TSTP Solution File: ITP176^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP176^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:42 EDT 2024

% Result   : Theorem 19.26s 5.93s
% Output   : Refutation 20.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  425
% Syntax   : Number of formulae    :  739 ( 351 unt; 113 typ;   0 def)
%            Number of atoms       : 1643 ( 715 equ;   6 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 4623 ( 212   ~;  29   |; 130   &;3730   @)
%                                         (   0 <=>; 522  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :   30 (  29 usr)
%            Number of type conns  :  266 ( 266   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   88 (  84 usr;  13 con; 0-3 aty)
%            Number of variables   : 1613 ( 176   ^1385   !;  52   ?;1613   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_Pr2109276827od_b_b_type,type,
    set_Pr2109276827od_b_b: $tType ).

thf(produc970027067od_b_b_type,type,
    produc970027067od_b_b: $tType ).

thf(set_Pr1071216121od_b_b_type,type,
    set_Pr1071216121od_b_b: $tType ).

thf(set_Pr2134561957od_b_b_type,type,
    set_Pr2134561957od_b_b: $tType ).

thf(set_Pr1021918435od_b_b_type,type,
    set_Pr1021918435od_b_b: $tType ).

thf(produc1052326083od_b_b_type,type,
    produc1052326083od_b_b: $tType ).

thf(produc1990339951od_b_b_type,type,
    produc1990339951od_b_b: $tType ).

thf(set_Pr2060523537od_b_b_type,type,
    set_Pr2060523537od_b_b: $tType ).

thf(set_Pr1906739389_b_b_b_type,type,
    set_Pr1906739389_b_b_b: $tType ).

thf(produc1605346267od_b_b_type,type,
    produc1605346267od_b_b: $tType ).

thf(produc276146823_b_b_b_type,type,
    produc276146823_b_b_b: $tType ).

thf(set_Pr306736955tant_a_type,type,
    set_Pr306736955tant_a: $tType ).

thf(set_Pr1324126435od_b_b_type,type,
    set_Pr1324126435od_b_b: $tType ).

thf(labele1835558936od_b_b_type,type,
    labele1835558936od_b_b: $tType ).

thf(set_Pr2007082183od_b_b_type,type,
    set_Pr2007082183od_b_b: $tType ).

thf(produc1367125253tant_a_type,type,
    produc1367125253tant_a: $tType ).

thf(produc1213276845od_b_b_type,type,
    produc1213276845od_b_b: $tType ).

thf(produc1168037607od_b_b_type,type,
    produc1168037607od_b_b: $tType ).

thf(labele1159362096nt_a_b_type,type,
    labele1159362096nt_a_b: $tType ).

thf(set_Pr621705391od_b_b_type,type,
    set_Pr621705391od_b_b: $tType ).

thf(set_Pr357419743_b_b_b_type,type,
    set_Pr357419743_b_b_b: $tType ).

thf(produc255402447od_b_b_type,type,
    produc255402447od_b_b: $tType ).

thf(produc2112523263_b_b_b_type,type,
    produc2112523263_b_b_b: $tType ).

thf(set_St761939237tant_a_type,type,
    set_St761939237tant_a: $tType ).

thf(set_Product_prod_b_b_type,type,
    set_Product_prod_b_b: $tType ).

thf(standard_Constant_a_type,type,
    standard_Constant_a: $tType ).

thf(product_prod_b_b_type,type,
    product_prod_b_b: $tType ).

thf(set_b_type,type,
    set_b: $tType ).

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

thf(equiv_1629197578_set_b_type,type,
    equiv_1629197578_set_b: set_Pr2109276827od_b_b > set_Product_prod_b_b > ( produc1213276845od_b_b > b > set_b ) > $o ).

thf(equiv_1036235914_set_b_type,type,
    equiv_1036235914_set_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > ( product_prod_b_b > b > set_b ) > $o ).

thf(equiv_167626658_set_b_type,type,
    equiv_167626658_set_b: set_Product_prod_b_b > set_Product_prod_b_b > ( b > b > set_b ) > $o ).

thf(equiv_1821124534_set_b_type,type,
    equiv_1821124534_set_b: set_Product_prod_b_b > ( b > set_b ) > $o ).

thf(equiv_2048442231od_b_b_type,type,
    equiv_2048442231od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).

thf(equiv_1125628061od_b_b_type,type,
    equiv_1125628061od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).

thf(equiv_equiv_b_type,type,
    equiv_equiv_b: set_b > set_Product_prod_b_b > $o ).

thf(equiv_proj_b_b_type,type,
    equiv_proj_b_b: set_Product_prod_b_b > b > set_b ).

thf(hilber46179633od_b_b_type,type,
    hilber46179633od_b_b: ( produc1213276845od_b_b > $o ) > produc1213276845od_b_b ).

thf(hilber620807523od_b_b_type,type,
    hilber620807523od_b_b: ( product_prod_b_b > $o ) > product_prod_b_b ).

thf(hilbert_Eps_b_type,type,
    hilbert_Eps_b: ( b > $o ) > b ).

thf(if_b_type,type,
    if_b: $o > b > b > b ).

thf(standard_S_Idt_a_type,type,
    standard_S_Idt_a: standard_Constant_a ).

thf(getRel904497637nt_a_b_type,type,
    getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b ).

thf(graph_792023598_b_b_b_type,type,
    graph_792023598_b_b_b: labele1835558936od_b_b > labele1159362096nt_a_b > set_Pr357419743_b_b_b > $o ).

thf(graph_222606102_a_b_b_type,type,
    graph_222606102_a_b_b: labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).

thf(labele170595300od_b_b_type,type,
    labele170595300od_b_b: set_Pr1021918435od_b_b > set_Product_prod_b_b > labele1835558936od_b_b ).

thf(labele1230159100nt_a_b_type,type,
    labele1230159100nt_a_b: set_Pr1324126435od_b_b > set_b > labele1159362096nt_a_b ).

thf(labele377702064od_b_b_type,type,
    labele377702064od_b_b: ( set_Pr1324126435od_b_b > set_b > set_Pr1324126435od_b_b ) > labele1159362096nt_a_b > set_Pr1324126435od_b_b ).

thf(labele1287464530_set_b_type,type,
    labele1287464530_set_b: ( set_Pr1324126435od_b_b > set_b > set_b ) > labele1159362096nt_a_b > set_b ).

thf(labele1741081071nt_a_b_type,type,
    labele1741081071nt_a_b: labele1159362096nt_a_b > set_Pr1324126435od_b_b ).

thf(labele1424214014nt_a_b_type,type,
    labele1424214014nt_a_b: labele1159362096nt_a_b > set_b ).

thf(restri446606278nt_a_b_type,type,
    restri446606278nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b ).

thf(order_653178932r_on_b_type,type,
    order_653178932r_on_b: set_b > set_Product_prod_b_b > $o ).

thf(bot_bo1734638456_b_b_o_type,type,
    bot_bo1734638456_b_b_o: standard_Constant_a > product_prod_b_b > $o ).

thf(bot_bo1167600078_b_b_o_type,type,
    bot_bo1167600078_b_b_o: produc1213276845od_b_b > $o ).

thf(bot_bo1302443370_b_b_o_type,type,
    bot_bo1302443370_b_b_o: product_prod_b_b > $o ).

thf(bot_bot_b_b_o_type,type,
    bot_bot_b_b_o: b > b > $o ).

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

thf(bot_bo1160111033tant_a_type,type,
    bot_bo1160111033tant_a: set_St761939237tant_a ).

thf(bot_bo1964903287od_b_b_type,type,
    bot_bo1964903287od_b_b: set_Pr1021918435od_b_b ).

thf(bot_bo1664927607od_b_b_type,type,
    bot_bo1664927607od_b_b: set_Pr1324126435od_b_b ).

thf(bot_bo1124087115_b_b_b_type,type,
    bot_bo1124087115_b_b_b: set_Pr357419743_b_b_b ).

thf(bot_bo1343651123od_b_b_type,type,
    bot_bo1343651123od_b_b: set_Product_prod_b_b ).

thf(bot_bot_set_b_type,type,
    bot_bot_set_b: set_b ).

thf(ord_le123089219od_b_b_type,type,
    ord_le123089219od_b_b: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).

thf(ord_le1036320359od_b_b_type,type,
    ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).

thf(ord_less_eq_set_b_type,type,
    ord_less_eq_set_b: set_b > set_b > $o ).

thf(produc1432590431od_b_b_type,type,
    produc1432590431od_b_b: standard_Constant_a > product_prod_b_b > produc1213276845od_b_b ).

thf(produc1580777273_b_b_b_type,type,
    produc1580777273_b_b_b: produc1213276845od_b_b > b > produc276146823_b_b_b ).

thf(produc732676669od_b_b_type,type,
    produc732676669od_b_b: product_prod_b_b > produc1213276845od_b_b > produc1052326083od_b_b ).

thf(produc1001682799_b_b_b_type,type,
    produc1001682799_b_b_b: product_prod_b_b > b > produc2112523263_b_b_b ).

thf(produc800495189od_b_b_type,type,
    produc800495189od_b_b: b > produc1213276845od_b_b > produc1605346267od_b_b ).

thf(produc1257047359od_b_b_type,type,
    produc1257047359od_b_b: b > product_prod_b_b > produc255402447od_b_b ).

thf(product_Pair_b_b_type,type,
    product_Pair_b_b: b > b > product_prod_b_b ).

thf(image_1916422435od_b_b_type,type,
    image_1916422435od_b_b: set_Pr1324126435od_b_b > set_St761939237tant_a > set_Product_prod_b_b ).

thf(image_763305007od_b_b_type,type,
    image_763305007od_b_b: set_Pr2109276827od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).

thf(image_1764625405_b_b_b_type,type,
    image_1764625405_b_b_b: set_Pr1906739389_b_b_b > set_Pr1324126435od_b_b > set_b ).

thf(image_532916993od_b_b_type,type,
    image_532916993od_b_b: set_Pr1071216121od_b_b > set_Product_prod_b_b > set_Pr1324126435od_b_b ).

thf(image_1928024979od_b_b_type,type,
    image_1928024979od_b_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).

thf(image_921732011_b_b_b_type,type,
    image_921732011_b_b_b: set_Pr357419743_b_b_b > set_Product_prod_b_b > set_b ).

thf(image_984343321od_b_b_type,type,
    image_984343321od_b_b: set_Pr2060523537od_b_b > set_b > set_Pr1324126435od_b_b ).

thf(image_1177096571od_b_b_type,type,
    image_1177096571od_b_b: set_Pr621705391od_b_b > set_b > set_Product_prod_b_b ).

thf(image_b_b_type,type,
    image_b_b: set_Product_prod_b_b > set_b > set_b ).

thf(converse_b_b_type,type,
    converse_b_b: set_Product_prod_b_b > set_Product_prod_b_b ).

thf(refl_on_b_type,type,
    refl_on_b: set_b > set_Product_prod_b_b > $o ).

thf(total_178717291od_b_b_type,type,
    total_178717291od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).

thf(total_on_b_type,type,
    total_on_b: set_b > set_Product_prod_b_b > $o ).

thf(collec279084418od_b_b_type,type,
    collec279084418od_b_b: ( produc1213276845od_b_b > $o ) > set_Pr1324126435od_b_b ).

thf(collec1481886546od_b_b_type,type,
    collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).

thf(collect_b_type,type,
    collect_b: ( b > $o ) > set_b ).

thf(insert1909710879tant_a_type,type,
    insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).

thf(insert2037698781od_b_b_type,type,
    insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).

thf(insert1952693431od_b_b_type,type,
    insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).

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

thf(is_sin1465183929od_b_b_type,type,
    is_sin1465183929od_b_b: set_Pr1324126435od_b_b > $o ).

thf(is_sin1713057243od_b_b_type,type,
    is_sin1713057243od_b_b: set_Product_prod_b_b > $o ).

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

thf(the_el329196508od_b_b_type,type,
    the_el329196508od_b_b: set_Product_prod_b_b > product_prod_b_b ).

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

thf(member1632892294tant_a_type,type,
    member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).

thf(member1516365892od_b_b_type,type,
    member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o ).

thf(member1417789726_b_b_b_type,type,
    member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o ).

thf(member4694106od_b_b_type,type,
    member4694106od_b_b: produc1052326083od_b_b > set_Pr1071216121od_b_b > $o ).

thf(member351494440_b_b_b_type,type,
    member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o ).

thf(member599505522od_b_b_type,type,
    member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o ).

thf(member641857272od_b_b_type,type,
    member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o ).

thf(member1285940496od_b_b_type,type,
    member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).

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

thf(g_type,type,
    g: labele1159362096nt_a_b ).

thf(p_type,type,
    p: b > b > $o ).

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

thf(x_type,type,
    x: b ).

thf(y_type,type,
    y: b ).

thf(107,axiom,
    ! [A: set_Product_prod_b_b,B: b > set_b] :
      ( ! [C: b,D: b] :
          ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
         => ( ( B @ C )
            = ( B @ D ) ) )
     => ( equiv_1821124534_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_congruentI) ).

thf(645,plain,
    ! [A: set_Product_prod_b_b,B: b > set_b] :
      ( ! [C: b,D: b] :
          ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
         => ( ( B @ C )
            = ( B @ D ) ) )
     => ( equiv_1821124534_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(233,axiom,
    ! [A: b > $o,B: b,C: b] :
      ( ( ( hilbert_Eps_b @ A )
        = B )
     => ( ( A @ C )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_some__eq__imp) ).

thf(1036,plain,
    ! [A: b > $o,B: b,C: b] :
      ( ( ( hilbert_Eps_b @ A )
        = B )
     => ( ( A @ C )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(158,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_b] :
      ( ( labele1424214014nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_labeled__graph_Osel_I2_J) ).

thf(809,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_b] :
      ( ( labele1424214014nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(254,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b] :
      ( ( refl_on_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_refl__onD) ).

thf(1105,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b] :
      ( ( refl_on_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(297,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: b,D: set_Pr1906739389_b_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ C ) @ D )
       => ( member_b @ C @ ( image_1764625405_b_b_b @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_rev__ImageI) ).

thf(1237,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: b,D: set_Pr1906739389_b_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ C ) @ D )
       => ( member_b @ C @ ( image_1764625405_b_b_b @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(279,axiom,
    ! [A: b > $o,B: b > $o] :
      ( ! [C: b] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( hilbert_Eps_b @ A )
        = ( hilbert_Eps_b @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Eps__cong) ).

thf(1179,plain,
    ! [A: b > $o,B: b > $o] :
      ( ! [C: b] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( hilbert_Eps_b @ A )
        = ( hilbert_Eps_b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(148,axiom,
    ! [A: labele1159362096nt_a_b] :
      ( ( labele1424214014nt_a_b @ ( restri446606278nt_a_b @ A ) )
      = ( labele1424214014nt_a_b @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_vertices__restrict) ).

thf(777,plain,
    ! [A: labele1159362096nt_a_b] :
      ( ( labele1424214014nt_a_b @ ( restri446606278nt_a_b @ A ) )
      = ( labele1424214014nt_a_b @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(256,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_252_is__singletonE) ).

thf(1110,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)],[256]) ).

thf(55,axiom,
    ! [A: product_prod_b_b] :
      ~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_emptyE) ).

thf(481,plain,
    ! [A: product_prod_b_b] :
      ~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(286,axiom,
    ! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_is__singletonI) ).

thf(1200,plain,
    ! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(217,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_110_Set_Oset__insert) ).

thf(977,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)],[217]) ).

thf(290,axiom,
    ! [A: b,B: b] :
      ( ( collect_b
        @ ^ [C: b] :
            ( ( C = A )
            | ( C = B ) ) )
      = ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_tuple__disj) ).

thf(1211,plain,
    ! [A: b,B: b] :
      ( ( collect_b
        @ ^ [C: b] :
            ( ( C = A )
            | ( C = B ) ) )
      = ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(119,axiom,
    ! [A: product_prod_b_b > $o,B: product_prod_b_b] :
      ( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_old_Oprod_Oinducts) ).

thf(683,plain,
    ! [A: product_prod_b_b > $o,B: product_prod_b_b] :
      ( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(243,axiom,
    ( bot_bot_set_b
    = ( collect_b
      @ ^ [A: b] : $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_empty__def) ).

thf(1068,plain,
    ( bot_bot_set_b
    = ( collect_b
      @ ^ [A: b] : $false ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(268,axiom,
    ! [A: b] :
      ( ( collect_b @ ( (=) @ b @ A ) )
      = ( insert_b @ A @ bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_singleton__conv2) ).

thf(1142,plain,
    ! [A: b] :
      ( ( collect_b @ ( (=) @ b @ A ) )
      = ( insert_b @ A @ bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(176,axiom,
    ! [A: set_b,B: b > $o,C: b > $o] :
      ( ? [D: b] :
          ( ( member_b @ D @ A )
          & ( B @ D ) )
     => ( ! [D: b] :
            ( ( ( member_b @ D @ A )
              & ( B @ D ) )
           => ( C @ D ) )
       => ( C
          @ ( hilbert_Eps_b
            @ ^ [D: b] :
                ( ( member_b @ D @ A )
                & ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_someI2__bex) ).

thf(861,plain,
    ! [A: set_b,B: b > $o,C: b > $o] :
      ( ? [D: b] :
          ( ( member_b @ D @ A )
          & ( B @ D ) )
     => ( ! [D: b] :
            ( ( ( member_b @ D @ A )
              & ( B @ D ) )
           => ( C @ D ) )
       => ( C
          @ ( hilbert_Eps_b
            @ ^ [D: b] :
                ( ( member_b @ D @ A )
                & ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(277,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_119_insertE) ).

thf(1173,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)],[277]) ).

thf(274,axiom,
    ! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
      ( ( A
        = ( restri446606278nt_a_b @ A ) )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
       => ( member_b @ C @ ( labele1424214014nt_a_b @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_getRel__dom_I2_J) ).

thf(1158,plain,
    ! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
      ( ( A
        = ( restri446606278nt_a_b @ A ) )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
       => ( member_b @ C @ ( labele1424214014nt_a_b @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(88,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001tf__b_T) ).

thf(582,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(136,axiom,
    ! [A: product_prod_b_b] :
      ~ ! [B: b,C: b] :
          ( A
         != ( product_Pair_b_b @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_old_Oprod_Oexhaust) ).

thf(741,plain,
    ! [A: product_prod_b_b] :
      ~ ! [B: b,C: b] :
          ( A
         != ( product_Pair_b_b @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(245,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_97_mk__disjoint__insert) ).

thf(1073,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)],[245]) ).

thf(180,axiom,
    ! [A: b > $o,B: b > $o] :
      ( ? [C: b] : ( A @ C )
     => ( ! [C: b] :
            ( ( A @ C )
           => ( B @ C ) )
       => ( B @ ( hilbert_Eps_b @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_someI2__ex) ).

thf(873,plain,
    ! [A: b > $o,B: b > $o] :
      ( ? [C: b] : ( A @ C )
     => ( ! [C: b] :
            ( ( A @ C )
           => ( B @ C ) )
       => ( B @ ( hilbert_Eps_b @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(288,axiom,
    ! [A: set_Product_prod_b_b,B: b] :
      ( ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
      = ( collect_b
        @ ^ [C: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Image__singleton) ).

thf(1205,plain,
    ! [A: set_Product_prod_b_b,B: b] :
      ( ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
      = ( collect_b
        @ ^ [C: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(42,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ? [C: set_Pr1324126435od_b_b] :
          ( ( B
            = ( insert2037698781od_b_b @ A @ C ) )
          & ~ ( member1516365892od_b_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_mk__disjoint__insert) ).

thf(440,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ? [C: set_Pr1324126435od_b_b] :
          ( ( B
            = ( insert2037698781od_b_b @ A @ C ) )
          & ~ ( member1516365892od_b_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(110,axiom,
    ! [A: b,B: b,C: set_Product_prod_b_b,D: b > b > $o] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
     => ( ! [E: b,F: b] :
            ( ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ F ) @ C )
           => ( D @ F @ E ) )
       => ( D @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_converse_Oinducts) ).

thf(655,plain,
    ! [A: b,B: b,C: set_Product_prod_b_b,D: b > b > $o] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
     => ( ! [E: b,F: b] :
            ( ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ F ) @ C )
           => ( D @ F @ E ) )
       => ( D @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(192,axiom,
    ! [A: b] : ( total_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_total__on__singleton) ).

thf(913,plain,
    ! [A: b] : ( total_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(203,axiom,
    refl_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_refl__on__empty) ).

thf(945,plain,
    refl_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(12,axiom,
    ! [A: product_prod_b_b > $o] :
      ( ( bot_bo1343651123od_b_b
        = ( collec1481886546od_b_b @ A ) )
      = ( ! [B: product_prod_b_b] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_empty__Collect__eq) ).

thf(340,plain,
    ! [A: product_prod_b_b > $o] :
      ( ( bot_bo1343651123od_b_b
        = ( collec1481886546od_b_b @ A ) )
      = ( ! [B: product_prod_b_b] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(252,axiom,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ( ( insert_b @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_insert__absorb) ).

thf(1095,plain,
    ! [A: b,B: set_b] :
      ( ( member_b @ A @ B )
     => ( ( insert_b @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(299,axiom,
    ! [A: set_b] :
      ( ( ! [B: b] :
            ~ ( member_b @ B @ A ) )
      = ( A = bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_all__not__in__conv) ).

thf(1243,plain,
    ! [A: set_b] :
      ( ( ! [B: b] :
            ~ ( member_b @ B @ A ) )
      = ( A = bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(169,axiom,
    ! [A: set_b] :
      ( ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A )
      = ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_graph__empty__e) ).

thf(841,plain,
    ! [A: set_b] :
      ( ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A )
      = ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(41,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( converse_b_b @ B ) )
     => ~ ! [C: b,D: b] :
            ( ( A
              = ( product_Pair_b_b @ D @ C ) )
           => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_converseE) ).

thf(436,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( converse_b_b @ B ) )
     => ~ ! [C: b,D: b] :
            ( ( A
              = ( product_Pair_b_b @ D @ C ) )
           => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(307,axiom,
    ! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: set_b] :
      ( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ C ) )
     => ~ ! [D: b] :
            ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ D @ A ) @ B )
           => ~ ( member_b @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ImageE) ).

thf(1265,plain,
    ! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: set_b] :
      ( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ C ) )
     => ~ ! [D: b] :
            ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ D @ A ) @ B )
           => ~ ( member_b @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(109,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ~ ! [C: set_Pr1324126435od_b_b] :
            ( ( B
              = ( insert2037698781od_b_b @ A @ C ) )
           => ( member1516365892od_b_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Set_Oset__insert) ).

thf(651,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ~ ! [C: set_Pr1324126435od_b_b] :
            ( ( B
              = ( insert2037698781od_b_b @ A @ C ) )
           => ( member1516365892od_b_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(294,axiom,
    ! [A: b,B: set_Pr1906739389_b_b_b,C: set_Pr1324126435od_b_b] :
      ( ( member_b @ A @ ( image_1764625405_b_b_b @ B @ C ) )
     => ~ ! [D: produc1213276845od_b_b] :
            ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ D @ A ) @ B )
           => ~ ( member1516365892od_b_b @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ImageE) ).

thf(1228,plain,
    ! [A: b,B: set_Pr1906739389_b_b_b,C: set_Pr1324126435od_b_b] :
      ( ( member_b @ A @ ( image_1764625405_b_b_b @ B @ C ) )
     => ~ ! [D: produc1213276845od_b_b] :
            ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ D @ A ) @ B )
           => ~ ( member1516365892od_b_b @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(303,axiom,
    ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) )
    = ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062) ).

thf(1254,plain,
    ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) )
    = ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(28,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( insert1952693431od_b_b @ A @ B )
     != bot_bo1343651123od_b_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_insert__not__empty) ).

thf(389,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( insert1952693431od_b_b @ A @ B )
     != bot_bo1343651123od_b_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(238,axiom,
    ! [A: b] :
      ( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ ( hilbert_Eps_b @ ( p @ A ) ) ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_vert__P) ).

thf(1055,plain,
    ! [A: b] :
      ( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ ( hilbert_Eps_b @ ( p @ A ) ) ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(23,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
      ( ~ ( member1516365892od_b_b @ A @ B )
     => ( ~ ( member1516365892od_b_b @ A @ C )
       => ( ( ( insert2037698781od_b_b @ A @ B )
            = ( insert2037698781od_b_b @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insert__ident) ).

thf(372,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
      ( ~ ( member1516365892od_b_b @ A @ B )
     => ( ~ ( member1516365892od_b_b @ A @ C )
       => ( ( ( insert2037698781od_b_b @ A @ B )
            = ( insert2037698781od_b_b @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(194,axiom,
    ! [A: b,B: set_b,C: produc1213276845od_b_b,D: set_Pr2060523537od_b_b] :
      ( ( member_b @ A @ B )
     => ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ C ) @ D )
       => ( member1516365892od_b_b @ C @ ( image_984343321od_b_b @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_rev__ImageI) ).

thf(917,plain,
    ! [A: b,B: set_b,C: produc1213276845od_b_b,D: set_Pr2060523537od_b_b] :
      ( ( member_b @ A @ B )
     => ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ C ) @ D )
       => ( member1516365892od_b_b @ C @ ( image_984343321od_b_b @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(157,axiom,
    ! [A: b,B: b,C: b,D: b] :
      ( ( ( product_Pair_b_b @ A @ B )
        = ( product_Pair_b_b @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Pair__inject) ).

thf(802,plain,
    ! [A: b,B: b,C: b,D: b] :
      ( ( ( product_Pair_b_b @ A @ B )
        = ( product_Pair_b_b @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(240,axiom,
    ! [A: product_prod_b_b,B: b,C: set_Pr357419743_b_b_b,D: set_Product_prod_b_b] :
      ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ B ) @ C )
     => ( ( member1285940496od_b_b @ A @ D )
       => ( member_b @ B @ ( image_921732011_b_b_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_ImageI) ).

thf(1059,plain,
    ! [A: product_prod_b_b,B: b,C: set_Pr357419743_b_b_b,D: set_Product_prod_b_b] :
      ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ B ) @ C )
     => ( ( member1285940496od_b_b @ A @ D )
       => ( member_b @ B @ ( image_921732011_b_b_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(205,axiom,
    refl_on_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_local_Orefl) ).

thf(949,plain,
    refl_on_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(75,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( ( insert1952693431od_b_b @ A @ B )
        = ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) )
      = ( ( A = C )
        & ( ord_le1036320359od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_singleton__insert__inj__eq_H) ).

thf(542,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( ( insert1952693431od_b_b @ A @ B )
        = ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) )
      = ( ( A = C )
        & ( ord_le1036320359od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(18,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( collec1481886546od_b_b
        @ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Collect__mem__eq) ).

thf(357,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( collec1481886546od_b_b
        @ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(283,axiom,
    ! [A: b,B: set_Product_prod_b_b,C: set_b] :
      ( ( member_b @ A @ ( image_b_b @ B @ C ) )
     => ~ ! [D: b] :
            ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B )
           => ~ ( member_b @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_ImageE) ).

thf(1191,plain,
    ! [A: b,B: set_Product_prod_b_b,C: set_b] :
      ( ( member_b @ A @ ( image_b_b @ B @ C ) )
     => ~ ! [D: b] :
            ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B )
           => ~ ( member_b @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(106,axiom,
    ! [A: product_prod_b_b > $o,B: product_prod_b_b] :
      ( ( ( A @ B )
       => ( ( collec1481886546od_b_b
            @ ^ [C: product_prod_b_b] :
                ( ( C = B )
                & ( A @ C ) ) )
          = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) )
      & ( ~ ( A @ B )
       => ( ( collec1481886546od_b_b
            @ ^ [C: product_prod_b_b] :
                ( ( C = B )
                & ( A @ C ) ) )
          = bot_bo1343651123od_b_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Collect__conv__if) ).

thf(638,plain,
    ! [A: product_prod_b_b > $o,B: product_prod_b_b] :
      ( ( ( A @ B )
       => ( ( collec1481886546od_b_b
            @ ^ [C: product_prod_b_b] :
                ( ( C = B )
                & ( A @ C ) ) )
          = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) )
      & ( ~ ( A @ B )
       => ( ( collec1481886546od_b_b
            @ ^ [C: product_prod_b_b] :
                ( ( C = B )
                & ( A @ C ) ) )
          = bot_bo1343651123od_b_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(214,axiom,
    ! [A: b > $o] :
      ( ( bot_bot_set_b
        = ( collect_b @ A ) )
      = ( ! [B: b] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_empty__Collect__eq) ).

thf(969,plain,
    ! [A: b > $o] :
      ( ( bot_bot_set_b
        = ( collect_b @ A ) )
      = ( ! [B: b] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(146,axiom,
    ( insert2037698781od_b_b
    = ( ^ [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
          ( collec279084418od_b_b
          @ ^ [C: produc1213276845od_b_b] :
              ( ( C = A )
              | ( member1516365892od_b_b @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_insert__compr) ).

thf(770,plain,
    ( insert2037698781od_b_b
    = ( ^ [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
          ( collec279084418od_b_b
          @ ^ [C: produc1213276845od_b_b] :
              ( ( C = A )
              | ( member1516365892od_b_b @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(3,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
      ( ! [C: produc1213276845od_b_b] :
          ( ( member1516365892od_b_b @ C @ A )
         => ( member1516365892od_b_b @ C @ B ) )
     => ( ord_le123089219od_b_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_subsetI) ).

thf(316,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
      ( ! [C: produc1213276845od_b_b] :
          ( ( member1516365892od_b_b @ C @ A )
         => ( member1516365892od_b_b @ C @ B ) )
     => ( ord_le123089219od_b_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(141,axiom,
    ( is_sin1713057243od_b_b
    = ( ^ [A: set_Product_prod_b_b] :
        ? [B: product_prod_b_b] :
          ( A
          = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_is__singleton__def) ).

thf(756,plain,
    ( is_sin1713057243od_b_b
    = ( ^ [A: set_Product_prod_b_b] :
        ? [B: product_prod_b_b] :
          ( A
          = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(152,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
     => ( ( A != B )
       => ( member1285940496od_b_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_insertE) ).

thf(789,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
     => ( ( A != B )
       => ( member1285940496od_b_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(5,axiom,
    ( bot_bo1343651123od_b_b
    = ( collec1481886546od_b_b @ bot_bo1302443370_b_b_o ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_bot__set__def) ).

thf(321,plain,
    ( bot_bo1343651123od_b_b
    = ( collec1481886546od_b_b @ bot_bo1302443370_b_b_o ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(24,axiom,
    ! [A: produc1213276845od_b_b] :
      ~ ! [B: standard_Constant_a,C: b,D: b] :
          ( A
         != ( produc1432590431od_b_b @ B @ ( product_Pair_b_b @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_prod__cases3) ).

thf(376,plain,
    ! [A: produc1213276845od_b_b] :
      ~ ! [B: standard_Constant_a,C: b,D: b] :
          ( A
         != ( produc1432590431od_b_b @ B @ ( product_Pair_b_b @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(266,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_250_is__singleton__def) ).

thf(1136,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)],[266]) ).

thf(65,axiom,
    ( is_sin1713057243od_b_b
    = ( ^ [A: set_Product_prod_b_b] :
          ( A
          = ( insert1952693431od_b_b @ ( the_el329196508od_b_b @ A ) @ bot_bo1343651123od_b_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_is__singleton__the__elem) ).

thf(514,plain,
    ( is_sin1713057243od_b_b
    = ( ^ [A: set_Product_prod_b_b] :
          ( A
          = ( insert1952693431od_b_b @ ( the_el329196508od_b_b @ A ) @ bot_bo1343651123od_b_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(271,axiom,
    ! [A: b,B: b,C: standard_Constant_a] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
     => ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
        @ ^ [D: b] : ( image_b_b @ ( getRel904497637nt_a_b @ C @ g ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_congr_I1_J) ).

thf(1151,plain,
    ! [A: b,B: b,C: standard_Constant_a] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
     => ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
        @ ^ [D: b] : ( image_b_b @ ( getRel904497637nt_a_b @ C @ g ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(15,axiom,
    ! [A: set_Pr1324126435od_b_b,B: standard_Constant_a] :
      ( ( image_1916422435od_b_b @ A @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) )
      = ( collec1481886546od_b_b
        @ ^ [C: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Image__singleton) ).

thf(348,plain,
    ! [A: set_Pr1324126435od_b_b,B: standard_Constant_a] :
      ( ( image_1916422435od_b_b @ A @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) )
      = ( collec1481886546od_b_b
        @ ^ [C: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(213,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: set_b] :
      ( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ C ) )
     => ~ ! [D: b] :
            ( ( member599505522od_b_b @ ( produc800495189od_b_b @ D @ A ) @ B )
           => ~ ( member_b @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_ImageE) ).

thf(966,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: set_b] :
      ( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ C ) )
     => ~ ! [D: b] :
            ( ( member599505522od_b_b @ ( produc800495189od_b_b @ D @ A ) @ B )
           => ~ ( member_b @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(177,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( ord_less_eq_set_b @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) @ ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_equiv__class__subset) ).

thf(866,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( ord_less_eq_set_b @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) @ ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(259,axiom,
    ! [A: set_b,B: b] : ( ord_less_eq_set_b @ A @ ( insert_b @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_subset__insertI) ).

thf(1119,plain,
    ! [A: set_b,B: b] : ( ord_less_eq_set_b @ A @ ( insert_b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(30,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( is_sin1713057243od_b_b @ A )
     => ~ ! [B: product_prod_b_b] :
            ( A
           != ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_is__singletonE) ).

thf(396,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( is_sin1713057243od_b_b @ A )
     => ~ ! [B: product_prod_b_b] :
            ( A
           != ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(223,axiom,
    ! [A: set_b,B: b] :
      ( ( A = bot_bot_set_b )
     => ~ ( member_b @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_equals0D) ).

thf(998,plain,
    ! [A: set_b,B: b] :
      ( ( A = bot_bot_set_b )
     => ~ ( member_b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(220,axiom,
    ! [A: b > $o,B: b] :
      ( ( A @ B )
     => ( ! [C: b] :
            ( ( A @ C )
           => ( C = B ) )
       => ( ( hilbert_Eps_b @ A )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_some__equality) ).

thf(988,plain,
    ! [A: b > $o,B: b] :
      ( ( A @ B )
     => ( ! [C: b] :
            ( ( A @ C )
           => ( C = B ) )
       => ( ( hilbert_Eps_b @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(94,axiom,
    ! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
      ( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_prod__cases) ).

thf(602,plain,
    ! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
      ( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(218,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( ( member_b @ D @ A )
         => ( ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
              = ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
            = ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_eq__equiv__class__iff) ).

thf(981,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( ( member_b @ D @ A )
         => ( ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
              = ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
            = ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(145,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ~ ! [C: set_Product_prod_b_b] :
            ( ( B
              = ( insert1952693431od_b_b @ A @ C ) )
           => ( member1285940496od_b_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Set_Oset__insert) ).

thf(766,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ~ ! [C: set_Product_prod_b_b] :
            ( ( B
              = ( insert1952693431od_b_b @ A @ C ) )
           => ( member1285940496od_b_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(181,axiom,
    ! [A: b,B: set_Product_prod_b_b,C: b] :
      ( ( member_b @ A @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
      = ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Image__singleton__iff) ).

thf(877,plain,
    ! [A: b,B: set_Product_prod_b_b,C: b] :
      ( ( member_b @ A @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
      = ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(122,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_singletonD) ).

thf(692,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(46,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b,D: set_Product_prod_b_b] :
      ( ~ ( member1285940496od_b_b @ A @ B )
     => ( ~ ( member1285940496od_b_b @ C @ D )
       => ( ( ( insert1952693431od_b_b @ A @ B )
            = ( insert1952693431od_b_b @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Product_prod_b_b] :
                  ( ( B
                    = ( insert1952693431od_b_b @ C @ E ) )
                  & ~ ( member1285940496od_b_b @ C @ E )
                  & ( D
                    = ( insert1952693431od_b_b @ A @ E ) )
                  & ~ ( member1285940496od_b_b @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_insert__eq__iff) ).

thf(452,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b,D: set_Product_prod_b_b] :
      ( ~ ( member1285940496od_b_b @ A @ B )
     => ( ~ ( member1285940496od_b_b @ C @ D )
       => ( ( ( insert1952693431od_b_b @ A @ B )
            = ( insert1952693431od_b_b @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Product_prod_b_b] :
                  ( ( B
                    = ( insert1952693431od_b_b @ C @ E ) )
                  & ~ ( member1285940496od_b_b @ C @ E )
                  & ( D
                    = ( insert1952693431od_b_b @ A @ E ) )
                  & ~ ( member1285940496od_b_b @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(195,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_emptyE) ).

thf(920,plain,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(25,axiom,
    ! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
      ( ! [C: standard_Constant_a,D: b,E: b] : ( A @ ( produc1432590431od_b_b @ C @ ( product_Pair_b_b @ D @ E ) ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_prod__induct3) ).

thf(380,plain,
    ! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
      ( ! [C: standard_Constant_a,D: b,E: b] : ( A @ ( produc1432590431od_b_b @ C @ ( product_Pair_b_b @ D @ E ) ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(117,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ B )
     => ( ( member1285940496od_b_b @ C @ A )
       => ( member1285940496od_b_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_in__mono) ).

thf(678,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ B )
     => ( ( member1285940496od_b_b @ C @ A )
       => ( member1285940496od_b_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(21,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ! [C: b,D: b] :
          ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
         => ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) )
     => ( ord_le1036320359od_b_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_subrelI) ).

thf(366,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ! [C: b,D: b] :
          ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
         => ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) )
     => ( ord_le1036320359od_b_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(72,axiom,
    ! [A: set_Product_prod_b_b,B: set_Pr2007082183od_b_b,C: product_prod_b_b] :
      ( ( equiv_1125628061od_b_b @ A @ B )
     => ( ( member1285940496od_b_b @ C @ A )
       => ( member1285940496od_b_b @ C @ ( image_1928024979od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_equiv__class__self) ).

thf(534,plain,
    ! [A: set_Product_prod_b_b,B: set_Pr2007082183od_b_b,C: product_prod_b_b] :
      ( ( equiv_1125628061od_b_b @ A @ B )
     => ( ( member1285940496od_b_b @ C @ A )
       => ( member1285940496od_b_b @ C @ ( image_1928024979od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(128,axiom,
    ! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
      ( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_old_Oprod_Oinducts) ).

thf(714,plain,
    ! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
      ( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(64,axiom,
    ( bot_bo1302443370_b_b_o
    = ( ^ [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_bot__empty__eq) ).

thf(512,plain,
    ( bot_bo1302443370_b_b_o
    = ( ^ [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(202,axiom,
    ! [A: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A @ B )
     => ( ord_less_eq_set_b @ A @ ( insert_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_subset__insertI2) ).

thf(942,plain,
    ! [A: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A @ B )
     => ( ord_less_eq_set_b @ A @ ( insert_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(272,axiom,
    ! [A: b > $o] :
      ( ( ( collect_b @ A )
        = bot_bot_set_b )
      = ( A = bot_bot_b_o ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_Collect__empty__eq__bot) ).

thf(1153,plain,
    ! [A: b > $o] :
      ( ( ( collect_b @ A )
        = bot_bot_set_b )
      = ( A = bot_bot_b_o ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(143,axiom,
    ( ord_le1036320359od_b_b
    = ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
        ! [C: product_prod_b_b] :
          ( ( member1285940496od_b_b @ C @ A )
         => ( member1285940496od_b_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_subset__eq) ).

thf(761,plain,
    ( ord_le1036320359od_b_b
    = ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
        ! [C: product_prod_b_b] :
          ( ( member1285940496od_b_b @ C @ A )
         => ( member1285940496od_b_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(235,axiom,
    ! [A: b,B: b > $o] :
      ( ( member_b @ A @ ( collect_b @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mem__Collect__eq) ).

thf(1047,plain,
    ! [A: b,B: b > $o] :
      ( ( member_b @ A @ ( collect_b @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(239,axiom,
    ( f
    = ( ^ [A: b] :
          ( if_b
          @ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
            = bot_bot_set_b )
          @ A
          @ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_f) ).

thf(1057,plain,
    ( f
    = ( ^ [A: b] :
          ( if_b
          @ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
            = bot_bot_set_b )
          @ A
          @ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(310,axiom,
    ! [A: b,B: set_b] :
      ( ( insert_b @ A @ ( insert_b @ A @ B ) )
      = ( insert_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insert__absorb2) ).

thf(1274,plain,
    ! [A: b,B: set_b] :
      ( ( insert_b @ A @ ( insert_b @ A @ B ) )
      = ( insert_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(10,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
      ( ( ord_le123089219od_b_b @ A @ B )
     => ( ( member1516365892od_b_b @ C @ A )
       => ( member1516365892od_b_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_in__mono) ).

thf(334,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
      ( ( ord_le123089219od_b_b @ A @ B )
     => ( ( member1516365892od_b_b @ C @ A )
       => ( member1516365892od_b_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(191,axiom,
    ! [A: b > $o] :
      ( ( ( collect_b @ A )
        = bot_bot_set_b )
      = ( ! [B: b] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Collect__empty__eq) ).

thf(910,plain,
    ! [A: b > $o] :
      ( ( ( collect_b @ A )
        = bot_bot_set_b )
      = ( ! [B: b] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(261,axiom,
    ! [A: set_b,B: set_b] :
      ( ! [C: b] :
          ( ( member_b @ C @ A )
         => ( member_b @ C @ B ) )
     => ( ord_less_eq_set_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_subsetI) ).

thf(1123,plain,
    ! [A: set_b,B: set_b] :
      ( ! [C: b] :
          ( ( member_b @ C @ A )
         => ( member_b @ C @ B ) )
     => ( ord_less_eq_set_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(292,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( refl_on_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( ( member_b @ C @ A )
          & ( member_b @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_refl__on__domain) ).

thf(1217,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( refl_on_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( ( member_b @ C @ A )
          & ( member_b @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(161,axiom,
    ! [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_singletonI) ).

thf(820,plain,
    ! [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(103,axiom,
    ! [A: b,B: b,C: b,D: b] :
      ( ( ( product_Pair_b_b @ A @ B )
        = ( product_Pair_b_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_old_Oprod_Oinject) ).

thf(630,plain,
    ! [A: b,B: b,C: b,D: b] :
      ( ( ( product_Pair_b_b @ A @ B )
        = ( product_Pair_b_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(40,axiom,
    ! [A: product_prod_b_b > $o,B: product_prod_b_b] :
      ( ( ( A @ B )
       => ( ( collec1481886546od_b_b
            @ ^ [C: product_prod_b_b] :
                ( ( B = C )
                & ( A @ C ) ) )
          = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) )
      & ( ~ ( A @ B )
       => ( ( collec1481886546od_b_b
            @ ^ [C: product_prod_b_b] :
                ( ( B = C )
                & ( A @ C ) ) )
          = bot_bo1343651123od_b_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Collect__conv__if2) ).

thf(429,plain,
    ! [A: product_prod_b_b > $o,B: product_prod_b_b] :
      ( ( ( A @ B )
       => ( ( collec1481886546od_b_b
            @ ^ [C: product_prod_b_b] :
                ( ( B = C )
                & ( A @ C ) ) )
          = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) )
      & ( ~ ( A @ B )
       => ( ( collec1481886546od_b_b
            @ ^ [C: product_prod_b_b] :
                ( ( B = C )
                & ( A @ C ) ) )
          = bot_bo1343651123od_b_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(160,axiom,
    ! [A: set_Product_prod_b_b,B: product_prod_b_b] :
      ( ( A = bot_bo1343651123od_b_b )
     => ~ ( member1285940496od_b_b @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_equals0D) ).

thf(815,plain,
    ! [A: set_Product_prod_b_b,B: product_prod_b_b] :
      ( ( A = bot_bo1343651123od_b_b )
     => ~ ( member1285940496od_b_b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(209,axiom,
    ( insert_b
    = ( ^ [A: b,B: set_b] :
          ( collect_b
          @ ^ [C: b] :
              ( ( C = A )
              | ( member_b @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_insert__compr) ).

thf(957,plain,
    ( insert_b
    = ( ^ [A: b,B: set_b] :
          ( collect_b
          @ ^ [C: b] :
              ( ( C = A )
              | ( member_b @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(187,axiom,
    ! [A: b > $o,B: b] :
      ( ? [C: b] :
          ( ( A @ C )
          & ! [D: b] :
              ( ( A @ D )
             => ( D = C ) ) )
     => ( ( A @ B )
       => ( ( hilbert_Eps_b @ A )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_some1__equality) ).

thf(894,plain,
    ! [A: b > $o,B: b] :
      ( ? [C: b] :
          ( ( A @ C )
          & ! [D: b] :
              ( ( A @ D )
             => ( D = C ) ) )
     => ( ( A @ B )
       => ( ( hilbert_Eps_b @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(51,axiom,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b
        @ ( hilber46179633od_b_b
          @ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
        @ A )
      = ( A != bot_bo1664927607od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_some__in__eq) ).

thf(467,plain,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b
        @ ( hilber46179633od_b_b
          @ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
        @ A )
      = ( A != bot_bo1664927607od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(56,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b] :
      ( ( collec1481886546od_b_b
        @ ^ [C: product_prod_b_b] :
            ( ( C = A )
            | ( C = B ) ) )
      = ( insert1952693431od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_tuple__disj) ).

thf(484,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b] :
      ( ( collec1481886546od_b_b
        @ ^ [C: product_prod_b_b] :
            ( ( C = A )
            | ( C = B ) ) )
      = ( insert1952693431od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(232,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( ord_less_eq_set_b @ B @ ( insert_b @ A @ C ) )
        = ( ord_less_eq_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_subset__insert) ).

thf(1032,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ~ ( member_b @ A @ B )
     => ( ( ord_less_eq_set_b @ B @ ( insert_b @ A @ C ) )
        = ( ord_less_eq_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(173,axiom,
    ! [A: set_b] :
      ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
      = ( A = bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_subset__empty) ).

thf(852,plain,
    ! [A: set_b] :
      ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
      = ( A = bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(113,axiom,
    ! [A: set_Pr1324126435od_b_b] :
      ( ! [B: produc1213276845od_b_b] :
          ~ ( member1516365892od_b_b @ B @ A )
     => ( A = bot_bo1664927607od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_equals0I) ).

thf(665,plain,
    ! [A: set_Pr1324126435od_b_b] :
      ( ! [B: produc1213276845od_b_b] :
          ~ ( member1516365892od_b_b @ B @ A )
     => ( A = bot_bo1664927607od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(185,axiom,
    ( equiv_proj_b_b
    = ( ^ [A: set_Product_prod_b_b,B: b] : ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_proj__def) ).

thf(889,plain,
    ( equiv_proj_b_b
    = ( ^ [A: set_Product_prod_b_b,B: b] : ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(49,axiom,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b] :
      ( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ bot_bo1664927607od_b_b ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_singletonD) ).

thf(461,plain,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b] :
      ( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ bot_bo1664927607od_b_b ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(78,axiom,
    ! [A: set_b,B: set_Product_prod_b_b] :
      ( ( refl_on_b @ A @ ( converse_b_b @ B ) )
      = ( refl_on_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_refl__on__converse) ).

thf(551,plain,
    ! [A: set_b,B: set_Product_prod_b_b] :
      ( ( refl_on_b @ A @ ( converse_b_b @ B ) )
      = ( refl_on_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(313,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b,D: b > b > set_b,E: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( equiv_167626658_set_b @ B @ C @ D )
       => ( ( member_b @ E @ A )
         => ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_congruent2__implies__congruent) ).

thf(1281,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b,D: b > b > set_b,E: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( equiv_167626658_set_b @ B @ C @ D )
       => ( ( member_b @ E @ A )
         => ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(47,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ ( converse_b_b @ B ) )
      = ( ord_le1036320359od_b_b @ ( converse_b_b @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_converse__subset__swap) ).

thf(456,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ ( converse_b_b @ B ) )
      = ( ord_le1036320359od_b_b @ ( converse_b_b @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(216,axiom,
    ! [A: labele1159362096nt_a_b,B: set_Product_prod_b_b] :
      ( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ bot_bot_set_b ) @ A @ B )
      = ( ( B = bot_bo1343651123od_b_b )
        & ( A
          = ( restri446606278nt_a_b @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_graph__homomorphism__empty) ).

thf(974,plain,
    ! [A: labele1159362096nt_a_b,B: set_Product_prod_b_b] :
      ( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ bot_bot_set_b ) @ A @ B )
      = ( ( B = bot_bo1343651123od_b_b )
        & ( A
          = ( restri446606278nt_a_b @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(227,axiom,
    ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_singletonI) ).

thf(1012,plain,
    ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(89,axiom,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
      = ( ? [D: b,E: b] :
            ( ( A = E )
            & ( B = D )
            & ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_converse_Osimps) ).

thf(583,plain,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
      = ( ? [D: b,E: b] :
            ( ( A = E )
            & ( B = D )
            & ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(165,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insertI2) ).

thf(830,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(67,axiom,
    ( bot_bot_b_b_o
    = ( ^ [A: b,B: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ bot_bo1343651123od_b_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_bot__empty__eq2) ).

thf(519,plain,
    ( bot_bot_b_b_o
    = ( ^ [A: b,B: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ bot_bo1343651123od_b_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(305,axiom,
    ! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_empty__subsetI) ).

thf(1259,plain,
    ! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(260,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_229_is__singleton__the__elem) ).

thf(1121,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)],[260]) ).

thf(242,axiom,
    ! [A: b > $o,B: b,C: b > $o] :
      ( ( A @ B )
     => ( ! [D: b] :
            ( ( A @ D )
           => ( C @ D ) )
       => ( C @ ( hilbert_Eps_b @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_someI2) ).

thf(1064,plain,
    ! [A: b > $o,B: b,C: b > $o] :
      ( ( A @ B )
     => ( ! [D: b] :
            ( ( A @ D )
           => ( C @ D ) )
       => ( C @ ( hilbert_Eps_b @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(32,axiom,
    ! [A: product_prod_b_b] :
    ? [B: b,C: b] :
      ( A
      = ( product_Pair_b_b @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_surj__pair) ).

thf(403,plain,
    ! [A: product_prod_b_b] :
    ? [B: b,C: b] :
      ( A
      = ( product_Pair_b_b @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(267,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_101_insert__eq__iff) ).

thf(1138,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)],[267]) ).

thf(178,axiom,
    ! [A: b,B: set_b,C: b] :
      ( ( ( insert_b @ A @ B )
        = ( insert_b @ C @ bot_bot_set_b ) )
      = ( ( A = C )
        & ( ord_less_eq_set_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_singleton__insert__inj__eq_H) ).

thf(869,plain,
    ! [A: b,B: set_b,C: b] :
      ( ( ( insert_b @ A @ B )
        = ( insert_b @ C @ bot_bot_set_b ) )
      = ( ( A = C )
        & ( ord_less_eq_set_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(97,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_b] :
      ( ( labele1741081071nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_labeled__graph_Osel_I1_J) ).

thf(610,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_b] :
      ( ( labele1741081071nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(60,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
      ( ( ord_le123089219od_b_b @ ( insert2037698781od_b_b @ A @ B ) @ C )
      = ( ( member1516365892od_b_b @ A @ C )
        & ( ord_le123089219od_b_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_insert__subset) ).

thf(499,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
      ( ( ord_le123089219od_b_b @ ( insert2037698781od_b_b @ A @ B ) @ C )
      = ( ( member1516365892od_b_b @ A @ C )
        & ( ord_le123089219od_b_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(250,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_empty__iff) ).

thf(1089,plain,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(296,axiom,
    ! [A: b] :
      ( ( hilbert_Eps_b @ ( (=) @ b @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_some__sym__eq__trivial) ).

thf(1234,plain,
    ! [A: b] :
      ( ( hilbert_Eps_b @ ( (=) @ b @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(150,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
      ( ( ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b )
        = ( insert1952693431od_b_b @ B @ C ) )
      = ( ( B = A )
        & ( ord_le1036320359od_b_b @ C @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_singleton__insert__inj__eq) ).

thf(783,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
      ( ( ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b )
        = ( insert1952693431od_b_b @ B @ C ) )
      = ( ( B = A )
        & ( ord_le1036320359od_b_b @ C @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(37,axiom,
    ! [A: b > $o,B: b > $o] :
      ( ! [C: b] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_Collect__mono) ).

thf(420,plain,
    ! [A: b > $o,B: b > $o] :
      ( ! [C: b] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(258,axiom,
    equiv_equiv_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_equiv) ).

thf(1118,plain,
    equiv_equiv_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(8,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
      ( ( ord_le123089219od_b_b @ A @ B )
     => ( ( member1516365892od_b_b @ C @ A )
       => ( member1516365892od_b_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_subsetD) ).

thf(328,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
      ( ( ord_le123089219od_b_b @ A @ B )
     => ( ( member1516365892od_b_b @ C @ A )
       => ( member1516365892od_b_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(280,axiom,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ord_less_eq_set_b @ ( insert_b @ A @ B ) @ C )
      = ( ( member_b @ A @ C )
        & ( ord_less_eq_set_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_insert__subset) ).

thf(1182,plain,
    ! [A: b,B: set_b,C: set_b] :
      ( ( ord_less_eq_set_b @ ( insert_b @ A @ B ) @ C )
      = ( ( member_b @ A @ C )
        & ( ord_less_eq_set_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(73,axiom,
    ( insert1952693431od_b_b
    = ( ^ [A: product_prod_b_b,B: set_Product_prod_b_b] :
          ( collec1481886546od_b_b
          @ ^ [C: product_prod_b_b] :
              ( ( C = A )
              | ( member1285940496od_b_b @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_insert__compr) ).

thf(537,plain,
    ( insert1952693431od_b_b
    = ( ^ [A: product_prod_b_b,B: set_Product_prod_b_b] :
          ( collec1481886546od_b_b
          @ ^ [C: product_prod_b_b] :
              ( ( C = A )
              | ( member1285940496od_b_b @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(114,axiom,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( collec279084418od_b_b
        @ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Collect__mem__eq) ).

thf(669,plain,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( collec279084418od_b_b
        @ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(120,axiom,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b] :
      ( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ bot_bo1664927607od_b_b ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_singleton__iff) ).

thf(686,plain,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b] :
      ( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ bot_bo1664927607od_b_b ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(69,axiom,
    ( bot_bo1343651123od_b_b
    = ( collec1481886546od_b_b
      @ ^ [A: product_prod_b_b] : $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_empty__def) ).

thf(526,plain,
    ( bot_bo1343651123od_b_b
    = ( collec1481886546od_b_b
      @ ^ [A: product_prod_b_b] : $false ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(291,axiom,
    ! [A: set_b] :
      ( ( ? [B: b] : ( member_b @ B @ A ) )
      = ( A != bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_ex__in__conv) ).

thf(1214,plain,
    ! [A: set_b] :
      ( ( ? [B: b] : ( member_b @ B @ A ) )
      = ( A != bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(125,axiom,
    ! [A: set_Product_prod_b_b] : ( ord_le1036320359od_b_b @ bot_bo1343651123od_b_b @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_bot_Oextremum) ).

thf(706,plain,
    ! [A: set_Product_prod_b_b] : ( ord_le1036320359od_b_b @ bot_bo1343651123od_b_b @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(79,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ B )
     => ( ( member1285940496od_b_b @ C @ A )
       => ( member1285940496od_b_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_subsetD) ).

thf(554,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ B )
     => ( ( member1285940496od_b_b @ C @ A )
       => ( member1285940496od_b_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(140,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( ( ^ [C: b,D: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A ) )
        = ( ^ [C: b,D: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_pred__equals__eq2) ).

thf(753,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( ( ^ [C: b,D: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A ) )
        = ( ^ [C: b,D: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(168,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
      ( ~ ( member1285940496od_b_b @ A @ B )
     => ( ( ord_le1036320359od_b_b @ B @ ( insert1952693431od_b_b @ A @ C ) )
        = ( ord_le1036320359od_b_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_subset__insert) ).

thf(837,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
      ( ~ ( member1285940496od_b_b @ A @ B )
     => ( ( ord_le1036320359od_b_b @ B @ ( insert1952693431od_b_b @ A @ C ) )
        = ( ord_le1036320359od_b_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(219,axiom,
    ! [A: b,B: set_b,C: b,D: set_Product_prod_b_b] :
      ( ( member_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ D )
       => ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_rev__ImageI) ).

thf(985,plain,
    ! [A: b,B: set_b,C: b,D: set_Product_prod_b_b] :
      ( ( member_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ D )
       => ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(301,axiom,
    ( bot_bot_set_b
    = ( collect_b @ bot_bot_b_o ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_bot__set__def) ).

thf(1249,plain,
    ( bot_bot_set_b
    = ( collect_b @ bot_bot_b_o ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(135,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
      = ( ( A = B )
        | ( member1285940496od_b_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_insert__iff) ).

thf(738,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
      = ( ( A = B )
        | ( member1285940496od_b_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(295,axiom,
    ! [A: b] :
      ( ( collect_b
        @ ^ [B: b] : ( B = A ) )
      = ( insert_b @ A @ bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_singleton__conv) ).

thf(1231,plain,
    ! [A: b] :
      ( ( collect_b
        @ ^ [B: b] : ( B = A ) )
      = ( insert_b @ A @ bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(264,axiom,
    ! [A: set_b] :
      ( ( member_b
        @ ( hilbert_Eps_b
          @ ^ [B: b] : ( member_b @ B @ A ) )
        @ A )
      = ( A != bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_some__in__eq) ).

thf(1131,plain,
    ! [A: set_b] :
      ( ( member_b
        @ ( hilbert_Eps_b
          @ ^ [B: b] : ( member_b @ B @ A ) )
        @ A )
      = ( A != bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(236,axiom,
    ! [A: set_b] :
      ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
      = ( A = bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_bot_Oextremum__unique) ).

thf(1050,plain,
    ! [A: set_b] :
      ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
      = ( A = bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(300,axiom,
    ! [A: b,B: b,C: set_b] :
      ( ( insert_b @ A @ ( insert_b @ B @ C ) )
      = ( insert_b @ B @ ( insert_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_insert__commute) ).

thf(1246,plain,
    ! [A: b,B: b,C: set_b] :
      ( ( insert_b @ A @ ( insert_b @ B @ C ) )
      = ( insert_b @ B @ ( insert_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(95,axiom,
    ! [A: labele1159362096nt_a_b,B: set_Pr357419743_b_b_b] :
      ( ( graph_792023598_b_b_b @ ( labele170595300od_b_b @ bot_bo1964903287od_b_b @ bot_bo1343651123od_b_b ) @ A @ B )
      = ( ( B = bot_bo1124087115_b_b_b )
        & ( A
          = ( restri446606278nt_a_b @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_graph__homomorphism__empty) ).

thf(605,plain,
    ! [A: labele1159362096nt_a_b,B: set_Pr357419743_b_b_b] :
      ( ( graph_792023598_b_b_b @ ( labele170595300od_b_b @ bot_bo1964903287od_b_b @ bot_bo1343651123od_b_b ) @ A @ B )
      = ( ( B = bot_bo1124087115_b_b_b )
        & ( A
          = ( restri446606278nt_a_b @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(29,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( ? [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
      = ( A != bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ex__in__conv) ).

thf(393,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( ? [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
      = ( A != bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(257,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
          = ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_equiv__class__eq) ).

thf(1114,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
          = ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(13,axiom,
    ( ord_le123089219od_b_b
    = ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
        ! [C: produc1213276845od_b_b] :
          ( ( member1516365892od_b_b @ C @ A )
         => ( member1516365892od_b_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_subset__iff) ).

thf(343,plain,
    ( ord_le123089219od_b_b
    = ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
        ! [C: produc1213276845od_b_b] :
          ( ( member1516365892od_b_b @ C @ A )
         => ( member1516365892od_b_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(230,axiom,
    ! [A: b] :
      ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
        = bot_bot_set_b )
      = ( ~ ( member_b @ A @ ( labele1424214014nt_a_b @ g ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_r2) ).

thf(1026,plain,
    ! [A: b] :
      ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
        = bot_bot_set_b )
      = ( ~ ( member_b @ A @ ( labele1424214014nt_a_b @ g ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(112,axiom,
    ! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
      ( ( ( produc1432590431od_b_b @ A @ B )
        = ( produc1432590431od_b_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_prod_Oinject) ).

thf(662,plain,
    ! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
      ( ( ( produc1432590431od_b_b @ A @ B )
        = ( produc1432590431od_b_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(197,axiom,
    ! [A: set_b] :
      ( ( collect_b
        @ ^ [B: b] : ( member_b @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Collect__mem__eq) ).

thf(926,plain,
    ! [A: set_b] :
      ( ( collect_b
        @ ^ [B: b] : ( member_b @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(287,axiom,
    ! [A: set_Pr621705391od_b_b] :
      ( ( image_1177096571od_b_b @ A @ bot_bot_set_b )
      = bot_bo1343651123od_b_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Image__empty2) ).

thf(1202,plain,
    ! [A: set_Pr621705391od_b_b] :
      ( ( image_1177096571od_b_b @ A @ bot_bot_set_b )
      = bot_bo1343651123od_b_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(153,axiom,
    ( ( converse_b_b @ bot_bo1343651123od_b_b )
    = bot_bo1343651123od_b_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_converse__empty) ).

thf(792,plain,
    ( ( converse_b_b @ bot_bo1343651123od_b_b )
    = bot_bo1343651123od_b_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(249,axiom,
    ! [A: b] :
      ( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_the__elem__eq) ).

thf(1086,plain,
    ! [A: b] :
      ( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(201,axiom,
    ! [A: set_Product_prod_b_b,B: b,C: b,D: set_b] :
      ( ( ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
        = ( image_b_b @ A @ ( insert_b @ C @ bot_bot_set_b ) ) )
     => ( ( equiv_equiv_b @ D @ A )
       => ( ( member_b @ C @ D )
         => ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_eq__equiv__class) ).

thf(938,plain,
    ! [A: set_Product_prod_b_b,B: b,C: b,D: set_b] :
      ( ( ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
        = ( image_b_b @ A @ ( insert_b @ C @ bot_bot_set_b ) ) )
     => ( ( equiv_equiv_b @ D @ A )
       => ( ( member_b @ C @ D )
         => ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(104,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_insertI1) ).

thf(633,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(19,axiom,
    ! [A: product_prod_b_b > $o] :
      ( ( ( collec1481886546od_b_b @ A )
        = bot_bo1343651123od_b_b )
      = ( A = bot_bo1302443370_b_b_o ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Collect__empty__eq__bot) ).

thf(360,plain,
    ! [A: product_prod_b_b > $o] :
      ( ( ( collec1481886546od_b_b @ A )
        = bot_bo1343651123od_b_b )
      = ( A = bot_bo1302443370_b_b_o ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(207,axiom,
    ! [A: b] : ( order_653178932r_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_linear__order__on__singleton) ).

thf(953,plain,
    ! [A: b] : ( order_653178932r_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(281,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: b,D: set_Pr357419743_b_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ C ) @ D )
       => ( member_b @ C @ ( image_921732011_b_b_b @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_rev__ImageI) ).

thf(1185,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: b,D: set_Pr357419743_b_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ C ) @ D )
       => ( member_b @ C @ ( image_921732011_b_b_b @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(154,axiom,
    ! [A: product_prod_b_b] : ( is_sin1713057243od_b_b @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_is__singletonI) ).

thf(794,plain,
    ! [A: product_prod_b_b] : ( is_sin1713057243od_b_b @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(90,axiom,
    ( labele1424214014nt_a_b
    = ( labele1287464530_set_b
      @ ^ [A: set_Pr1324126435od_b_b,B: set_b] : B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_vertices__def) ).

thf(586,plain,
    ( labele1424214014nt_a_b
    = ( labele1287464530_set_b
      @ ^ [A: set_Pr1324126435od_b_b,B: set_b] : B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(35,axiom,
    ! [A: set_Pr357419743_b_b_b,B: product_prod_b_b] :
      ( ( image_921732011_b_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
      = ( collect_b
        @ ^ [C: b] : ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Image__singleton) ).

thf(412,plain,
    ! [A: set_Pr357419743_b_b_b,B: product_prod_b_b] :
      ( ( image_921732011_b_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
      = ( collect_b
        @ ^ [C: b] : ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(139,axiom,
    ! [A: b > $o,B: b > $o] :
      ( ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) )
      = ( ! [C: b] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_Collect__mono__iff) ).

thf(750,plain,
    ! [A: b > $o,B: b > $o] :
      ( ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) )
      = ( ! [C: b] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(302,axiom,
    ! [A: b,B: b,C: set_Product_prod_b_b,D: set_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
     => ( ( member_b @ A @ D )
       => ( member_b @ B @ ( image_b_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_ImageI) ).

thf(1251,plain,
    ! [A: b,B: b,C: set_Product_prod_b_b,D: set_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
     => ( ( member_b @ A @ D )
       => ( member_b @ B @ ( image_b_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(163,axiom,
    ! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
      ( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
     => ~ ! [D: standard_Constant_a] :
            ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B )
           => ~ ( member1632892294tant_a @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ImageE) ).

thf(824,plain,
    ! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
      ( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
     => ~ ! [D: standard_Constant_a] :
            ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B )
           => ~ ( member1632892294tant_a @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(137,axiom,
    ! [A: labele1159362096nt_a_b] :
      ( A
      = ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_labeled__graph_Oexhaust__sel) ).

thf(745,plain,
    ! [A: labele1159362096nt_a_b] :
      ( A
      = ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(85,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b
        @ ( hilber620807523od_b_b
          @ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
        @ A )
      = ( A != bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_some__in__eq) ).

thf(573,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b
        @ ( hilber620807523od_b_b
          @ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
        @ A )
      = ( A != bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(121,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ( ( insert2037698781od_b_b @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_insert__absorb) ).

thf(689,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ( ( insert2037698781od_b_b @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(43,axiom,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
     => ( ( A != B )
       => ( member1516365892od_b_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_insertE) ).

thf(444,plain,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
     => ( ( A != B )
       => ( member1516365892od_b_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(189,axiom,
    ! [A: b] :
      ( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
      = ( p @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_r1) ).

thf(904,plain,
    ! [A: b] :
      ( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
      = ( p @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(38,axiom,
    ! [A: b,B: b] :
      ( ( if_b @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001tf__b_T) ).

thf(423,plain,
    ! [A: b,B: b] :
      ( ( if_b @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(225,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( member_b @ C @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_equiv__class__self) ).

thf(1007,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( member_b @ C @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(133,axiom,
    ! [A: set_Product_prod_b_b,B: product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
      = ( ( A = bot_bo1343651123od_b_b )
        | ( A
          = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_subset__singleton__iff) ).

thf(732,plain,
    ! [A: set_Product_prod_b_b,B: product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
      = ( ( A = bot_bo1343651123od_b_b )
        | ( A
          = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(147,axiom,
    ! [A: set_Product_prod_b_b,B: product_prod_b_b > $o,C: product_prod_b_b > $o] :
      ( ? [D: product_prod_b_b] :
          ( ( member1285940496od_b_b @ D @ A )
          & ( B @ D ) )
     => ( ! [D: product_prod_b_b] :
            ( ( ( member1285940496od_b_b @ D @ A )
              & ( B @ D ) )
           => ( C @ D ) )
       => ( C
          @ ( hilber620807523od_b_b
            @ ^ [D: product_prod_b_b] :
                ( ( member1285940496od_b_b @ D @ A )
                & ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_someI2__bex) ).

thf(772,plain,
    ! [A: set_Product_prod_b_b,B: product_prod_b_b > $o,C: product_prod_b_b > $o] :
      ( ? [D: product_prod_b_b] :
          ( ( member1285940496od_b_b @ D @ A )
          & ( B @ D ) )
     => ( ! [D: product_prod_b_b] :
            ( ( ( member1285940496od_b_b @ D @ A )
              & ( B @ D ) )
           => ( C @ D ) )
       => ( C
          @ ( hilber620807523od_b_b
            @ ^ [D: product_prod_b_b] :
                ( ( member1285940496od_b_b @ D @ A )
                & ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(87,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr2109276827od_b_b,C: set_Product_prod_b_b,D: produc1213276845od_b_b > b > set_b,E: produc1213276845od_b_b] :
      ( ( equiv_2048442231od_b_b @ A @ B )
     => ( ( equiv_1629197578_set_b @ B @ C @ D )
       => ( ( member1516365892od_b_b @ E @ A )
         => ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_congruent2__implies__congruent) ).

thf(579,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr2109276827od_b_b,C: set_Product_prod_b_b,D: produc1213276845od_b_b > b > set_b,E: produc1213276845od_b_b] :
      ( ( equiv_2048442231od_b_b @ A @ B )
     => ( ( equiv_1629197578_set_b @ B @ C @ D )
       => ( ( member1516365892od_b_b @ E @ A )
         => ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(304,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_113_insertI2) ).

thf(1256,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)],[304]) ).

thf(76,axiom,
    ! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
      ( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
      = ( ? [D: standard_Constant_a] :
            ( ( member1632892294tant_a @ D @ C )
            & ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Image__iff) ).

thf(545,plain,
    ! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
      ( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
      = ( ? [D: standard_Constant_a] :
            ( ( member1632892294tant_a @ D @ C )
            & ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(309,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_154_singleton__iff) ).

thf(1271,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)],[309]) ).

thf(251,axiom,
    ! [A: b] :
      ( ( hilbert_Eps_b
        @ ^ [B: b] : ( B = A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_some__eq__trivial) ).

thf(1092,plain,
    ! [A: b] :
      ( ( hilbert_Eps_b
        @ ^ [B: b] : ( B = A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(115,axiom,
    ! [A: product_prod_b_b > $o,B: product_prod_b_b] :
      ( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_prod__cases) ).

thf(672,plain,
    ! [A: product_prod_b_b > $o,B: product_prod_b_b] :
      ( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(284,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: b] :
      ( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
      = ( member599505522od_b_b @ ( produc800495189od_b_b @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Image__singleton__iff) ).

thf(1194,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: b] :
      ( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
      = ( member599505522od_b_b @ ( produc800495189od_b_b @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(118,axiom,
    ( bot_bo1167600078_b_b_o
    = ( ^ [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_bot__empty__eq) ).

thf(681,plain,
    ( bot_bo1167600078_b_b_o
    = ( ^ [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(222,axiom,
    ! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_insertI1) ).

thf(996,plain,
    ! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(99,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
      ( ~ ( member1285940496od_b_b @ A @ B )
     => ( ~ ( member1285940496od_b_b @ A @ C )
       => ( ( ( insert1952693431od_b_b @ A @ B )
            = ( insert1952693431od_b_b @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insert__ident) ).

thf(616,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
      ( ~ ( member1285940496od_b_b @ A @ B )
     => ( ~ ( member1285940496od_b_b @ A @ C )
       => ( ( ( insert1952693431od_b_b @ A @ B )
            = ( insert1952693431od_b_b @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(93,axiom,
    ! [A: produc1213276845od_b_b] :
      ~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_emptyE) ).

thf(599,plain,
    ! [A: produc1213276845od_b_b] :
      ~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(188,axiom,
    ! [A: set_b] :
      ( ! [B: b] :
          ~ ( member_b @ B @ A )
     => ( A = bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_equals0I) ).

thf(900,plain,
    ! [A: set_b] :
      ( ! [B: b] :
          ~ ( member_b @ B @ A )
     => ( A = bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(33,axiom,
    ! [A: product_prod_b_b] :
      ( ( collec1481886546od_b_b @ ( (=) @ product_prod_b_b @ A ) )
      = ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_singleton__conv2) ).

thf(406,plain,
    ! [A: product_prod_b_b] :
      ( ( collec1481886546od_b_b @ ( (=) @ product_prod_b_b @ A ) )
      = ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(63,axiom,
    ! [A: labele1159362096nt_a_b] :
      ( ( restri446606278nt_a_b @ ( restri446606278nt_a_b @ A ) )
      = ( restri446606278nt_a_b @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_restrict__idemp) ).

thf(509,plain,
    ! [A: labele1159362096nt_a_b] :
      ( ( restri446606278nt_a_b @ ( restri446606278nt_a_b @ A ) )
      = ( restri446606278nt_a_b @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(182,axiom,
    ! [A: set_Pr357419743_b_b_b] :
      ( ( image_921732011_b_b_b @ A @ bot_bo1343651123od_b_b )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Image__empty2) ).

thf(880,plain,
    ! [A: set_Pr357419743_b_b_b] :
      ( ( image_921732011_b_b_b @ A @ bot_bo1343651123od_b_b )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(108,axiom,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_converseD) ).

thf(649,plain,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(54,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
      ( ~ ( member1516365892od_b_b @ A @ B )
     => ( ( ord_le123089219od_b_b @ B @ ( insert2037698781od_b_b @ A @ C ) )
        = ( ord_le123089219od_b_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_subset__insert) ).

thf(477,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
      ( ~ ( member1516365892od_b_b @ A @ B )
     => ( ( ord_le123089219od_b_b @ B @ ( insert2037698781od_b_b @ A @ C ) )
        = ( ord_le123089219od_b_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(247,axiom,
    order_653178932r_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_lnear__order__on__empty) ).

thf(1080,plain,
    order_653178932r_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(142,axiom,
    ! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: standard_Constant_a] :
      ( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
      = ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Image__singleton__iff) ).

thf(758,plain,
    ! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: standard_Constant_a] :
      ( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
      = ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(6,axiom,
    ! [A: product_prod_b_b > $o] :
      ( ( ( collec1481886546od_b_b @ A )
        = bot_bo1343651123od_b_b )
      = ( ! [B: product_prod_b_b] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Collect__empty__eq) ).

thf(323,plain,
    ! [A: product_prod_b_b > $o] :
      ( ( ( collec1481886546od_b_b @ A )
        = bot_bo1343651123od_b_b )
      = ( ! [B: product_prod_b_b] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(171,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A: set_b,B: set_b] :
        ! [C: b] :
          ( ( member_b @ C @ A )
         => ( member_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_subset__eq) ).

thf(848,plain,
    ( ord_less_eq_set_b
    = ( ^ [A: set_b,B: set_b] :
        ! [C: b] :
          ( ( member_b @ C @ A )
         => ( member_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(231,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_157_singletonD) ).

thf(1029,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)],[231]) ).

thf(212,axiom,
    ( total_on_b
    = ( ^ [A: set_b,B: set_Product_prod_b_b] :
        ! [C: b] :
          ( ( member_b @ C @ A )
         => ! [D: b] :
              ( ( member_b @ D @ A )
             => ( ( C != D )
               => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
                  | ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_total__on__def) ).

thf(964,plain,
    ( total_on_b
    = ( ^ [A: set_b,B: set_Product_prod_b_b] :
        ! [C: b] :
          ( ( member_b @ C @ A )
         => ! [D: b] :
              ( ( member_b @ D @ A )
             => ( ( C != D )
               => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
                  | ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(193,axiom,
    ( g
    = ( restri446606278nt_a_b @ g ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).

thf(915,plain,
    ( g
    = ( restri446606278nt_a_b @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(229,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
        = ( ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
            = ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
          & ( member_b @ C @ A )
          & ( member_b @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_equiv__class__eq__iff) ).

thf(1022,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( equiv_equiv_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
        = ( ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
            = ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
          & ( member_b @ C @ A )
          & ( member_b @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(199,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_33_insert__iff) ).

thf(932,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)],[199]) ).

thf(14,axiom,
    ! [A: set_Pr2007082183od_b_b] :
      ( ( image_1928024979od_b_b @ A @ bot_bo1343651123od_b_b )
      = bot_bo1343651123od_b_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Image__empty2) ).

thf(345,plain,
    ! [A: set_Pr2007082183od_b_b] :
      ( ( image_1928024979od_b_b @ A @ bot_bo1343651123od_b_b )
      = bot_bo1343651123od_b_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(175,axiom,
    ! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: b] :
      ( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
      = ( member641857272od_b_b @ ( produc1257047359od_b_b @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Image__singleton__iff) ).

thf(858,plain,
    ! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: b] :
      ( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
      = ( member641857272od_b_b @ ( produc1257047359od_b_b @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(156,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr2109276827od_b_b,C: produc1213276845od_b_b] :
      ( ( equiv_2048442231od_b_b @ A @ B )
     => ( ( member1516365892od_b_b @ C @ A )
       => ( member1516365892od_b_b @ C @ ( image_763305007od_b_b @ B @ ( insert2037698781od_b_b @ C @ bot_bo1664927607od_b_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_equiv__class__self) ).

thf(799,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr2109276827od_b_b,C: produc1213276845od_b_b] :
      ( ( equiv_2048442231od_b_b @ A @ B )
     => ( ( member1516365892od_b_b @ C @ A )
       => ( member1516365892od_b_b @ C @ ( image_763305007od_b_b @ B @ ( insert2037698781od_b_b @ C @ bot_bo1664927607od_b_b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(275,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( refl_on_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( member_b @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_refl__onD1) ).

thf(1162,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( refl_on_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( member_b @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(68,axiom,
    ! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b] :
      ( ( A = bot_bo1664927607od_b_b )
     => ~ ( member1516365892od_b_b @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_equals0D) ).

thf(521,plain,
    ! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b] :
      ( ( A = bot_bo1664927607od_b_b )
     => ~ ( member1516365892od_b_b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(210,axiom,
    ! [A: set_b,B: b > $o] :
      ( ord_less_eq_set_b
      @ ( collect_b
        @ ^ [C: b] :
            ( ( member_b @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_Collect__subset) ).

thf(959,plain,
    ! [A: set_b,B: b > $o] :
      ( ord_less_eq_set_b
      @ ( collect_b
        @ ^ [C: b] :
            ( ( member_b @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(164,axiom,
    ! [A: product_prod_b_b] :
      ( ( collec1481886546od_b_b
        @ ^ [B: product_prod_b_b] : ( B = A ) )
      = ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_singleton__conv) ).

thf(827,plain,
    ! [A: product_prod_b_b] :
      ( ( collec1481886546od_b_b
        @ ^ [B: product_prod_b_b] : ( B = A ) )
      = ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(149,axiom,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( ! [B: produc1213276845od_b_b] :
            ~ ( member1516365892od_b_b @ B @ A ) )
      = ( A = bot_bo1664927607od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_all__not__in__conv) ).

thf(780,plain,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( ! [B: produc1213276845od_b_b] :
            ~ ( member1516365892od_b_b @ B @ A ) )
      = ( A = bot_bo1664927607od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(183,axiom,
    ! [A: standard_Constant_a,B: b,C: b] :
      ( ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
      = ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_graph__single) ).

thf(883,plain,
    ! [A: standard_Constant_a,B: b,C: b] :
      ( ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
      = ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(82,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
      ( ( ~ ( member1516365892od_b_b @ A @ B )
       => ( A = C ) )
     => ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_insertCI) ).

thf(563,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
      ( ( ~ ( member1516365892od_b_b @ A @ B )
       => ( A = C ) )
     => ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(62,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ! [B: product_prod_b_b] :
          ~ ( member1285940496od_b_b @ B @ A )
     => ( A = bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_equals0I) ).

thf(505,plain,
    ! [A: set_Product_prod_b_b] :
      ( ! [B: product_prod_b_b] :
          ~ ( member1285940496od_b_b @ B @ A )
     => ( A = bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(234,axiom,
    ! [A: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A @ B )
     => ( ord_less_eq_set_b @ ( insert_b @ C @ A ) @ ( insert_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_insert__mono) ).

thf(1044,plain,
    ! [A: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A @ B )
     => ( ord_less_eq_set_b @ ( insert_b @ C @ A ) @ ( insert_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(123,axiom,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( A != bot_bo1664927607od_b_b )
     => ( ! [B: produc1213276845od_b_b,C: produc1213276845od_b_b] :
            ( ( member1516365892od_b_b @ B @ A )
           => ( ( member1516365892od_b_b @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1465183929od_b_b @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_is__singletonI_H) ).

thf(695,plain,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( A != bot_bo1664927607od_b_b )
     => ( ! [B: produc1213276845od_b_b,C: produc1213276845od_b_b] :
            ( ( member1516365892od_b_b @ B @ A )
           => ( ( member1516365892od_b_b @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1465183929od_b_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(278,axiom,
    ! [A: b,B: product_prod_b_b,C: set_Pr621705391od_b_b,D: set_b] :
      ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ B ) @ C )
     => ( ( member_b @ A @ D )
       => ( member1285940496od_b_b @ B @ ( image_1177096571od_b_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_ImageI) ).

thf(1176,plain,
    ! [A: b,B: product_prod_b_b,C: set_Pr621705391od_b_b,D: set_b] :
      ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ B ) @ C )
     => ( ( member_b @ A @ D )
       => ( member1285940496od_b_b @ B @ ( image_1177096571od_b_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(96,axiom,
    ( labele1741081071nt_a_b
    = ( labele377702064od_b_b
      @ ^ [A: set_Pr1324126435od_b_b,B: set_b] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_edges__def) ).

thf(608,plain,
    ( labele1741081071nt_a_b
    = ( labele377702064od_b_b
      @ ^ [A: set_Pr1324126435od_b_b,B: set_b] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(39,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
     => ( A = bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_bot_Oextremum__uniqueI) ).

thf(426,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
     => ( A = bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(289,axiom,
    ! [A: b,B: set_b,C: product_prod_b_b,D: set_Pr621705391od_b_b] :
      ( ( member_b @ A @ B )
     => ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ C ) @ D )
       => ( member1285940496od_b_b @ C @ ( image_1177096571od_b_b @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rev__ImageI) ).

thf(1208,plain,
    ! [A: b,B: set_b,C: product_prod_b_b,D: set_Pr621705391od_b_b] :
      ( ( member_b @ A @ B )
     => ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ C ) @ D )
       => ( member1285940496od_b_b @ C @ ( image_1177096571od_b_b @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(71,axiom,
    ! [A: labele1159362096nt_a_b] :
      ( ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_labeled__graph_Ocollapse) ).

thf(531,plain,
    ! [A: labele1159362096nt_a_b] :
      ( ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(77,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( ( converse_b_b @ A )
        = ( converse_b_b @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_converse__inject) ).

thf(548,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( ( converse_b_b @ A )
        = ( converse_b_b @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(311,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b,D: set_b] :
      ( ( ord_le1036320359od_b_b @ A @ B )
     => ( ( ord_less_eq_set_b @ C @ D )
       => ( ord_less_eq_set_b @ ( image_b_b @ A @ C ) @ ( image_b_b @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_Image__mono) ).

thf(1277,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b,D: set_b] :
      ( ( ord_le1036320359od_b_b @ A @ B )
     => ( ( ord_less_eq_set_b @ C @ D )
       => ( ord_less_eq_set_b @ ( image_b_b @ A @ C ) @ ( image_b_b @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(159,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ ( converse_b_b @ A ) @ ( converse_b_b @ B ) )
      = ( ord_le1036320359od_b_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_converse__mono) ).

thf(812,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ ( converse_b_b @ A ) @ ( converse_b_b @ B ) )
      = ( ord_le1036320359od_b_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(248,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_36_insertCI) ).

thf(1081,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)],[248]) ).

thf(66,axiom,
    ! [A: product_prod_b_b] :
      ~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_empty__iff) ).

thf(516,plain,
    ! [A: product_prod_b_b] :
      ~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(269,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( image_b_b @ A @ bot_bot_set_b )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Image__empty2) ).

thf(1145,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( image_b_b @ A @ bot_bot_set_b )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(58,axiom,
    ! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
      ( ( ( produc1432590431od_b_b @ A @ B )
        = ( produc1432590431od_b_b @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_Pair__inject) ).

thf(490,plain,
    ! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
      ( ( ( produc1432590431od_b_b @ A @ B )
        = ( produc1432590431od_b_b @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(116,axiom,
    ! [A: set_b,B: set_Product_prod_b_b] :
      ( ( order_653178932r_on_b @ A @ ( converse_b_b @ B ) )
      = ( order_653178932r_on_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_linear__order__on__converse) ).

thf(675,plain,
    ! [A: set_b,B: set_Product_prod_b_b] :
      ( ( order_653178932r_on_b @ A @ ( converse_b_b @ B ) )
      = ( order_653178932r_on_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(265,axiom,
    ! [A: b] :
      ( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062) ).

thf(1134,plain,
    ! [A: b] :
      ( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(57,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
      = ( A = bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_subset__empty) ).

thf(487,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
      = ( A = bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(174,axiom,
    ! [A: b,B: produc1213276845od_b_b,C: set_Pr2060523537od_b_b,D: set_b] :
      ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ B ) @ C )
     => ( ( member_b @ A @ D )
       => ( member1516365892od_b_b @ B @ ( image_984343321od_b_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_ImageI) ).

thf(855,plain,
    ! [A: b,B: produc1213276845od_b_b,C: set_Pr2060523537od_b_b,D: set_b] :
      ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ B ) @ C )
     => ( ( member_b @ A @ D )
       => ( member1516365892od_b_b @ B @ ( image_984343321od_b_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(273,axiom,
    ! [A: b,B: b,C: standard_Constant_a] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
     => ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
        @ ^ [D: b] : ( image_b_b @ ( converse_b_b @ ( getRel904497637nt_a_b @ C @ g ) ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_congr_I2_J) ).

thf(1156,plain,
    ! [A: b,B: b,C: standard_Constant_a] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
     => ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
        @ ^ [D: b] : ( image_b_b @ ( converse_b_b @ ( getRel904497637nt_a_b @ C @ g ) ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(34,axiom,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b > $o] :
      ( ( member1516365892od_b_b @ A @ ( collec279084418od_b_b @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_mem__Collect__eq) ).

thf(409,plain,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b > $o] :
      ( ( member1516365892od_b_b @ A @ ( collec279084418od_b_b @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(253,axiom,
    ! [A: b > $o,B: b] :
      ( ( ( A @ B )
       => ( ( collect_b
            @ ^ [C: b] :
                ( ( C = B )
                & ( A @ C ) ) )
          = ( insert_b @ B @ bot_bot_set_b ) ) )
      & ( ~ ( A @ B )
       => ( ( collect_b
            @ ^ [C: b] :
                ( ( C = B )
                & ( A @ C ) ) )
          = bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Collect__conv__if) ).

thf(1098,plain,
    ! [A: b > $o,B: b] :
      ( ( ( A @ B )
       => ( ( collect_b
            @ ^ [C: b] :
                ( ( C = B )
                & ( A @ C ) ) )
          = ( insert_b @ B @ bot_bot_set_b ) ) )
      & ( ~ ( A @ B )
       => ( ( collect_b
            @ ^ [C: b] :
                ( ( C = B )
                & ( A @ C ) ) )
          = bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(221,axiom,
    ! [A: b > $o,B: b] :
      ( ( A @ B )
     => ( A @ ( hilbert_Eps_b @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_someI) ).

thf(993,plain,
    ! [A: b > $o,B: b] :
      ( ( A @ B )
     => ( A @ ( hilbert_Eps_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(127,axiom,
    ! [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ bot_bo1664927607od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_singletonI) ).

thf(712,plain,
    ! [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ bot_bo1664927607od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(80,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b] :
      ( ( ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b )
        = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_singleton__inject) ).

thf(557,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b] :
      ( ( ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b )
        = ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(224,axiom,
    ! [A: b,B: set_b] :
      ( ( insert_b @ A @ B )
     != bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_insert__not__empty) ).

thf(1003,plain,
    ! [A: b,B: set_b] :
      ( ( insert_b @ A @ B )
     != bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(244,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_147_singleton__inject) ).

thf(1070,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)],[244]) ).

thf(179,axiom,
    member1285940496od_b_b @ ( product_Pair_b_b @ x @ y ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062_Ix_M_Ay_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062) ).

thf(872,plain,
    member1285940496od_b_b @ ( product_Pair_b_b @ x @ y ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(237,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A: set_b,B: set_b] :
        ! [C: b] :
          ( ( member_b @ C @ A )
         => ( member_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_subset__iff) ).

thf(1053,plain,
    ( ord_less_eq_set_b
    = ( ^ [A: set_b,B: set_b] :
        ! [C: b] :
          ( ( member_b @ C @ A )
         => ( member_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(129,axiom,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( ? [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
      = ( A != bot_bo1664927607od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_ex__in__conv) ).

thf(717,plain,
    ! [A: set_Pr1324126435od_b_b] :
      ( ( ? [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
      = ( A != bot_bo1664927607od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(61,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
      ( ( ( ^ [C: standard_Constant_a,D: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A ) )
        = ( ^ [C: standard_Constant_a,D: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_pred__equals__eq2) ).

thf(502,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
      ( ( ( ^ [C: standard_Constant_a,D: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A ) )
        = ( ^ [C: standard_Constant_a,D: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(190,axiom,
    ! [A: b,B: b,C: set_b] :
      ( ( ( insert_b @ A @ bot_bot_set_b )
        = ( insert_b @ B @ C ) )
      = ( ( B = A )
        & ( ord_less_eq_set_b @ C @ ( insert_b @ A @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_singleton__insert__inj__eq) ).

thf(907,plain,
    ! [A: b,B: b,C: set_b] :
      ( ( ( insert_b @ A @ bot_bot_set_b )
        = ( insert_b @ B @ C ) )
      = ( ( B = A )
        & ( ord_less_eq_set_b @ C @ ( insert_b @ A @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(9,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1071216121od_b_b,C: set_Product_prod_b_b] :
      ( ( member1516365892od_b_b @ A @ ( image_532916993od_b_b @ B @ C ) )
     => ~ ! [D: product_prod_b_b] :
            ( ( member4694106od_b_b @ ( produc732676669od_b_b @ D @ A ) @ B )
           => ~ ( member1285940496od_b_b @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ImageE) ).

thf(331,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1071216121od_b_b,C: set_Product_prod_b_b] :
      ( ( member1516365892od_b_b @ A @ ( image_532916993od_b_b @ B @ C ) )
     => ~ ! [D: product_prod_b_b] :
            ( ( member4694106od_b_b @ ( produc732676669od_b_b @ D @ A ) @ B )
           => ~ ( member1285940496od_b_b @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(282,axiom,
    ! [A: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( member_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_subsetD) ).

thf(1188,plain,
    ! [A: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( member_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(52,axiom,
    ! [A: set_Product_prod_b_b,B: b > set_b,C: b,D: b] :
      ( ( equiv_1821124534_set_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
       => ( ( B @ C )
          = ( B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_congruentD) ).

thf(470,plain,
    ! [A: set_Product_prod_b_b,B: b > set_b,C: b,D: b] :
      ( ( equiv_1821124534_set_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
       => ( ( B @ C )
          = ( B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(86,axiom,
    ! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
      ( ( ( produc1432590431od_b_b @ A @ B )
        = ( produc1432590431od_b_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_old_Oprod_Oinject) ).

thf(576,plain,
    ! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
      ( ( ( produc1432590431od_b_b @ A @ B )
        = ( produc1432590431od_b_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(124,axiom,
    ! [A: produc1213276845od_b_b] :
    ? [B: standard_Constant_a,C: product_prod_b_b] :
      ( A
      = ( produc1432590431od_b_b @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_surj__pair) ).

thf(703,plain,
    ! [A: produc1213276845od_b_b] :
    ? [B: standard_Constant_a,C: product_prod_b_b] :
      ( A
      = ( produc1432590431od_b_b @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(98,axiom,
    ! [A: standard_Constant_a,B: set_St761939237tant_a,C: product_prod_b_b,D: set_Pr1324126435od_b_b] :
      ( ( member1632892294tant_a @ A @ B )
     => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ C ) @ D )
       => ( member1285940496od_b_b @ C @ ( image_1916422435od_b_b @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rev__ImageI) ).

thf(613,plain,
    ! [A: standard_Constant_a,B: set_St761939237tant_a,C: product_prod_b_b,D: set_Pr1324126435od_b_b] :
      ( ( member1632892294tant_a @ A @ B )
     => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ C ) @ D )
       => ( member1285940496od_b_b @ C @ ( image_1916422435od_b_b @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(293,axiom,
    ! [A: b > $o,B: b] :
      ( ( ( A @ B )
       => ( ( collect_b
            @ ^ [C: b] :
                ( ( B = C )
                & ( A @ C ) ) )
          = ( insert_b @ B @ bot_bot_set_b ) ) )
      & ( ~ ( A @ B )
       => ( ( collect_b
            @ ^ [C: b] :
                ( ( B = C )
                & ( A @ C ) ) )
          = bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Collect__conv__if2) ).

thf(1221,plain,
    ! [A: b > $o,B: b] :
      ( ( ( A @ B )
       => ( ( collect_b
            @ ^ [C: b] :
                ( ( B = C )
                & ( A @ C ) ) )
          = ( insert_b @ B @ bot_bot_set_b ) ) )
      & ( ~ ( A @ B )
       => ( ( collect_b
            @ ^ [C: b] :
                ( ( B = C )
                & ( A @ C ) ) )
          = bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(132,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( ~ ( member1285940496od_b_b @ A @ B )
       => ( A = C ) )
     => ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_insertCI) ).

thf(727,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
      ( ( ~ ( member1285940496od_b_b @ A @ B )
       => ( A = C ) )
     => ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(27,axiom,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ! [C: product_prod_b_b] :
          ( ( member1285940496od_b_b @ C @ A )
         => ( member1285940496od_b_b @ C @ B ) )
     => ( ord_le1036320359od_b_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_subsetI) ).

thf(386,plain,
    ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
      ( ! [C: product_prod_b_b] :
          ( ( member1285940496od_b_b @ C @ A )
         => ( member1285940496od_b_b @ C @ B ) )
     => ( ord_le1036320359od_b_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(1,conjecture,
    ( ( hilbert_Eps_b
      @ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) )
    = ( hilbert_Eps_b
      @ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( hilbert_Eps_b
      @ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) )
   != ( hilbert_Eps_b
      @ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(314,plain,
    ( ( hilbert_Eps_b
      @ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) )
   != ( hilbert_Eps_b
      @ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(84,axiom,
    ( bot_bo1734638456_b_b_o
    = ( ^ [A: standard_Constant_a,B: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ bot_bo1664927607od_b_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_bot__empty__eq2) ).

thf(571,plain,
    ( bot_bo1734638456_b_b_o
    = ( ^ [A: standard_Constant_a,B: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ bot_bo1664927607od_b_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(59,axiom,
    ! [A: set_Pr2007082183od_b_b] : ( total_178717291od_b_b @ bot_bo1343651123od_b_b @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_total__on__empty) ).

thf(497,plain,
    ! [A: set_Pr2007082183od_b_b] : ( total_178717291od_b_b @ bot_bo1343651123od_b_b @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(298,axiom,
    ! [A: b] :
      ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
       != bot_bot_set_b )
     => ( ( hilbert_Eps_b @ ( p @ ( hilbert_Eps_b @ ( p @ A ) ) ) )
        = ( hilbert_Eps_b @ ( p @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_P__eq) ).

thf(1240,plain,
    ! [A: b] :
      ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
       != bot_bot_set_b )
     => ( ( hilbert_Eps_b @ ( p @ ( hilbert_Eps_b @ ( p @ A ) ) ) )
        = ( hilbert_Eps_b @ ( p @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(102,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_singleton__iff) ).

thf(627,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(45,axiom,
    ! [A: set_Product_prod_b_b,B: product_prod_b_b > $o] :
      ( ord_le1036320359od_b_b
      @ ( collec1481886546od_b_b
        @ ^ [C: product_prod_b_b] :
            ( ( member1285940496od_b_b @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_Collect__subset) ).

thf(450,plain,
    ! [A: set_Product_prod_b_b,B: product_prod_b_b > $o] :
      ( ord_le1036320359od_b_b
      @ ( collec1481886546od_b_b
        @ ^ [C: product_prod_b_b] :
            ( ( member1285940496od_b_b @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(20,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( ! [B: product_prod_b_b] :
            ~ ( member1285940496od_b_b @ B @ A ) )
      = ( A = bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_all__not__in__conv) ).

thf(363,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( ! [B: product_prod_b_b] :
            ~ ( member1285940496od_b_b @ B @ A ) )
      = ( A = bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(74,axiom,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
      ( ! [C: standard_Constant_a,D: product_prod_b_b] :
          ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A )
         => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) )
     => ( ord_le123089219od_b_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_subrelI) ).

thf(539,plain,
    ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
      ( ! [C: standard_Constant_a,D: product_prod_b_b] :
          ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A )
         => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) )
     => ( ord_le123089219od_b_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(186,axiom,
    ! [A: b,B: set_Product_prod_b_b,C: set_b] :
      ( ( member_b @ A @ ( image_b_b @ B @ C ) )
      = ( ? [D: b] :
            ( ( member_b @ D @ C )
            & ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Image__iff) ).

thf(891,plain,
    ! [A: b,B: set_Product_prod_b_b,C: set_b] :
      ( ( member_b @ A @ ( image_b_b @ B @ C ) )
      = ( ? [D: b] :
            ( ( member_b @ D @ C )
            & ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(262,axiom,
    ! [A: set_b] :
      ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
     => ( A = bot_bot_set_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_bot_Oextremum__uniqueI) ).

thf(1126,plain,
    ! [A: set_b] :
      ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
     => ( A = bot_bot_set_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(226,axiom,
    ! [A: b] : ( refl_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_refl__on__singleton) ).

thf(1010,plain,
    ! [A: b] : ( refl_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(170,axiom,
    ! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
      ( ( A
        = ( restri446606278nt_a_b @ A ) )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
       => ( member_b @ B @ ( labele1424214014nt_a_b @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_getRel__dom_I1_J) ).

thf(844,plain,
    ! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
      ( ( A
        = ( restri446606278nt_a_b @ A ) )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
       => ( member_b @ B @ ( labele1424214014nt_a_b @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(255,axiom,
    ( bot_bot_b_o
    = ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_bot__empty__eq) ).

thf(1108,plain,
    ( bot_bot_b_o
    = ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(91,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( A != bot_bo1343651123od_b_b )
     => ( ! [B: product_prod_b_b,C: product_prod_b_b] :
            ( ( member1285940496od_b_b @ B @ A )
           => ( ( member1285940496od_b_b @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1713057243od_b_b @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_is__singletonI_H) ).

thf(588,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( A != bot_bo1343651123od_b_b )
     => ( ! [B: product_prod_b_b,C: product_prod_b_b] :
            ( ( member1285940496od_b_b @ B @ A )
           => ( ( member1285940496od_b_b @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1713057243od_b_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(211,axiom,
    ! [A: b,B: set_Pr357419743_b_b_b,C: set_Product_prod_b_b] :
      ( ( member_b @ A @ ( image_921732011_b_b_b @ B @ C ) )
     => ~ ! [D: product_prod_b_b] :
            ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ D @ A ) @ B )
           => ~ ( member1285940496od_b_b @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_ImageE) ).

thf(961,plain,
    ! [A: b,B: set_Pr357419743_b_b_b,C: set_Product_prod_b_b] :
      ( ( member_b @ A @ ( image_921732011_b_b_b @ B @ C ) )
     => ~ ! [D: product_prod_b_b] :
            ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ D @ A ) @ B )
           => ~ ( member1285940496od_b_b @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(4,axiom,
    ! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b > $o] :
      ( ord_le123089219od_b_b
      @ ( collec279084418od_b_b
        @ ^ [C: produc1213276845od_b_b] :
            ( ( member1516365892od_b_b @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_Collect__subset) ).

thf(319,plain,
    ! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b > $o] :
      ( ord_le123089219od_b_b
      @ ( collec279084418od_b_b
        @ ^ [C: produc1213276845od_b_b] :
            ( ( member1516365892od_b_b @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(138,axiom,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ ( converse_b_b @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_converse_Ointros) ).

thf(748,plain,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ ( converse_b_b @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(241,axiom,
    ( p
    = ( ^ [A: b,B: b] : ( member_b @ B @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_P) ).

thf(1062,plain,
    ( p
    = ( ^ [A: b,B: b] : ( member_b @ B @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(204,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_151_doubleton__eq__iff) ).

thf(946,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)],[204]) ).

thf(16,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: produc1213276845od_b_b,D: set_Pr1071216121od_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A @ C ) @ D )
       => ( member1516365892od_b_b @ C @ ( image_532916993od_b_b @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rev__ImageI) ).

thf(351,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: produc1213276845od_b_b,D: set_Pr1071216121od_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A @ C ) @ D )
       => ( member1516365892od_b_b @ C @ ( image_532916993od_b_b @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(151,axiom,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
      = ( ( A = B )
        | ( member1516365892od_b_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_insert__iff) ).

thf(786,plain,
    ! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
      ( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
      = ( ( A = B )
        | ( member1516365892od_b_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(83,axiom,
    ! [A: produc1213276845od_b_b] :
      ~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_empty__iff) ).

thf(568,plain,
    ! [A: produc1213276845od_b_b] :
      ~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(198,axiom,
    ! [A: b > $o,B: b] :
      ( ( A @ B )
     => ( A @ ( hilbert_Eps_b @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_tfl__some) ).

thf(929,plain,
    ! [A: b > $o,B: b] :
      ( ( A @ B )
     => ( A @ ( hilbert_Eps_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(246,axiom,
    ! [A: set_b] :
      ( ( image_b_b @ bot_bo1343651123od_b_b @ A )
      = bot_bot_set_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Image__empty1) ).

thf(1077,plain,
    ! [A: set_b] :
      ( ( image_b_b @ bot_bo1343651123od_b_b @ A )
      = bot_bot_set_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(144,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ( ( insert1952693431od_b_b @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_insert__absorb) ).

thf(763,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ( ( insert1952693431od_b_b @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(26,axiom,
    ! [A: set_b,B: set_Product_prod_b_b] :
      ( ( total_on_b @ A @ ( converse_b_b @ B ) )
      = ( total_on_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_total__on__converse) ).

thf(383,plain,
    ! [A: set_b,B: set_Product_prod_b_b] :
      ( ( total_on_b @ A @ ( converse_b_b @ B ) )
      = ( total_on_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(100,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b,D: set_Pr1324126435od_b_b] :
      ( ~ ( member1516365892od_b_b @ A @ B )
     => ( ~ ( member1516365892od_b_b @ C @ D )
       => ( ( ( insert2037698781od_b_b @ A @ B )
            = ( insert2037698781od_b_b @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Pr1324126435od_b_b] :
                  ( ( B
                    = ( insert2037698781od_b_b @ C @ E ) )
                  & ~ ( member1516365892od_b_b @ C @ E )
                  & ( D
                    = ( insert2037698781od_b_b @ A @ E ) )
                  & ~ ( member1516365892od_b_b @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_insert__eq__iff) ).

thf(620,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b,D: set_Pr1324126435od_b_b] :
      ( ~ ( member1516365892od_b_b @ A @ B )
     => ( ~ ( member1516365892od_b_b @ C @ D )
       => ( ( ( insert2037698781od_b_b @ A @ B )
            = ( insert2037698781od_b_b @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Pr1324126435od_b_b] :
                  ( ( B
                    = ( insert2037698781od_b_b @ C @ E ) )
                  & ~ ( member1516365892od_b_b @ C @ E )
                  & ( D
                    = ( insert2037698781od_b_b @ A @ E ) )
                  & ~ ( member1516365892od_b_b @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(44,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ ( insert1952693431od_b_b @ A @ B ) @ C )
      = ( ( member1285940496od_b_b @ A @ C )
        & ( ord_le1036320359od_b_b @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_insert__subset) ).

thf(447,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ ( insert1952693431od_b_b @ A @ B ) @ C )
      = ( ( member1285940496od_b_b @ A @ C )
        & ( ord_le1036320359od_b_b @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(312,axiom,
    member1516365892od_b_b @ ( produc1432590431od_b_b @ standard_S_Idt_a @ ( product_Pair_b_b @ x @ y ) ) @ ( labele1741081071nt_a_b @ g ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168__092_060open_062_IS__Idt_M_Ax_M_Ay_J_A_092_060in_062_Aedges_AG_092_060close_062) ).

thf(1280,plain,
    member1516365892od_b_b @ ( produc1432590431od_b_b @ standard_S_Idt_a @ ( product_Pair_b_b @ x @ y ) ) @ ( labele1741081071nt_a_b @ g ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(166,axiom,
    ( ord_le1036320359od_b_b
    = ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
        ! [C: product_prod_b_b] :
          ( ( member1285940496od_b_b @ C @ A )
         => ( member1285940496od_b_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_subset__iff) ).

thf(833,plain,
    ( ord_le1036320359od_b_b
    = ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
        ! [C: product_prod_b_b] :
          ( ( member1285940496od_b_b @ C @ A )
         => ( member1285940496od_b_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(270,axiom,
    ! [A: b,B: b > $o] :
      ( ( insert_b @ A @ ( collect_b @ B ) )
      = ( collect_b
        @ ^ [C: b] :
            ( ( C != A )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_insert__Collect) ).

thf(1148,plain,
    ! [A: b,B: b > $o] :
      ( ( insert_b @ A @ ( collect_b @ B ) )
      = ( collect_b
        @ ^ [C: b] :
            ( ( C != A )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(134,axiom,
    ! [A: standard_Constant_a,B: product_prod_b_b,C: set_Pr1324126435od_b_b,D: set_St761939237tant_a] :
      ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ C )
     => ( ( member1632892294tant_a @ A @ D )
       => ( member1285940496od_b_b @ B @ ( image_1916422435od_b_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_ImageI) ).

thf(735,plain,
    ! [A: standard_Constant_a,B: product_prod_b_b,C: set_Pr1324126435od_b_b,D: set_St761939237tant_a] :
      ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ C )
     => ( ( member1632892294tant_a @ A @ D )
       => ( member1285940496od_b_b @ B @ ( image_1916422435od_b_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(206,axiom,
    ! [A: produc1213276845od_b_b,B: b,C: set_Pr1906739389_b_b_b,D: set_Pr1324126435od_b_b] :
      ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ B ) @ C )
     => ( ( member1516365892od_b_b @ A @ D )
       => ( member_b @ B @ ( image_1764625405_b_b_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_ImageI) ).

thf(950,plain,
    ! [A: produc1213276845od_b_b,B: b,C: set_Pr1906739389_b_b_b,D: set_Pr1324126435od_b_b] :
      ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ B ) @ C )
     => ( ( member1516365892od_b_b @ A @ D )
       => ( member_b @ B @ ( image_1764625405_b_b_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(167,axiom,
    ! [A: set_Product_prod_b_b] : ( ord_le1036320359od_b_b @ bot_bo1343651123od_b_b @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_empty__subsetI) ).

thf(835,plain,
    ! [A: set_Product_prod_b_b] : ( ord_le1036320359od_b_b @ bot_bo1343651123od_b_b @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(7,axiom,
    ( ord_le123089219od_b_b
    = ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
        ! [C: produc1213276845od_b_b] :
          ( ( member1516365892od_b_b @ C @ A )
         => ( member1516365892od_b_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_subset__eq) ).

thf(326,plain,
    ( ord_le123089219od_b_b
    = ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
        ! [C: produc1213276845od_b_b] :
          ( ( member1516365892od_b_b @ C @ A )
         => ( member1516365892od_b_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(53,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1071216121od_b_b,C: product_prod_b_b] :
      ( ( member1516365892od_b_b @ A @ ( image_532916993od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) )
      = ( member4694106od_b_b @ ( produc732676669od_b_b @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Image__singleton__iff) ).

thf(474,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1071216121od_b_b,C: product_prod_b_b] :
      ( ( member1516365892od_b_b @ A @ ( image_532916993od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) )
      = ( member4694106od_b_b @ ( produc732676669od_b_b @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(105,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
      = ( A = bot_bo1343651123od_b_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_bot_Oextremum__unique) ).

thf(635,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
      = ( A = bot_bo1343651123od_b_b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(208,axiom,
    ! [A: b > $o] :
      ( ? [B: b] : ( A @ B )
     => ( A @ ( hilbert_Eps_b @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_someI__ex) ).

thf(955,plain,
    ! [A: b > $o] :
      ( ? [B: b] : ( A @ B )
     => ( A @ ( hilbert_Eps_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(155,axiom,
    ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
      ( ( ( ( labele1741081071nt_a_b @ A )
          = ( labele1741081071nt_a_b @ B ) )
        & ( ( labele1424214014nt_a_b @ A )
          = ( labele1424214014nt_a_b @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_labeled__graph_Oexpand) ).

thf(796,plain,
    ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
      ( ( ( ( labele1741081071nt_a_b @ A )
          = ( labele1741081071nt_a_b @ B ) )
        & ( ( labele1424214014nt_a_b @ A )
          = ( labele1424214014nt_a_b @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(31,axiom,
    ! [A: product_prod_b_b] :
      ( ( the_el329196508od_b_b @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_the__elem__eq) ).

thf(400,plain,
    ! [A: product_prod_b_b] :
      ( ( the_el329196508od_b_b @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(285,axiom,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( refl_on_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( member_b @ D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_refl__onD2) ).

thf(1197,plain,
    ! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
      ( ( refl_on_b @ A @ B )
     => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
       => ( member_b @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(130,axiom,
    ! [A: b > $o,B: b > $o] :
      ( ! [C: b] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect_b @ A )
        = ( collect_b @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Collect__cong) ).

thf(720,plain,
    ! [A: b > $o,B: b > $o] :
      ( ! [C: b] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect_b @ A )
        = ( collect_b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(276,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_246_is__singletonI_H) ).

thf(1165,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)],[276]) ).

thf(184,axiom,
    ! [A: set_b,B: b] :
      ( ( ord_less_eq_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
      = ( ( A = bot_bot_set_b )
        | ( A
          = ( insert_b @ B @ bot_bot_set_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_subset__singleton__iff) ).

thf(886,plain,
    ! [A: set_b,B: b] :
      ( ( ord_less_eq_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
      = ( ( A = bot_bot_set_b )
        | ( A
          = ( insert_b @ B @ bot_bot_set_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(36,axiom,
    ! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b > $o,C: produc1213276845od_b_b > $o] :
      ( ? [D: produc1213276845od_b_b] :
          ( ( member1516365892od_b_b @ D @ A )
          & ( B @ D ) )
     => ( ! [D: produc1213276845od_b_b] :
            ( ( ( member1516365892od_b_b @ D @ A )
              & ( B @ D ) )
           => ( C @ D ) )
       => ( C
          @ ( hilber46179633od_b_b
            @ ^ [D: produc1213276845od_b_b] :
                ( ( member1516365892od_b_b @ D @ A )
                & ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_someI2__bex) ).

thf(415,plain,
    ! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b > $o,C: produc1213276845od_b_b > $o] :
      ( ? [D: produc1213276845od_b_b] :
          ( ( member1516365892od_b_b @ D @ A )
          & ( B @ D ) )
     => ( ! [D: produc1213276845od_b_b] :
            ( ( ( member1516365892od_b_b @ D @ A )
              & ( B @ D ) )
           => ( C @ D ) )
       => ( C
          @ ( hilber46179633od_b_b
            @ ^ [D: produc1213276845od_b_b] :
                ( ( member1516365892od_b_b @ D @ A )
                & ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(101,axiom,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
      = ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_converse__iff) ).

thf(624,plain,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
      = ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(50,axiom,
    ! [A: set_Product_prod_b_b,B: set_Pr2007082183od_b_b,C: set_Product_prod_b_b,D: product_prod_b_b > b > set_b,E: product_prod_b_b] :
      ( ( equiv_1125628061od_b_b @ A @ B )
     => ( ( equiv_1036235914_set_b @ B @ C @ D )
       => ( ( member1285940496od_b_b @ E @ A )
         => ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_congruent2__implies__congruent) ).

thf(464,plain,
    ! [A: set_Product_prod_b_b,B: set_Pr2007082183od_b_b,C: set_Product_prod_b_b,D: product_prod_b_b > b > set_b,E: product_prod_b_b] :
      ( ( equiv_1125628061od_b_b @ A @ B )
     => ( ( equiv_1036235914_set_b @ B @ C @ D )
       => ( ( member1285940496od_b_b @ E @ A )
         => ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(263,axiom,
    ! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_bot_Oextremum) ).

thf(1129,plain,
    ! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(306,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_107_insert__ident) ).

thf(1261,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)],[306]) ).

thf(308,axiom,
    ! [A: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( member_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_in__mono) ).

thf(1268,plain,
    ! [A: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A @ B )
     => ( ( member_b @ C @ A )
       => ( member_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(92,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b,C: product_prod_b_b,D: product_prod_b_b] :
      ( ( ( insert1952693431od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
        = ( insert1952693431od_b_b @ C @ ( insert1952693431od_b_b @ D @ bot_bo1343651123od_b_b ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_doubleton__eq__iff) ).

thf(596,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b,C: product_prod_b_b,D: product_prod_b_b] :
      ( ( ( insert1952693431od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
        = ( insert1952693431od_b_b @ C @ ( insert1952693431od_b_b @ D @ bot_bo1343651123od_b_b ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(70,axiom,
    ! [A: set_Product_prod_b_b] :
      ( ( converse_b_b @ ( converse_b_b @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_converse__converse) ).

thf(528,plain,
    ! [A: set_Product_prod_b_b] :
      ( ( converse_b_b @ ( converse_b_b @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(48,axiom,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_converse_Ocases) ).

thf(459,plain,
    ! [A: b,B: b,C: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
     => ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(131,axiom,
    ! [A: produc1213276845od_b_b] :
      ~ ! [B: standard_Constant_a,C: product_prod_b_b] :
          ( A
         != ( produc1432590431od_b_b @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_old_Oprod_Oexhaust) ).

thf(723,plain,
    ! [A: produc1213276845od_b_b] :
      ~ ! [B: standard_Constant_a,C: product_prod_b_b] :
          ( A
         != ( produc1432590431od_b_b @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(162,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_insertI1) ).

thf(822,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(172,axiom,
    ( f
    = ( ^ [A: b] :
          ( if_b
          @ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
            = bot_bot_set_b )
          @ A
          @ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062) ).

thf(850,plain,
    ( f
    = ( ^ [A: b] :
          ( if_b
          @ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
            = bot_bot_set_b )
          @ A
          @ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(22,axiom,
    ! [A: b,B: b,C: b,D: b] :
      ( ( ( product_Pair_b_b @ A @ B )
        = ( product_Pair_b_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_prod_Oinject) ).

thf(369,plain,
    ! [A: b,B: b,C: b,D: b] :
      ( ( ( product_Pair_b_b @ A @ B )
        = ( product_Pair_b_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(11,axiom,
    ! [A: product_prod_b_b,B: product_prod_b_b > $o] :
      ( ( member1285940496od_b_b @ A @ ( collec1481886546od_b_b @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_mem__Collect__eq) ).

thf(337,plain,
    ! [A: product_prod_b_b,B: product_prod_b_b > $o] :
      ( ( member1285940496od_b_b @ A @ ( collec1481886546od_b_b @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(17,axiom,
    ! [A: product_prod_b_b,B: produc1213276845od_b_b,C: set_Pr1071216121od_b_b,D: set_Product_prod_b_b] :
      ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A @ B ) @ C )
     => ( ( member1285940496od_b_b @ A @ D )
       => ( member1516365892od_b_b @ B @ ( image_532916993od_b_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_ImageI) ).

thf(354,plain,
    ! [A: product_prod_b_b,B: produc1213276845od_b_b,C: set_Pr1071216121od_b_b,D: set_Product_prod_b_b] :
      ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A @ B ) @ C )
     => ( ( member1285940496od_b_b @ A @ D )
       => ( member1516365892od_b_b @ B @ ( image_532916993od_b_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(200,axiom,
    ! [A: b,B: set_Pr357419743_b_b_b,C: product_prod_b_b] :
      ( ( member_b @ A @ ( image_921732011_b_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) )
      = ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Image__singleton__iff) ).

thf(935,plain,
    ! [A: b,B: set_Pr357419743_b_b_b,C: product_prod_b_b] :
      ( ( member_b @ A @ ( image_921732011_b_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) )
      = ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(196,axiom,
    ! [A: b > $o] :
      ( ( A @ ( hilbert_Eps_b @ A ) )
      = ( ? [B: b] : ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_some__eq__ex) ).

thf(923,plain,
    ! [A: b > $o] :
      ( ( A @ ( hilbert_Eps_b @ A ) )
      = ( ? [B: b] : ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(111,axiom,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insertI2) ).

thf(659,plain,
    ! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
      ( ( member1516365892od_b_b @ A @ B )
     => ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(81,axiom,
    ! [A: b,B: b] :
      ( ( if_b @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001tf__b_T) ).

thf(560,plain,
    ! [A: b,B: b] :
      ( ( if_b @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(126,axiom,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ? [C: set_Product_prod_b_b] :
          ( ( B
            = ( insert1952693431od_b_b @ A @ C ) )
          & ~ ( member1285940496od_b_b @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_mk__disjoint__insert) ).

thf(708,plain,
    ! [A: product_prod_b_b,B: set_Product_prod_b_b] :
      ( ( member1285940496od_b_b @ A @ B )
     => ? [C: set_Product_prod_b_b] :
          ( ( B
            = ( insert1952693431od_b_b @ A @ C ) )
          & ~ ( member1285940496od_b_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(228,axiom,
    ! [A: set_b,B: set_Product_prod_b_b] :
      ( ! [C: b,D: b] :
          ( ( member_b @ C @ A )
         => ( ( member_b @ D @ A )
           => ( ( C != D )
             => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
                | ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ) )
     => ( total_on_b @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_total__onI) ).

thf(1014,plain,
    ! [A: set_b,B: set_Product_prod_b_b] :
      ( ! [C: b,D: b] :
          ( ( member_b @ C @ A )
         => ( ( member_b @ D @ A )
           => ( ( C != D )
             => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
                | ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ) )
     => ( total_on_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(215,axiom,
    ! [A: set_Product_prod_b_b] : ( total_on_b @ bot_bot_set_b @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_total__on__empty) ).

thf(972,plain,
    ! [A: set_Product_prod_b_b] : ( total_on_b @ bot_bot_set_b @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(1287,plain,
    $false,
    inference(e,[status(thm)],[645,1036,809,1105,1237,1179,777,1110,481,1200,977,1211,683,1068,1142,861,1173,1158,582,741,1073,873,1205,440,655,913,945,340,1095,1243,841,436,1265,651,1228,1254,389,1055,372,917,802,1059,949,542,357,1191,638,969,770,316,756,789,321,376,1136,514,1151,348,966,866,1119,396,998,988,602,981,766,877,692,452,920,380,678,366,534,714,512,942,1153,761,1047,1057,1274,334,910,1123,1217,820,630,429,815,957,894,467,484,1032,852,665,889,461,551,1281,456,974,1012,583,830,519,1259,1121,1064,403,1138,869,610,499,1089,1234,783,420,1118,328,1182,537,669,686,526,1214,706,554,753,837,985,1249,738,1231,1131,1050,1246,605,393,1114,343,1026,662,926,1202,792,1086,938,633,360,953,1185,794,586,412,750,1251,824,745,573,689,444,904,423,1007,732,772,579,1256,545,1271,1092,672,1194,681,996,616,599,900,406,509,880,649,477,1080,758,323,848,1029,964,915,1022,932,345,858,799,1162,521,959,827,780,883,563,505,1044,695,1176,608,426,1208,531,548,1277,812,1081,516,1145,490,675,1134,487,855,1156,409,1098,993,712,557,1003,1070,872,1053,717,502,907,331,1188,470,576,703,613,1221,727,386,314,571,497,1240,627,450,363,539,891,1126,1010,844,1108,588,961,319,748,1062,946,351,786,568,929,1077,763,383,620,447,1280,833,1148,735,950,835,326,474,635,955,796,400,1197,720,1165,886,415,624,464,1129,1261,1268,596,528,459,723,822,850,369,337,354,935,923,659,560,708,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : ITP176^1 : TPTP v8.2.0. Released v7.5.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n012.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat May 18 16:26:54 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.00/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.17/1.36  % [INFO] 	 Parsing done (390ms). 
% 2.17/1.38  % [INFO] 	 Running in sequential loop mode. 
% 3.23/1.75  % [INFO] 	 eprover registered as external prover. 
% 3.23/1.75  % [INFO] 	 cvc4 registered as external prover. 
% 3.23/1.76  % [INFO] 	 Scanning for conjecture ... 
% 3.71/1.92  % [INFO] 	 Found a conjecture (or negated_conjecture) and 358 axioms. Running axiom selection ... 
% 4.28/2.09  % [INFO] 	 Axiom selection finished. Selected 311 axioms (removed 47 axioms). 
% 4.91/2.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 5.23/2.37  % [INFO] 	 Type checking passed. 
% 5.23/2.38  % [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 ... 
% 19.26/5.92  % External prover 'e' found a proof!
% 19.26/5.92  % [INFO] 	 Killing All external provers ... 
% 19.26/5.92  % Time passed: 5439ms (effective reasoning time: 4538ms)
% 19.26/5.92  % 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)>
% 19.26/5.92  % Axioms used in derivation (311): fact_205_converseD, fact_58_pred__equals__eq2, fact_172_congr_I2_J, fact_116_insertI1, fact_14_Image__empty2, fact_309_empty__subsetI, fact_343_bot_Oextremum__unique, fact_117_insertI1, fact_127_Collect__mem__eq, fact_176_prod_Oinject, fact_41_ImageI, fact_281_total__on__def, fact_5__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062, fact_322_Collect__subset, fact_231_refl__on__converse, fact_59_pred__equals__eq2, fact_318_singleton__insert__inj__eq, fact_292_graph__homomorphism__empty, fact_265_congruentI, fact_8_singleton__conv2, fact_342_bot_Oextremum__uniqueI, fact_187_labeled__graph_Oexpand, fact_268_equiv__class__self, fact_107_insert__ident, fact_285_total__on__empty, fact_202_converseE, fact_348_subset__insert, fact_310_empty__subsetI, fact_336_in__mono, fact_226_equiv, fact_115_insertI2, fact_140_some__eq__ex, fact_299_congruent2__implies__congruent, fact_239_refl__onD1, fact_104_insert__absorb, fact_351_subset__insertI, fact_158_singletonD, fact_174_the__elem__eq, fact_207_bot__set__def, fact_232_is__singletonI, fact_114_insertI2, fact_294_linear__order__on__converse, fact_149_insert__not__empty, fact_216_old_Oprod_Oexhaust, fact_350_subset__insert, fact_110_Set_Oset__insert, fact_225_local_Orefl, fact_217_prod__induct3, fact_70_Image__iff, fact_165_some__in__eq, fact_60_rev__ImageI, fact_50_f, fact_141_someI2__bex, fact_186__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062, fact_15_Image__empty2, fact_106_insert__absorb, fact_24_Collect__empty__eq, fact_130_Collect__cong, fact_86_ex__in__conv, fact_96_emptyE, fact_228_getRel__dom_I2_J, fact_236_refl__onD, fact_1_assms_I1_J, fact_51_Image__singleton__iff, fact_48_ImageI, fact_148_singleton__inject, fact_284_total__onI, fact_199_converse_Ocases, fact_331_subset__eq, fact_276_total__on__singleton, fact_45_ImageI, fact_180_converse__converse, fact_3_P, fact_16_Image__empty2, fact_301_congruent2__implies__congruent, fact_296_vertices__def, fact_252_is__singletonE, fact_326_subset__iff, fact_71_Image__iff, fact_266_congruentD, fact_168__092_060open_062_IS__Idt_M_Ax_M_Ay_J_A_092_060in_062_Aedges_AG_092_060close_062, fact_251_is__singleton__def, fact_317_singleton__insert__inj__eq_H, fact_329_subset__eq, fact_352_subset__insertI2, fact_53_Image__singleton__iff, fact_157_singletonD, help_If_1_1_If_001tf__b_T, fact_155_singleton__iff, fact_105_insert__absorb, fact_100_insert__commute, fact_354_subset__singleton__iff, fact_316_singleton__insert__inj__eq_H, fact_2_P__eq, fact_223_surj__pair, fact_29_empty__iff, fact_311_subset__empty, fact_338_converse__subset__swap, fact_170_r2, fact_26_all__not__in__conv, fact_325_Collect__mono, fact_221_prod__cases, fact_98_mk__disjoint__insert, fact_339_subrelI, fact_253_is__singletonE, fact_4__092_060open_062_Ix_M_Ay_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062, fact_89_equals0I, fact_143_someI2__bex, fact_209_bot__empty__eq, fact_30_empty__iff, fact_295_edges__def, fact_255_equiv__class__eq__iff, fact_345_bot_Oextremum, fact_335_in__mono, fact_328_subset__iff, fact_150_insert__not__empty, fact_128_Collect__mem__eq, fact_113_insertI2, fact_138_insert__compr, fact_177_old_Oprod_Oinject, fact_83_Image__singleton, fact_269_equiv__class__self, fact_278_total__on__converse, fact_6_singleton__conv, fact_344_bot_Oextremum__unique, fact_349_subset__insert, fact_146_someI2, fact_103_insert__eq__iff, fact_190_converse_Oinducts, fact_208_bot__empty__eq, fact_315_insert__subset, fact_289_labeled__graph_Oexhaust__sel, fact_287_labeled__graph_Osel_I2_J, fact_333_subsetD, fact_125_mem__Collect__eq, fact_81_ImageE, fact_12_Image__empty1, fact_229_is__singleton__the__elem, fact_163_some__in__eq, fact_175_prod_Oinject, fact_27_all__not__in__conv, fact_95_emptyE, fact_22_empty__Collect__eq, fact_133_empty__def, fact_13_Image__empty2, fact_139_some1__equality, fact_144_someI2__ex, fact_243_refl__on__empty, fact_290_linear__order__on__singleton, fact_247_is__singletonI_H, fact_78_ImageE, fact_49_ImageI, fact_111_Set_Oset__insert, fact_68_rev__ImageI, fact_72_ImageE, fact_227_getRel__dom_I1_J, fact_82_Image__singleton, fact_314_insert__subset, fact_64_rev__ImageI, fact_320_Image__mono, fact_33_insert__iff, fact_25_Collect__empty__eq, fact_90_equals0I, fact_93_equals0D, fact_39_some__sym__eq__trivial, fact_302_proj__def, fact_65_rev__ImageI, fact_34_insert__iff, fact_222_prod__cases, fact_32_insert__absorb2, fact_323_Collect__subset, fact_74_ImageE, fact_260_equiv__class__eq, fact_122_some__eq__imp, fact_20_some__equality, fact_94_emptyE, fact_288_labeled__graph_Osel_I1_J, fact_87_ex__in__conv, fact_270_Collect__empty__eq__bot, fact_118_insertI1, fact_215_old_Oprod_Oexhaust, fact_250_is__singleton__def, fact_156_singletonD, fact_160_Collect__conv__if2, fact_263_eq__equiv__class, fact_126_mem__Collect__eq, fact_330_subset__eq, fact_136_insert__compr, fact_212_bot__empty__eq2, fact_233_is__singletonI, fact_28_all__not__in__conv, fact_280_graph__empty__e, fact_17_singletonI, fact_246_is__singletonI_H, fact_321_Collect__subset, fact_38_insertCI, fact_196_converse_Osimps, fact_142_someI2__bex, fact_11_tuple__disj, fact_334_subsetD, fact_91_equals0D, fact_40_ImageI, fact_319_singleton__insert__inj__eq, fact_230_is__singleton__the__elem, fact_80_ImageE, fact_62_rev__ImageI, fact_31_empty__iff, fact_213_old_Oprod_Oinducts, fact_286_total__on__empty, fact_183_converse__iff, fact_145_someI__ex, fact_88_equals0I, fact_324_Collect__mono__iff, fact_97_mk__disjoint__insert, fact_99_mk__disjoint__insert, fact_137_insert__compr, fact_305_subsetI, fact_275_refl__on__domain, fact_341_bot_Oextremum__uniqueI, fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062, fact_173_the__elem__eq, fact_123_tfl__some, fact_211_bot__empty__eq2, fact_52_Image__singleton__iff, fact_35_insert__iff, fact_124_mem__Collect__eq, fact_193_converse_Ointros, fact_184_vertices__restrict, fact_164_some__in__eq, fact_178_old_Oprod_Oinject, fact_220_Pair__inject, fact_23_empty__Collect__eq, fact_353_subset__singleton__iff, fact_279_labeled__graph_Ocollapse, fact_57_Image__singleton__iff, fact_248_refl__on__singleton, fact_109_insert__ident, fact_337_in__mono, fact_108_insert__ident, fact_293_graph__homomorphism__empty, fact_169_restrict__idemp, fact_54_Image__singleton__iff, fact_242_refl__onD2, fact_152_doubleton__eq__iff, fact_73_ImageE, fact_271_Collect__empty__eq__bot, fact_327_subset__iff, fact_312_subset__empty, fact_119_insertE, fact_300_congruent2__implies__congruent, fact_224_surj__pair, fact_132_someI, fact_308_converse__mono, fact_210_bot__empty__eq, fact_112_Set_Oset__insert, fact_77_ImageE, fact_161_Collect__conv__if, fact_267_equiv__class__self, fact_129_Collect__mem__eq, fact_7_singleton__conv, fact_346_bot_Oextremum, fact_121_insertE, fact_307_subsetI, fact_61_rev__ImageI, fact_214_old_Oprod_Oinducts, fact_134_empty__def, fact_36_insertCI, fact_131_Eps__cong, fact_18_singletonI, fact_102_insert__eq__iff, fact_135_insert__Collect, fact_147_singleton__inject, fact_151_doubleton__eq__iff, fact_218_prod__cases3, fact_120_insertE, fact_159_Collect__conv__if2, fact_258_eq__equiv__class__iff, fact_154_singleton__iff, fact_44_ImageI, fact_10_tuple__disj, fact_332_subsetD, fact_162_Collect__conv__if, help_If_3_1_If_001tf__b_T, fact_306_subsetI, fact_37_insertCI, fact_171_r1, fact_55_Image__singleton__iff, fact_185_converse__empty, fact_21_some__eq__trivial, fact_166_congr_I1_J, fact_19_singletonI, fact_297_lnear__order__on__empty, fact_69_rev__ImageI, fact_153_singleton__iff, fact_85_ex__in__conv, help_If_2_1_If_001tf__b_T, fact_92_equals0D, fact_219_Pair__inject, fact_179_converse__inject, fact_84_Image__singleton, fact_347_insert__mono, fact_272_graph__single, fact_101_insert__eq__iff, fact_206_bot__set__def, fact_245_is__singletonI_H, fact_167_vert__P, fact_9_singleton__conv2, fact_340_subrelI, fact_313_insert__subset, fact_303_equiv__class__subset, fact_42_ImageI
% 19.26/5.92  % No. of inferences in proof: 626
% 19.26/5.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5439 ms resp. 4538 ms w/o parsing
% 20.37/6.15  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.37/6.16  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------