
    ( ( (=) @ b )
    = ( ^ [A: b,B: b] :
          ( ( ord_less_eq_b @ A @ B )
          & ( ord_less_eq_b @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(6,axiom,
    ( is_singleton_b
    = ( ^ [A: set_b] :
        ? [B: b] :
          ( A
          = ( insert_b @ B @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_is__singleton__def) ).

thf(161,plain,
    ( is_singleton_b
    = ( ^ [A: set_b] :
        ? [B: b] :
          ( A
          = ( insert_b @ B @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(87,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( bot_bot_set_b
        = ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C ) )
      = ( ~ ( member_b @ A @ C )
        & ( bot_bot_set_b
          = ( inf_inf_set_b @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_insert__disjoint_I2_J) ).

thf(444,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( bot_bot_set_b
        = ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C ) )
      = ( ~ ( member_b @ A @ C )
        & ( bot_bot_set_b
          = ( inf_inf_set_b @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(122,axiom,
    ( inf_inf_set_b
    = ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_inf__sup__aci_I1_J) ).

thf(562,plain,
    ( inf_inf_set_b
    = ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(15,axiom,
    ! [A: b,B: set_b,C: b] :
      ( ( member_b @ A @ B )
     => ( member_b @ A @ ( insert_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_insertI2) ).

thf(191,plain,
    ! [A: b,B: set_b,C: b] :
      ( ( member_b @ A @ B )
     => ( member_b @ A @ ( insert_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(126,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ( member_b @ A @ B )
       => ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
          = ( insert_b @ A @ ( inf_inf_set_b @ C @ B ) ) ) )
      & ( ~ ( member_b @ A @ B )
       => ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
          = ( inf_inf_set_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_Int__insert__left) ).

thf(579,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ( member_b @ A @ B )
       => ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
          = ( insert_b @ A @ ( inf_inf_set_b @ C @ B ) ) ) )
      & ( ~ ( member_b @ A @ B )
       => ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
          = ( inf_inf_set_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(44,axiom,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_antisym) ).

thf(281,plain,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(37,axiom,
    ! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_insertI1) ).

thf(259,plain,
    ! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(80,axiom,
    ( inf_inf_set_b
    = ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_inf_Ocommute) ).

thf(413,plain,
    ( inf_inf_set_b
    = ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(74,axiom,
    ! [A: b,B: b] :
      ( ( A != B )
      = ( ? [C: set_b] :
            ( ( topolo1276428102open_b @ C )
            & ( member_b @ A @ C )
            & ~ ( member_b @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_separation__t1) ).

thf(391,plain,
    ! [A: b,B: b] :
      ( ( A != B )
      = ( ? [C: set_b] :
            ( ( topolo1276428102open_b @ C )
            & ( member_b @ A @ C )
            & ~ ( member_b @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(71,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_inf_Oleft__commute) ).

thf(382,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(4,axiom,
    ! [A: b,B: b,C: b] :
      ( ( ( ord_less_eq_b @ A @ B )
       => ~ ( ord_less_eq_b @ B @ C ) )
     => ( ( ( ord_less_eq_b @ B @ A )
         => ~ ( ord_less_eq_b @ A @ C ) )
       => ( ( ( ord_less_eq_b @ A @ C )
           => ~ ( ord_less_eq_b @ C @ B ) )
         => ( ( ( ord_less_eq_b @ C @ B )
             => ~ ( ord_less_eq_b @ B @ A ) )
           => ( ( ( ord_less_eq_b @ B @ C )
               => ~ ( ord_less_eq_b @ C @ A ) )
             => ~ ( ( ord_less_eq_b @ C @ A )
                 => ~ ( ord_less_eq_b @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_le__cases3) ).

thf(144,plain,
    ! [A: b,B: b,C: b] :
      ( ( ( ord_less_eq_b @ A @ B )
       => ~ ( ord_less_eq_b @ B @ C ) )
     => ( ( ( ord_less_eq_b @ B @ A )
         => ~ ( ord_less_eq_b @ A @ C ) )
       => ( ( ( ord_less_eq_b @ A @ C )
           => ~ ( ord_less_eq_b @ C @ B ) )
         => ( ( ( ord_less_eq_b @ C @ B )
             => ~ ( ord_less_eq_b @ B @ A ) )
           => ( ( ( ord_less_eq_b @ B @ C )
               => ~ ( ord_less_eq_b @ C @ A ) )
             => ~ ( ( ord_less_eq_b @ C @ A )
                 => ~ ( ord_less_eq_b @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(101,axiom,
    ( bot_bot_b_o
    = ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_bot__empty__eq) ).

thf(498,plain,
    ( bot_bot_b_o
    = ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(24,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
        = ( minus_minus_set_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_insert__Diff1) ).

thf(219,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
        = ( minus_minus_set_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(69,axiom,
    ! [A: set_b,B: b,C: set_b] :
      ( ( ( inf_inf_set_b @ A @ ( insert_b @ B @ C ) )
        = bot_bot_set_b )
      = ( ~ ( member_b @ B @ A )
        & ( ( inf_inf_set_b @ A @ C )
          = bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_disjoint__insert_I1_J) ).

thf(377,plain,
    ! [A: set_b,B: b,C: set_b] :
      ( ( ( inf_inf_set_b @ A @ ( insert_b @ B @ C ) )
        = bot_bot_set_b )
      = ( ~ ( member_b @ B @ A )
        & ( ( inf_inf_set_b @ A @ C )
          = bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(66,axiom,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ~ ! [C: set_b] :
            ( ( B
              = ( insert_b @ A @ C ) )
           => ( member_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Set_Oset__insert) ).

thf(362,plain,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ~ ! [C: set_b] :
            ( ( B
              = ( insert_b @ A @ C ) )
           => ( member_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(32,axiom,
    ! [A: set_b,B: b] :
      ( ( topolo1276428102open_b @ A )
     => ( topolo1276428102open_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_open__delete) ).

thf(245,plain,
    ! [A: set_b,B: b] :
      ( ( topolo1276428102open_b @ A )
     => ( topolo1276428102open_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(136,axiom,
    ! [A: set_b,B: set_b] :
      ( ( topolo1276428102open_b @ A )
     => ( ( topolo1276428102open_b @ B )
       => ( topolo1276428102open_b @ ( inf_inf_set_b @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_open__Int) ).

thf(616,plain,
    ! [A: set_b,B: set_b] :
      ( ( topolo1276428102open_b @ A )
     => ( ( topolo1276428102open_b @ B )
       => ( topolo1276428102open_b @ ( inf_inf_set_b @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(41,axiom,
    ! [A: b,B: b > b,C: b,D: b] :
      ( ( ord_less_eq_b @ A @ ( B @ C ) )
     => ( ( ord_less_eq_b @ C @ D )
       => ( ! [E: b,F: b] :
              ( ( ord_less_eq_b @ E @ F )
             => ( ord_less_eq_b @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_b @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_order__subst1) ).

thf(271,plain,
    ! [A: b,B: b > b,C: b,D: b] :
      ( ( ord_less_eq_b @ A @ ( B @ C ) )
     => ( ( ord_less_eq_b @ C @ D )
       => ( ! [E: b,F: b] :
              ( ( ord_less_eq_b @ E @ F )
             => ( ord_less_eq_b @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_b @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(100,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
        = ( insert_b @ A @ ( inf_inf_set_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Int__insert__left__if1) ).

thf(494,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ B )
     => ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
        = ( insert_b @ A @ ( inf_inf_set_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(114,axiom,
    ! [A: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ A @ B )
        = bot_bot_set_b )
     => ( ( minus_minus_set_b @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_Diff__triv) ).

thf(535,plain,
    ! [A: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ A @ B )
        = bot_bot_set_b )
     => ( ( minus_minus_set_b @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(134,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_inf_Oleft__idem) ).

thf(609,plain,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

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

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

thf(140,plain,
    ~ thesis,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(22,axiom,
    ! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_is__singletonI) ).

thf(213,plain,
    ! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(34,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ C ) )
      = ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_insert__inter__insert) ).

thf(251,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ C ) )
      = ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(57,axiom,
    ! [A: set_b] :
      ( ( is_singleton_b @ A )
     => ~ ! [B: b] :
            ( A
           != ( insert_b @ B @ bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_is__singletonE) ).

thf(330,plain,
    ! [A: set_b] :
      ( ( is_singleton_b @ A )
     => ~ ! [B: b] :
            ( A
           != ( insert_b @ B @ bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(76,axiom,
    ! [A: b,B: b] :
      ( ( A != B )
     => ? [C: set_b] :
          ( ( topolo1276428102open_b @ C )
          & ( ( member_b @ A @ C )
           != ( member_b @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_t0__space) ).

thf(399,plain,
    ! [A: b,B: b] :
      ( ( A != B )
     => ? [C: set_b] :
          ( ( topolo1276428102open_b @ C )
          & ( ( member_b @ A @ C )
           != ( member_b @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(43,axiom,
    ! [A: b,B: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( minus_minus_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ bot_bot_set_b ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Diff__insert__absorb) ).

thf(278,plain,
    ! [A: b,B: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( minus_minus_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ bot_bot_set_b ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(25,axiom,
    ! [A: b,B: b,C: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_ord__le__eq__trans) ).

thf(223,plain,
    ! [A: b,B: b,C: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(75,axiom,
    ! [A: set_b,B: set_b] :
      ( ! [C: b] :
          ( ( member_b @ C @ A )
         => ~ ( member_b @ C @ B ) )
     => ( ( inf_inf_set_b @ A @ B )
        = bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Int__emptyI) ).

thf(394,plain,
    ! [A: set_b,B: set_b] :
      ( ! [C: b] :
          ( ( member_b @ C @ A )
         => ~ ( member_b @ C @ B ) )
     => ( ( inf_inf_set_b @ A @ B )
        = bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(104,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_inf__idem) ).

thf(505,plain,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(108,axiom,
    ! [A: set_b,B: b,C: set_b] :
      ( ( bot_bot_set_b
        = ( inf_inf_set_b @ A @ ( insert_b @ B @ C ) ) )
      = ( ~ ( member_b @ B @ A )
        & ( bot_bot_set_b
          = ( inf_inf_set_b @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_disjoint__insert_I2_J) ).

thf(516,plain,
    ! [A: set_b,B: b,C: set_b] :
      ( ( bot_bot_set_b
        = ( inf_inf_set_b @ A @ ( insert_b @ B @ C ) ) )
      = ( ~ ( member_b @ B @ A )
        & ( bot_bot_set_b
          = ( inf_inf_set_b @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(119,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
      = ( inf_inf_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_inf_Oright__idem) ).

thf(553,plain,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
      = ( inf_inf_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(16,axiom,
    ( is_singleton_b
    = ( ^ [A: set_b] :
          ( A
          = ( insert_b @ ( the_elem_b @ A ) @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_is__singleton__the__elem) ).

thf(194,plain,
    ( is_singleton_b
    = ( ^ [A: set_b] :
          ( A
          = ( insert_b @ ( the_elem_b @ A ) @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(117,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
     => ( member_b @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_IntD2) ).

thf(544,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
     => ( member_b @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(95,axiom,
    ( ( ( f @ x0 )
     != a2 )
   => ? [A: set_b,B: set_b] :
        ( ( topolo1276428102open_b @ A )
        & ( topolo1276428102open_b @ B )
        & ( member_b @ ( f @ x0 ) @ A )
        & ( member_b @ a2 @ B )
        & ( ( inf_inf_set_b @ A @ B )
          = bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).

thf(470,plain,
    ( ( ( f @ x0 )
     != a2 )
   => ? [A: set_b,B: set_b] :
        ( ( topolo1276428102open_b @ A )
        & ( topolo1276428102open_b @ B )
        & ( member_b @ ( f @ x0 ) @ A )
        & ( member_b @ a2 @ B )
        & ( ( inf_inf_set_b @ A @ B )
          = bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(125,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ A )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Int__empty__left) ).

thf(576,plain,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ A )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(131,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ bot_bot_set_b )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_inf__bot__right) ).

thf(600,plain,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ bot_bot_set_b )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(10,axiom,
    ! [A: set_b,B: set_b] :
      ( ( minus_minus_set_b @ A @ ( minus_minus_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Diff__Diff__Int) ).

thf(175,plain,
    ! [A: set_b,B: set_b] :
      ( ( minus_minus_set_b @ A @ ( minus_minus_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(124,axiom,
    ! [A: set_b,B: set_b,C: set_b,D: set_b] :
      ( ( A
        = ( inf_inf_set_b @ B @ C ) )
     => ( ( inf_inf_set_b @ D @ A )
        = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_boolean__algebra__cancel_Oinf2) ).

thf(571,plain,
    ! [A: set_b,B: set_b,C: set_b,D: set_b] :
      ( ( A
        = ( inf_inf_set_b @ B @ C ) )
     => ( ( inf_inf_set_b @ D @ A )
        = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(135,axiom,
    ! [A: set_b] :
      ( ! [B: b] :
          ~ ( member_b @ B @ A )
     => ( A = bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_equals0I) ).

thf(612,plain,
    ! [A: set_b] :
      ( ! [B: b] :
          ~ ( member_b @ B @ A )
     => ( A = bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(89,axiom,
    ! [A: b,B: b] :
      ( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_singleton__iff) ).

thf(450,plain,
    ! [A: b,B: b] :
      ( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(120,axiom,
    ! [A: b,B: b] :
      ( ( A != B )
      = ( ? [C: set_b] :
            ( ( topolo1276428102open_b @ C )
            & ( ( member_b @ A @ C )
             != ( member_b @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_separation__t0) ).

thf(556,plain,
    ! [A: b,B: b] :
      ( ( A != B )
      = ( ? [C: set_b] :
            ( ( topolo1276428102open_b @ C )
            & ( ( member_b @ A @ C )
             != ( member_b @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(110,axiom,
    ( a2
   != ( f @ x0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).

thf(524,plain,
    ( a2
   != ( f @ x0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(96,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
     => ( member_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_IntD1) ).

thf(482,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
     => ( member_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(19,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Int__Diff) ).

thf(203,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
      = ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(53,axiom,
    ! [A: b] : ( ord_less_eq_b @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_dual__order_Orefl) ).

thf(319,plain,
    ! [A: b] : ( ord_less_eq_b @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(50,axiom,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ? [C: set_b] :
          ( ( B
            = ( insert_b @ A @ C ) )
          & ~ ( member_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_mk__disjoint__insert) ).

thf(304,plain,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ? [C: set_b] :
          ( ( B
            = ( insert_b @ A @ C ) )
          & ~ ( member_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(5,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
     => ( member_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_DiffD1) ).

thf(158,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
     => ( member_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(9,axiom,
    ! [A: b,B: b,C: b > b,D: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ ( C @ B ) @ D )
       => ( ! [E: b,F: b] :
              ( ( ord_less_eq_b @ E @ F )
             => ( ord_less_eq_b @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_b @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_order__subst2) ).

thf(171,plain,
    ! [A: b,B: b,C: b > b,D: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ ( C @ B ) @ D )
       => ( ! [E: b,F: b] :
              ( ( ord_less_eq_b @ E @ F )
             => ( ord_less_eq_b @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_b @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(82,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_emptyE) ).

thf(418,plain,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(47,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ( member_b @ A @ B )
       => ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
          = ( minus_minus_set_b @ C @ B ) ) )
      & ( ~ ( member_b @ A @ B )
       => ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
          = ( insert_b @ A @ ( minus_minus_set_b @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_insert__Diff__if) ).

thf(290,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ( member_b @ A @ B )
       => ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
          = ( minus_minus_set_b @ C @ B ) ) )
      & ( ~ ( member_b @ A @ B )
       => ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
          = ( insert_b @ A @ ( minus_minus_set_b @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(28,axiom,
    ! [A: b,B: b] :
      ( ~ ( ord_less_eq_b @ A @ B )
     => ( ord_less_eq_b @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_le__cases) ).

thf(235,plain,
    ! [A: b,B: b] :
      ( ~ ( ord_less_eq_b @ A @ B )
     => ( ord_less_eq_b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(62,axiom,
    ! [A: b,B: b,C: set_b] :
      ( ( member_b @ A @ ( insert_b @ B @ C ) )
      = ( ( A = B )
        | ( member_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_insert__iff) ).

thf(346,plain,
    ! [A: b,B: b,C: set_b] :
      ( ( member_b @ A @ ( insert_b @ B @ C ) )
      = ( ( A = B )
        | ( member_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(46,axiom,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_insert__Diff) ).

thf(287,plain,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(49,axiom,
    ! [A: b,B: set_b,C: b,D: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ~ ( member_b @ C @ D )
       => ( ( ( insert_b @ A @ B )
            = ( insert_b @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_b] :
                  ( ( B
                    = ( insert_b @ C @ E ) )
                  & ~ ( member_b @ C @ E )
                  & ( D
                    = ( insert_b @ A @ E ) )
                  & ~ ( member_b @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_insert__eq__iff) ).

thf(300,plain,
    ! [A: b,B: set_b,C: b,D: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ~ ( member_b @ C @ D )
       => ( ( ( insert_b @ A @ B )
            = ( insert_b @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_b] :
                  ( ( B
                    = ( insert_b @ C @ E ) )
                  & ~ ( member_b @ C @ E )
                  & ( D
                    = ( insert_b @ A @ E ) )
                  & ~ ( member_b @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(138,axiom,
    ( ~ ! [A: set_b] :
          ( ( ( topolo1276428102open_b @ A )
            & ( member_b @ ( f @ x0 ) @ A ) )
         => ? [B: set_a] :
              ( ( topolo1276428101open_a @ B )
              & ( member_a @ x0 @ B )
              & ! [C: a] :
                  ( ( member_a @ C @ B )
                 => ( ( ord_less_eq_b @ ( f @ C ) @ ( f @ x0 ) )
                   => ( member_b @ ( f @ C ) @ A ) ) ) ) )
   => ~ ( lower_464587817at_a_b @ x0 @ f ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_calculation) ).

thf(620,plain,
    ( ~ ! [A: set_b] :
          ( ( ( topolo1276428102open_b @ A )
            & ( member_b @ ( f @ x0 ) @ A ) )
         => ? [B: set_a] :
              ( ( topolo1276428101open_a @ B )
              & ( member_a @ x0 @ B )
              & ! [C: a] :
                  ( ( member_a @ C @ B )
                 => ( ( ord_less_eq_b @ ( f @ C ) @ ( f @ x0 ) )
                   => ( member_b @ ( f @ C ) @ A ) ) ) ) )
   => ~ ( lower_464587817at_a_b @ x0 @ f ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(88,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C )
        = bot_bot_set_b )
      = ( ~ ( member_b @ A @ C )
        & ( ( inf_inf_set_b @ B @ C )
          = bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_insert__disjoint_I1_J) ).

thf(447,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C )
        = bot_bot_set_b )
      = ( ~ ( member_b @ A @ C )
        & ( ( inf_inf_set_b @ B @ C )
          = bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(86,axiom,
    ! [A: b,B: b] :
      ( ( A != B )
     => ? [C: set_b,D: set_b] :
          ( ( topolo1276428102open_b @ C )
          & ( topolo1276428102open_b @ D )
          & ( member_b @ A @ C )
          & ( member_b @ B @ D )
          & ( ( inf_inf_set_b @ C @ D )
            = bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_hausdorff) ).

thf(432,plain,
    ! [A: b,B: b] :
      ( ( A != B )
     => ? [C: set_b,D: set_b] :
          ( ( topolo1276428102open_b @ C )
          & ( topolo1276428102open_b @ D )
          & ( member_b @ A @ C )
          & ( member_b @ B @ D )
          & ( ( inf_inf_set_b @ C @ D )
            = bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(79,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Int__absorb) ).

thf(410,plain,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(12,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
     => ~ ( member_b @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_DiffD2) ).

thf(183,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
     => ~ ( member_b @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(132,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_inf_Oidem) ).

thf(603,plain,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(123,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ( member_b @ A @ B )
       => ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
          = ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) )
      & ( ~ ( member_b @ A @ B )
       => ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
          = ( inf_inf_set_b @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Int__insert__right) ).

thf(564,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ( member_b @ A @ B )
       => ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
          = ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) )
      & ( ~ ( member_b @ A @ B )
       => ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
          = ( inf_inf_set_b @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(21,axiom,
    ! [A: b,B: b,C: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ C @ A )
       => ( ord_less_eq_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_dual__order_Otrans) ).

thf(210,plain,
    ! [A: b,B: b,C: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ C @ A )
       => ( ord_less_eq_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(40,axiom,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_antisym__conv) ).

thf(268,plain,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(113,axiom,
    ! [A: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ A @ B )
        = bot_bot_set_b )
      = ( ! [C: b] :
            ( ( member_b @ C @ A )
           => ~ ( member_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_disjoint__iff) ).

thf(532,plain,
    ! [A: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ A @ B )
        = bot_bot_set_b )
      = ( ! [C: b] :
            ( ( member_b @ C @ A )
           => ~ ( member_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(81,axiom,
    ! [A: b,B: b] :
      ( ( A != B )
      = ( ? [C: set_b,D: set_b] :
            ( ( topolo1276428102open_b @ C )
            & ( topolo1276428102open_b @ D )
            & ( member_b @ A @ C )
            & ( member_b @ B @ D )
            & ( ( inf_inf_set_b @ C @ D )
              = bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_separation__t2) ).

thf(415,plain,
    ! [A: b,B: b] :
      ( ( A != B )
      = ( ? [C: set_b,D: set_b] :
            ( ( topolo1276428102open_b @ C )
            & ( topolo1276428102open_b @ D )
            & ( member_b @ A @ C )
            & ( member_b @ B @ D )
            & ( ( inf_inf_set_b @ C @ D )
              = bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(30,axiom,
    ! [A: set_b,B: b,C: set_b] :
      ( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
      = ( minus_minus_set_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_Diff__insert2) ).

thf(239,plain,
    ! [A: set_b,B: b,C: set_b] :
      ( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
      = ( minus_minus_set_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(31,axiom,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ ( inf_inf_set_b @ C @ B ) )
      = ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_Diff__Int2) ).

thf(242,plain,
    ! [A: set_b,B: set_b,C: set_b] :
      ( ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ ( inf_inf_set_b @ C @ B ) )
      = ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(139,axiom,
    ! [A: set_b,B: set_b] :
      ( ( ( topolo1276428102open_b @ A )
        & ( topolo1276428102open_b @ B )
        & ( member_b @ ( f @ x0 ) @ A )
        & ( member_b @ a2 @ B )
        & ( ( inf_inf_set_b @ A @ B )
          = bot_bot_set_b ) )
     => thesis ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(624,plain,
    ! [A: set_b,B: set_b] :
      ( ( ( topolo1276428102open_b @ A )
        & ( topolo1276428102open_b @ B )
        & ( member_b @ ( f @ x0 ) @ A )
        & ( member_b @ a2 @ B )
        & ( ( inf_inf_set_b @ A @ B )
          = bot_bot_set_b ) )
     => thesis ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(93,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
      = ( inf_inf_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_inf__right__idem) ).

thf(464,plain,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
      = ( inf_inf_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(92,axiom,
    ! [A: set_b,B: set_b,C: set_b,D: set_b] :
      ( ( A
        = ( inf_inf_set_b @ B @ C ) )
     => ( ( inf_inf_set_b @ A @ D )
        = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_boolean__algebra__cancel_Oinf1) ).

thf(459,plain,
    ! [A: set_b,B: set_b,C: set_b,D: set_b] :
      ( ( A
        = ( inf_inf_set_b @ B @ C ) )
     => ( ( inf_inf_set_b @ A @ D )
        = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(11,axiom,
    ! [A: b,B: set_b,C: b] :
      ( ( ~ ( member_b @ A @ B )
       => ( A = C ) )
     => ( member_b @ A @ ( insert_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_insertCI) ).

thf(178,plain,
    ! [A: b,B: set_b,C: b] :
      ( ( ~ ( member_b @ A @ B )
       => ( A = C ) )
     => ( member_b @ A @ ( insert_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(68,axiom,
    ! [A: set_b] :
      ( ( A != bot_bot_set_b )
     => ( ! [B: b,C: b] :
            ( ( member_b @ B @ A )
           => ( ( member_b @ C @ A )
             => ( B = C ) ) )
       => ( is_singleton_b @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_is__singletonI_H) ).

thf(369,plain,
    ! [A: set_b] :
      ( ( A != bot_bot_set_b )
     => ( ! [B: b,C: b] :
            ( ( member_b @ B @ A )
           => ( ( member_b @ C @ A )
             => ( B = C ) ) )
       => ( is_singleton_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(7,axiom,
    ! [A: b > b > $o,B: b,C: b] :
      ( ! [D: b,E: b] :
          ( ( ord_less_eq_b @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: b,E: b] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_linorder__wlog) ).

thf(163,plain,
    ! [A: b > b > $o,B: b,C: b] :
      ( ! [D: b,E: b] :
          ( ( ord_less_eq_b @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: b,E: b] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(18,axiom,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ( ( insert_b @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_insert__absorb) ).

thf(200,plain,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ( ( insert_b @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(35,axiom,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
      | ( ord_less_eq_b @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_linear) ).

thf(254,plain,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
      | ( ord_less_eq_b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(59,axiom,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ A )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_dual__order_Oantisym) ).

thf(337,plain,
    ! [A: b,B: b] :
      ( ( ord_less_eq_b @ A @ B )
     => ( ( ord_less_eq_b @ B @ A )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(23,axiom,
    ! [A: b,B: b] :
      ( ( A = B )
     => ( ord_less_eq_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_eq__refl) ).

thf(215,plain,
    ! [A: b,B: b] :
      ( ( A = B )
     => ( ord_less_eq_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(99,axiom,
    ! [A: set_b] :
      ( ( ? [B: b] : ( member_b @ B @ A ) )
      = ( A != bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_ex__in__conv) ).

thf(491,plain,
    ! [A: set_b] :
      ( ( ? [B: b] : ( member_b @ B @ A ) )
      = ( A != bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(27,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
      = ( ( member_b @ A @ B )
        & ~ ( member_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Diff__iff) ).

thf(232,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
      = ( ( member_b @ A @ B )
        & ~ ( member_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(628,plain,
    $false,
    inference(e,[status(thm)],[352,503,327,308,511,597,385,500,340,538,404,185,619,196,559,421,606,284,228,261,321,485,514,453,428,527,206,248,380,546,366,334,349,297,424,407,275,467,456,324,519,188,388,169,593,141,256,488,590,266,360,508,311,541,530,586,343,237,161,444,562,191,579,281,259,413,391,382,144,498,219,377,362,245,616,271,494,535,609,140,213,251,330,399,278,223,394,505,516,553,194,544,470,576,600,175,571,612,450,556,524,482,203,319,304,158,171,418,290,235,346,287,300,620,447,432,410,183,603,564,210,268,532,415,239,242,624,464,459,178,369,163,200,254,337,215,491,232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ITP115^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.39  % Computer : n025.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit : 300
% 0.17/0.39  % WCLimit  : 300
% 0.17/0.39  % DateTime : Sat May 18 16:01:09 EDT 2024
% 0.17/0.39  % CPUTime  : 
% 1.00/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.87/1.15  % [INFO] 	 Parsing done (256ms). 
% 1.87/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.74/1.50  % [INFO] 	 eprover registered as external prover. 
% 2.74/1.50  % [INFO] 	 cvc4 registered as external prover. 
% 2.74/1.51  % [INFO] 	 Scanning for conjecture ... 
% 3.02/1.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 356 axioms. Running axiom selection ... 
% 3.19/1.69  % [INFO] 	 Axiom selection finished. Selected 137 axioms (removed 219 axioms). 
% 3.73/1.82  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.73/1.84  % [INFO] 	 Type checking passed. 
% 3.73/1.85  % [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 ... 
% 8.56/3.13  % External prover 'e' found a proof!
% 8.56/3.13  % [INFO] 	 Killing All external provers ... 
% 8.56/3.13  % Time passed: 2569ms (effective reasoning time: 1970ms)
% 8.56/3.13  % 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)>
% 8.56/3.14  % Axioms used in derivation (137): fact_101_disjoint__iff, fact_59_boolean__algebra__cancel_Oinf2, fact_20_inf_Oleft__idem, fact_342_is__singleton__the__elem, fact_61_boolean__algebra__cancel_Oinf1, fact_189_dual__order_Oantisym, fact_248_Diff__Int2, fact_116_insert__disjoint_I1_J, fact_236_doubleton__eq__iff, fact_32_inf_Oright__idem, fact_135_singletonI, fact_71_Int__left__commute, fact_340_Int__Diff__disjoint, fact_51_inf__commute, fact_337_Diff__triv, fact_151_Diff__cancel, fact_97_Int__empty__right, fact_9_inf__bot__right, fact_195_order__class_Oorder_Oantisym, fact_106_Set_Ois__empty__def, fact_149_empty__Diff, fact_232_singletonD, fact_196_ord__le__eq__trans, fact_202_le__cases, fact_28_empty__iff, fact_211_Diff__insert__absorb, fact_118_insert__disjoint_I2_J, fact_57_inf_Oassoc, fact_34_inf__left__idem, fact_123_insert__iff, fact_183_insert__eq__iff, fact_65_inf__sup__aci_I2_J, fact_145_Int__insert__right__if1, fact_92_separation__t0, fact_208_ord__eq__le__subst, fact_194_order__trans, fact_163_is__singletonI, fact_199_antisym__conv, fact_120_order__refl, fact_137_Int__insert__left__if0, fact_157_disjoint__insert_I2_J, fact_13_IntI, fact_95_disjoint__iff__not__equal, fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062, fact_161_insert__Diff__single, fact_173_insertI1, fact_4_open__empty, fact_39_ex__in__conv, fact_242_Int__insert__left, fact_85_IntD2, fact_75_Int__commute, fact_197_ord__eq__le__trans, fact_165_DiffE, fact_36__092_060open_062_092_060forall_062S_O_Aopen_AS_A_092_060and_062_Af_Ax0_A_092_060in_062_AS_A_092_060longrightarrow_062_A_I_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062x_H_092_060in_062T_O_Af_Ax_H_A_092_060le_062_Af_Ax0_A_092_060longrightarrow_062_Af_Ax_H_A_092_060in_062_AS_J_J_092_060close_062, fact_45_emptyE, fact_63_inf__sup__aci_I1_J, fact_185_insert__Diff__if, fact_205_antisym, fact_192_linorder__wlog, fact_26_all__not__in__conv, fact_125_DiffI, fact_2_open__Int, fact_167_DiffD1, fact_147_Diff__empty, fact_206_eq__iff, fact_203_eq__refl, fact_215_insert__Diff, fact_103_Int__emptyI, fact_55_inf__assoc, fact_230_is__singletonE, fact_112_is__singletonI_H, fact_10_hausdorff, fact_18_inf__idem, fact_193_dual__order_Orefl, fact_190_dual__order_Oeq__iff, fact_204_linear, fact_171_insertE, fact_153_Diff__insert0, fact_139_Int__insert__left__if1, fact_228_is__singleton__def, fact_7_inf__bot__left, fact_175_insertI2, fact_41_equals0I, fact_155_insert__Diff1, fact_47_inf__left__commute, fact_69_inf__sup__aci_I4_J, fact_177_Set_Oset__insert, fact_43_equals0D, fact_209_order__subst2, fact_234_singleton__iff, fact_344_the__elem__eq, fact_210_order__subst1, fact_252_Diff__Int__distrib, fact_91_separation__t1, fact_217_Diff__insert, fact_246_Int__Diff, fact_11_separation__t2, fact_207_ord__le__eq__subst, fact_250_Diff__Diff__Int, fact_121_insertCI, fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062, fact_16_inf_Oidem, fact_105_calculation, fact_141_insert__inter__insert, fact_73_Int__left__absorb, fact_159_disjoint__insert_I1_J, fact_77_Int__absorb, fact_67_inf__sup__aci_I3_J, fact_15_Int__iff, fact_87_IntD1, fact_254_Diff__Int__distrib2, fact_187_mk__disjoint__insert, fact_179_insert__ident, fact_201_order_Otrans, fact_200_le__cases3, fact_114_Diff__disjoint, fact_198_order__class_Oorder_Oeq__iff, fact_169_DiffD2, fact_79_Int__assoc, fact_53_inf_Ocommute, fact_238_insert__not__empty, fact_339_open__delete, conj_0, fact_49_inf_Oleft__commute, fact_240_singleton__inject, fact_94_t0__space, fact_127_Diff__iff, fact_244_Int__insert__right, fact_143_Int__insert__right__if0, fact_89_IntE, fact_191_dual__order_Otrans, fact_213_Diff__insert2, fact_99_Int__empty__left, fact_93_t1__space, fact_30_inf__right__idem, fact_110_bot__empty__eq, fact_181_insert__absorb
% 8.56/3.14  % No. of inferences in proof: 278
% 8.56/3.14  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2569 ms resp. 1970 ms w/o parsing
% 8.98/3.22  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.98/3.22  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------