Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP180^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:07:04 AM UTC 2026

% Result   : Theorem 54.07s 11.41s
% Output   : Refutation 50.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  341
% Syntax   : Number of formulae    :  684 ( 384 unt;   0 typ;   0 def)
%            Number of atoms       : 1752 ( 896 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 5647 ( 262   ~;  54   |; 146   &;4635   @)
%                                         (   0 <=>; 550  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Number of types       :   44 (  43 usr)
%            Number of type conns  :  156 ( 156   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  137 ( 135 usr;  25 con; 0-3 aty)
%            Number of variables   : 1690 (  48   ^;1596   !;  46   ?;1690   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_Pr361461255at_nat_type,type,
    set_Pr361461255at_nat: $tType ).

thf(set_Pr1326571566_V_nat_type,type,
    set_Pr1326571566_V_nat: $tType ).

thf(set_Pr1007924423_V_nat_type,type,
    set_Pr1007924423_V_nat: $tType ).

thf(set_Pr872354016od_V_V_type,type,
    set_Pr872354016od_V_V: $tType ).

thf(produc1269720746od_V_V_type,type,
    produc1269720746od_V_V: $tType ).

thf(set_Pr597600647_V_nat_type,type,
    set_Pr597600647_V_nat: $tType ).

thf(labele506073123_V_nat_type,type,
    labele506073123_V_nat: $tType ).

thf(set_Pr2015814777od_V_V_type,type,
    set_Pr2015814777od_V_V: $tType ).

thf(set_Pr1056235617_nat_V_type,type,
    set_Pr1056235617_nat_V: $tType ).

thf(produc1082089497od_V_V_type,type,
    produc1082089497od_V_V: $tType ).

thf(set_Pr473545225_V_nat_type,type,
    set_Pr473545225_V_nat: $tType ).

thf(set_Pr1058435079_V_nat_type,type,
    set_Pr1058435079_V_nat: $tType ).

thf(produc778275879_V_nat_type,type,
    produc778275879_V_nat: $tType ).

thf(produc651414759nt_V_V_type,type,
    produc651414759nt_V_V: $tType ).

thf(labele201426742od_V_V_type,type,
    labele201426742od_V_V: $tType ).

thf(set_Pr951255342od_V_V_type,type,
    set_Pr951255342od_V_V: $tType ).

thf(produc1443401592od_V_V_type,type,
    produc1443401592od_V_V: $tType ).

thf(set_Pr257494450_V_V_V_type,type,
    set_Pr257494450_V_V_V: $tType ).

thf(set_Pr744279122od_V_V_type,type,
    set_Pr744279122od_V_V: $tType ).

thf(set_Pr1498723630od_V_V_type,type,
    set_Pr1498723630od_V_V: $tType ).

thf(labele236903175od_V_V_type,type,
    labele236903175od_V_V: $tType ).

thf(set_Pr2022779335od_V_V_type,type,
    set_Pr2022779335od_V_V: $tType ).

thf(produc1699571228od_V_V_type,type,
    produc1699571228od_V_V: $tType ).

thf(produc1113554040od_V_V_type,type,
    produc1113554040od_V_V: $tType ).

thf(set_la14611914_V_nat_type,type,
    set_la14611914_V_nat: $tType ).

thf(produc522115815od_V_V_type,type,
    produc522115815od_V_V: $tType ).

thf(labele2128733290_V_nat_type,type,
    labele2128733290_V_nat: $tType ).

thf(allego859987871tant_V_type,type,
    allego859987871tant_V: $tType ).

thf(labele2115946735nt_V_V_type,type,
    labele2115946735nt_V_V: $tType ).

thf(set_Pr1228022213_V_V_V_type,type,
    set_Pr1228022213_V_V_V: $tType ).

thf(labele788688367nt_V_V_type,type,
    labele788688367nt_V_V: $tType ).

thf(set_St1111633946tant_V_type,type,
    set_St1111633946tant_V: $tType ).

thf(set_Pr53436518_nat_V_type,type,
    set_Pr53436518_nat_V: $tType ).

thf(set_Product_prod_V_V_type,type,
    set_Product_prod_V_V: $tType ).

thf(set_Product_prod_V_V2_type,type,
    set_Product_prod_V_V2: $tType ).

thf(set_Product_prod_V_V3_type,type,
    set_Product_prod_V_V3: $tType ).

thf(standard_Constant_V_type,type,
    standard_Constant_V: $tType ).

thf(product_prod_V_V_type,type,
    product_prod_V_V: $tType ).

thf(product_prod_V_V2_type,type,
    product_prod_V_V2: $tType ).

thf(set_V_type,type,
    set_V: $tType ).

thf(set_V2_type,type,
    set_V2: $tType ).

thf(v_type,type,
    v: $tType ).

thf(v2_type,type,
    v2: $tType ).

thf(bNF_Gr320641027od_V_V_decl,type,
    bNF_Gr320641027od_V_V: set_St1111633946tant_V > ( standard_Constant_V > product_prod_V_V ) > set_Pr744279122od_V_V ).

thf(bNF_Gr17960482_V_nat_decl,type,
    bNF_Gr17960482_V_nat: set_la14611914_V_nat > ( labele2128733290_V_nat > labele2128733290_V_nat ) > set_Pr1058435079_V_nat ).

thf(bNF_Gr480427157_V_V_V_decl,type,
    bNF_Gr480427157_V_V_V: set_Pr744279122od_V_V > ( produc1699571228od_V_V > v ) > set_Pr257494450_V_V_V ).

thf(bNF_Gr1069958334_V_V_V_decl,type,
    bNF_Gr1069958334_V_V_V: set_Product_prod_V_V > ( product_prod_V_V > v ) > set_Pr1228022213_V_V_V ).

thf(bNF_Gr_V_V_decl,type,
    bNF_Gr_V_V: set_V2 > ( v2 > v ) > set_Product_prod_V_V2 ).

thf(bNF_Gr_V_V2_decl,type,
    bNF_Gr_V_V2: set_V > ( v > v ) > set_Product_prod_V_V ).

thf(comp_V1480932210od_V_V_decl,type,
    comp_V1480932210od_V_V: ( v > produc1699571228od_V_V ) > ( produc1699571228od_V_V > v ) > produc1699571228od_V_V > produc1699571228od_V_V ).

thf(comp_V772749048od_V_V_decl,type,
    comp_V772749048od_V_V: ( v > product_prod_V_V ) > ( product_prod_V_V > v ) > product_prod_V_V > product_prod_V_V ).

thf(comp_V_V_V_decl,type,
    comp_V_V_V: ( v > v2 ) > ( v2 > v ) > v2 > v2 ).

thf(comp_V_V_V2_decl,type,
    comp_V_V_V2: ( v > v ) > ( v > v ) > v > v ).

thf(standard_S_Bot_V_decl,type,
    standard_S_Bot_V: standard_Constant_V ).

thf(standard_S_Const_V_decl,type,
    standard_S_Const_V: v2 > standard_Constant_V ).

thf(standard_S_Top_V_decl,type,
    standard_S_Top_V: standard_Constant_V ).

thf(getRel2057312683od_V_V_decl,type,
    getRel2057312683od_V_V: standard_Constant_V > labele201426742od_V_V > set_Pr2015814777od_V_V ).

thf(getRel1902920892od_V_V_decl,type,
    getRel1902920892od_V_V: standard_Constant_V > labele236903175od_V_V > set_Pr2022779335od_V_V ).

thf(getRel632961956nt_V_V_decl,type,
    getRel632961956nt_V_V: standard_Constant_V > labele788688367nt_V_V > set_Product_prod_V_V3 ).

thf(getRel1432786916nt_V_V_decl,type,
    getRel1432786916nt_V_V: standard_Constant_V > labele2115946735nt_V_V > set_Product_prod_V_V ).

thf(semant993842370nt_V_V_decl,type,
    semant993842370nt_V_V: labele2115946735nt_V_V > allego859987871tant_V > set_Product_prod_V_V ).

thf(edge_p669293514tant_V_decl,type,
    edge_p669293514tant_V: set_Pr257494450_V_V_V > set_Pr872354016od_V_V > set_Pr744279122od_V_V > $o ).

thf(edge_p1776314003tant_V_decl,type,
    edge_p1776314003tant_V: set_Pr1228022213_V_V_V > set_Pr951255342od_V_V > set_Pr744279122od_V_V > $o ).

thf(edge_p1322161019tant_V_decl,type,
    edge_p1322161019tant_V: set_Product_prod_V_V2 > set_Pr1498723630od_V_V > set_Pr744279122od_V_V > $o ).

thf(edge_p1560004099tant_V_decl,type,
    edge_p1560004099tant_V: set_Product_prod_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > $o ).

thf(graph_227683057_nat_V_decl,type,
    graph_227683057_nat_V: labele506073123_V_nat > labele2115946735nt_V_V > set_Pr1056235617_nat_V > $o ).

thf(graph_840721237_V_V_V_decl,type,
    graph_840721237_V_V_V: labele236903175od_V_V > labele2115946735nt_V_V > set_Pr1228022213_V_V_V > $o ).

thf(graph_1808119_V_V_V_decl,type,
    graph_1808119_V_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).

thf(graph_1141886696nt_V_V_decl,type,
    graph_1141886696nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).

thf(labele1193521135_V_nat_decl,type,
    labele1193521135_V_nat: set_Pr1326571566_V_nat > set_Pr1058435079_V_nat > labele506073123_V_nat ).

thf(labele94156371od_V_V_decl,type,
    labele94156371od_V_V: set_Pr951255342od_V_V > set_Product_prod_V_V > labele236903175od_V_V ).

thf(labele712009229nt_V_V_decl,type,
    labele712009229nt_V_V: set_Pr744279122od_V_V > set_V > labele2115946735nt_V_V ).

thf(labele1794513953od_V_V_decl,type,
    labele1794513953od_V_V: labele201426742od_V_V > set_Pr872354016od_V_V ).

thf(labele668941254od_V_V_decl,type,
    labele668941254od_V_V: labele236903175od_V_V > set_Pr951255342od_V_V ).

thf(labele1469545390nt_V_V_decl,type,
    labele1469545390nt_V_V: labele788688367nt_V_V > set_Pr1498723630od_V_V ).

thf(labele515735386nt_V_V_decl,type,
    labele515735386nt_V_V: labele2115946735nt_V_V > set_Pr744279122od_V_V ).

thf(labele1328382418od_V_V_decl,type,
    labele1328382418od_V_V: labele201426742od_V_V > set_Pr744279122od_V_V ).

thf(labele1822884081_V_nat_decl,type,
    labele1822884081_V_nat: labele506073123_V_nat > set_Pr1058435079_V_nat ).

thf(labele981584981od_V_V_decl,type,
    labele981584981od_V_V: labele236903175od_V_V > set_Product_prod_V_V ).

thf(labele1152678333nt_V_V_decl,type,
    labele1152678333nt_V_V: labele788688367nt_V_V > set_V2 ).

thf(labele1134902411nt_V_V_decl,type,
    labele1134902411nt_V_V: labele2115946735nt_V_V > set_V ).

thf(map_gr157381846tant_V_decl,type,
    map_gr157381846tant_V: set_Pr257494450_V_V_V > labele201426742od_V_V > labele2115946735nt_V_V ).

thf(map_gr875022471tant_V_decl,type,
    map_gr875022471tant_V: set_Pr1228022213_V_V_V > labele236903175od_V_V > labele2115946735nt_V_V ).

thf(map_gr530397039tant_V_decl,type,
    map_gr530397039tant_V: set_Product_prod_V_V2 > labele788688367nt_V_V > labele2115946735nt_V_V ).

thf(map_gr907434255tant_V_decl,type,
    map_gr907434255tant_V: set_Product_prod_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).

thf(restri1699516426od_V_V_decl,type,
    restri1699516426od_V_V: labele201426742od_V_V > labele201426742od_V_V ).

thf(restri1932147897_V_nat_decl,type,
    restri1932147897_V_nat: labele506073123_V_nat > labele506073123_V_nat ).

thf(restri1502575645od_V_V_decl,type,
    restri1502575645od_V_V: labele236903175od_V_V > labele236903175od_V_V ).

thf(restri175070597nt_V_V_decl,type,
    restri175070597nt_V_V: labele788688367nt_V_V > labele788688367nt_V_V ).

thf(restri1305980611nt_V_V_decl,type,
    restri1305980611nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V ).

thf(sup_su693515134od_V_V_decl,type,
    sup_su693515134od_V_V: set_Pr744279122od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).

thf(sup_su1043134939_V_nat_decl,type,
    sup_su1043134939_V_nat: set_Pr1058435079_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).

thf(sup_su551882943od_V_V_decl,type,
    sup_su551882943od_V_V: set_Product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V ).

thf(sup_sup_set_V_decl,type,
    sup_sup_set_V: set_V2 > set_V2 > set_V2 ).

thf(sup_sup_set_V2_decl,type,
    sup_sup_set_V2: set_V > set_V > set_V ).

thf(bot_bo2024487199_V_V_o_decl,type,
    bot_bo2024487199_V_V_o: produc1699571228od_V_V > $o ).

thf(bot_bo1078500394_nat_o_decl,type,
    bot_bo1078500394_nat_o: produc778275879_V_nat > $o ).

thf(bot_bo1168561222_V_V_o_decl,type,
    bot_bo1168561222_V_V_o: product_prod_V_V > $o ).

thf(bot_bot_V_o_decl,type,
    bot_bot_V_o: v2 > $o ).

thf(bot_bot_V_o2_decl,type,
    bot_bot_V_o2: v > $o ).

thf(bot_bo1053950006_V_nat_decl,type,
    bot_bo1053950006_V_nat: set_la14611914_V_nat ).

thf(bot_bo634818242_V_nat_decl,type,
    bot_bo634818242_V_nat: set_Pr1326571566_V_nat ).

thf(bot_bo451843010od_V_V_decl,type,
    bot_bo451843010od_V_V: set_Pr951255342od_V_V ).

thf(bot_bo667804902od_V_V_decl,type,
    bot_bo667804902od_V_V: set_Pr744279122od_V_V ).

thf(bot_bo323535987at_nat_decl,type,
    bot_bo323535987at_nat: set_Pr361461255at_nat ).

thf(bot_bo1196823539_V_nat_decl,type,
    bot_bo1196823539_V_nat: set_Pr597600647_V_nat ).

thf(bot_bo907687539_V_nat_decl,type,
    bot_bo907687539_V_nat: set_Pr1058435079_V_nat ).

thf(bot_bo1834032757_V_nat_decl,type,
    bot_bo1834032757_V_nat: set_Pr473545225_V_nat ).

thf(bot_bo2057106227_V_nat_decl,type,
    bot_bo2057106227_V_nat: set_Pr1007924423_V_nat ).

thf(bot_bo1708783349_nat_V_decl,type,
    bot_bo1708783349_nat_V: set_Pr1056235617_nat_V ).

thf(bot_bo12878899od_V_V_decl,type,
    bot_bo12878899od_V_V: set_Pr2022779335od_V_V ).

thf(bot_bo688400985_V_V_V_decl,type,
    bot_bo688400985_V_V_V: set_Pr1228022213_V_V_V ).

thf(bot_bo1389414743od_V_V_decl,type,
    bot_bo1389414743od_V_V: set_Product_prod_V_V ).

thf(bot_bot_set_V_decl,type,
    bot_bot_set_V: set_V2 ).

thf(bot_bot_set_V2_decl,type,
    bot_bot_set_V2: set_V ).

thf(produc2132932316od_V_V_decl,type,
    produc2132932316od_V_V: standard_Constant_V > produc1082089497od_V_V > produc1269720746od_V_V ).

thf(produc1482441770od_V_V_decl,type,
    produc1482441770od_V_V: standard_Constant_V > produc522115815od_V_V > produc1443401592od_V_V ).

thf(produc1171747370od_V_V_decl,type,
    produc1171747370od_V_V: standard_Constant_V > product_prod_V_V2 > produc1113554040od_V_V ).

thf(produc107991630od_V_V_decl,type,
    produc107991630od_V_V: standard_Constant_V > product_prod_V_V > produc1699571228od_V_V ).

thf(produc698429463_V_nat_decl,type,
    produc698429463_V_nat: labele2128733290_V_nat > labele2128733290_V_nat > produc778275879_V_nat ).

thf(produc533118295nt_V_V_decl,type,
    produc533118295nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > produc651414759nt_V_V ).

thf(produc1736057425od_V_V_decl,type,
    produc1736057425od_V_V: produc1699571228od_V_V > produc1699571228od_V_V > produc1082089497od_V_V ).

thf(produc1905750615od_V_V_decl,type,
    produc1905750615od_V_V: product_prod_V_V > product_prod_V_V > produc522115815od_V_V ).

thf(product_Pair_V_V_decl,type,
    product_Pair_V_V: v2 > v2 > product_prod_V_V2 ).

thf(product_Pair_V_V2_decl,type,
    product_Pair_V_V2: v > v > product_prod_V_V ).

thf(id_on_1882925319_V_nat_decl,type,
    id_on_1882925319_V_nat: set_la14611914_V_nat > set_Pr1058435079_V_nat ).

thf(id_on_1491482303od_V_V_decl,type,
    id_on_1491482303od_V_V: set_Pr744279122od_V_V > set_Pr2015814777od_V_V ).

thf(id_on_558037444_V_nat_decl,type,
    id_on_558037444_V_nat: set_Pr1058435079_V_nat > set_Pr1007924423_V_nat ).

thf(id_on_2125509800od_V_V_decl,type,
    id_on_2125509800od_V_V: set_Product_prod_V_V > set_Pr2022779335od_V_V ).

thf(id_on_V_decl,type,
    id_on_V: set_V2 > set_Product_prod_V_V3 ).

thf(id_on_V2_decl,type,
    id_on_V2: set_V > set_Product_prod_V_V ).

thf(conseq1236301781_nat_V_decl,type,
    conseq1236301781_nat_V: set_Pr1058435079_V_nat > labele2115946735nt_V_V > $o ).

thf(extens1533825066_V_V_V_decl,type,
    extens1533825066_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).

thf(mainta1342478555od_V_V_decl,type,
    mainta1342478555od_V_V: produc778275879_V_nat > labele201426742od_V_V > $o ).

thf(mainta922614952_V_nat_decl,type,
    mainta922614952_V_nat: produc778275879_V_nat > labele506073123_V_nat > $o ).

thf(mainta1984786828od_V_V_decl,type,
    mainta1984786828od_V_V: produc778275879_V_nat > labele236903175od_V_V > $o ).

thf(mainta1026355316_nat_V_decl,type,
    mainta1026355316_nat_V: produc778275879_V_nat > labele788688367nt_V_V > $o ).

thf(mainta197426964_nat_V_decl,type,
    mainta197426964_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > $o ).

thf(mainta1699210777_V_V_V_decl,type,
    mainta1699210777_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > $o ).

thf(collec1840263537od_V_V_decl,type,
    collec1840263537od_V_V: ( produc1699571228od_V_V > $o ) > set_Pr744279122od_V_V ).

thf(collec1411521682_V_nat_decl,type,
    collec1411521682_V_nat: ( produc778275879_V_nat > $o ) > set_Pr1058435079_V_nat ).

thf(collec2040633974od_V_V_decl,type,
    collec2040633974od_V_V: ( product_prod_V_V > $o ) > set_Product_prod_V_V ).

thf(collect_V_decl,type,
    collect_V: ( v2 > $o ) > set_V2 ).

thf(collect_V2_decl,type,
    collect_V2: ( v > $o ) > set_V ).

thf(insert1818834324tant_V_decl,type,
    insert1818834324tant_V: standard_Constant_V > set_St1111633946tant_V > set_St1111633946tant_V ).

thf(insert213439034_V_nat_decl,type,
    insert213439034_V_nat: labele2128733290_V_nat > set_la14611914_V_nat > set_la14611914_V_nat ).

thf(insert135842892od_V_V_decl,type,
    insert135842892od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).

thf(insert481364471_V_nat_decl,type,
    insert481364471_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).

thf(insert2024285275od_V_V_decl,type,
    insert2024285275od_V_V: product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V ).

thf(insert_V2_decl,type,
    insert_V2: v > set_V > set_V ).

thf(standa434642387_V_nat_decl,type,
    standa434642387_V_nat: set_Pr1058435079_V_nat > set_Pr361461255at_nat ).

thf(standa1571708471od_V_V_decl,type,
    standa1571708471od_V_V: set_Product_prod_V_V > set_Pr597600647_V_nat ).

thf(standa1897115807ules_V_decl,type,
    standa1897115807ules_V: set_V2 > set_Pr1058435079_V_nat ).

thf(standa294833961ules_V_decl,type,
    standa294833961ules_V: set_V > set_Pr473545225_V_nat ).

thf(standa1568205529ules_V_decl,type,
    standa1568205529ules_V: set_St1111633946tant_V > set_Pr1058435079_V_nat ).

thf(standa1319953089tant_V_decl,type,
    standa1319953089tant_V: produc778275879_V_nat ).

thf(standa157301464ules_V_decl,type,
    standa157301464ules_V: set_V2 > set_St1111633946tant_V > set_Pr1058435079_V_nat ).

thf(standa214871990tant_V_decl,type,
    standa214871990tant_V: standard_Constant_V > produc778275879_V_nat ).

thf(member1542015739tant_V_decl,type,
    member1542015739tant_V: standard_Constant_V > set_St1111633946tant_V > $o ).

thf(member600445121od_V_V_decl,type,
    member600445121od_V_V: produc1269720746od_V_V > set_Pr872354016od_V_V > $o ).

thf(member361435663od_V_V_decl,type,
    member361435663od_V_V: produc1443401592od_V_V > set_Pr951255342od_V_V > $o ).

thf(member1416643087od_V_V_decl,type,
    member1416643087od_V_V: produc1113554040od_V_V > set_Pr1498723630od_V_V > $o ).

thf(member1010391347od_V_V_decl,type,
    member1010391347od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > $o ).

thf(member1886821968_V_nat_decl,type,
    member1886821968_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > $o ).

thf(member785416642od_V_V_decl,type,
    member785416642od_V_V: produc1082089497od_V_V > set_Pr2015814777od_V_V > $o ).

thf(member134497296od_V_V_decl,type,
    member134497296od_V_V: produc522115815od_V_V > set_Pr2022779335od_V_V > $o ).

thf(member1990987792od_V_V_decl,type,
    member1990987792od_V_V: product_prod_V_V2 > set_Product_prod_V_V3 > $o ).

thf(member2015049524od_V_V_decl,type,
    member2015049524od_V_V: product_prod_V_V > set_Product_prod_V_V > $o ).

thf(member_V_decl,type,
    member_V: v2 > set_V2 > $o ).

thf(member_V2_decl,type,
    member_V2: v > set_V > $o ).

thf(c_decl,type,
    c: set_V2 ).

thf(g_decl,type,
    g: labele2115946735nt_V_V ).

thf(l_decl,type,
    l: set_St1111633946tant_V ).

thf(h_decl,type,
    h: v > v ).

thf(m_decl,type,
    m: v2 > v ).

thf(x_decl,type,
    x: v ).

thf(xa_decl,type,
    xa: v2 ).

thf(y_decl,type,
    y: v2 ).

thf(94,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ A @ B ) )
      = ( sup_su1043134939_V_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_sup_Oleft__idem) ).

thf(645,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ A @ B ) )
      = ( sup_su1043134939_V_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(329,axiom,
    ! [A: v,B: v,C: standard_Constant_V,D: labele2115946735nt_V_V,E: v > v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ C @ D ) )
     => ( ( member_V2 @ A @ ( labele1134902411nt_V_V @ D ) )
       => ( ( member_V2 @ B @ ( labele1134902411nt_V_V @ D ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ A ) @ ( E @ B ) ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ D ) @ E ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_getRel__hom) ).

thf(1411,plain,
    ! [A: v,B: v,C: standard_Constant_V,D: labele2115946735nt_V_V,E: v > v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ C @ D ) )
     => ( ( member_V2 @ A @ ( labele1134902411nt_V_V @ D ) )
       => ( ( member_V2 @ B @ ( labele1134902411nt_V_V @ D ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ A ) @ ( E @ B ) ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ D ) @ E ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(259,axiom,
    ! [A: product_prod_V_V > $o,B: product_prod_V_V] :
      ( ! [C: v,D: v] : ( A @ ( product_Pair_V_V2 @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_old_Oprod_Oinducts) ).

thf(1168,plain,
    ! [A: product_prod_V_V > $o,B: product_prod_V_V] :
      ( ! [C: v,D: v] : ( A @ ( product_Pair_V_V2 @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(239,axiom,
    ( bot_bot_V_o
    = ( ^ [A: v2] : ( member_V @ A @ bot_bot_set_V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_bot__empty__eq) ).

thf(1105,plain,
    ( bot_bot_V_o
    = ( ^ [A: v2] : ( member_V @ A @ bot_bot_set_V ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(301,axiom,
    member_V @ y @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__C1_C_I2_J) ).

thf(1315,plain,
    member_V @ y @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(70,axiom,
    ! [A: v2,B: v2,C: set_V2] :
      ( ( A = B )
     => ( ( member_V @ A @ C )
       => ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ B ) @ ( id_on_V @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Id__on__eqI) ).

thf(555,plain,
    ! [A: v2,B: v2,C: set_V2] :
      ( ( A = B )
     => ( ( member_V @ A @ C )
       => ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ B ) @ ( id_on_V @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(99,axiom,
    ! [A: labele2115946735nt_V_V,B: set_Product_prod_V_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( map_gr907434255tant_V @ B @ A )
        = ( restri1305980611nt_V_V @ ( map_gr907434255tant_V @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_map__graph__preserves__restricted) ).

thf(666,plain,
    ! [A: labele2115946735nt_V_V,B: set_Product_prod_V_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( map_gr907434255tant_V @ B @ A )
        = ( restri1305980611nt_V_V @ ( map_gr907434255tant_V @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(88,axiom,
    ! [A: produc778275879_V_nat] :
      ~ ( member1886821968_V_nat @ A @ bot_bo907687539_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_emptyE) ).

thf(628,plain,
    ! [A: produc778275879_V_nat] :
      ~ ( member1886821968_V_nat @ A @ bot_bo907687539_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(214,axiom,
    ( ( standa434642387_V_nat @ bot_bo907687539_V_nat )
    = bot_bo323535987at_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_constant__rules__empty) ).

thf(1031,plain,
    ( ( standa434642387_V_nat @ bot_bo907687539_V_nat )
    = bot_bo323535987at_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(293,axiom,
    member_V2 @ x @ ( labele1134902411nt_V_V @ g ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_x) ).

thf(1290,plain,
    member_V2 @ x @ ( labele1134902411nt_V_V @ g ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(340,axiom,
    ! [A: product_prod_V_V,B: labele236903175od_V_V,C: product_prod_V_V,D: standard_Constant_V,E: product_prod_V_V > v,F: v,G: v] :
      ( ( member2015049524od_V_V @ A @ ( labele981584981od_V_V @ B ) )
     => ( ( member2015049524od_V_V @ C @ ( labele981584981od_V_V @ B ) )
       => ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ C ) @ ( getRel1902920892od_V_V @ D @ B ) )
         => ( ( ( E @ A )
              = F )
           => ( ( ( E @ C )
                = G )
             => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ ( getRel1432786916nt_V_V @ D @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_getRel__map__fn) ).

thf(1443,plain,
    ! [A: product_prod_V_V,B: labele236903175od_V_V,C: product_prod_V_V,D: standard_Constant_V,E: product_prod_V_V > v,F: v,G: v] :
      ( ( member2015049524od_V_V @ A @ ( labele981584981od_V_V @ B ) )
     => ( ( member2015049524od_V_V @ C @ ( labele981584981od_V_V @ B ) )
       => ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ C ) @ ( getRel1902920892od_V_V @ D @ B ) )
         => ( ( ( E @ A )
              = F )
           => ( ( ( E @ C )
                = G )
             => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ ( getRel1432786916nt_V_V @ D @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(202,axiom,
    ! [A: set_V,B: set_V,C: v] :
      ( ( ( sup_sup_set_V2 @ A @ B )
        = ( insert_V2 @ C @ bot_bot_set_V2 ) )
      = ( ( ( A = bot_bot_set_V2 )
          & ( B
            = ( insert_V2 @ C @ bot_bot_set_V2 ) ) )
        | ( ( A
            = ( insert_V2 @ C @ bot_bot_set_V2 ) )
          & ( B = bot_bot_set_V2 ) )
        | ( ( A
            = ( insert_V2 @ C @ bot_bot_set_V2 ) )
          & ( B
            = ( insert_V2 @ C @ bot_bot_set_V2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Un__singleton__iff) ).

thf(994,plain,
    ! [A: set_V,B: set_V,C: v] :
      ( ( ( sup_sup_set_V2 @ A @ B )
        = ( insert_V2 @ C @ bot_bot_set_V2 ) )
      = ( ( ( A = bot_bot_set_V2 )
          & ( B
            = ( insert_V2 @ C @ bot_bot_set_V2 ) ) )
        | ( ( A
            = ( insert_V2 @ C @ bot_bot_set_V2 ) )
          & ( B = bot_bot_set_V2 ) )
        | ( ( A
            = ( insert_V2 @ C @ bot_bot_set_V2 ) )
          & ( B
            = ( insert_V2 @ C @ bot_bot_set_V2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(333,axiom,
    ! [A: produc522115815od_V_V,B: set_Product_prod_V_V] :
      ( ( member134497296od_V_V @ A @ ( id_on_2125509800od_V_V @ B ) )
     => ~ ! [C: product_prod_V_V] :
            ( ( member2015049524od_V_V @ C @ B )
           => ( A
             != ( produc1905750615od_V_V @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Id__onE) ).

thf(1422,plain,
    ! [A: produc522115815od_V_V,B: set_Product_prod_V_V] :
      ( ( member134497296od_V_V @ A @ ( id_on_2125509800od_V_V @ B ) )
     => ~ ! [C: product_prod_V_V] :
            ( ( member2015049524od_V_V @ C @ B )
           => ( A
             != ( produc1905750615od_V_V @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(122,axiom,
    ! [A: v > $o] :
      ( ( ( collect_V2 @ A )
        = bot_bot_set_V2 )
      = ( ! [B: v] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Collect__empty__eq) ).

thf(741,plain,
    ! [A: v > $o] :
      ( ( ( collect_V2 @ A )
        = bot_bot_set_V2 )
      = ( ! [B: v] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(166,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ( ( insert481364471_V_nat @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_insert__absorb) ).

thf(878,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ( ( insert481364471_V_nat @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(260,axiom,
    ~ ! [A: v] :
        ~ ( member_V2 @ A @ ( labele1134902411nt_V_V @ g ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(1173,plain,
    ~ ! [A: v] :
        ~ ( member_V2 @ A @ ( labele1134902411nt_V_V @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(77,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ! [B: produc778275879_V_nat] :
          ~ ( member1886821968_V_nat @ B @ A )
     => ( A = bot_bo907687539_V_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_equals0I) ).

thf(582,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ! [B: produc778275879_V_nat] :
          ~ ( member1886821968_V_nat @ B @ A )
     => ( A = bot_bo907687539_V_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(130,axiom,
    ( standa157301464ules_V
    = ( ^ [A: set_V2,B: set_St1111633946tant_V] : ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ ( standa1897115807ules_V @ A ) @ ( standa1568205529ules_V @ B ) ) @ ( insert481364471_V_nat @ ( standa214871990tant_V @ standard_S_Top_V ) @ ( insert481364471_V_nat @ standa1319953089tant_V @ bot_bo907687539_V_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_standard__rules__def) ).

thf(762,plain,
    ( standa157301464ules_V
    = ( ^ [A: set_V2,B: set_St1111633946tant_V] : ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ ( standa1897115807ules_V @ A ) @ ( standa1568205529ules_V @ B ) ) @ ( insert481364471_V_nat @ ( standa214871990tant_V @ standard_S_Top_V ) @ ( insert481364471_V_nat @ standa1319953089tant_V @ bot_bo907687539_V_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(17,axiom,
    ( bot_bo907687539_V_nat
    = ( collec1411521682_V_nat @ bot_bo1078500394_nat_o ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_bot__set__def) ).

thf(385,plain,
    ( bot_bo907687539_V_nat
    = ( collec1411521682_V_nat @ bot_bo1078500394_nat_o ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(63,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( insert2024285275od_V_V @ A @ B )
     != bot_bo1389414743od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_insert__not__empty) ).

thf(533,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( insert2024285275od_V_V @ A @ B )
     != bot_bo1389414743od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(141,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( ! [B: produc778275879_V_nat] :
            ~ ( member1886821968_V_nat @ B @ A ) )
      = ( A = bot_bo907687539_V_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_all__not__in__conv) ).

thf(797,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( ! [B: produc778275879_V_nat] :
            ~ ( member1886821968_V_nat @ B @ A ) )
      = ( A = bot_bo907687539_V_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(276,axiom,
    ! [A: labele788688367nt_V_V,B: v2 > v,C: set_Pr744279122od_V_V] :
      ( ! [D: standard_Constant_V,E: v2,F: v2] :
          ( ( member1416643087od_V_V @ ( produc1171747370od_V_V @ D @ ( product_Pair_V_V @ E @ F ) ) @ ( labele1469545390nt_V_V @ A ) )
         => ( ( member_V @ E @ ( labele1152678333nt_V_V @ A ) )
           => ( ( member_V @ F @ ( labele1152678333nt_V_V @ A ) )
             => ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
     => ( edge_p1322161019tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ A ) @ B ) @ ( labele1469545390nt_V_V @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_edge__preserving__on__graphI) ).

thf(1233,plain,
    ! [A: labele788688367nt_V_V,B: v2 > v,C: set_Pr744279122od_V_V] :
      ( ! [D: standard_Constant_V,E: v2,F: v2] :
          ( ( member1416643087od_V_V @ ( produc1171747370od_V_V @ D @ ( product_Pair_V_V @ E @ F ) ) @ ( labele1469545390nt_V_V @ A ) )
         => ( ( member_V @ E @ ( labele1152678333nt_V_V @ A ) )
           => ( ( member_V @ F @ ( labele1152678333nt_V_V @ A ) )
             => ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
     => ( edge_p1322161019tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ A ) @ B ) @ ( labele1469545390nt_V_V @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(225,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_UnI1) ).

thf(1063,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(273,axiom,
    ! [A: standard_Constant_V,B: v,C: v] :
      ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ ( labele515735386nt_V_V @ g ) )
      = ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ ( h @ B ) @ ( h @ C ) ) ) @ ( labele515735386nt_V_V @ g ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_h_I4_J) ).

thf(1222,plain,
    ! [A: standard_Constant_V,B: v,C: v] :
      ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ ( labele515735386nt_V_V @ g ) )
      = ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ ( h @ B ) @ ( h @ C ) ) ) @ ( labele515735386nt_V_V @ g ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(100,axiom,
    ! [A: labele506073123_V_nat] :
      ( ( A
        = ( restri1932147897_V_nat @ A ) )
     => ( ( mainta922614952_V_nat @ standa1319953089tant_V @ A )
        = ( ( labele1822884081_V_nat @ A )
         != bot_bo907687539_V_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_nonempty__rule) ).

thf(670,plain,
    ! [A: labele506073123_V_nat] :
      ( ( A
        = ( restri1932147897_V_nat @ A ) )
     => ( ( mainta922614952_V_nat @ standa1319953089tant_V @ A )
        = ( ( labele1822884081_V_nat @ A )
         != bot_bo907687539_V_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(283,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ C ) )
      = ( ( A = B )
        | ( member2015049524od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_insert__iff) ).

thf(1260,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ C ) )
      = ( ( A = B )
        | ( member2015049524od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(110,axiom,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ C ) )
      = ( ( A = B )
        | ( member1886821968_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_insert__iff) ).

thf(698,plain,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ C ) )
      = ( ( A = B )
        | ( member1886821968_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(278,axiom,
    ! [A: produc1699571228od_V_V,B: labele201426742od_V_V,C: produc1699571228od_V_V,D: standard_Constant_V,E: produc1699571228od_V_V > v,F: v,G: v] :
      ( ( member1010391347od_V_V @ A @ ( labele1328382418od_V_V @ B ) )
     => ( ( member1010391347od_V_V @ C @ ( labele1328382418od_V_V @ B ) )
       => ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ C ) @ ( getRel2057312683od_V_V @ D @ B ) )
         => ( ( ( E @ A )
              = F )
           => ( ( ( E @ C )
                = G )
             => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ ( getRel1432786916nt_V_V @ D @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_getRel__map__fn) ).

thf(1243,plain,
    ! [A: produc1699571228od_V_V,B: labele201426742od_V_V,C: produc1699571228od_V_V,D: standard_Constant_V,E: produc1699571228od_V_V > v,F: v,G: v] :
      ( ( member1010391347od_V_V @ A @ ( labele1328382418od_V_V @ B ) )
     => ( ( member1010391347od_V_V @ C @ ( labele1328382418od_V_V @ B ) )
       => ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ C ) @ ( getRel2057312683od_V_V @ D @ B ) )
         => ( ( ( E @ A )
              = F )
           => ( ( ( E @ C )
                = G )
             => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ ( getRel1432786916nt_V_V @ D @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(339,axiom,
    ( ( getRel1432786916nt_V_V @ standard_S_Bot_V @ g )
    = bot_bo1389414743od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_cf) ).

thf(1441,plain,
    ( ( getRel1432786916nt_V_V @ standard_S_Bot_V @ g )
    = bot_bo1389414743od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(27,axiom,
    ! [A: set_V] :
      ( ( sup_sup_set_V2 @ A @ bot_bot_set_V2 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_sup__bot_Oright__neutral) ).

thf(417,plain,
    ! [A: set_V] :
      ( ( sup_sup_set_V2 @ A @ bot_bot_set_V2 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(219,axiom,
    ! [A: product_prod_V_V > $o] :
      ( ( bot_bo1389414743od_V_V
        = ( collec2040633974od_V_V @ A ) )
      = ( ! [B: product_prod_V_V] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_empty__Collect__eq) ).

thf(1046,plain,
    ! [A: product_prod_V_V > $o] :
      ( ( bot_bo1389414743od_V_V
        = ( collec2040633974od_V_V @ A ) )
      = ( ! [B: product_prod_V_V] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(72,axiom,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( insert_V2 @ A @ ( insert_V2 @ B @ bot_bot_set_V2 ) )
        = ( insert_V2 @ C @ ( insert_V2 @ D @ bot_bot_set_V2 ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_doubleton__eq__iff) ).

thf(565,plain,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( insert_V2 @ A @ ( insert_V2 @ B @ bot_bot_set_V2 ) )
        = ( insert_V2 @ C @ ( insert_V2 @ D @ bot_bot_set_V2 ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(275,axiom,
    ! [A: v,B: set_V,C: v > v,D: v] :
      ( ( ~ ( member_V2 @ A @ B )
        | ( ( C @ A )
         != D ) )
     => ~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ D ) @ ( bNF_Gr_V_V2 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Gr__not__in) ).

thf(1228,plain,
    ! [A: v,B: set_V,C: v > v,D: v] :
      ( ( ~ ( member_V2 @ A @ B )
        | ( ( C @ A )
         != D ) )
     => ~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ D ) @ ( bNF_Gr_V_V2 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(96,axiom,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( insert481364471_V_nat @ A @ ( insert481364471_V_nat @ B @ C ) )
      = ( insert481364471_V_nat @ B @ ( insert481364471_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_insert__commute) ).

thf(651,plain,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( insert481364471_V_nat @ A @ ( insert481364471_V_nat @ B @ C ) )
      = ( insert481364471_V_nat @ B @ ( insert481364471_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(151,axiom,
    ! [A: set_Pr744279122od_V_V,B: produc1699571228od_V_V] :
      ( ( A = bot_bo667804902od_V_V )
     => ~ ( member1010391347od_V_V @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_equals0D) ).

thf(829,plain,
    ! [A: set_Pr744279122od_V_V,B: produc1699571228od_V_V] :
      ( ( A = bot_bo667804902od_V_V )
     => ~ ( member1010391347od_V_V @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(236,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ? [C: set_Pr1058435079_V_nat] :
          ( ( B
            = ( insert481364471_V_nat @ A @ C ) )
          & ~ ( member1886821968_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_mk__disjoint__insert) ).

thf(1095,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ? [C: set_Pr1058435079_V_nat] :
          ( ( B
            = ( insert481364471_V_nat @ A @ C ) )
          & ~ ( member1886821968_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(19,axiom,
    ! [A: v,B: set_V,C: set_V] :
      ( ( ~ ( member_V2 @ A @ B )
       => ( member_V2 @ A @ C ) )
     => ( member_V2 @ A @ ( sup_sup_set_V2 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_UnCI) ).

thf(389,plain,
    ! [A: v,B: set_V,C: set_V] :
      ( ( ~ ( member_V2 @ A @ B )
       => ( member_V2 @ A @ C ) )
     => ( member_V2 @ A @ ( sup_sup_set_V2 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(222,axiom,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( ~ ( member_V @ A @ B )
       => ( member_V @ A @ C ) )
     => ( member_V @ A @ ( sup_sup_set_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_UnCI) ).

thf(1055,plain,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( ~ ( member_V @ A @ B )
       => ( member_V @ A @ C ) )
     => ( member_V @ A @ ( sup_sup_set_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(138,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: labele2115946735nt_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
     => ( ( graph_1808119_V_V_V @ B @ C @ ( id_on_V2 @ ( labele1134902411nt_V_V @ B ) ) )
       => ( graph_1808119_V_V_V @ A @ C @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_subgraph__trans) ).

thf(785,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: labele2115946735nt_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
     => ( ( graph_1808119_V_V_V @ B @ C @ ( id_on_V2 @ ( labele1134902411nt_V_V @ B ) ) )
       => ( graph_1808119_V_V_V @ A @ C @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(13,axiom,
    ! [A: v2] :
      ~ ( member_V @ A @ bot_bot_set_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_emptyE) ).

thf(372,plain,
    ! [A: v2] :
      ~ ( member_V @ A @ bot_bot_set_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(285,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_singletonD) ).

thf(1264,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(85,axiom,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ C ) )
     => ( ( A != B )
       => ( member1010391347od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_insertE) ).

thf(619,plain,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ C ) )
     => ( ( A != B )
       => ( member1010391347od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(3,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( ~ ( member1010391347od_V_V @ A @ B )
       => ( member1010391347od_V_V @ A @ C ) )
     => ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_UnCI) ).

thf(344,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( ~ ( member1010391347od_V_V @ A @ B )
       => ( member1010391347od_V_V @ A @ C ) )
     => ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(189,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: product_prod_V_V,D: product_prod_V_V] :
      ( ( ( insert2024285275od_V_V @ A @ ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
        = ( insert2024285275od_V_V @ C @ ( insert2024285275od_V_V @ D @ bot_bo1389414743od_V_V ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_doubleton__eq__iff) ).

thf(949,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: product_prod_V_V,D: product_prod_V_V] :
      ( ( ( insert2024285275od_V_V @ A @ ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
        = ( insert2024285275od_V_V @ C @ ( insert2024285275od_V_V @ D @ bot_bo1389414743od_V_V ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(41,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ A @ B ) @ B )
      = ( sup_su1043134939_V_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_sup_Oright__idem) ).

thf(460,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ A @ B ) @ B )
      = ( sup_su1043134939_V_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(177,axiom,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ C ) )
      = ( ( A = B )
        | ( member1010391347od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_insert__iff) ).

thf(917,plain,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ C ) )
      = ( ( A = B )
        | ( member1010391347od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(126,axiom,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_singleton__iff) ).

thf(751,plain,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(300,axiom,
    ( ( mainta197426964_nat_V @ standa1319953089tant_V @ g )
    = ( ( labele1134902411nt_V_V @ g )
     != bot_bot_set_V2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85__092_060open_062maintained_Anonempty__rule_AG_H_A_061_A_Ivertices_AG_H_A_092_060noteq_062_A_123_125_J_092_060close_062) ).

thf(1313,plain,
    ( ( mainta197426964_nat_V @ standa1319953089tant_V @ g )
    = ( ( labele1134902411nt_V_V @ g )
     != bot_bot_set_V2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(290,axiom,
    ! [A: v2,B: v2] :
      ( ( ( standard_S_Const_V @ A )
        = ( standard_S_Const_V @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Standard__Constant_Oinject) ).

thf(1279,plain,
    ! [A: v2,B: v2] :
      ( ( ( standard_S_Const_V @ A )
        = ( standard_S_Const_V @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(183,axiom,
    ( ( standa1897115807ules_V @ bot_bot_set_V )
    = bot_bo907687539_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_constant__rules__empty) ).

thf(934,plain,
    ( ( standa1897115807ules_V @ bot_bot_set_V )
    = bot_bo907687539_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(7,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: set_Product_prod_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ C )
     => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_extensible__refl) ).

thf(357,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: set_Product_prod_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ C )
     => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(223,axiom,
    ! [A: v] : ( member_V2 @ A @ ( insert_V2 @ A @ bot_bot_set_V2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_singletonI) ).

thf(1059,plain,
    ! [A: v] : ( member_V2 @ A @ ( insert_V2 @ A @ bot_bot_set_V2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(248,axiom,
    ! [A: product_prod_V_V] : ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_singletonI) ).

thf(1132,plain,
    ! [A: product_prod_V_V] : ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(172,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_UnI2) ).

thf(902,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(233,axiom,
    ( ( id_on_558037444_V_nat @ bot_bo907687539_V_nat )
    = bot_bo2057106227_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Id__on__empty) ).

thf(1087,plain,
    ( ( id_on_558037444_V_nat @ bot_bo907687539_V_nat )
    = bot_bo2057106227_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(253,axiom,
    ! [A: v,B: v,C: set_V,D: v > v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( bNF_Gr_V_V2 @ C @ D ) )
     => ( member_V2 @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_GrD1) ).

thf(1147,plain,
    ! [A: v,B: v,C: set_V,D: v > v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( bNF_Gr_V_V2 @ C @ D ) )
     => ( member_V2 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(167,axiom,
    ! [A: v,B: set_V,C: v] :
      ( ( ~ ( member_V2 @ A @ B )
       => ( A = C ) )
     => ( member_V2 @ A @ ( insert_V2 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_insertCI) ).

thf(881,plain,
    ! [A: v,B: set_V,C: v] :
      ( ( ~ ( member_V2 @ A @ B )
       => ( A = C ) )
     => ( member_V2 @ A @ ( insert_V2 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(237,axiom,
    ! [A: labele2115946735nt_V_V] :
      ( ( labele712009229nt_V_V @ ( labele515735386nt_V_V @ A ) @ ( labele1134902411nt_V_V @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_labeled__graph_Ocollapse) ).

thf(1100,plain,
    ! [A: labele2115946735nt_V_V] :
      ( ( labele712009229nt_V_V @ ( labele515735386nt_V_V @ A ) @ ( labele1134902411nt_V_V @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(194,axiom,
    ! [A: v,B: v] :
      ( ( member_V2 @ A @ ( insert_V2 @ B @ bot_bot_set_V2 ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_singleton__iff) ).

thf(969,plain,
    ! [A: v,B: v] :
      ( ( member_V2 @ A @ ( insert_V2 @ B @ bot_bot_set_V2 ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(83,axiom,
    ! [A: v] :
      ~ ( member_V2 @ A @ bot_bot_set_V2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_empty__iff) ).

thf(606,plain,
    ! [A: v] :
      ~ ( member_V2 @ A @ bot_bot_set_V2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(51,axiom,
    ! [A: set_Pr744279122od_V_V,B: set_V] :
      ( ( labele515735386nt_V_V @ ( labele712009229nt_V_V @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_labeled__graph_Osel_I1_J) ).

thf(492,plain,
    ! [A: set_Pr744279122od_V_V,B: set_V] :
      ( ( labele515735386nt_V_V @ ( labele712009229nt_V_V @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(297,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( A = B )
     => ( ( member2015049524od_V_V @ A @ C )
       => ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ B ) @ ( id_on_2125509800od_V_V @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Id__on__eqI) ).

thf(1302,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( A = B )
     => ( ( member2015049524od_V_V @ A @ C )
       => ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ B ) @ ( id_on_2125509800od_V_V @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(80,axiom,
    ! [A: produc1699571228od_V_V > $o,B: produc1699571228od_V_V] :
      ( ! [C: standard_Constant_V,D: product_prod_V_V] : ( A @ ( produc107991630od_V_V @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_old_Oprod_Oinducts) ).

thf(591,plain,
    ! [A: produc1699571228od_V_V > $o,B: produc1699571228od_V_V] :
      ( ! [C: standard_Constant_V,D: product_prod_V_V] : ( A @ ( produc107991630od_V_V @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(316,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] : ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_insertI1) ).

thf(1373,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] : ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(152,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_insertI2) ).

thf(834,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(193,axiom,
    ! [A: set_Pr744279122od_V_V,B: set_V] :
      ( ( labele1134902411nt_V_V @ ( labele712009229nt_V_V @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_labeled__graph_Osel_I2_J) ).

thf(966,plain,
    ! [A: set_Pr744279122od_V_V,B: set_V] :
      ( ( labele1134902411nt_V_V @ ( labele712009229nt_V_V @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(148,axiom,
    ! [A: set_Product_prod_V_V] :
      ( ( sup_su551882943od_V_V @ bot_bo1389414743od_V_V @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_Un__empty__left) ).

thf(821,plain,
    ! [A: set_Product_prod_V_V] :
      ( ( sup_su551882943od_V_V @ bot_bo1389414743od_V_V @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(4,axiom,
    ! [A: v,B: set_V,C: set_V] :
      ( ( member_V2 @ A @ ( sup_sup_set_V2 @ B @ C ) )
      = ( ( member_V2 @ A @ B )
        | ( member_V2 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Un__iff) ).

thf(348,plain,
    ! [A: v,B: set_V,C: set_V] :
      ( ( member_V2 @ A @ ( sup_sup_set_V2 @ B @ C ) )
      = ( ( member_V2 @ A @ B )
        | ( member_V2 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(75,axiom,
    ! [A: labele2115946735nt_V_V] :
      ( ( restri1305980611nt_V_V @ ( restri1305980611nt_V_V @ A ) )
      = ( restri1305980611nt_V_V @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_restrict__idemp) ).

thf(574,plain,
    ! [A: labele2115946735nt_V_V] :
      ( ( restri1305980611nt_V_V @ ( restri1305980611nt_V_V @ A ) )
      = ( restri1305980611nt_V_V @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(173,axiom,
    ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( bot_bo1389414743od_V_V
        = ( sup_su551882943od_V_V @ A @ B ) )
      = ( ( A = bot_bo1389414743od_V_V )
        & ( B = bot_bo1389414743od_V_V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_sup__bot_Oneutr__eq__iff) ).

thf(905,plain,
    ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( bot_bo1389414743od_V_V
        = ( sup_su551882943od_V_V @ A @ B ) )
      = ( ( A = bot_bo1389414743od_V_V )
        & ( B = bot_bo1389414743od_V_V ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(47,axiom,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: standard_Constant_V,D: product_prod_V_V] :
      ( ( ( produc107991630od_V_V @ A @ B )
        = ( produc107991630od_V_V @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_prod_Oinject) ).

thf(480,plain,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: standard_Constant_V,D: product_prod_V_V] :
      ( ( ( produc107991630od_V_V @ A @ B )
        = ( produc107991630od_V_V @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(318,axiom,
    ! [A: v,B: v,C: set_V,D: v > v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( bNF_Gr_V_V2 @ C @ D ) )
     => ( ( D @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_GrD2) ).

thf(1377,plain,
    ! [A: v,B: v,C: set_V,D: v > v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( bNF_Gr_V_V2 @ C @ D ) )
     => ( ( D @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(90,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( ( insert135842892od_V_V @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_insert__absorb) ).

thf(634,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( ( insert135842892od_V_V @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(228,axiom,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ B ) @ ( id_on_1491482303od_V_V @ C ) )
      = ( ( A = B )
        & ( member1010391347od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Id__on__iff) ).

thf(1072,plain,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ B ) @ ( id_on_1491482303od_V_V @ C ) )
      = ( ( A = B )
        & ( member1010391347od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(243,axiom,
    ! [A: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( standa1568205529ules_V @ l ) )
     => ( mainta197426964_nat_V @ A @ g ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129__092_060open_062maintainedA_A_Iidentity__rules_AL_J_AG_H_092_060close_062) ).

thf(1119,plain,
    ! [A: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( standa1568205529ules_V @ l ) )
     => ( mainta197426964_nat_V @ A @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(325,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ~ ! [C: set_Product_prod_V_V] :
            ( ( B
              = ( insert2024285275od_V_V @ A @ C ) )
           => ( member2015049524od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_Set_Oset__insert) ).

thf(1394,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ~ ! [C: set_Product_prod_V_V] :
            ( ( B
              = ( insert2024285275od_V_V @ A @ C ) )
           => ( member2015049524od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(312,axiom,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( product_Pair_V_V2 @ A @ B )
        = ( product_Pair_V_V2 @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Pair__inject) ).

thf(1351,plain,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( product_Pair_V_V2 @ A @ B )
        = ( product_Pair_V_V2 @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(98,axiom,
    ! [A: labele2115946735nt_V_V,B: v > v,C: v > v] :
      ( ! [D: v] :
          ( ( member_V2 @ D @ ( labele1134902411nt_V_V @ A ) )
         => ( ( B @ D )
            = ( C @ D ) ) )
     => ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A )
        = ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_map__graph__fn__eqI) ).

thf(660,plain,
    ! [A: labele2115946735nt_V_V,B: v > v,C: v > v] :
      ( ! [D: v] :
          ( ( member_V2 @ D @ ( labele1134902411nt_V_V @ A ) )
         => ( ( B @ D )
            = ( C @ D ) ) )
     => ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A )
        = ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(200,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_sup__idem) ).

thf(988,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(336,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ B @ C ) )
      = ( ( member2015049524od_V_V @ A @ B )
        | ( member2015049524od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Un__iff) ).

thf(1433,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ B @ C ) )
      = ( ( member2015049524od_V_V @ A @ B )
        | ( member2015049524od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(268,axiom,
    ! [A: standard_Constant_V,B: v,C: v] :
      ( ( labele712009229nt_V_V @ ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ bot_bo667804902od_V_V ) @ ( insert_V2 @ B @ ( insert_V2 @ C @ bot_bot_set_V2 ) ) )
      = ( restri1305980611nt_V_V @ ( labele712009229nt_V_V @ ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ bot_bo667804902od_V_V ) @ ( insert_V2 @ B @ ( insert_V2 @ C @ bot_bot_set_V2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_graph__single) ).

thf(1201,plain,
    ! [A: standard_Constant_V,B: v,C: v] :
      ( ( labele712009229nt_V_V @ ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ bot_bo667804902od_V_V ) @ ( insert_V2 @ B @ ( insert_V2 @ C @ bot_bot_set_V2 ) ) )
      = ( restri1305980611nt_V_V @ ( labele712009229nt_V_V @ ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ bot_bo667804902od_V_V ) @ ( insert_V2 @ B @ ( insert_V2 @ C @ bot_bot_set_V2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(198,axiom,
    ! [A: v,B: set_V,C: set_V] :
      ( ~ ( member_V2 @ A @ B )
     => ( ~ ( member_V2 @ A @ C )
       => ( ( ( insert_V2 @ A @ B )
            = ( insert_V2 @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_insert__ident) ).

thf(981,plain,
    ! [A: v,B: set_V,C: set_V] :
      ( ~ ( member_V2 @ A @ B )
     => ( ~ ( member_V2 @ A @ C )
       => ( ( ( insert_V2 @ A @ B )
            = ( insert_V2 @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(132,axiom,
    ! [A: set_V2] :
      ( ( collect_V
        @ ^ [B: v2] : ( member_V @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Collect__mem__eq) ).

thf(766,plain,
    ! [A: set_V2] :
      ( ( collect_V
        @ ^ [B: v2] : ( member_V @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(21,axiom,
    ! [A: set_V2] :
      ( ( ? [B: v2] : ( member_V @ B @ A ) )
      = ( A != bot_bot_set_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_ex__in__conv) ).

thf(397,plain,
    ! [A: set_V2] :
      ( ( ? [B: v2] : ( member_V @ B @ A ) )
      = ( A != bot_bot_set_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(106,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( ? [B: produc778275879_V_nat] : ( member1886821968_V_nat @ B @ A ) )
      = ( A != bot_bo907687539_V_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_ex__in__conv) ).

thf(687,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( ? [B: produc778275879_V_nat] : ( member1886821968_V_nat @ B @ A ) )
      = ( A != bot_bo907687539_V_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(178,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: labele2115946735nt_V_V,D: set_Product_prod_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
     => ( ( graph_1808119_V_V_V @ C @ A @ D )
       => ( graph_1808119_V_V_V @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_subgraph__preserves__hom) ).

thf(920,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: labele2115946735nt_V_V,D: set_Product_prod_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
     => ( ( graph_1808119_V_V_V @ C @ A @ D )
       => ( graph_1808119_V_V_V @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(62,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ~ ( member1886821968_V_nat @ A @ B )
     => ( ~ ( member1886821968_V_nat @ A @ C )
       => ( ( ( insert481364471_V_nat @ A @ B )
            = ( insert481364471_V_nat @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_insert__ident) ).

thf(529,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ~ ( member1886821968_V_nat @ A @ B )
     => ( ~ ( member1886821968_V_nat @ A @ C )
       => ( ( ( insert481364471_V_nat @ A @ B )
            = ( insert481364471_V_nat @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(338,axiom,
    ! [A: v,B: v,C: set_V] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( id_on_V2 @ C ) )
      = ( ( A = B )
        & ( member_V2 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Id__on__iff) ).

thf(1438,plain,
    ! [A: v,B: v,C: set_V] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( id_on_V2 @ C ) )
      = ( ( A = B )
        & ( member_V2 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(255,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( ~ ( member2015049524od_V_V @ A @ B )
       => ( member2015049524od_V_V @ A @ C ) )
     => ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_UnCI) ).

thf(1153,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( ~ ( member2015049524od_V_V @ A @ B )
       => ( member2015049524od_V_V @ A @ C ) )
     => ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(11,axiom,
    ! [A: set_V] :
      ( ( sup_sup_set_V2 @ bot_bot_set_V2 @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_sup__bot_Oleft__neutral) ).

thf(366,plain,
    ! [A: set_V] :
      ( ( sup_sup_set_V2 @ bot_bot_set_V2 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(124,axiom,
    ! [A: produc1699571228od_V_V] :
      ~ ( member1010391347od_V_V @ A @ bot_bo667804902od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_empty__iff) ).

thf(746,plain,
    ! [A: produc1699571228od_V_V] :
      ~ ( member1010391347od_V_V @ A @ bot_bo667804902od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(136,axiom,
    ! [A: v,B: set_V] : ( member_V2 @ A @ ( insert_V2 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_insertI1) ).

thf(778,plain,
    ! [A: v,B: set_V] : ( member_V2 @ A @ ( insert_V2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(108,axiom,
    ! [A: labele2115946735nt_V_V] :
      ( ( graph_1808119_V_V_V @ A @ A @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
      = ( A
        = ( restri1305980611nt_V_V @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_subgraph__refl) ).

thf(693,plain,
    ! [A: labele2115946735nt_V_V] :
      ( ( graph_1808119_V_V_V @ A @ A @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
      = ( A
        = ( restri1305980611nt_V_V @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(31,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: labele2115946735nt_V_V,D: set_Product_prod_V_V] :
      ( ( mainta1699210777_V_V_V @ ( produc533118295nt_V_V @ A @ B ) @ C )
     => ( ( graph_1808119_V_V_V @ A @ C @ D )
       => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A @ B ) @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_maintainedD) ).

thf(429,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: labele2115946735nt_V_V,D: set_Product_prod_V_V] :
      ( ( mainta1699210777_V_V_V @ ( produc533118295nt_V_V @ A @ B ) @ C )
     => ( ( graph_1808119_V_V_V @ A @ C @ D )
       => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A @ B ) @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(139,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat,D: set_Pr1058435079_V_nat] :
      ( ~ ( member1886821968_V_nat @ A @ B )
     => ( ~ ( member1886821968_V_nat @ C @ D )
       => ( ( ( insert481364471_V_nat @ A @ B )
            = ( insert481364471_V_nat @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Pr1058435079_V_nat] :
                  ( ( B
                    = ( insert481364471_V_nat @ C @ E ) )
                  & ~ ( member1886821968_V_nat @ C @ E )
                  & ( D
                    = ( insert481364471_V_nat @ A @ E ) )
                  & ~ ( member1886821968_V_nat @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_insert__eq__iff) ).

thf(788,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat,D: set_Pr1058435079_V_nat] :
      ( ~ ( member1886821968_V_nat @ A @ B )
     => ( ~ ( member1886821968_V_nat @ C @ D )
       => ( ( ( insert481364471_V_nat @ A @ B )
            = ( insert481364471_V_nat @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Pr1058435079_V_nat] :
                  ( ( B
                    = ( insert481364471_V_nat @ C @ E ) )
                  & ~ ( member1886821968_V_nat @ C @ E )
                  & ( D
                    = ( insert481364471_V_nat @ A @ E ) )
                  & ~ ( member1886821968_V_nat @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(146,axiom,
    ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( ( sup_su551882943od_V_V @ A @ B )
        = bot_bo1389414743od_V_V )
      = ( ( A = bot_bo1389414743od_V_V )
        & ( B = bot_bo1389414743od_V_V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Un__empty) ).

thf(815,plain,
    ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( ( sup_su551882943od_V_V @ A @ B )
        = bot_bo1389414743od_V_V )
      = ( ( A = bot_bo1389414743od_V_V )
        & ( B = bot_bo1389414743od_V_V ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(218,axiom,
    ! [A: v,B: set_V] :
      ( ( insert_V2 @ A @ B )
     != bot_bot_set_V2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_insert__not__empty) ).

thf(1042,plain,
    ! [A: v,B: set_V] :
      ( ( insert_V2 @ A @ B )
     != bot_bot_set_V2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(190,axiom,
    ! [A: labele2115946735nt_V_V,B: v > v,C: v > v,D: produc778275879_V_nat] :
      ( ! [E: v] :
          ( ( member_V2 @ E @ ( labele1134902411nt_V_V @ A ) )
         => ( ( comp_V_V_V2 @ B @ C @ E )
            = E ) )
     => ( ( A
          = ( restri1305980611nt_V_V @ A ) )
       => ( ( mainta197426964_nat_V @ D @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ C ) @ A ) )
         => ( mainta197426964_nat_V @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_maintained__preserved__by__isomorphism) ).

thf(952,plain,
    ! [A: labele2115946735nt_V_V,B: v > v,C: v > v,D: produc778275879_V_nat] :
      ( ! [E: v] :
          ( ( member_V2 @ E @ ( labele1134902411nt_V_V @ A ) )
         => ( ( comp_V_V_V2 @ B @ C @ E )
            = E ) )
     => ( ( A
          = ( restri1305980611nt_V_V @ A ) )
       => ( ( mainta197426964_nat_V @ D @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ C ) @ A ) )
         => ( mainta197426964_nat_V @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(43,axiom,
    ! [A: produc778275879_V_nat > $o] :
      ( ( bot_bo907687539_V_nat
        = ( collec1411521682_V_nat @ A ) )
      = ( ! [B: produc778275879_V_nat] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_empty__Collect__eq) ).

thf(467,plain,
    ! [A: produc778275879_V_nat > $o] :
      ( ( bot_bo907687539_V_nat
        = ( collec1411521682_V_nat @ A ) )
      = ( ! [B: produc778275879_V_nat] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(314,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ C ) )
     => ( ( A != B )
       => ( member2015049524od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_insertE) ).

thf(1365,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ C ) )
     => ( ( A != B )
       => ( member2015049524od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(87,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ ( insert481364471_V_nat @ A @ B ) @ C )
      = ( insert481364471_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Un__insert__left) ).

thf(625,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ ( insert481364471_V_nat @ A @ B ) @ C )
      = ( insert481364471_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(33,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_UnI2) ).

thf(435,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(60,axiom,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: set_St1111633946tant_V,D: standard_Constant_V > product_prod_V_V] :
      ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ B ) @ ( bNF_Gr320641027od_V_V @ C @ D ) )
     => ( member1542015739tant_V @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_GrD1) ).

thf(522,plain,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: set_St1111633946tant_V,D: standard_Constant_V > product_prod_V_V] :
      ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ B ) @ ( bNF_Gr320641027od_V_V @ C @ D ) )
     => ( member1542015739tant_V @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(128,axiom,
    ! [A: labele2115946735nt_V_V] : ( graph_1808119_V_V_V @ ( restri1305980611nt_V_V @ A ) @ ( restri1305980611nt_V_V @ A ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_graph__homomorphism__Id) ).

thf(757,plain,
    ! [A: labele2115946735nt_V_V] : ( graph_1808119_V_V_V @ ( restri1305980611nt_V_V @ A ) @ ( restri1305980611nt_V_V @ A ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(69,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( insert481364471_V_nat @ A @ B )
     != bot_bo907687539_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_insert__not__empty) ).

thf(551,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( insert481364471_V_nat @ A @ B )
     != bot_bo907687539_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(324,axiom,
    ! [A: v2] :
      ( ( member_V @ A @ c )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ A ) @ ( m @ A ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ A ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_m) ).

thf(1392,plain,
    ! [A: v2] :
      ( ( member_V @ A @ c )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ A ) @ ( m @ A ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ A ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(155,axiom,
    ! [A: v,B: set_V,C: set_V] :
      ( ( ( insert_V2 @ A @ bot_bot_set_V2 )
        = ( sup_sup_set_V2 @ B @ C ) )
      = ( ( ( B = bot_bot_set_V2 )
          & ( C
            = ( insert_V2 @ A @ bot_bot_set_V2 ) ) )
        | ( ( B
            = ( insert_V2 @ A @ bot_bot_set_V2 ) )
          & ( C = bot_bot_set_V2 ) )
        | ( ( B
            = ( insert_V2 @ A @ bot_bot_set_V2 ) )
          & ( C
            = ( insert_V2 @ A @ bot_bot_set_V2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_singleton__Un__iff) ).

thf(842,plain,
    ! [A: v,B: set_V,C: set_V] :
      ( ( ( insert_V2 @ A @ bot_bot_set_V2 )
        = ( sup_sup_set_V2 @ B @ C ) )
      = ( ( ( B = bot_bot_set_V2 )
          & ( C
            = ( insert_V2 @ A @ bot_bot_set_V2 ) ) )
        | ( ( B
            = ( insert_V2 @ A @ bot_bot_set_V2 ) )
          & ( C = bot_bot_set_V2 ) )
        | ( ( B
            = ( insert_V2 @ A @ bot_bot_set_V2 ) )
          & ( C
            = ( insert_V2 @ A @ bot_bot_set_V2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(196,axiom,
    ! [A: produc1699571228od_V_V] :
      ~ ! [B: standard_Constant_V,C: product_prod_V_V] :
          ( A
         != ( produc107991630od_V_V @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_old_Oprod_Oexhaust) ).

thf(974,plain,
    ! [A: produc1699571228od_V_V] :
      ~ ! [B: standard_Constant_V,C: product_prod_V_V] :
          ( A
         != ( produc107991630od_V_V @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(104,axiom,
    ( insert481364471_V_nat
    = ( ^ [A: produc778275879_V_nat] : ( sup_su1043134939_V_nat @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insert__is__Un) ).

thf(682,plain,
    ( insert481364471_V_nat
    = ( ^ [A: produc778275879_V_nat] : ( sup_su1043134939_V_nat @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(328,axiom,
    ! [A: v2] :
      ( standard_S_Top_V
     != ( standard_S_Const_V @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Standard__Constant_Odistinct_I5_J) ).

thf(1407,plain,
    ! [A: v2] :
      ( standard_S_Top_V
     != ( standard_S_Const_V @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(294,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_UnI1) ).

thf(1291,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(114,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
      = ( ( A
          = ( restri1305980611nt_V_V @ A ) )
        & ( B
          = ( restri1305980611nt_V_V @ B ) )
        & ( ( graph_1141886696nt_V_V @ A @ B )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_subgraph__def) ).

thf(710,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
      = ( ( A
          = ( restri1305980611nt_V_V @ A ) )
        & ( B
          = ( restri1305980611nt_V_V @ B ) )
        & ( ( graph_1141886696nt_V_V @ A @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(59,axiom,
    ! [A: produc1699571228od_V_V] :
      ~ ( member1010391347od_V_V @ A @ bot_bo667804902od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_emptyE) ).

thf(519,plain,
    ! [A: produc1699571228od_V_V] :
      ~ ( member1010391347od_V_V @ A @ bot_bo667804902od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(234,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Un__empty__left) ).

thf(1089,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(251,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_UnI2) ).

thf(1143,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(206,axiom,
    ! [A: set_Product_prod_V_V] :
      ( ( sup_su551882943od_V_V @ A @ bot_bo1389414743od_V_V )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_Un__empty__right) ).

thf(1006,plain,
    ! [A: set_Product_prod_V_V] :
      ( ( sup_su551882943od_V_V @ A @ bot_bo1389414743od_V_V )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(28,axiom,
    ! [A: v2] :
      ~ ( member_V @ A @ bot_bot_set_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_empty__iff) ).

thf(420,plain,
    ! [A: v2] :
      ~ ( member_V @ A @ bot_bot_set_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(160,axiom,
    ! [A: product_prod_V_V > $o] :
      ( ( ( collec2040633974od_V_V @ A )
        = bot_bo1389414743od_V_V )
      = ( ! [B: product_prod_V_V] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Collect__empty__eq) ).

thf(857,plain,
    ! [A: product_prod_V_V > $o] :
      ( ( ( collec2040633974od_V_V @ A )
        = bot_bo1389414743od_V_V )
      = ( ! [B: product_prod_V_V] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(317,axiom,
    ( ( m @ xa )
    = ( m @ y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__C1_C_I3_J) ).

thf(1375,plain,
    ( ( m @ xa )
    = ( m @ y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(244,axiom,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: standard_Constant_V,D: labele201426742od_V_V,E: produc1699571228od_V_V > v] :
      ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ B ) @ ( getRel2057312683od_V_V @ C @ D ) )
     => ( ( member1010391347od_V_V @ A @ ( labele1328382418od_V_V @ D ) )
       => ( ( member1010391347od_V_V @ B @ ( labele1328382418od_V_V @ D ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ A ) @ ( E @ B ) ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ D ) @ E ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_getRel__hom) ).

thf(1121,plain,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: standard_Constant_V,D: labele201426742od_V_V,E: produc1699571228od_V_V > v] :
      ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ B ) @ ( getRel2057312683od_V_V @ C @ D ) )
     => ( ( member1010391347od_V_V @ A @ ( labele1328382418od_V_V @ D ) )
       => ( ( member1010391347od_V_V @ B @ ( labele1328382418od_V_V @ D ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ A ) @ ( E @ B ) ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ D ) @ E ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(313,axiom,
    ! [A: produc1699571228od_V_V] :
      ~ ! [B: standard_Constant_V,C: v,D: v] :
          ( A
         != ( produc107991630od_V_V @ B @ ( product_Pair_V_V2 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_prod__cases3) ).

thf(1361,plain,
    ! [A: produc1699571228od_V_V] :
      ~ ! [B: standard_Constant_V,C: v,D: v] :
          ( A
         != ( produc107991630od_V_V @ B @ ( product_Pair_V_V2 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(64,axiom,
    ! [A: set_Product_prod_V_V] :
      ( ( sup_su551882943od_V_V @ A @ bot_bo1389414743od_V_V )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_sup__bot_Oright__neutral) ).

thf(537,plain,
    ! [A: set_Product_prod_V_V] :
      ( ( sup_su551882943od_V_V @ A @ bot_bo1389414743od_V_V )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(330,axiom,
    ? [A: v2 > v] :
    ! [B: v2] :
      ( ( member_V @ B @ c )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( A @ B ) @ ( A @ B ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ B ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).

thf(1414,plain,
    ? [A: v2 > v] :
    ! [B: v2] :
      ( ( member_V @ B @ c )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( A @ B ) @ ( A @ B ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ B ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(91,axiom,
    ! [A: set_V] :
      ( ( ? [B: v] : ( member_V2 @ B @ A ) )
      = ( A != bot_bot_set_V2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_ex__in__conv) ).

thf(637,plain,
    ! [A: set_V] :
      ( ( ? [B: v] : ( member_V2 @ B @ A ) )
      = ( A != bot_bot_set_V2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(50,axiom,
    ! [A: set_V] :
      ( ( collect_V2
        @ ^ [B: v] : ( member_V2 @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Collect__mem__eq) ).

thf(489,plain,
    ! [A: set_V] :
      ( ( collect_V2
        @ ^ [B: v] : ( member_V2 @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(332,axiom,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( product_Pair_V_V2 @ A @ B )
        = ( product_Pair_V_V2 @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_old_Oprod_Oinject) ).

thf(1419,plain,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( product_Pair_V_V2 @ A @ B )
        = ( product_Pair_V_V2 @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(213,axiom,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: set_St1111633946tant_V,D: standard_Constant_V > product_prod_V_V] :
      ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ B ) @ ( bNF_Gr320641027od_V_V @ C @ D ) )
     => ( ( D @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_GrD2) ).

thf(1028,plain,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: set_St1111633946tant_V,D: standard_Constant_V > product_prod_V_V] :
      ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ B ) @ ( bNF_Gr320641027od_V_V @ C @ D ) )
     => ( ( D @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(231,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] : ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_insertI1) ).

thf(1082,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] : ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(229,axiom,
    ! [A: set_V,B: v] :
      ( ( A = bot_bot_set_V2 )
     => ~ ( member_V2 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_equals0D) ).

thf(1075,plain,
    ! [A: set_V,B: v] :
      ( ( A = bot_bot_set_V2 )
     => ~ ( member_V2 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(46,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: produc1699571228od_V_V,D: set_Pr744279122od_V_V] :
      ( ~ ( member1010391347od_V_V @ A @ B )
     => ( ~ ( member1010391347od_V_V @ C @ D )
       => ( ( ( insert135842892od_V_V @ A @ B )
            = ( insert135842892od_V_V @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Pr744279122od_V_V] :
                  ( ( B
                    = ( insert135842892od_V_V @ C @ E ) )
                  & ~ ( member1010391347od_V_V @ C @ E )
                  & ( D
                    = ( insert135842892od_V_V @ A @ E ) )
                  & ~ ( member1010391347od_V_V @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_insert__eq__iff) ).

thf(476,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: produc1699571228od_V_V,D: set_Pr744279122od_V_V] :
      ( ~ ( member1010391347od_V_V @ A @ B )
     => ( ~ ( member1010391347od_V_V @ C @ D )
       => ( ( ( insert135842892od_V_V @ A @ B )
            = ( insert135842892od_V_V @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Pr744279122od_V_V] :
                  ( ( B
                    = ( insert135842892od_V_V @ C @ E ) )
                  & ~ ( member1010391347od_V_V @ C @ E )
                  & ( D
                    = ( insert135842892od_V_V @ A @ E ) )
                  & ~ ( member1010391347od_V_V @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(103,axiom,
    ! [A: set_Pr744279122od_V_V] :
      ( ( ! [B: produc1699571228od_V_V] :
            ~ ( member1010391347od_V_V @ B @ A ) )
      = ( A = bot_bo667804902od_V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_all__not__in__conv) ).

thf(679,plain,
    ! [A: set_Pr744279122od_V_V] :
      ( ( ! [B: produc1699571228od_V_V] :
            ~ ( member1010391347od_V_V @ B @ A ) )
      = ( A = bot_bo667804902od_V_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(217,axiom,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat] :
      ( ( ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat )
        = ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_singleton__inject) ).

thf(1039,plain,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat] :
      ( ( ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat )
        = ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(199,axiom,
    ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V,C: product_prod_V_V] :
      ( ( ( sup_su551882943od_V_V @ A @ B )
        = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) )
      = ( ( ( A = bot_bo1389414743od_V_V )
          & ( B
            = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) ) )
        | ( ( A
            = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) )
          & ( B = bot_bo1389414743od_V_V ) )
        | ( ( A
            = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) )
          & ( B
            = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Un__singleton__iff) ).

thf(985,plain,
    ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V,C: product_prod_V_V] :
      ( ( ( sup_su551882943od_V_V @ A @ B )
        = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) )
      = ( ( ( A = bot_bo1389414743od_V_V )
          & ( B
            = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) ) )
        | ( ( A
            = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) )
          & ( B = bot_bo1389414743od_V_V ) )
        | ( ( A
            = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) )
          & ( B
            = ( insert2024285275od_V_V @ C @ bot_bo1389414743od_V_V ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(111,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_sup_Oidem) ).

thf(701,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(296,axiom,
    ! [A: set_Product_prod_V_V,B: product_prod_V_V] :
      ( ( A = bot_bo1389414743od_V_V )
     => ~ ( member2015049524od_V_V @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_equals0D) ).

thf(1297,plain,
    ! [A: set_Product_prod_V_V,B: product_prod_V_V] :
      ( ( A = bot_bo1389414743od_V_V )
     => ~ ( member2015049524od_V_V @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(121,axiom,
    ! [A: labele2115946735nt_V_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( mainta197426964_nat_V @ standa1319953089tant_V @ A )
        = ( ( labele1134902411nt_V_V @ A )
         != bot_bot_set_V2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_nonempty__rule) ).

thf(738,plain,
    ! [A: labele2115946735nt_V_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( mainta197426964_nat_V @ standa1319953089tant_V @ A )
        = ( ( labele1134902411nt_V_V @ A )
         != bot_bot_set_V2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(320,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V > $o] :
      ( ( member2015049524od_V_V @ A @ ( collec2040633974od_V_V @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mem__Collect__eq) ).

thf(1382,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V > $o] :
      ( ( member2015049524od_V_V @ A @ ( collec2040633974od_V_V @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(97,axiom,
    ! [A: labele2115946735nt_V_V,B: v > v,C: produc778275879_V_nat] :
      ( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) @ A @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) ) ) )
     => ( ! [D: v] :
            ( ( member_V2 @ D @ ( labele1134902411nt_V_V @ A ) )
           => ( ( comp_V_V_V2 @ B @ B @ D )
              = ( B @ D ) ) )
       => ( ( mainta197426964_nat_V @ C @ A )
         => ( mainta197426964_nat_V @ C @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_idemp__embedding__maintained__preserved) ).

thf(654,plain,
    ! [A: labele2115946735nt_V_V,B: v > v,C: produc778275879_V_nat] :
      ( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) @ A @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) ) ) )
     => ( ! [D: v] :
            ( ( member_V2 @ D @ ( labele1134902411nt_V_V @ A ) )
           => ( ( comp_V_V_V2 @ B @ B @ D )
              = ( B @ D ) ) )
       => ( ( mainta197426964_nat_V @ C @ A )
         => ( mainta197426964_nat_V @ C @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(40,axiom,
    ! [A: standard_Constant_V,B: set_St1111633946tant_V,C: standard_Constant_V > product_prod_V_V] :
      ( ( bNF_Gr320641027od_V_V @ ( insert1818834324tant_V @ A @ B ) @ C )
      = ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( C @ A ) ) @ ( bNF_Gr320641027od_V_V @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Gr__insert) ).

thf(457,plain,
    ! [A: standard_Constant_V,B: set_St1111633946tant_V,C: standard_Constant_V > product_prod_V_V] :
      ( ( bNF_Gr320641027od_V_V @ ( insert1818834324tant_V @ A @ B ) @ C )
      = ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( C @ A ) ) @ ( bNF_Gr320641027od_V_V @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(175,axiom,
    ! [A: labele236903175od_V_V] :
      ( ( A
        = ( restri1502575645od_V_V @ A ) )
     => ( ( mainta1984786828od_V_V @ standa1319953089tant_V @ A )
        = ( ( labele981584981od_V_V @ A )
         != bot_bo1389414743od_V_V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_nonempty__rule) ).

thf(911,plain,
    ! [A: labele236903175od_V_V] :
      ( ( A
        = ( restri1502575645od_V_V @ A ) )
     => ( ( mainta1984786828od_V_V @ standa1319953089tant_V @ A )
        = ( ( labele981584981od_V_V @ A )
         != bot_bo1389414743od_V_V ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(55,axiom,
    ! [A: labele2115946735nt_V_V] :
      ( ( map_gr907434255tant_V @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) @ A )
      = ( restri1305980611nt_V_V @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_map__graph__fn__id_I2_J) ).

thf(503,plain,
    ! [A: labele2115946735nt_V_V] :
      ( ( map_gr907434255tant_V @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) @ A )
      = ( restri1305980611nt_V_V @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(86,axiom,
    ! [A: v,B: set_V,C: v] :
      ( ( member_V2 @ A @ B )
     => ( member_V2 @ A @ ( insert_V2 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_insertI2) ).

thf(622,plain,
    ! [A: v,B: set_V,C: v] :
      ( ( member_V2 @ A @ B )
     => ( member_V2 @ A @ ( insert_V2 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(153,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) )
     => ( ~ ( member1886821968_V_nat @ A @ B )
       => ( member1886821968_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_UnE) ).

thf(837,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) )
     => ( ~ ( member1886821968_V_nat @ A @ B )
       => ( member1886821968_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(304,axiom,
    member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).

thf(1324,plain,
    member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(20,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: labele2115946735nt_V_V] :
      ( ! [D: set_Product_prod_V_V] :
          ( ( graph_1808119_V_V_V @ A @ B @ D )
         => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A @ C ) @ B @ D ) )
     => ( mainta1699210777_V_V_V @ ( produc533118295nt_V_V @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_maintainedI) ).

thf(393,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: labele2115946735nt_V_V] :
      ( ! [D: set_Product_prod_V_V] :
          ( ( graph_1808119_V_V_V @ A @ B @ D )
         => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A @ C ) @ B @ D ) )
     => ( mainta1699210777_V_V_V @ ( produc533118295nt_V_V @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(284,axiom,
    mainta197426964_nat_V @ standa1319953089tant_V @ g,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_ne) ).

thf(1263,plain,
    mainta197426964_nat_V @ standa1319953089tant_V @ g,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(203,axiom,
    standard_S_Top_V != standard_S_Bot_V,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Standard__Constant_Odistinct_I1_J) ).

thf(997,plain,
    standard_S_Top_V != standard_S_Bot_V,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(58,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( B
          = ( restri1305980611nt_V_V @ B ) )
       => ( ( graph_1141886696nt_V_V @ A @ B )
          = ( restri1305980611nt_V_V @ ( graph_1141886696nt_V_V @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_graph__union__preserves__restrict) ).

thf(515,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( B
          = ( restri1305980611nt_V_V @ B ) )
       => ( ( graph_1141886696nt_V_V @ A @ B )
          = ( restri1305980611nt_V_V @ ( graph_1141886696nt_V_V @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(254,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: v,D: v,E: allego859987871tant_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ C @ D ) @ ( semant993842370nt_V_V @ A @ E ) )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ C @ D ) @ ( semant993842370nt_V_V @ B @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_subgraph__semantics) ).

thf(1150,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: v,D: v,E: allego859987871tant_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ C @ D ) @ ( semant993842370nt_V_V @ A @ E ) )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ C @ D ) @ ( semant993842370nt_V_V @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(307,axiom,
    ! [A: product_prod_V_V] :
      ~ ( member2015049524od_V_V @ A @ bot_bo1389414743od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_empty__iff) ).

thf(1333,plain,
    ! [A: product_prod_V_V] :
      ~ ( member2015049524od_V_V @ A @ bot_bo1389414743od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(1,conjecture,
    member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(343,plain,
    ~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(140,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ~ ! [C: set_Pr744279122od_V_V] :
            ( ( B
              = ( insert135842892od_V_V @ A @ C ) )
           => ( member1010391347od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Set_Oset__insert) ).

thf(792,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ~ ! [C: set_Pr744279122od_V_V] :
            ( ( B
              = ( insert135842892od_V_V @ A @ C ) )
           => ( member1010391347od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(185,axiom,
    ( insert_V2
    = ( ^ [A: v] : ( sup_sup_set_V2 @ ( insert_V2 @ A @ bot_bot_set_V2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_insert__is__Un) ).

thf(938,plain,
    ( insert_V2
    = ( ^ [A: v] : ( sup_sup_set_V2 @ ( insert_V2 @ A @ bot_bot_set_V2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(264,axiom,
    ! [A: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ ( standa1897115807ules_V @ c ) @ ( standa1568205529ules_V @ l ) ) @ ( insert481364471_V_nat @ ( standa214871990tant_V @ standard_S_Top_V ) @ ( insert481364471_V_nat @ standa1319953089tant_V @ bot_bo907687539_V_nat ) ) ) )
     => ( mainta197426964_nat_V @ A @ g ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_mnt) ).

thf(1187,plain,
    ! [A: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ ( standa1897115807ules_V @ c ) @ ( standa1568205529ules_V @ l ) ) @ ( insert481364471_V_nat @ ( standa214871990tant_V @ standard_S_Top_V ) @ ( insert481364471_V_nat @ standa1319953089tant_V @ bot_bo907687539_V_nat ) ) ) )
     => ( mainta197426964_nat_V @ A @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(78,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ A @ B ) )
      = ( sup_su1043134939_V_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_sup__left__idem) ).

thf(586,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ A @ B ) )
      = ( sup_su1043134939_V_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(116,axiom,
    ( ( id_on_1882925319_V_nat @ bot_bo1053950006_V_nat )
    = bot_bo907687539_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Id__on__empty) ).

thf(718,plain,
    ( ( id_on_1882925319_V_nat @ bot_bo1053950006_V_nat )
    = bot_bo907687539_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(180,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat > $o] :
      ( ( ? [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ ( sup_su1043134939_V_nat @ A @ B ) )
            & ( C @ D ) ) )
      = ( ? [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ A )
            & ( C @ D ) )
        | ? [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ B )
            & ( C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_bex__Un) ).

thf(926,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat > $o] :
      ( ( ? [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ ( sup_su1043134939_V_nat @ A @ B ) )
            & ( C @ D ) ) )
      = ( ? [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ A )
            & ( C @ D ) )
        | ? [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ B )
            & ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(252,axiom,
    graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_h_I3_J) ).

thf(1146,plain,
    graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(238,axiom,
    ! [A: v2,B: set_V2] :
      ( ( member_V @ A @ B )
     => ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ A ) @ ( id_on_V @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Id__onI) ).

thf(1103,plain,
    ! [A: v2,B: set_V2] :
      ( ( member_V @ A @ B )
     => ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ A ) @ ( id_on_V @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(149,axiom,
    ( bot_bo2024487199_V_V_o
    = ( ^ [A: produc1699571228od_V_V] : ( member1010391347od_V_V @ A @ bot_bo667804902od_V_V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_bot__empty__eq) ).

thf(824,plain,
    ( bot_bo2024487199_V_V_o
    = ( ^ [A: produc1699571228od_V_V] : ( member1010391347od_V_V @ A @ bot_bo667804902od_V_V ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(288,axiom,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: allego859987871tant_V,E: v > v] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( semant993842370nt_V_V @ A @ D ) )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ B ) @ ( E @ C ) ) @ ( semant993842370nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ E ) @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_map__graph__in) ).

thf(1273,plain,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: allego859987871tant_V,E: v > v] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( semant993842370nt_V_V @ A @ D ) )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ B ) @ ( E @ C ) ) @ ( semant993842370nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ E ) @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(36,axiom,
    ! [A: set_V] :
      ( ( sup_sup_set_V2 @ A @ bot_bot_set_V2 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Un__empty__right) ).

thf(444,plain,
    ! [A: set_V] :
      ( ( sup_sup_set_V2 @ A @ bot_bot_set_V2 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(14,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ B @ C ) )
     => ( ~ ( member1010391347od_V_V @ A @ B )
       => ( member1010391347od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_UnE) ).

thf(375,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ B @ C ) )
     => ( ~ ( member1010391347od_V_V @ A @ B )
       => ( member1010391347od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(29,axiom,
    ! [A: set_V,B: set_V] :
      ( ( ( sup_sup_set_V2 @ A @ B )
        = bot_bot_set_V2 )
      = ( ( A = bot_bot_set_V2 )
        & ( B = bot_bot_set_V2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Un__empty) ).

thf(423,plain,
    ! [A: set_V,B: set_V] :
      ( ( ( sup_sup_set_V2 @ A @ B )
        = bot_bot_set_V2 )
      = ( ( A = bot_bot_set_V2 )
        & ( B = bot_bot_set_V2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(23,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] :
      ( ( labele1134902411nt_V_V @ ( graph_1141886696nt_V_V @ A @ B ) )
      = ( sup_sup_set_V2 @ ( labele1134902411nt_V_V @ A ) @ ( labele1134902411nt_V_V @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_graph__union__vertices) ).

thf(402,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] :
      ( ( labele1134902411nt_V_V @ ( graph_1141886696nt_V_V @ A @ B ) )
      = ( sup_sup_set_V2 @ ( labele1134902411nt_V_V @ A ) @ ( labele1134902411nt_V_V @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(323,axiom,
    ! [A: v,B: set_V,C: v > v] :
      ( ( bNF_Gr_V_V2 @ ( insert_V2 @ A @ B ) @ C )
      = ( insert2024285275od_V_V @ ( product_Pair_V_V2 @ A @ ( C @ A ) ) @ ( bNF_Gr_V_V2 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Gr__insert) ).

thf(1389,plain,
    ! [A: v,B: set_V,C: v > v] :
      ( ( bNF_Gr_V_V2 @ ( insert_V2 @ A @ B ) @ C )
      = ( insert2024285275od_V_V @ ( product_Pair_V_V2 @ A @ ( C @ A ) ) @ ( bNF_Gr_V_V2 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(134,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ bot_bo907687539_V_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_sup__bot_Oright__neutral) ).

thf(772,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ bot_bo907687539_V_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(322,axiom,
    mainta197426964_nat_V @ ( standa214871990tant_V @ standard_S_Top_V ) @ g,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_tr) ).

thf(1388,plain,
    mainta197426964_nat_V @ ( standa214871990tant_V @ standard_S_Top_V ) @ g,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(245,axiom,
    ( g
    = ( restri1305980611nt_V_V @ g ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_gr_I1_J) ).

thf(1124,plain,
    ( g
    = ( restri1305980611nt_V_V @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(165,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat )
        = ( sup_su1043134939_V_nat @ B @ C ) )
      = ( ( ( B = bot_bo907687539_V_nat )
          & ( C
            = ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ) )
        | ( ( B
            = ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) )
          & ( C = bot_bo907687539_V_nat ) )
        | ( ( B
            = ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) )
          & ( C
            = ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_singleton__Un__iff) ).

thf(875,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat )
        = ( sup_su1043134939_V_nat @ B @ C ) )
      = ( ( ( B = bot_bo907687539_V_nat )
          & ( C
            = ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ) )
        | ( ( B
            = ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) )
          & ( C = bot_bo907687539_V_nat ) )
        | ( ( B
            = ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) )
          & ( C
            = ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(150,axiom,
    ! [A: v2,B: v2 > $o] :
      ( ( member_V @ A @ ( collect_V @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_mem__Collect__eq) ).

thf(826,plain,
    ! [A: v2,B: v2 > $o] :
      ( ( member_V @ A @ ( collect_V @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(76,axiom,
    ! [A: produc1082089497od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member785416642od_V_V @ A @ ( id_on_1491482303od_V_V @ B ) )
     => ~ ! [C: produc1699571228od_V_V] :
            ( ( member1010391347od_V_V @ C @ B )
           => ( A
             != ( produc1736057425od_V_V @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Id__onE) ).

thf(577,plain,
    ! [A: produc1082089497od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member785416642od_V_V @ A @ ( id_on_1491482303od_V_V @ B ) )
     => ~ ! [C: produc1699571228od_V_V] :
            ( ( member1010391347od_V_V @ C @ B )
           => ( A
             != ( produc1736057425od_V_V @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(281,axiom,
    member_V @ xa @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C1_C_I1_J) ).

thf(1256,plain,
    member_V @ xa @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(67,axiom,
    ! [A: set_Pr744279122od_V_V] :
      ( ( collec1840263537od_V_V
        @ ^ [B: produc1699571228od_V_V] : ( member1010391347od_V_V @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Collect__mem__eq) ).

thf(545,plain,
    ! [A: set_Pr744279122od_V_V] :
      ( ( collec1840263537od_V_V
        @ ^ [B: produc1699571228od_V_V] : ( member1010391347od_V_V @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(184,axiom,
    ( ( comp_V_V_V2 @ h @ h )
    = h ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_h_I1_J) ).

thf(936,plain,
    ( ( comp_V_V_V2 @ h @ h )
    = h ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(16,axiom,
    ! [A: v > v,B: v > v,C: v > v] :
      ( ( comp_V_V_V2 @ ( comp_V_V_V2 @ A @ B ) @ C )
      = ( comp_V_V_V2 @ A @ ( comp_V_V_V2 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_comp__assoc) ).

thf(382,plain,
    ! [A: v > v,B: v > v,C: v > v] :
      ( ( comp_V_V_V2 @ ( comp_V_V_V2 @ A @ B ) @ C )
      = ( comp_V_V_V2 @ A @ ( comp_V_V_V2 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(240,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat] :
      ( ( ~ ( member1886821968_V_nat @ A @ B )
       => ( A = C ) )
     => ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_insertCI) ).

thf(1107,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat] :
      ( ( ~ ( member1886821968_V_nat @ A @ B )
       => ( A = C ) )
     => ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(277,axiom,
    ! [A: set_Product_prod_V_V] :
      ( ! [B: product_prod_V_V] :
          ~ ( member2015049524od_V_V @ B @ A )
     => ( A = bot_bo1389414743od_V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_equals0I) ).

thf(1239,plain,
    ! [A: set_Product_prod_V_V] :
      ( ! [B: product_prod_V_V] :
          ~ ( member2015049524od_V_V @ B @ A )
     => ( A = bot_bo1389414743od_V_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(235,axiom,
    ! [A: v > v] :
      ( ( bNF_Gr_V_V2 @ bot_bot_set_V2 @ A )
      = bot_bo1389414743od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Gr__empty) ).

thf(1092,plain,
    ! [A: v > v] :
      ( ( bNF_Gr_V_V2 @ bot_bot_set_V2 @ A )
      = bot_bo1389414743od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(112,axiom,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_singletonD) ).

thf(704,plain,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(65,axiom,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ bot_bo667804902od_V_V ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_singletonD) ).

thf(540,plain,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ bot_bo667804902od_V_V ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(115,axiom,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: set_Pr744279122od_V_V] :
      ( ( A = B )
     => ( ( member1010391347od_V_V @ A @ C )
       => ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ B ) @ ( id_on_1491482303od_V_V @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Id__on__eqI) ).

thf(713,plain,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,C: set_Pr744279122od_V_V] :
      ( ( A = B )
     => ( ( member1010391347od_V_V @ A @ C )
       => ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ B ) @ ( id_on_1491482303od_V_V @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(53,axiom,
    ! [A: labele2115946735nt_V_V] :
      ( A
      = ( labele712009229nt_V_V @ ( labele515735386nt_V_V @ A ) @ ( labele1134902411nt_V_V @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_labeled__graph_Oexhaust__sel) ).

thf(498,plain,
    ! [A: labele2115946735nt_V_V] :
      ( A
      = ( labele712009229nt_V_V @ ( labele515735386nt_V_V @ A ) @ ( labele1134902411nt_V_V @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(131,axiom,
    ( graph_1141886696nt_V_V
    = ( ^ [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] : ( labele712009229nt_V_V @ ( sup_su693515134od_V_V @ ( labele515735386nt_V_V @ A ) @ ( labele515735386nt_V_V @ B ) ) @ ( sup_sup_set_V2 @ ( labele1134902411nt_V_V @ A ) @ ( labele1134902411nt_V_V @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_graph__union__def) ).

thf(764,plain,
    ( graph_1141886696nt_V_V
    = ( ^ [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] : ( labele712009229nt_V_V @ ( sup_su693515134od_V_V @ ( labele515735386nt_V_V @ A ) @ ( labele515735386nt_V_V @ B ) ) @ ( sup_sup_set_V2 @ ( labele1134902411nt_V_V @ A ) @ ( labele1134902411nt_V_V @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(270,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_singleton__iff) ).

thf(1209,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(291,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ A ) @ ( id_on_2125509800od_V_V @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Id__onI) ).

thf(1282,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ A ) @ ( id_on_2125509800od_V_V @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(208,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) )
      = ( ( member1886821968_V_nat @ A @ B )
        | ( member1886821968_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Un__iff) ).

thf(1011,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) )
      = ( ( member1886821968_V_nat @ A @ B )
        | ( member1886821968_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(15,axiom,
    ! [A: v > v,B: v > v,C: v > v,D: v] :
      ( ( ( comp_V_V_V2 @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_comp__eq__dest__lhs) ).

thf(377,plain,
    ! [A: v > v,B: v > v,C: v > v,D: v] :
      ( ( ( comp_V_V_V2 @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(57,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: produc1699571228od_V_V] :
      ( ( ~ ( member1010391347od_V_V @ A @ B )
       => ( A = C ) )
     => ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_insertCI) ).

thf(509,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: produc1699571228od_V_V] :
      ( ( ~ ( member1010391347od_V_V @ A @ B )
       => ( A = C ) )
     => ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(298,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ B @ C ) )
     => ( ~ ( member2015049524od_V_V @ A @ B )
       => ( member2015049524od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_UnE) ).

thf(1307,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ ( sup_su551882943od_V_V @ B @ C ) )
     => ( ~ ( member2015049524od_V_V @ A @ B )
       => ( member2015049524od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(9,axiom,
    ! [A: v,B: set_V,C: set_V] :
      ( ( member_V2 @ A @ ( sup_sup_set_V2 @ B @ C ) )
     => ( ~ ( member_V2 @ A @ B )
       => ( member_V2 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_UnE) ).

thf(362,plain,
    ! [A: v,B: set_V,C: set_V] :
      ( ( member_V2 @ A @ ( sup_sup_set_V2 @ B @ C ) )
     => ( ~ ( member_V2 @ A @ B )
       => ( member_V2 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(38,axiom,
    ! [A: v > v,B: v > v,C: v > v,D: v > v] :
      ( ( ( comp_V_V_V2 @ A @ B )
        = ( comp_V_V_V2 @ C @ D ) )
     => ! [E: v] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_comp__eq__elim) ).

thf(451,plain,
    ! [A: v > v,B: v > v,C: v > v,D: v > v] :
      ( ( ( comp_V_V_V2 @ A @ B )
        = ( comp_V_V_V2 @ C @ D ) )
     => ! [E: v] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(18,axiom,
    ( bot_bot_set_V2
    = ( collect_V2 @ bot_bot_V_o2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_bot__set__def) ).

thf(387,plain,
    ( bot_bot_set_V2
    = ( collect_V2 @ bot_bot_V_o2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(230,axiom,
    ( bot_bot_V_o2
    = ( ^ [A: v] : ( member_V2 @ A @ bot_bot_set_V2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_bot__empty__eq) ).

thf(1080,plain,
    ( bot_bot_V_o2
    = ( ^ [A: v] : ( member_V2 @ A @ bot_bot_set_V2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(89,axiom,
    ! [A: produc1699571228od_V_V] :
    ? [B: standard_Constant_V,C: product_prod_V_V] :
      ( A
      = ( produc107991630od_V_V @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_surj__pair) ).

thf(631,plain,
    ! [A: produc1699571228od_V_V] :
    ? [B: standard_Constant_V,C: product_prod_V_V] :
      ( A
      = ( produc107991630od_V_V @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(309,axiom,
    ! [A: labele236903175od_V_V,B: v > product_prod_V_V,C: product_prod_V_V > v,D: produc778275879_V_nat] :
      ( ! [E: product_prod_V_V] :
          ( ( member2015049524od_V_V @ E @ ( labele981584981od_V_V @ A ) )
         => ( ( comp_V772749048od_V_V @ B @ C @ E )
            = E ) )
     => ( ( A
          = ( restri1502575645od_V_V @ A ) )
       => ( ( mainta197426964_nat_V @ D @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ A ) @ C ) @ A ) )
         => ( mainta1984786828od_V_V @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_maintained__preserved__by__isomorphism) ).

thf(1339,plain,
    ! [A: labele236903175od_V_V,B: v > product_prod_V_V,C: product_prod_V_V > v,D: produc778275879_V_nat] :
      ( ! [E: product_prod_V_V] :
          ( ( member2015049524od_V_V @ E @ ( labele981584981od_V_V @ A ) )
         => ( ( comp_V772749048od_V_V @ B @ C @ E )
            = E ) )
     => ( ( A
          = ( restri1502575645od_V_V @ A ) )
       => ( ( mainta197426964_nat_V @ D @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ A ) @ C ) @ A ) )
         => ( mainta1984786828od_V_V @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(84,axiom,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: standard_Constant_V,D: product_prod_V_V] :
      ( ( ( produc107991630od_V_V @ A @ B )
        = ( produc107991630od_V_V @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Pair__inject) ).

thf(609,plain,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: standard_Constant_V,D: product_prod_V_V] :
      ( ( ( produc107991630od_V_V @ A @ B )
        = ( produc107991630od_V_V @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(48,axiom,
    ! [A: v,B: v > $o] :
      ( ( member_V2 @ A @ ( collect_V2 @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_mem__Collect__eq) ).

thf(483,plain,
    ! [A: v,B: v > $o] :
      ( ( member_V2 @ A @ ( collect_V2 @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(157,axiom,
    ! [A: labele2128733290_V_nat,B: labele2115946735nt_V_V] : ( mainta197426964_nat_V @ ( produc698429463_V_nat @ A @ A ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_maintained__refl) ).

thf(848,plain,
    ! [A: labele2128733290_V_nat,B: labele2115946735nt_V_V] : ( mainta197426964_nat_V @ ( produc698429463_V_nat @ A @ A ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(305,axiom,
    ! [A: labele2115946735nt_V_V,B: v > v,C: set_Pr744279122od_V_V] :
      ( ! [D: standard_Constant_V,E: v,F: v] :
          ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ E @ F ) ) @ ( labele515735386nt_V_V @ A ) )
         => ( ( member_V2 @ E @ ( labele1134902411nt_V_V @ A ) )
           => ( ( member_V2 @ F @ ( labele1134902411nt_V_V @ A ) )
             => ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
     => ( edge_p1560004099tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ ( labele515735386nt_V_V @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_edge__preserving__on__graphI) ).

thf(1325,plain,
    ! [A: labele2115946735nt_V_V,B: v > v,C: set_Pr744279122od_V_V] :
      ( ! [D: standard_Constant_V,E: v,F: v] :
          ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ E @ F ) ) @ ( labele515735386nt_V_V @ A ) )
         => ( ( member_V2 @ E @ ( labele1134902411nt_V_V @ A ) )
           => ( ( member_V2 @ F @ ( labele1134902411nt_V_V @ A ) )
             => ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
     => ( edge_p1560004099tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ ( labele515735386nt_V_V @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(133,axiom,
    ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( ( sup_su551882943od_V_V @ A @ B )
        = bot_bo1389414743od_V_V )
      = ( ( A = bot_bo1389414743od_V_V )
        & ( B = bot_bo1389414743od_V_V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_sup__bot_Oeq__neutr__iff) ).

thf(769,plain,
    ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( ( sup_su551882943od_V_V @ A @ B )
        = bot_bo1389414743od_V_V )
      = ( ( A = bot_bo1389414743od_V_V )
        & ( B = bot_bo1389414743od_V_V ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(261,axiom,
    ! [A: v,B: v,C: standard_Constant_V,D: labele2115946735nt_V_V,E: labele2115946735nt_V_V] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ C @ D ) )
     => ( ( graph_1808119_V_V_V @ D @ E @ ( id_on_V2 @ ( labele1134902411nt_V_V @ D ) ) )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_getRel__subgraph) ).

thf(1177,plain,
    ! [A: v,B: v,C: standard_Constant_V,D: labele2115946735nt_V_V,E: labele2115946735nt_V_V] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ C @ D ) )
     => ( ( graph_1808119_V_V_V @ D @ E @ ( id_on_V2 @ ( labele1134902411nt_V_V @ D ) ) )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(257,axiom,
    ! [A: set_Product_prod_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V,D: v,E: v,F: v,G: v,H: standard_Constant_V] :
      ( ( edge_p1560004099tant_V @ A @ B @ C )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ D @ E ) @ A )
       => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ A )
         => ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ H @ ( product_Pair_V_V2 @ D @ F ) ) @ B )
           => ( member1010391347od_V_V @ ( produc107991630od_V_V @ H @ ( product_Pair_V_V2 @ E @ G ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_edge__preserving__atomic) ).

thf(1162,plain,
    ! [A: set_Product_prod_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V,D: v,E: v,F: v,G: v,H: standard_Constant_V] :
      ( ( edge_p1560004099tant_V @ A @ B @ C )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ D @ E ) @ A )
       => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ A )
         => ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ H @ ( product_Pair_V_V2 @ D @ F ) ) @ B )
           => ( member1010391347od_V_V @ ( produc107991630od_V_V @ H @ ( product_Pair_V_V2 @ E @ G ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(119,axiom,
    ! [A: produc1699571228od_V_V > $o,B: produc1699571228od_V_V] :
      ( ! [C: standard_Constant_V,D: product_prod_V_V] : ( A @ ( produc107991630od_V_V @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_prod__cases) ).

thf(726,plain,
    ! [A: produc1699571228od_V_V > $o,B: produc1699571228od_V_V] :
      ( ! [C: standard_Constant_V,D: product_prod_V_V] : ( A @ ( produc107991630od_V_V @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(187,axiom,
    ! [A: labele2115946735nt_V_V,B: set_Product_prod_V_V] :
      ( ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ bot_bot_set_V2 ) @ A @ B )
      = ( ( B = bot_bo1389414743od_V_V )
        & ( A
          = ( restri1305980611nt_V_V @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_graph__homomorphism__empty) ).

thf(943,plain,
    ! [A: labele2115946735nt_V_V,B: set_Product_prod_V_V] :
      ( ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ bot_bot_set_V2 ) @ A @ B )
      = ( ( B = bot_bo1389414743od_V_V )
        & ( A
          = ( restri1305980611nt_V_V @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(211,axiom,
    ! [A: produc778275879_V_nat] :
      ~ ( member1886821968_V_nat @ A @ bot_bo907687539_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_empty__iff) ).

thf(1022,plain,
    ! [A: produc778275879_V_nat] :
      ~ ( member1886821968_V_nat @ A @ bot_bo907687539_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(182,axiom,
    ( insert2024285275od_V_V
    = ( ^ [A: product_prod_V_V] : ( sup_su551882943od_V_V @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_insert__is__Un) ).

thf(932,plain,
    ( insert2024285275od_V_V
    = ( ^ [A: product_prod_V_V] : ( sup_su551882943od_V_V @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(224,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] : ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_insertI1) ).

thf(1061,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] : ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(267,axiom,
    ! [A: v,B: v,C: standard_Constant_V,D: labele2115946735nt_V_V,E: v,F: set_Product_prod_V_V,G: v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ C @ D ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ E ) @ F )
       => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ G ) @ F )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ E @ G ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr907434255tant_V @ F @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_getRel__homR) ).

thf(1198,plain,
    ! [A: v,B: v,C: standard_Constant_V,D: labele2115946735nt_V_V,E: v,F: set_Product_prod_V_V,G: v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ C @ D ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ E ) @ F )
       => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ G ) @ F )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ E @ G ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr907434255tant_V @ F @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(191,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: set_Product_prod_V_V,D: allego859987871tant_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ C )
     => ( ( ( semant993842370nt_V_V @ A @ D )
         != bot_bo1389414743od_V_V )
       => ( ( semant993842370nt_V_V @ B @ D )
         != bot_bo1389414743od_V_V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_graph__homomorphism__nonempty) ).

thf(959,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: set_Product_prod_V_V,D: allego859987871tant_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ C )
     => ( ( ( semant993842370nt_V_V @ A @ D )
         != bot_bo1389414743od_V_V )
       => ( ( semant993842370nt_V_V @ B @ D )
         != bot_bo1389414743od_V_V ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(137,axiom,
    ! [A: set_Pr1058435079_V_nat,B: produc778275879_V_nat] :
      ( ( A = bot_bo907687539_V_nat )
     => ~ ( member1886821968_V_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_equals0D) ).

thf(780,plain,
    ! [A: set_Pr1058435079_V_nat,B: produc778275879_V_nat] :
      ( ( A = bot_bo907687539_V_nat )
     => ~ ( member1886821968_V_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(241,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ A @ B ) @ C )
      = ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_Un__assoc) ).

thf(1113,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ A @ B ) @ C )
      = ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(204,axiom,
    ! [A: labele2115946735nt_V_V] :
      ( ( labele1134902411nt_V_V @ ( restri1305980611nt_V_V @ A ) )
      = ( labele1134902411nt_V_V @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_vertices__restrict) ).

thf(1000,plain,
    ! [A: labele2115946735nt_V_V] :
      ( ( labele1134902411nt_V_V @ ( restri1305980611nt_V_V @ A ) )
      = ( labele1134902411nt_V_V @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(34,axiom,
    ! [A: set_V] :
      ( ( sup_sup_set_V2 @ bot_bot_set_V2 @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Un__empty__left) ).

thf(438,plain,
    ! [A: set_V] :
      ( ( sup_sup_set_V2 @ bot_bot_set_V2 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(226,axiom,
    ! [A: set_Pr744279122od_V_V] :
      ( ! [B: produc1699571228od_V_V] :
          ~ ( member1010391347od_V_V @ B @ A )
     => ( A = bot_bo667804902od_V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_equals0I) ).

thf(1066,plain,
    ! [A: set_Pr744279122od_V_V] :
      ( ! [B: produc1699571228od_V_V] :
          ~ ( member1010391347od_V_V @ B @ A )
     => ( A = bot_bo667804902od_V_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(163,axiom,
    ! [A: v,B: set_V,C: v,D: set_V] :
      ( ~ ( member_V2 @ A @ B )
     => ( ~ ( member_V2 @ C @ D )
       => ( ( ( insert_V2 @ A @ B )
            = ( insert_V2 @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_V] :
                  ( ( B
                    = ( insert_V2 @ C @ E ) )
                  & ~ ( member_V2 @ C @ E )
                  & ( D
                    = ( insert_V2 @ A @ E ) )
                  & ~ ( member_V2 @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_insert__eq__iff) ).

thf(868,plain,
    ! [A: v,B: set_V,C: v,D: set_V] :
      ( ~ ( member_V2 @ A @ B )
     => ( ~ ( member_V2 @ C @ D )
       => ( ( ( insert_V2 @ A @ B )
            = ( insert_V2 @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_V] :
                  ( ( B
                    = ( insert_V2 @ C @ E ) )
                  & ~ ( member_V2 @ C @ E )
                  & ( D
                    = ( insert_V2 @ A @ E ) )
                  & ~ ( member_V2 @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(45,axiom,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V > $o] :
      ( ( member1010391347od_V_V @ A @ ( collec1840263537od_V_V @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_mem__Collect__eq) ).

thf(473,plain,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V > $o] :
      ( ( member1010391347od_V_V @ A @ ( collec1840263537od_V_V @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(30,axiom,
    ! [A: labele2128733290_V_nat,B: set_la14611914_V_nat,C: labele2128733290_V_nat > labele2128733290_V_nat] :
      ( ( bNF_Gr17960482_V_nat @ ( insert213439034_V_nat @ A @ B ) @ C )
      = ( insert481364471_V_nat @ ( produc698429463_V_nat @ A @ ( C @ A ) ) @ ( bNF_Gr17960482_V_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Gr__insert) ).

thf(426,plain,
    ! [A: labele2128733290_V_nat,B: set_la14611914_V_nat,C: labele2128733290_V_nat > labele2128733290_V_nat] :
      ( ( bNF_Gr17960482_V_nat @ ( insert213439034_V_nat @ A @ B ) @ C )
      = ( insert481364471_V_nat @ ( produc698429463_V_nat @ A @ ( C @ A ) ) @ ( bNF_Gr17960482_V_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(79,axiom,
    ( ( id_on_V2 @ bot_bot_set_V2 )
    = bot_bo1389414743od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Id__on__empty) ).

thf(589,plain,
    ( ( id_on_V2 @ bot_bot_set_V2 )
    = bot_bo1389414743od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(68,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V )
        = ( sup_su551882943od_V_V @ B @ C ) )
      = ( ( ( B = bot_bo1389414743od_V_V )
          & ( C
            = ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ) )
        | ( ( B
            = ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) )
          & ( C = bot_bo1389414743od_V_V ) )
        | ( ( B
            = ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) )
          & ( C
            = ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_singleton__Un__iff) ).

thf(548,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V )
        = ( sup_su551882943od_V_V @ B @ C ) )
      = ( ( ( B = bot_bo1389414743od_V_V )
          & ( C
            = ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ) )
        | ( ( B
            = ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) )
          & ( C = bot_bo1389414743od_V_V ) )
        | ( ( B
            = ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) )
          & ( C
            = ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(289,axiom,
    ! [A: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( standa157301464ules_V @ c @ l ) )
     => ( mainta197426964_nat_V @ A @ g ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_assms_I1_J) ).

thf(1277,plain,
    ! [A: produc778275879_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( standa157301464ules_V @ c @ l ) )
     => ( mainta197426964_nat_V @ A @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(125,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ A ) @ ( id_on_1491482303od_V_V @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Id__onI) ).

thf(749,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ A ) @ ( id_on_1491482303od_V_V @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(127,axiom,
    ! [A: v] :
      ~ ( member_V2 @ A @ bot_bot_set_V2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_emptyE) ).

thf(754,plain,
    ! [A: v] :
      ~ ( member_V2 @ A @ bot_bot_set_V2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(220,axiom,
    ! [A: v,B: v] :
      ( ( ( insert_V2 @ A @ bot_bot_set_V2 )
        = ( insert_V2 @ B @ bot_bot_set_V2 ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_singleton__inject) ).

thf(1049,plain,
    ! [A: v,B: v] :
      ( ( ( insert_V2 @ A @ bot_bot_set_V2 )
        = ( insert_V2 @ B @ bot_bot_set_V2 ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(249,axiom,
    ! [A: labele201426742od_V_V,B: produc1699571228od_V_V > v,C: set_Pr744279122od_V_V] :
      ( ! [D: standard_Constant_V,E: produc1699571228od_V_V,F: produc1699571228od_V_V] :
          ( ( member600445121od_V_V @ ( produc2132932316od_V_V @ D @ ( produc1736057425od_V_V @ E @ F ) ) @ ( labele1794513953od_V_V @ A ) )
         => ( ( member1010391347od_V_V @ E @ ( labele1328382418od_V_V @ A ) )
           => ( ( member1010391347od_V_V @ F @ ( labele1328382418od_V_V @ A ) )
             => ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
     => ( edge_p669293514tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ A ) @ B ) @ ( labele1794513953od_V_V @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_edge__preserving__on__graphI) ).

thf(1134,plain,
    ! [A: labele201426742od_V_V,B: produc1699571228od_V_V > v,C: set_Pr744279122od_V_V] :
      ( ! [D: standard_Constant_V,E: produc1699571228od_V_V,F: produc1699571228od_V_V] :
          ( ( member600445121od_V_V @ ( produc2132932316od_V_V @ D @ ( produc1736057425od_V_V @ E @ F ) ) @ ( labele1794513953od_V_V @ A ) )
         => ( ( member1010391347od_V_V @ E @ ( labele1328382418od_V_V @ A ) )
           => ( ( member1010391347od_V_V @ F @ ( labele1328382418od_V_V @ A ) )
             => ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
     => ( edge_p669293514tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ A ) @ B ) @ ( labele1794513953od_V_V @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(95,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ A @ B ) )
      = ( sup_su1043134939_V_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_Un__left__absorb) ).

thf(648,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ A @ B ) )
      = ( sup_su1043134939_V_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(61,axiom,
    ! [A: set_Pr744279122od_V_V,B: set_V,C: labele2115946735nt_V_V,D: set_Product_prod_V_V,E: set_Pr744279122od_V_V] :
      ( ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ A @ B ) @ C @ D )
     => ( ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ ( labele712009229nt_V_V @ A @ B ) @ ( labele712009229nt_V_V @ E @ B ) ) @ C @ D )
        = ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ E @ B ) @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_extensible__refl__concr) ).

thf(525,plain,
    ! [A: set_Pr744279122od_V_V,B: set_V,C: labele2115946735nt_V_V,D: set_Product_prod_V_V,E: set_Pr744279122od_V_V] :
      ( ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ A @ B ) @ C @ D )
     => ( ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ ( labele712009229nt_V_V @ A @ B ) @ ( labele712009229nt_V_V @ E @ B ) ) @ C @ D )
        = ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ E @ B ) @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(205,axiom,
    ! [A: v > $o] :
      ( ( bot_bot_set_V2
        = ( collect_V2 @ A ) )
      = ( ! [B: v] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_empty__Collect__eq) ).

thf(1003,plain,
    ! [A: v > $o] :
      ( ( bot_bot_set_V2
        = ( collect_V2 @ A ) )
      = ( ! [B: v] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(107,axiom,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: standard_Constant_V,D: product_prod_V_V] :
      ( ( ( produc107991630od_V_V @ A @ B )
        = ( produc107991630od_V_V @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_old_Oprod_Oinject) ).

thf(690,plain,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: standard_Constant_V,D: product_prod_V_V] :
      ( ( ( produc107991630od_V_V @ A @ B )
        = ( produc107991630od_V_V @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(92,axiom,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( member_V @ A @ ( sup_sup_set_V @ B @ C ) )
      = ( ( member_V @ A @ B )
        | ( member_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Un__iff) ).

thf(640,plain,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( member_V @ A @ ( sup_sup_set_V @ B @ C ) )
      = ( ( member_V @ A @ B )
        | ( member_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(212,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_sup__bot_Oleft__neutral) ).

thf(1025,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(168,axiom,
    ! [A: set_V] :
      ( ! [B: v] :
          ~ ( member_V2 @ B @ A )
     => ( A = bot_bot_set_V2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_equals0I) ).

thf(887,plain,
    ! [A: set_V] :
      ( ! [B: v] :
          ~ ( member_V2 @ B @ A )
     => ( A = bot_bot_set_V2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(26,axiom,
    ! [A: set_V,B: set_V] :
      ( ( bot_bot_set_V2
        = ( sup_sup_set_V2 @ A @ B ) )
      = ( ( A = bot_bot_set_V2 )
        & ( B = bot_bot_set_V2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_sup__bot_Oneutr__eq__iff) ).

thf(414,plain,
    ! [A: set_V,B: set_V] :
      ( ( bot_bot_set_V2
        = ( sup_sup_set_V2 @ A @ B ) )
      = ( ( A = bot_bot_set_V2 )
        & ( B = bot_bot_set_V2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(280,axiom,
    ! [A: product_prod_V_V] :
      ~ ! [B: v,C: v] :
          ( A
         != ( product_Pair_V_V2 @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_old_Oprod_Oexhaust) ).

thf(1252,plain,
    ! [A: product_prod_V_V] :
      ~ ! [B: v,C: v] :
          ( A
         != ( product_Pair_V_V2 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(315,axiom,
    ! [A: product_prod_V_V > $o,B: product_prod_V_V] :
      ( ! [C: v,D: v] : ( A @ ( product_Pair_V_V2 @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_prod__cases) ).

thf(1368,plain,
    ! [A: product_prod_V_V > $o,B: product_prod_V_V] :
      ( ! [C: v,D: v] : ( A @ ( product_Pair_V_V2 @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(286,axiom,
    ! [A: product_prod_V_V,B: set_V] :
      ( ( member2015049524od_V_V @ A @ ( id_on_V2 @ B ) )
     => ~ ! [C: v] :
            ( ( member_V2 @ C @ B )
           => ( A
             != ( product_Pair_V_V2 @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Id__onE) ).

thf(1267,plain,
    ! [A: product_prod_V_V,B: set_V] :
      ( ( member2015049524od_V_V @ A @ ( id_on_V2 @ B ) )
     => ~ ! [C: v] :
            ( ( member_V2 @ C @ B )
           => ( A
             != ( product_Pair_V_V2 @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(25,axiom,
    ! [A: set_V2,B: v2] :
      ( ( A = bot_bot_set_V )
     => ~ ( member_V @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_equals0D) ).

thf(409,plain,
    ! [A: set_V2,B: v2] :
      ( ( A = bot_bot_set_V )
     => ~ ( member_V @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(227,axiom,
    ! [A: produc1699571228od_V_V] : ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ A @ bot_bo667804902od_V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_singletonI) ).

thf(1070,plain,
    ! [A: produc1699571228od_V_V] : ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ A @ bot_bo667804902od_V_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(164,axiom,
    ! [A: produc778275879_V_nat > $o] :
      ( ( ( collec1411521682_V_nat @ A )
        = bot_bo907687539_V_nat )
      = ( ! [B: produc778275879_V_nat] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Collect__empty__eq) ).

thf(872,plain,
    ! [A: produc778275879_V_nat > $o] :
      ( ( ( collec1411521682_V_nat @ A )
        = bot_bo907687539_V_nat )
      = ( ! [B: produc778275879_V_nat] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(274,axiom,
    ! [A: set_Product_prod_V_V] :
      ( ( collec2040633974od_V_V
        @ ^ [B: product_prod_V_V] : ( member2015049524od_V_V @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Collect__mem__eq) ).

thf(1225,plain,
    ! [A: set_Product_prod_V_V] :
      ( ( collec2040633974od_V_V
        @ ^ [B: product_prod_V_V] : ( member2015049524od_V_V @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(113,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( bot_bo907687539_V_nat
        = ( sup_su1043134939_V_nat @ A @ B ) )
      = ( ( A = bot_bo907687539_V_nat )
        & ( B = bot_bo907687539_V_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_sup__bot_Oneutr__eq__iff) ).

thf(707,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( bot_bo907687539_V_nat
        = ( sup_su1043134939_V_nat @ A @ B ) )
      = ( ( A = bot_bo907687539_V_nat )
        & ( B = bot_bo907687539_V_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(101,axiom,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ C ) )
     => ( ( A != B )
       => ( member1886821968_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_insertE) ).

thf(673,plain,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ C ) )
     => ( ( A != B )
       => ( member1886821968_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(335,axiom,
    member2015049524od_V_V @ ( product_Pair_V_V2 @ x @ x ) @ ( getRel1432786916nt_V_V @ standard_S_Top_V @ g ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_top__nonempty) ).

thf(1432,plain,
    member2015049524od_V_V @ ( product_Pair_V_V2 @ x @ x ) @ ( getRel1432786916nt_V_V @ standard_S_Top_V @ g ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(342,axiom,
    ! [A: set_Product_prod_V_V] :
      ( ( ! [B: product_prod_V_V] :
            ~ ( member2015049524od_V_V @ B @ A ) )
      = ( A = bot_bo1389414743od_V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_all__not__in__conv) ).

thf(1452,plain,
    ! [A: set_Product_prod_V_V] :
      ( ( ! [B: product_prod_V_V] :
            ~ ( member2015049524od_V_V @ B @ A ) )
      = ( A = bot_bo1389414743od_V_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(35,axiom,
    ! [A: v,B: set_V,C: set_V] :
      ( ( member_V2 @ A @ B )
     => ( member_V2 @ A @ ( sup_sup_set_V2 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_UnI1) ).

thf(441,plain,
    ! [A: v,B: set_V,C: set_V] :
      ( ( member_V2 @ A @ B )
     => ( member_V2 @ A @ ( sup_sup_set_V2 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(42,axiom,
    ! [A: labele2115946735nt_V_V,B: v > v] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( graph_1808119_V_V_V @ A @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_graph__homo) ).

thf(463,plain,
    ! [A: labele2115946735nt_V_V,B: v > v] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( graph_1808119_V_V_V @ A @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(44,axiom,
    ! [A: labele2115946735nt_V_V,B: v > v,C: v > v] :
      ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ ( comp_V_V_V2 @ B @ C ) ) @ A )
      = ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ C ) @ A ) ) @ B ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_map__graph__fn__comp) ).

thf(470,plain,
    ! [A: labele2115946735nt_V_V,B: v > v,C: v > v] :
      ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ ( comp_V_V_V2 @ B @ C ) ) @ A )
      = ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ C ) @ A ) ) @ B ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(144,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ~ ! [C: set_Pr1058435079_V_nat] :
            ( ( B
              = ( insert481364471_V_nat @ A @ C ) )
           => ( member1886821968_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_Set_Oset__insert) ).

thf(808,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( member1886821968_V_nat @ A @ B )
     => ~ ! [C: set_Pr1058435079_V_nat] :
            ( ( B
              = ( insert481364471_V_nat @ A @ C ) )
           => ( member1886821968_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(8,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ B @ C ) )
      = ( ( member1010391347od_V_V @ A @ B )
        | ( member1010391347od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_Un__iff) ).

thf(359,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ B @ C ) )
      = ( ( member1010391347od_V_V @ A @ B )
        | ( member1010391347od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(272,axiom,
    ! [A: v2] :
      ( standard_S_Bot_V
     != ( standard_S_Const_V @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Standard__Constant_Odistinct_I9_J) ).

thf(1218,plain,
    ! [A: v2] :
      ( standard_S_Bot_V
     != ( standard_S_Const_V @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(308,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( ( insert2024285275od_V_V @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_insert__absorb) ).

thf(1336,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( ( insert2024285275od_V_V @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(93,axiom,
    ( bot_bo1078500394_nat_o
    = ( ^ [A: produc778275879_V_nat] : ( member1886821968_V_nat @ A @ bot_bo907687539_V_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_bot__empty__eq) ).

thf(643,plain,
    ( bot_bo1078500394_nat_o
    = ( ^ [A: produc778275879_V_nat] : ( member1886821968_V_nat @ A @ bot_bo907687539_V_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(327,axiom,
    ! [A: set_Product_prod_V_V] :
      ( ( ? [B: product_prod_V_V] : ( member2015049524od_V_V @ B @ A ) )
      = ( A != bot_bo1389414743od_V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_ex__in__conv) ).

thf(1404,plain,
    ! [A: set_Product_prod_V_V] :
      ( ( ? [B: product_prod_V_V] : ( member2015049524od_V_V @ B @ A ) )
      = ( A != bot_bo1389414743od_V_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(123,axiom,
    ( ( standa1571708471od_V_V @ bot_bo1389414743od_V_V )
    = bot_bo1196823539_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_constant__rules__empty) ).

thf(744,plain,
    ( ( standa1571708471od_V_V @ bot_bo1389414743od_V_V )
    = bot_bo1196823539_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(282,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_insertI2) ).

thf(1257,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(292,axiom,
    ! [A: labele236903175od_V_V,B: product_prod_V_V > v,C: set_Pr744279122od_V_V] :
      ( ! [D: standard_Constant_V,E: product_prod_V_V,F: product_prod_V_V] :
          ( ( member361435663od_V_V @ ( produc1482441770od_V_V @ D @ ( produc1905750615od_V_V @ E @ F ) ) @ ( labele668941254od_V_V @ A ) )
         => ( ( member2015049524od_V_V @ E @ ( labele981584981od_V_V @ A ) )
           => ( ( member2015049524od_V_V @ F @ ( labele981584981od_V_V @ A ) )
             => ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
     => ( edge_p1776314003tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ A ) @ B ) @ ( labele668941254od_V_V @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_edge__preserving__on__graphI) ).

thf(1284,plain,
    ! [A: labele236903175od_V_V,B: product_prod_V_V > v,C: set_Pr744279122od_V_V] :
      ( ! [D: standard_Constant_V,E: product_prod_V_V,F: product_prod_V_V] :
          ( ( member361435663od_V_V @ ( produc1482441770od_V_V @ D @ ( produc1905750615od_V_V @ E @ F ) ) @ ( labele668941254od_V_V @ A ) )
         => ( ( member2015049524od_V_V @ E @ ( labele981584981od_V_V @ A ) )
           => ( ( member2015049524od_V_V @ F @ ( labele981584981od_V_V @ A ) )
             => ( member1010391347od_V_V @ ( produc107991630od_V_V @ D @ ( product_Pair_V_V2 @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
     => ( edge_p1776314003tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ A ) @ B ) @ ( labele668941254od_V_V @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(221,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: set_Product_prod_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
     => ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ C @ A ) @ ( map_gr907434255tant_V @ C @ B ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_map__graph__preserves__subgraph) ).

thf(1052,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: set_Product_prod_V_V] :
      ( ( graph_1808119_V_V_V @ A @ B @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
     => ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ C @ A ) @ ( map_gr907434255tant_V @ C @ B ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(334,axiom,
    ! [A: produc1699571228od_V_V > $o,B: produc1699571228od_V_V] :
      ( ! [C: standard_Constant_V,D: v,E: v] : ( A @ ( produc107991630od_V_V @ C @ ( product_Pair_V_V2 @ D @ E ) ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod__induct3) ).

thf(1427,plain,
    ! [A: produc1699571228od_V_V > $o,B: produc1699571228od_V_V] :
      ( ! [C: standard_Constant_V,D: v,E: v] : ( A @ ( produc107991630od_V_V @ C @ ( product_Pair_V_V2 @ D @ E ) ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(74,axiom,
    ! [A: v,B: v,C: set_V] :
      ( ( member_V2 @ A @ ( insert_V2 @ B @ C ) )
      = ( ( A = B )
        | ( member_V2 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_insert__iff) ).

thf(571,plain,
    ! [A: v,B: v,C: set_V] :
      ( ( member_V2 @ A @ ( insert_V2 @ B @ C ) )
      = ( ( A = B )
        | ( member_V2 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(287,axiom,
    member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ xa ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).

thf(1272,plain,
    member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ xa ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(201,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat] :
      ( ( ( sup_su1043134939_V_nat @ A @ B )
        = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) )
      = ( ( ( A = bot_bo907687539_V_nat )
          & ( B
            = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) ) )
        | ( ( A
            = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) )
          & ( B = bot_bo907687539_V_nat ) )
        | ( ( A
            = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) )
          & ( B
            = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Un__singleton__iff) ).

thf(991,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat] :
      ( ( ( sup_su1043134939_V_nat @ A @ B )
        = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) )
      = ( ( ( A = bot_bo907687539_V_nat )
          & ( B
            = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) ) )
        | ( ( A
            = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) )
          & ( B = bot_bo907687539_V_nat ) )
        | ( ( A
            = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) )
          & ( B
            = ( insert481364471_V_nat @ C @ bot_bo907687539_V_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(197,axiom,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ bot_bo667804902od_V_V ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_singleton__iff) ).

thf(978,plain,
    ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V] :
      ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ bot_bo667804902od_V_V ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(250,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: standard_Constant_V,D: labele236903175od_V_V,E: product_prod_V_V > v] :
      ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ B ) @ ( getRel1902920892od_V_V @ C @ D ) )
     => ( ( member2015049524od_V_V @ A @ ( labele981584981od_V_V @ D ) )
       => ( ( member2015049524od_V_V @ B @ ( labele981584981od_V_V @ D ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ A ) @ ( E @ B ) ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ D ) @ E ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_getRel__hom) ).

thf(1140,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: standard_Constant_V,D: labele236903175od_V_V,E: product_prod_V_V > v] :
      ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ B ) @ ( getRel1902920892od_V_V @ C @ D ) )
     => ( ( member2015049524od_V_V @ A @ ( labele981584981od_V_V @ D ) )
       => ( ( member2015049524od_V_V @ B @ ( labele981584981od_V_V @ D ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ A ) @ ( E @ B ) ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ D ) @ E ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(156,axiom,
    ! [A: v,B: v] :
      ( ( member_V2 @ A @ ( insert_V2 @ B @ bot_bot_set_V2 ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_singletonD) ).

thf(845,plain,
    ! [A: v,B: v] :
      ( ( member_V2 @ A @ ( insert_V2 @ B @ bot_bot_set_V2 ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(262,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: product_prod_V_V,D: set_Product_prod_V_V] :
      ( ~ ( member2015049524od_V_V @ A @ B )
     => ( ~ ( member2015049524od_V_V @ C @ D )
       => ( ( ( insert2024285275od_V_V @ A @ B )
            = ( insert2024285275od_V_V @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Product_prod_V_V] :
                  ( ( B
                    = ( insert2024285275od_V_V @ C @ E ) )
                  & ~ ( member2015049524od_V_V @ C @ E )
                  & ( D
                    = ( insert2024285275od_V_V @ A @ E ) )
                  & ~ ( member2015049524od_V_V @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_insert__eq__iff) ).

thf(1180,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: product_prod_V_V,D: set_Product_prod_V_V] :
      ( ~ ( member2015049524od_V_V @ A @ B )
     => ( ~ ( member2015049524od_V_V @ C @ D )
       => ( ( ( insert2024285275od_V_V @ A @ B )
            = ( insert2024285275od_V_V @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Product_prod_V_V] :
                  ( ( B
                    = ( insert2024285275od_V_V @ C @ E ) )
                  & ~ ( member2015049524od_V_V @ C @ E )
                  & ( D
                    = ( insert2024285275od_V_V @ A @ E ) )
                  & ~ ( member2015049524od_V_V @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(256,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ? [C: set_Product_prod_V_V] :
          ( ( B
            = ( insert2024285275od_V_V @ A @ C ) )
          & ~ ( member2015049524od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_mk__disjoint__insert) ).

thf(1157,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V] :
      ( ( member2015049524od_V_V @ A @ B )
     => ? [C: set_Product_prod_V_V] :
          ( ( B
            = ( insert2024285275od_V_V @ A @ C ) )
          & ~ ( member2015049524od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(52,axiom,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( member_V @ A @ B )
     => ( member_V @ A @ ( sup_sup_set_V @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_UnI1) ).

thf(495,plain,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( member_V @ A @ B )
     => ( member_V @ A @ ( sup_sup_set_V @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(129,axiom,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( member_V @ A @ B )
     => ( member_V @ A @ ( sup_sup_set_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_UnI2) ).

thf(759,plain,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( member_V @ A @ B )
     => ( member_V @ A @ ( sup_sup_set_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(169,axiom,
    ! [A: v,B: set_V] :
      ( ( member_V2 @ A @ B )
     => ? [C: set_V] :
          ( ( B
            = ( insert_V2 @ A @ C ) )
          & ~ ( member_V2 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_mk__disjoint__insert) ).

thf(891,plain,
    ! [A: v,B: set_V] :
      ( ( member_V2 @ A @ B )
     => ? [C: set_V] :
          ( ( B
            = ( insert_V2 @ A @ C ) )
          & ~ ( member_V2 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(246,axiom,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( product_Pair_V_V2 @ A @ B )
        = ( product_Pair_V_V2 @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_prod_Oinject) ).

thf(1126,plain,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( product_Pair_V_V2 @ A @ B )
        = ( product_Pair_V_V2 @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(302,axiom,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: standard_Constant_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( getRel1432786916nt_V_V @ D @ A ) )
       => ( member_V2 @ C @ ( labele1134902411nt_V_V @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_getRel__dom_I2_J) ).

thf(1316,plain,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: standard_Constant_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( getRel1432786916nt_V_V @ D @ A ) )
       => ( member_V2 @ C @ ( labele1134902411nt_V_V @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(232,axiom,
    ! [A: set_Pr1058435079_V_nat,B: labele2115946735nt_V_V,C: produc778275879_V_nat] :
      ( ( conseq1236301781_nat_V @ A @ B )
     => ( ( member1886821968_V_nat @ C @ A )
       => ( mainta197426964_nat_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_consequence__graphD_I1_J) ).

thf(1084,plain,
    ! [A: set_Pr1058435079_V_nat,B: labele2115946735nt_V_V,C: produc778275879_V_nat] :
      ( ( conseq1236301781_nat_V @ A @ B )
     => ( ( member1886821968_V_nat @ C @ A )
       => ( mainta197426964_nat_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(341,axiom,
    ~ ! [A: v2 > v] :
        ~ ! [B: v2] :
            ( ( member_V @ B @ c )
           => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( A @ B ) @ ( A @ B ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ B ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(1448,plain,
    ~ ! [A: v2 > v] :
        ~ ! [B: v2] :
            ( ( member_V @ B @ c )
           => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( A @ B ) @ ( A @ B ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ B ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(265,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ~ ( member2015049524od_V_V @ A @ B )
     => ( ~ ( member2015049524od_V_V @ A @ C )
       => ( ( ( insert2024285275od_V_V @ A @ B )
            = ( insert2024285275od_V_V @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_insert__ident) ).

thf(1189,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: set_Product_prod_V_V] :
      ( ~ ( member2015049524od_V_V @ A @ B )
     => ( ~ ( member2015049524od_V_V @ A @ C )
       => ( ( ( insert2024285275od_V_V @ A @ B )
            = ( insert2024285275od_V_V @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(192,axiom,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: produc778275879_V_nat,D: produc778275879_V_nat] :
      ( ( ( insert481364471_V_nat @ A @ ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
        = ( insert481364471_V_nat @ C @ ( insert481364471_V_nat @ D @ bot_bo907687539_V_nat ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_doubleton__eq__iff) ).

thf(963,plain,
    ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: produc778275879_V_nat,D: produc778275879_V_nat] :
      ( ( ( insert481364471_V_nat @ A @ ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
        = ( insert481364471_V_nat @ C @ ( insert481364471_V_nat @ D @ bot_bo907687539_V_nat ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(170,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) )
      = ( sup_su1043134939_V_nat @ B @ ( sup_su1043134939_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_Un__left__commute) ).

thf(896,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ B @ C ) )
      = ( sup_su1043134939_V_nat @ B @ ( sup_su1043134939_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(188,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ bot_bo907687539_V_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Un__empty__right) ).

thf(946,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ bot_bo907687539_V_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(5,axiom,
    ! [A: set_V2] :
      ( ( ! [B: v2] :
            ~ ( member_V @ B @ A ) )
      = ( A = bot_bot_set_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_all__not__in__conv) ).

thf(351,plain,
    ! [A: set_V2] :
      ( ( ! [B: v2] :
            ~ ( member_V @ B @ A ) )
      = ( A = bot_bot_set_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(120,axiom,
    ! [A: labele201426742od_V_V,B: v > produc1699571228od_V_V,C: produc1699571228od_V_V > v,D: produc778275879_V_nat] :
      ( ! [E: produc1699571228od_V_V] :
          ( ( member1010391347od_V_V @ E @ ( labele1328382418od_V_V @ A ) )
         => ( ( comp_V1480932210od_V_V @ B @ C @ E )
            = E ) )
     => ( ( A
          = ( restri1699516426od_V_V @ A ) )
       => ( ( mainta197426964_nat_V @ D @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ A ) @ C ) @ A ) )
         => ( mainta1342478555od_V_V @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_maintained__preserved__by__isomorphism) ).

thf(731,plain,
    ! [A: labele201426742od_V_V,B: v > produc1699571228od_V_V,C: produc1699571228od_V_V > v,D: produc778275879_V_nat] :
      ( ! [E: produc1699571228od_V_V] :
          ( ( member1010391347od_V_V @ E @ ( labele1328382418od_V_V @ A ) )
         => ( ( comp_V1480932210od_V_V @ B @ C @ E )
            = E ) )
     => ( ( A
          = ( restri1699516426od_V_V @ A ) )
       => ( ( mainta197426964_nat_V @ D @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ A ) @ C ) @ A ) )
         => ( mainta1342478555od_V_V @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(145,axiom,
    ! [A: set_Product_prod_V_V,B: labele2115946735nt_V_V] : ( edge_p1560004099tant_V @ A @ ( labele515735386nt_V_V @ B ) @ ( labele515735386nt_V_V @ ( map_gr907434255tant_V @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_map__graph__edge__preserving) ).

thf(813,plain,
    ! [A: set_Product_prod_V_V,B: labele2115946735nt_V_V] : ( edge_p1560004099tant_V @ A @ ( labele515735386nt_V_V @ B ) @ ( labele515735386nt_V_V @ ( map_gr907434255tant_V @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(321,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ B ) @ ( id_on_2125509800od_V_V @ C ) )
      = ( ( A = B )
        & ( member2015049524od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Id__on__iff) ).

thf(1385,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V,C: set_Product_prod_V_V] :
      ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ B ) @ ( id_on_2125509800od_V_V @ C ) )
      = ( ( A = B )
        & ( member2015049524od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(73,axiom,
    ! [A: product_prod_V_V,B: product_prod_V_V] :
      ( ( ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V )
        = ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_singleton__inject) ).

thf(568,plain,
    ! [A: product_prod_V_V,B: product_prod_V_V] :
      ( ( ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V )
        = ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(176,axiom,
    ! [A: labele2115946735nt_V_V,B: set_Pr1056235617_nat_V] :
      ( ( graph_227683057_nat_V @ ( labele1193521135_V_nat @ bot_bo634818242_V_nat @ bot_bo907687539_V_nat ) @ A @ B )
      = ( ( B = bot_bo1708783349_nat_V )
        & ( A
          = ( restri1305980611nt_V_V @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_graph__homomorphism__empty) ).

thf(914,plain,
    ! [A: labele2115946735nt_V_V,B: set_Pr1056235617_nat_V] :
      ( ( graph_227683057_nat_V @ ( labele1193521135_V_nat @ bot_bo634818242_V_nat @ bot_bo907687539_V_nat ) @ A @ B )
      = ( ( B = bot_bo1708783349_nat_V )
        & ( A
          = ( restri1305980611nt_V_V @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(295,axiom,
    ! [A: v2] :
    ? [B: v] :
      ( ( member_V @ A @ c )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ B ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ A ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__092_060open_062_092_060forall_062c_O_A_092_060exists_062v_O_Ac_A_092_060in_062_AC_A_092_060longrightarrow_062_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).

thf(1294,plain,
    ! [A: v2] :
    ? [B: v] :
      ( ( member_V @ A @ c )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ B ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ A ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(181,axiom,
    ! [A: labele2115946735nt_V_V,B: set_Pr1228022213_V_V_V] :
      ( ( graph_840721237_V_V_V @ ( labele94156371od_V_V @ bot_bo451843010od_V_V @ bot_bo1389414743od_V_V ) @ A @ B )
      = ( ( B = bot_bo688400985_V_V_V )
        & ( A
          = ( restri1305980611nt_V_V @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_graph__homomorphism__empty) ).

thf(929,plain,
    ! [A: labele2115946735nt_V_V,B: set_Pr1228022213_V_V_V] :
      ( ( graph_840721237_V_V_V @ ( labele94156371od_V_V @ bot_bo451843010od_V_V @ bot_bo1389414743od_V_V ) @ A @ B )
      = ( ( B = bot_bo688400985_V_V_V )
        & ( A
          = ( restri1305980611nt_V_V @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(266,axiom,
    ! [A: v,B: v,C: set_V] :
      ( ( A = B )
     => ( ( member_V2 @ A @ C )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( id_on_V2 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Id__on__eqI) ).

thf(1193,plain,
    ! [A: v,B: v,C: set_V] :
      ( ( A = B )
     => ( ( member_V2 @ A @ C )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( id_on_V2 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(271,axiom,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: product_prod_V_V] :
      ( ( ~ ( member2015049524od_V_V @ A @ B )
       => ( A = C ) )
     => ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insertCI) ).

thf(1212,plain,
    ! [A: product_prod_V_V,B: set_Product_prod_V_V,C: product_prod_V_V] :
      ( ( ~ ( member2015049524od_V_V @ A @ B )
       => ( A = C ) )
     => ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(171,axiom,
    ! [A: set_Pr1058435079_V_nat,B: produc778275879_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( insert481364471_V_nat @ B @ C ) )
      = ( insert481364471_V_nat @ B @ ( sup_su1043134939_V_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_Un__insert__right) ).

thf(899,plain,
    ! [A: set_Pr1058435079_V_nat,B: produc778275879_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ ( insert481364471_V_nat @ B @ C ) )
      = ( insert481364471_V_nat @ B @ ( sup_su1043134939_V_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(105,axiom,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: set_St1111633946tant_V,D: standard_Constant_V > product_prod_V_V] :
      ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ B ) @ ( bNF_Gr320641027od_V_V @ C @ D ) )
      = ( ( member1542015739tant_V @ A @ C )
        & ( ( D @ A )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_in__Gr) ).

thf(684,plain,
    ! [A: standard_Constant_V,B: product_prod_V_V,C: set_St1111633946tant_V,D: standard_Constant_V > product_prod_V_V] :
      ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ B ) @ ( bNF_Gr320641027od_V_V @ C @ D ) )
      = ( ( member1542015739tant_V @ A @ C )
        & ( ( D @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(299,axiom,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: allego859987871tant_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( semant993842370nt_V_V @ A @ D ) )
       => ( member_V2 @ C @ ( labele1134902411nt_V_V @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_semantics__in__vertices_I2_J) ).

thf(1309,plain,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: allego859987871tant_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( semant993842370nt_V_V @ A @ D ) )
       => ( member_V2 @ C @ ( labele1134902411nt_V_V @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(142,axiom,
    ! [A: v,B: set_V] :
      ( ( member_V2 @ A @ B )
     => ( ( insert_V2 @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_insert__absorb) ).

thf(800,plain,
    ! [A: v,B: set_V] :
      ( ( member_V2 @ A @ B )
     => ( ( insert_V2 @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(242,axiom,
    ! [A: labele2115946735nt_V_V,B: v > v] :
      ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A )
      = ( restri1305980611nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_map__graph__fn__graphI) ).

thf(1116,plain,
    ! [A: labele2115946735nt_V_V,B: v > v] :
      ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A )
      = ( restri1305980611nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ A ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(311,axiom,
    ! [A: product_prod_V_V] :
      ~ ( member2015049524od_V_V @ A @ bot_bo1389414743od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_emptyE) ).

thf(1348,plain,
    ! [A: product_prod_V_V] :
      ~ ( member2015049524od_V_V @ A @ bot_bo1389414743od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(37,axiom,
    ! [A: set_V2] :
      ( ! [B: v2] :
          ~ ( member_V @ B @ A )
     => ( A = bot_bot_set_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_equals0I) ).

thf(447,plain,
    ! [A: set_V2] :
      ( ! [B: v2] :
          ~ ( member_V @ B @ A )
     => ( A = bot_bot_set_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(32,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_UnI1) ).

thf(432,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( member1010391347od_V_V @ A @ ( sup_su693515134od_V_V @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(147,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_Un__absorb) ).

thf(818,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(319,axiom,
    ! [A: v2] :
      ( ( member_V @ A @ c )
     => ? [B: v] : ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ B ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ A ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__092_060open_062_092_060And_062c_O_Ac_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_092_060exists_062v_O_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).

thf(1380,plain,
    ! [A: v2] :
      ( ( member_V @ A @ c )
     => ? [B: v] : ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ B ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ A ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(24,axiom,
    ! [A: v > v,B: v > v,C: v > v,D: v > v,E: v] :
      ( ( ( comp_V_V_V2 @ A @ B )
        = ( comp_V_V_V2 @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_comp__eq__dest) ).

thf(405,plain,
    ! [A: v > v,B: v > v,C: v > v,D: v > v,E: v] :
      ( ( ( comp_V_V_V2 @ A @ B )
        = ( comp_V_V_V2 @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(159,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: produc1699571228od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_insertI2) ).

thf(854,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: produc1699571228od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(279,axiom,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: allego859987871tant_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( semant993842370nt_V_V @ A @ D ) )
       => ( member_V2 @ B @ ( labele1134902411nt_V_V @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_semantics__in__vertices_I1_J) ).

thf(1248,plain,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: allego859987871tant_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( semant993842370nt_V_V @ A @ D ) )
       => ( member_V2 @ B @ ( labele1134902411nt_V_V @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(162,axiom,
    ! [A: v2,B: v2,C: set_V2] :
      ( ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ B ) @ ( id_on_V @ C ) )
      = ( ( A = B )
        & ( member_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Id__on__iff) ).

thf(865,plain,
    ! [A: v2,B: v2,C: set_V2] :
      ( ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ B ) @ ( id_on_V @ C ) )
      = ( ( A = B )
        & ( member_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(82,axiom,
    ! [A: set_V] :
      ( ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ A )
      = ( restri1305980611nt_V_V @ ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_graph__empty__e) ).

thf(603,plain,
    ! [A: set_V] :
      ( ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ A )
      = ( restri1305980611nt_V_V @ ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(337,axiom,
    ! [A: v,B: set_V] :
      ( ( member_V2 @ A @ B )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ A ) @ ( id_on_V2 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Id__onI) ).

thf(1436,plain,
    ! [A: v,B: set_V] :
      ( ( member_V2 @ A @ B )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ A ) @ ( id_on_V2 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(56,axiom,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_sup__bot__left) ).

thf(506,plain,
    ! [A: set_Pr1058435079_V_nat] :
      ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(109,axiom,
    ( sup_su1043134939_V_nat
    = ( ^ [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] : ( sup_su1043134939_V_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_Un__commute) ).

thf(696,plain,
    ( sup_su1043134939_V_nat
    = ( ^ [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] : ( sup_su1043134939_V_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(310,axiom,
    ( bot_bo1168561222_V_V_o
    = ( ^ [A: product_prod_V_V] : ( member2015049524od_V_V @ A @ bot_bo1389414743od_V_V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_bot__empty__eq) ).

thf(1346,plain,
    ( bot_bo1168561222_V_V_o
    = ( ^ [A: product_prod_V_V] : ( member2015049524od_V_V @ A @ bot_bo1389414743od_V_V ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(215,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ~ ( member1010391347od_V_V @ A @ B )
     => ( ~ ( member1010391347od_V_V @ A @ C )
       => ( ( ( insert135842892od_V_V @ A @ B )
            = ( insert135842892od_V_V @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_insert__ident) ).

thf(1033,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V,C: set_Pr744279122od_V_V] :
      ( ~ ( member1010391347od_V_V @ A @ B )
     => ( ~ ( member1010391347od_V_V @ A @ C )
       => ( ( ( insert135842892od_V_V @ A @ B )
            = ( insert135842892od_V_V @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(22,axiom,
    ( comp_V_V_V2
    = ( ^ [A: v > v,B: v > v,C: v] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_comp__def) ).

thf(400,plain,
    ( comp_V_V_V2
    = ( ^ [A: v > v,B: v > v,C: v] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(117,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( ( sup_su1043134939_V_nat @ A @ B )
        = bot_bo907687539_V_nat )
      = ( ( A = bot_bo907687539_V_nat )
        & ( B = bot_bo907687539_V_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_sup__bot_Oeq__neutr__iff) ).

thf(720,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( ( sup_su1043134939_V_nat @ A @ B )
        = bot_bo907687539_V_nat )
      = ( ( A = bot_bo907687539_V_nat )
        & ( B = bot_bo907687539_V_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(258,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: set_Product_prod_V_V,D: v,E: v,F: allego859987871tant_V,G: v,H: v] :
      ( ( graph_1808119_V_V_V @ A @ B @ C )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ D @ E ) @ ( semant993842370nt_V_V @ A @ F ) )
       => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ D @ G ) @ C )
         => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ E @ H ) @ C )
           => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ G @ H ) @ ( semant993842370nt_V_V @ B @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_graph__homomorphism__semantics) ).

thf(1165,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V,C: set_Product_prod_V_V,D: v,E: v,F: allego859987871tant_V,G: v,H: v] :
      ( ( graph_1808119_V_V_V @ A @ B @ C )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ D @ E ) @ ( semant993842370nt_V_V @ A @ F ) )
       => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ D @ G ) @ C )
         => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ E @ H ) @ C )
           => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ G @ H ) @ ( semant993842370nt_V_V @ B @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(154,axiom,
    ! [A: set_Product_prod_V_V] :
      ( ( sup_su551882943od_V_V @ bot_bo1389414743od_V_V @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_sup__bot_Oleft__neutral) ).

thf(839,plain,
    ! [A: set_Product_prod_V_V] :
      ( ( sup_su551882943od_V_V @ bot_bo1389414743od_V_V @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(247,axiom,
    ! [A: v2,B: v2,C: standard_Constant_V,D: labele788688367nt_V_V,E: v2 > v] :
      ( ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ B ) @ ( getRel632961956nt_V_V @ C @ D ) )
     => ( ( member_V @ A @ ( labele1152678333nt_V_V @ D ) )
       => ( ( member_V @ B @ ( labele1152678333nt_V_V @ D ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ A ) @ ( E @ B ) ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ D ) @ E ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_getRel__hom) ).

thf(1129,plain,
    ! [A: v2,B: v2,C: standard_Constant_V,D: labele788688367nt_V_V,E: v2 > v] :
      ( ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ B ) @ ( getRel632961956nt_V_V @ C @ D ) )
     => ( ( member_V @ A @ ( labele1152678333nt_V_V @ D ) )
       => ( ( member_V @ B @ ( labele1152678333nt_V_V @ D ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( E @ A ) @ ( E @ B ) ) @ ( getRel1432786916nt_V_V @ C @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ D ) @ E ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(161,axiom,
    ! [A: standard_Constant_V,B: set_St1111633946tant_V,C: standard_Constant_V > product_prod_V_V,D: product_prod_V_V] :
      ( ( ~ ( member1542015739tant_V @ A @ B )
        | ( ( C @ A )
         != D ) )
     => ~ ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ D ) @ ( bNF_Gr320641027od_V_V @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Gr__not__in) ).

thf(860,plain,
    ! [A: standard_Constant_V,B: set_St1111633946tant_V,C: standard_Constant_V > product_prod_V_V,D: product_prod_V_V] :
      ( ( ~ ( member1542015739tant_V @ A @ B )
        | ( ( C @ A )
         != D ) )
     => ~ ( member1010391347od_V_V @ ( produc107991630od_V_V @ A @ D ) @ ( bNF_Gr320641027od_V_V @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(81,axiom,
    ! [A: labele788688367nt_V_V,B: v > v2,C: v2 > v,D: produc778275879_V_nat] :
      ( ! [E: v2] :
          ( ( member_V @ E @ ( labele1152678333nt_V_V @ A ) )
         => ( ( comp_V_V_V @ B @ C @ E )
            = E ) )
     => ( ( A
          = ( restri175070597nt_V_V @ A ) )
       => ( ( mainta197426964_nat_V @ D @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ A ) @ C ) @ A ) )
         => ( mainta1026355316_nat_V @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_maintained__preserved__by__isomorphism) ).

thf(596,plain,
    ! [A: labele788688367nt_V_V,B: v > v2,C: v2 > v,D: produc778275879_V_nat] :
      ( ! [E: v2] :
          ( ( member_V @ E @ ( labele1152678333nt_V_V @ A ) )
         => ( ( comp_V_V_V @ B @ C @ E )
            = E ) )
     => ( ( A
          = ( restri175070597nt_V_V @ A ) )
       => ( ( mainta197426964_nat_V @ D @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ A ) @ C ) @ A ) )
         => ( mainta1026355316_nat_V @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(210,axiom,
    ! [A: v,B: v,C: set_V] :
      ( ( member_V2 @ A @ ( insert_V2 @ B @ C ) )
     => ( ( A != B )
       => ( member_V2 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_insertE) ).

thf(1019,plain,
    ! [A: v,B: v,C: set_V] :
      ( ( member_V2 @ A @ ( insert_V2 @ B @ C ) )
     => ( ( A != B )
       => ( member_V2 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(174,axiom,
    ! [A: labele2115946735nt_V_V] :
      ( ( graph_1808119_V_V_V @ A @ ( restri1305980611nt_V_V @ A ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
      = ( A
        = ( restri1305980611nt_V_V @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_subgraph__restrict) ).

thf(908,plain,
    ! [A: labele2115946735nt_V_V] :
      ( ( graph_1808119_V_V_V @ A @ ( restri1305980611nt_V_V @ A ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) )
      = ( A
        = ( restri1305980611nt_V_V @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(118,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat > $o] :
      ( ( ! [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ ( sup_su1043134939_V_nat @ A @ B ) )
           => ( C @ D ) ) )
      = ( ! [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ A )
           => ( C @ D ) )
        & ! [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ B )
           => ( C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_ball__Un) ).

thf(723,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat,C: produc778275879_V_nat > $o] :
      ( ( ! [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ ( sup_su1043134939_V_nat @ A @ B ) )
           => ( C @ D ) ) )
      = ( ! [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ A )
           => ( C @ D ) )
        & ! [D: produc778275879_V_nat] :
            ( ( member1886821968_V_nat @ D @ B )
           => ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(158,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( ~ ( member1886821968_V_nat @ A @ B )
       => ( member1886821968_V_nat @ A @ C ) )
     => ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_UnCI) ).

thf(850,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat,C: set_Pr1058435079_V_nat] :
      ( ( ~ ( member1886821968_V_nat @ A @ B )
       => ( member1886821968_V_nat @ A @ C ) )
     => ( member1886821968_V_nat @ A @ ( sup_su1043134939_V_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(326,axiom,
    ! [A: v2,B: labele788688367nt_V_V,C: v2,D: standard_Constant_V,E: v2 > v,F: v,G: v] :
      ( ( member_V @ A @ ( labele1152678333nt_V_V @ B ) )
     => ( ( member_V @ C @ ( labele1152678333nt_V_V @ B ) )
       => ( ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ C ) @ ( getRel632961956nt_V_V @ D @ B ) )
         => ( ( ( E @ A )
              = F )
           => ( ( ( E @ C )
                = G )
             => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ ( getRel1432786916nt_V_V @ D @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_getRel__map__fn) ).

thf(1399,plain,
    ! [A: v2,B: labele788688367nt_V_V,C: v2,D: standard_Constant_V,E: v2 > v,F: v,G: v] :
      ( ( member_V @ A @ ( labele1152678333nt_V_V @ B ) )
     => ( ( member_V @ C @ ( labele1152678333nt_V_V @ B ) )
       => ( ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ C ) @ ( getRel632961956nt_V_V @ D @ B ) )
         => ( ( ( E @ A )
              = F )
           => ( ( ( E @ C )
                = G )
             => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ ( getRel1432786916nt_V_V @ D @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(54,axiom,
    ( ( standa294833961ules_V @ bot_bot_set_V2 )
    = bot_bo1834032757_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_constant__rules__empty) ).

thf(501,plain,
    ( ( standa294833961ules_V @ bot_bot_set_V2 )
    = bot_bo1834032757_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(12,axiom,
    ! [A: set_V,B: set_V] :
      ( ( ( sup_sup_set_V2 @ A @ B )
        = bot_bot_set_V2 )
      = ( ( A = bot_bot_set_V2 )
        & ( B = bot_bot_set_V2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_sup__bot_Oeq__neutr__iff) ).

thf(369,plain,
    ! [A: set_V,B: set_V] :
      ( ( ( sup_sup_set_V2 @ A @ B )
        = bot_bot_set_V2 )
      = ( ( A = bot_bot_set_V2 )
        & ( B = bot_bot_set_V2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(306,axiom,
    ! [A: produc778275879_V_nat] :
      ( ( mainta197426964_nat_V @ A @ g )
     => ( mainta197426964_nat_V @ A @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_mg) ).

thf(1331,plain,
    ! [A: produc778275879_V_nat] :
      ( ( mainta197426964_nat_V @ A @ g )
     => ( mainta197426964_nat_V @ A @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(49,axiom,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] :
      ( ( ( ( labele515735386nt_V_V @ A )
          = ( labele515735386nt_V_V @ B ) )
        & ( ( labele1134902411nt_V_V @ A )
          = ( labele1134902411nt_V_V @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_labeled__graph_Oexpand) ).

thf(486,plain,
    ! [A: labele2115946735nt_V_V,B: labele2115946735nt_V_V] :
      ( ( ( ( labele515735386nt_V_V @ A )
          = ( labele515735386nt_V_V @ B ) )
        & ( ( labele1134902411nt_V_V @ A )
          = ( labele1134902411nt_V_V @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(143,axiom,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ? [C: set_Pr744279122od_V_V] :
          ( ( B
            = ( insert135842892od_V_V @ A @ C ) )
          & ~ ( member1010391347od_V_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_mk__disjoint__insert) ).

thf(803,plain,
    ! [A: produc1699571228od_V_V,B: set_Pr744279122od_V_V] :
      ( ( member1010391347od_V_V @ A @ B )
     => ? [C: set_Pr744279122od_V_V] :
          ( ( B
            = ( insert135842892od_V_V @ A @ C ) )
          & ~ ( member1010391347od_V_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(303,axiom,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: standard_Constant_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( getRel1432786916nt_V_V @ D @ A ) )
       => ( member_V2 @ B @ ( labele1134902411nt_V_V @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_getRel__dom_I1_J) ).

thf(1320,plain,
    ! [A: labele2115946735nt_V_V,B: v,C: v,D: standard_Constant_V] :
      ( ( A
        = ( restri1305980611nt_V_V @ A ) )
     => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ C ) @ ( getRel1432786916nt_V_V @ D @ A ) )
       => ( member_V2 @ B @ ( labele1134902411nt_V_V @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(186,axiom,
    ! [A: set_V] :
      ( ( ! [B: v] :
            ~ ( member_V2 @ B @ A ) )
      = ( A = bot_bot_set_V2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_all__not__in__conv) ).

thf(940,plain,
    ! [A: set_V] :
      ( ( ! [B: v] :
            ~ ( member_V2 @ B @ A ) )
      = ( A = bot_bot_set_V2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(6,axiom,
    ! [A: v,B: set_V,C: set_V] :
      ( ( member_V2 @ A @ B )
     => ( member_V2 @ A @ ( sup_sup_set_V2 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_UnI2) ).

thf(354,plain,
    ! [A: v,B: set_V,C: set_V] :
      ( ( member_V2 @ A @ B )
     => ( member_V2 @ A @ ( sup_sup_set_V2 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(207,axiom,
    ! [A: produc778275879_V_nat] : ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_singletonI) ).

thf(1009,plain,
    ! [A: produc778275879_V_nat] : ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(179,axiom,
    ! [A: labele2128733290_V_nat > labele2128733290_V_nat] :
      ( ( bNF_Gr17960482_V_nat @ bot_bo1053950006_V_nat @ A )
      = bot_bo907687539_V_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Gr__empty) ).

thf(923,plain,
    ! [A: labele2128733290_V_nat > labele2128733290_V_nat] :
      ( ( bNF_Gr17960482_V_nat @ bot_bo1053950006_V_nat @ A )
      = bot_bo907687539_V_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(263,axiom,
    ! [A: product_prod_V_V] :
    ? [B: v,C: v] :
      ( A
      = ( product_Pair_V_V2 @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_surj__pair) ).

thf(1184,plain,
    ! [A: product_prod_V_V] :
    ? [B: v,C: v] :
      ( A
      = ( product_Pair_V_V2 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(66,axiom,
    ( bot_bo1389414743od_V_V
    = ( collec2040633974od_V_V @ bot_bo1168561222_V_V_o ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_bot__set__def) ).

thf(543,plain,
    ( bot_bo1389414743od_V_V
    = ( collec2040633974od_V_V @ bot_bo1168561222_V_V_o ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(331,axiom,
    ! [A: v,B: v,C: set_V,D: v > v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( bNF_Gr_V_V2 @ C @ D ) )
      = ( ( member_V2 @ A @ C )
        & ( ( D @ A )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_in__Gr) ).

thf(1416,plain,
    ! [A: v,B: v,C: set_V,D: v > v] :
      ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( bNF_Gr_V_V2 @ C @ D ) )
      = ( ( member_V2 @ A @ C )
        & ( ( D @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(102,axiom,
    ! [A: set_Pr744279122od_V_V] :
      ( ( ? [B: produc1699571228od_V_V] : ( member1010391347od_V_V @ B @ A ) )
      = ( A != bot_bo667804902od_V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_ex__in__conv) ).

thf(676,plain,
    ! [A: set_Pr744279122od_V_V] :
      ( ( ? [B: produc1699571228od_V_V] : ( member1010391347od_V_V @ B @ A ) )
      = ( A != bot_bo667804902od_V_V ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(269,axiom,
    ! [A: v,B: labele2115946735nt_V_V,C: v,D: standard_Constant_V,E: v > v,F: v,G: v] :
      ( ( member_V2 @ A @ ( labele1134902411nt_V_V @ B ) )
     => ( ( member_V2 @ C @ ( labele1134902411nt_V_V @ B ) )
       => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ C ) @ ( getRel1432786916nt_V_V @ D @ B ) )
         => ( ( ( E @ A )
              = F )
           => ( ( ( E @ C )
                = G )
             => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ ( getRel1432786916nt_V_V @ D @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_getRel__map__fn) ).

thf(1204,plain,
    ! [A: v,B: labele2115946735nt_V_V,C: v,D: standard_Constant_V,E: v > v,F: v,G: v] :
      ( ( member_V2 @ A @ ( labele1134902411nt_V_V @ B ) )
     => ( ( member_V2 @ C @ ( labele1134902411nt_V_V @ B ) )
       => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ C ) @ ( getRel1432786916nt_V_V @ D @ B ) )
         => ( ( ( E @ A )
              = F )
           => ( ( ( E @ C )
                = G )
             => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ F @ G ) @ ( getRel1432786916nt_V_V @ D @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(39,axiom,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( ( sup_su1043134939_V_nat @ A @ B )
        = bot_bo907687539_V_nat )
      = ( ( A = bot_bo907687539_V_nat )
        & ( B = bot_bo907687539_V_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_Un__empty) ).

thf(454,plain,
    ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( ( sup_su1043134939_V_nat @ A @ B )
        = bot_bo907687539_V_nat )
      = ( ( A = bot_bo907687539_V_nat )
        & ( B = bot_bo907687539_V_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(10,axiom,
    ( comp_V_V_V2
    = ( ^ [A: v > v,B: v > v,C: v] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_comp__apply) ).

thf(364,plain,
    ( comp_V_V_V2
    = ( ^ [A: v > v,B: v > v,C: v] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(216,axiom,
    ( ( id_on_2125509800od_V_V @ bot_bo1389414743od_V_V )
    = bot_bo12878899od_V_V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Id__on__empty) ).

thf(1037,plain,
    ( ( id_on_2125509800od_V_V @ bot_bo1389414743od_V_V )
    = bot_bo12878899od_V_V ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(135,axiom,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( insert481364471_V_nat @ A @ ( insert481364471_V_nat @ A @ B ) )
      = ( insert481364471_V_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_insert__absorb2) ).

thf(775,plain,
    ! [A: produc778275879_V_nat,B: set_Pr1058435079_V_nat] :
      ( ( insert481364471_V_nat @ A @ ( insert481364471_V_nat @ A @ B ) )
      = ( insert481364471_V_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(71,axiom,
    ! [A: product_prod_V_V2,B: set_V2] :
      ( ( member1990987792od_V_V @ A @ ( id_on_V @ B ) )
     => ~ ! [C: v2] :
            ( ( member_V @ C @ B )
           => ( A
             != ( product_Pair_V_V @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Id__onE) ).

thf(560,plain,
    ! [A: product_prod_V_V2,B: set_V2] :
      ( ( member1990987792od_V_V @ A @ ( id_on_V @ B ) )
     => ~ ! [C: v2] :
            ( ( member_V @ C @ B )
           => ( A
             != ( product_Pair_V_V @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(209,axiom,
    ! [A: v,B: set_V] :
      ( ( member_V2 @ A @ B )
     => ~ ! [C: set_V] :
            ( ( B
              = ( insert_V2 @ A @ C ) )
           => ( member_V2 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_Set_Oset__insert) ).

thf(1014,plain,
    ! [A: v,B: set_V] :
      ( ( member_V2 @ A @ B )
     => ~ ! [C: set_V] :
            ( ( B
              = ( insert_V2 @ A @ C ) )
           => ( member_V2 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(195,axiom,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( member_V @ A @ ( sup_sup_set_V @ B @ C ) )
     => ( ~ ( member_V @ A @ B )
       => ( member_V @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_UnE) ).

thf(972,plain,
    ! [A: v2,B: set_V2,C: set_V2] :
      ( ( member_V @ A @ ( sup_sup_set_V @ B @ C ) )
     => ( ~ ( member_V @ A @ B )
       => ( member_V @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(4580,plain,
    $false,
    inference(e,[status(thm)],[645,1411,1168,1105,1315,555,666,628,1031,1290,1443,994,1422,741,878,1173,582,762,385,533,797,1233,1063,1222,670,1260,698,1243,1441,417,1046,565,1228,651,829,1095,389,1055,785,372,1264,619,344,949,460,917,751,1313,1279,934,357,1059,1132,902,1087,1147,881,1100,969,606,492,1302,591,1373,834,966,821,348,574,905,480,1377,634,1072,1119,1394,1351,660,988,1433,1201,981,766,397,687,920,529,1438,1153,366,746,778,693,429,788,815,1042,952,467,1365,625,435,522,757,551,1392,842,974,682,1407,1291,710,519,1089,1143,1006,420,857,1375,1121,1361,537,1414,637,489,1419,1028,1082,1075,476,679,1039,985,701,1297,738,1382,654,457,911,503,622,837,1324,393,1263,997,515,1150,1333,343,792,938,1187,586,718,926,1146,1103,824,1273,444,375,423,402,1389,772,1388,1124,875,826,577,1256,545,936,382,1107,1239,1092,704,540,713,498,764,1209,1282,1011,377,509,1307,362,451,387,1080,631,1339,609,483,848,1325,769,1177,1162,726,943,1022,932,1061,1198,959,780,1113,1000,438,1066,868,473,426,589,548,1277,749,754,1049,1134,648,525,1003,690,640,1025,887,414,1252,1368,1267,409,1070,872,1225,707,673,1432,1452,441,463,470,808,359,1218,1336,643,1404,744,1257,1284,1052,1427,571,1272,991,978,1140,845,1180,1157,495,759,891,1126,1316,1084,1448,1189,963,896,946,351,731,813,1385,568,914,1294,929,1193,1212,899,684,1309,800,1116,1348,447,432,818,1380,405,854,1248,865,603,1436,506,696,1346,1033,400,720,1165,839,1129,860,596,1019,908,723,850,1399,501,369,1331,486,803,1320,940,354,1009,923,1184,543,1416,676,1204,454,364,1037,775,560,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : ITP180^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21  % Computer : n013.cluster.edu
% 0.10/0.21  % Model    : x86_64 x86_64
% 0.10/0.21  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21  % Memory   : 8046.5625MB
% 0.10/0.21  % OS       : Linux 6.8.0-71-generic
% 0.10/0.21  % CPULimit : 300
% 0.10/0.21  % WCLimit  : 300
% 0.10/0.21  % DateTime : Tue Sep 29 20:06:21 UTC 2026
% 0.10/0.21  % CPUTime  : 
% 0.10/0.21  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.03/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.39/1.21  % [INFO] 	 Parsing done (412ms). 
% 2.39/1.23  % [INFO] 	 Running in sequential loop mode. 
% 3.68/1.61  % [INFO] 	 eprover registered as external prover. 
% 3.68/1.61  % [INFO] 	 Scanning for conjecture ... 
% 3.98/1.78  % [INFO] 	 Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ... 
% 4.49/1.97  % [INFO] 	 Axiom selection finished. Selected 340 axioms (removed 15 axioms). 
% 5.49/2.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 5.49/2.28  % [INFO] 	 Type checking passed. 
% 5.49/2.28  % [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 ... 
% 54.07/11.40  % External prover 'e' found a proof!
% 54.07/11.40  % [INFO] 	 Killing All external provers ... 
% 54.07/11.40  % Time passed: 11055ms (effective reasoning time: 10169ms)
% 54.07/11.41  % 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)>
% 54.07/11.41  % Axioms used in derivation (340): fact_323_UnE, fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_25_getRel__map__fn, fact_168_bot__empty__eq, fact_316_UnI1, fact_329_graph__homomorphism__nonempty, fact_265_mk__disjoint__insert, fact_54_Collect__mem__eq, fact_310_bex__Un, fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_36_getRel__dom_I1_J, fact_99_Id__on__iff, fact_151_comp__def, fact_53_mem__Collect__eq, fact_195_Un__iff, fact_15_top__nonempty, fact_330_labeled__graph_Oexhaust__sel, fact_120_empty__iff, fact_331_standard__rules__def, fact_26_getRel__map__fn, fact_80_vertices__restrict, fact_125_all__not__in__conv, fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_42_old_Oprod_Oexhaust, fact_336_maintainedD, fact_144_equals0I, fact_189_insertCI, fact_62_subgraph__refl, fact_225_Gr__insert, fact_141_equals0I, fact_145_equals0I, fact_322_UnE, fact_155_comp__eq__dest__lhs, fact_115_Collect__empty__eq, fact_351_sup_Oleft__idem, fact_226_extensible__refl__concr, fact_48_prod__cases, fact_220_constant__rules__empty, fact_22_surj__pair, fact_300_insertI1, fact_14_m, fact_137_equals0D, fact_100_Id__on__iff, fact_252_singleton__iff, fact_260_singleton__inject, fact_29_getRel__hom, fact_59_map__graph__fn__id_I2_J, fact_82_map__graph__fn__comp, fact_229_insert__is__Un, fact_60_map__graph__fn__graphI, fact_343_sup__bot_Oleft__neutral, fact_276_insert__absorb, fact_214_graph__union__preserves__restrict, fact_282_insert__ident, fact_142_equals0I, fact_38_getRel__subgraph, fact_341_sup__bot_Oneutr__eq__iff, fact_70_Gr__empty, fact_352_sup__idem, fact_223_Gr__insert, fact_176_map__graph__in, fact_312_UnI2, fact_309_ball__Un, fact_194_Un__iff, fact_71_restrict__idemp, fact_91_Id__onE, fact_31_getRel__hom, fact_183_insert__absorb2, fact_325_UnE, fact_340_sup__bot_Oneutr__eq__iff, fact_171_bot__set__def, fact_245_singletonD, fact_24_h_I1_J, fact_2__C1_C_I3_J, fact_30_getRel__hom, fact_285_insert__ident, fact_321_UnE, fact_3__C1_C_I1_J, fact_199_UnCI, fact_73_in__Gr, fact_256_doubleton__eq__iff, fact_4__C1_C_I2_J, fact_308_insertE, fact_237_graph__union__def, fact_49_mg, fact_46_Pair__inject, fact_174_edge__preserving__atomic, fact_114_Collect__empty__eq, fact_178_maintainedI, fact_290_Set_Oset__insert, fact_277_insert__absorb, fact_206_singletonI, fact_347_sup__bot_Oeq__neutr__iff, fact_299_insertI1, fact_164_map__graph__edge__preserving, fact_246_singletonD, fact_175_mnt, fact_239_Un__empty__left, fact_105_map__graph__fn__eqI, fact_278_insert__absorb, fact_297_insertI2, fact_35_Standard__Constant_Odistinct_I9_J, fact_179_graph__homomorphism__empty, fact_8_h_I3_J, fact_90_idemp__embedding__maintained__preserved, fact_83_assms_I1_J, fact_96_Id__on__eqI, fact_55_Collect__mem__eq, fact_188_insert__iff, fact_132_emptyE, fact_16_cf, fact_149_ex__in__conv, fact_92_Id__onE, fact_116_empty__iff, fact_248_singletonD, fact_37_getRel__dom_I2_J, fact_111_empty__Collect__eq, fact_78_Id__onI, fact_89_maintained__preserved__by__isomorphism, fact_294_insertI2, fact_337_sup__bot_Oright__neutral, fact_64_graph__homomorphism__Id, fact_34_Standard__Constant_Odistinct_I5_J, fact_196_Un__iff, fact_197_Un__iff, fact_106_tr, fact_275_insert__eq__iff, fact_339_sup__bot_Oright__neutral, fact_205_singletonI, fact_263_mk__disjoint__insert, fact_217_extensible__refl, fact_139_equals0D, fact_33_Standard__Constant_Odistinct_I1_J, fact_257_insert__not__empty, fact_95_Id__on__eqI, fact_346_sup__bot_Oeq__neutr__iff, fact_77_Id__onI, fact_242_Un__empty__right, fact_291_Un__commute, fact_268_Un__left__commute, fact_230_insert__is__Un, fact_231_Un__singleton__iff, fact_258_insert__not__empty, fact_152_comp__assoc, fact_119_empty__iff, fact_213_Un__insert__left, fact_234_singleton__Un__iff, fact_333_semantics__in__vertices_I1_J, fact_219_constant__rules__empty, fact_261_singleton__inject, fact_327_labeled__graph_Osel_I1_J, fact_227_graph__single, fact_150_ex__in__conv, fact_147_ex__in__conv, fact_143_equals0I, fact_193_insertCI, fact_74_Gr__not__in, fact_166_bot__empty__eq, fact_134_emptyE, fact_306_insertE, fact_221_constant__rules__empty, fact_305_insertE, fact_344_sup__bot_Oleft__neutral, fact_12_old_Oprod_Oinject, fact_128_nonempty__rule, fact_267_mk__disjoint__insert, fact_129__092_060open_062maintainedA_A_Iidentity__rules_AL_J_AG_H_092_060close_062, fact_292_Un__absorb, fact_20__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_133_emptyE, fact_11_prod_Oinject, fact_118_empty__iff, fact_342_sup__bot_Oneutr__eq__iff, fact_209_Un__empty, fact_51_mem__Collect__eq, fact_172_bot__set__def, fact_135_emptyE, fact_153_comp__eq__dest, fact_295_insertI2, fact_254_doubleton__eq__iff, fact_76_Id__onI, fact_184_insert__iff, fact_238_Un__empty__left, fact_72_in__Gr, fact_159_edge__preserving__on__graphI, fact_103_subgraph__preserves__hom, fact_127_nonempty__rule, fact_232_Un__singleton__iff, fact_136_equals0D, fact_101_Id__on__iff, fact_0_x, fact_273_insert__eq__iff, fact_272_insert__eq__iff, fact_349_sup_Oright__idem, fact_270_Un__left__absorb, fact_84_ne, fact_286_Set_Oset__insert, fact_271_insert__eq__iff, fact_224_Gr__insert, fact_326_labeled__graph_Osel_I2_J, fact_210_Un__empty, fact_212_Un__insert__right, fact_203_UnCI, fact_288_Set_Oset__insert, fact_117_empty__iff, fact_235_singleton__Un__iff, fact_191_insertCI, fact_186_insert__iff, fact_123_all__not__in__conv, fact_68_Id__on__empty, fact_170_bot__set__def, fact_350_sup__left__idem, fact_63_subgraph__restrict, fact_251_singleton__iff, fact_138_equals0D, fact_180_graph__homomorphism__empty, fact_320_UnI1, fact_75_Gr__not__in, fact_97_Id__on__eqI, fact_110_empty__Collect__eq, fact_165_bot__empty__eq, fact_146_ex__in__conv, fact_124_all__not__in__conv, fact_262_singleton__inject, fact_353_sup_Oidem, fact_161_GrD2, fact_218_graph__empty__e, fact_47_prod__cases, fact_163_GrD1, fact_315_UnI2, fact_211_Un__empty, fact_243_Un__empty__right, fact_45_Pair__inject, fact_32_getRel__hom, fact_148_ex__in__conv, fact_236_singleton__Un__iff, fact_348_sup__bot_Oeq__neutr__iff, fact_88_maintained__preserved__by__isomorphism, fact_79_Id__onI, fact_9_Standard__Constant_Oinject, fact_58_graph__homo, fact_57_Collect__mem__eq, fact_304_insertE, fact_354_sup__bot__left, fact_264_mk__disjoint__insert, fact_247_singletonD, fact_113_Collect__empty__eq, fact_200_UnCI, fact_13_old_Oprod_Oinject, fact_167_bot__empty__eq, fact_98_Id__on__eqI, fact_140_equals0D, fact_7_gr_I1_J, fact_27_getRel__map__fn, fact_43_prod__induct3, fact_130_labeled__graph_Oexpand, fact_233_Un__singleton__iff, fact_21_getRel__homR, fact_241_Un__empty__right, fact_338_sup__bot_Oright__neutral, fact_65_Id__on__empty, fact_17__092_060open_062_092_060And_062c_O_Ac_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_092_060exists_062v_O_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_40_old_Oprod_Oinducts, fact_281_insert__ident, fact_56_Collect__mem__eq, fact_66_Id__on__empty, fact_126_nonempty__rule, fact_41_old_Oprod_Oexhaust, fact_287_Set_Oset__insert, fact_190_insertCI, fact_253_singleton__iff, fact_94_Id__onE, fact_39_old_Oprod_Oinducts, fact_334_subgraph__semantics, fact_154_comp__eq__elim, fact_102_Id__on__iff, fact_5__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_317_UnI1, fact_44_prod__cases3, fact_156_edge__preserving__on__graphI, fact_293_insertI2, fact_298_insertI1, fact_259_insert__not__empty, fact_185_insert__iff, fact_81_map__graph__preserves__restricted, fact_314_UnI2, fact_207_singletonI, fact_122_all__not__in__conv, fact_345_sup__bot_Oleft__neutral, fact_86_maintained__preserved__by__isomorphism, fact_222_constant__rules__empty, fact_87_maintained__preserved__by__isomorphism, fact_198_Un__iff, fact_215_graph__union__vertices, fact_10_prod_Oinject, fact_319_UnI1, fact_109_comp__apply, fact_181_graph__homomorphism__empty, fact_28_getRel__map__fn, fact_157_edge__preserving__on__graphI, fact_311_UnI2, fact_302_insertI1, fact_269_insert__commute, fact_158_edge__preserving__on__graphI, fact_121_all__not__in__conv, fact_50_mem__Collect__eq, fact_324_UnE, fact_208_singletonI, fact_18__092_060open_062_092_060forall_062c_O_A_092_060exists_062v_O_Ac_A_092_060in_062_AC_A_092_060longrightarrow_062_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_23_surj__pair, fact_107_h_I4_J, fact_332_semantics__in__vertices_I2_J, fact_283_insert__ident, fact_67_Id__on__empty, fact_250_singleton__iff, fact_318_UnI1, fact_52_mem__Collect__eq, fact_328_graph__homomorphism__semantics, fact_228_insert__is__Un, fact_202_UnCI, fact_162_GrD1, fact_255_doubleton__eq__iff, fact_104_subgraph__trans, fact_280_insert__absorb, fact_240_Un__empty__left, fact_160_GrD2, fact_69_Gr__empty, fact_201_UnCI, fact_108_maintained__refl, fact_131_emptyE, fact_303_Un__assoc, fact_182_subgraph__def, fact_313_UnI2, fact_173_consequence__graphD_I1_J, fact_216_labeled__graph_Ocollapse, fact_61_map__graph__preserves__subgraph, fact_85__092_060open_062maintained_Anonempty__rule_AG_H_A_061_A_Ivertices_AG_H_A_092_060noteq_062_A_123_125_J_092_060close_062, fact_112_empty__Collect__eq, fact_93_Id__onE, fact_169_bot__empty__eq
% 54.07/11.41  % No. of inferences in proof: 684
% 54.07/11.41  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11055 ms resp. 10169 ms w/o parsing
% 50.04/11.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 50.04/11.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------