TSTP Solution File: ITP178^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP178^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:43 EDT 2024

% Result   : Theorem 23.70s 7.57s
% Output   : Refutation 24.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  499
% Syntax   : Number of formulae    :  826 ( 257 unt; 174 typ;   0 def)
%            Number of atoms       : 1867 ( 671 equ;  12 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 6888 ( 168   ~;   2   |; 257   &;5681   @)
%                                         (   0 <=>; 780  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Number of types       :   42 (  41 usr)
%            Number of type conns  :  307 ( 307   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  136 ( 133 usr;  14 con; 0-6 aty)
%            Number of variables   : 1914 (  98   ^1726   !;  90   ?;1914   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_Pr2123625671_a_nat_type,type,
    set_Pr2123625671_a_nat: $tType ).

thf(produc116665063_a_nat_type,type,
    produc116665063_a_nat: $tType ).

thf(set_Pr924198087_a_nat_type,type,
    set_Pr924198087_a_nat: $tType ).

thf(produc398057191_a_nat_type,type,
    produc398057191_a_nat: $tType ).

thf(set_Pr1173424071_b_nat_type,type,
    set_Pr1173424071_b_nat: $tType ).

thf(set_Pr1839611079term_b_type,type,
    set_Pr1839611079term_b: $tType ).

thf(produc446386919_b_nat_type,type,
    produc446386919_b_nat: $tType ).

thf(produc1116408039term_b_type,type,
    produc1116408039term_b: $tType ).

thf(set_Pr1987088711_a_nat_type,type,
    set_Pr1987088711_a_nat: $tType ).

thf(set_Pr665622551at_nat_type,type,
    set_Pr665622551at_nat: $tType ).

thf(produc1871334759_a_nat_type,type,
    produc1871334759_a_nat: $tType ).

thf(produc1391440311at_nat_type,type,
    produc1391440311at_nat: $tType ).

thf(set_Pr551076371_b_nat_type,type,
    set_Pr551076371_b_nat: $tType ).

thf(set_Pr1647387645at_nat_type,type,
    set_Pr1647387645at_nat: $tType ).

thf(set_Pr1490359111at_nat_type,type,
    set_Pr1490359111at_nat: $tType ).

thf(set_Pr1163220871term_b_type,type,
    set_Pr1163220871term_b: $tType ).

thf(set_Pr2041158302at_nat_type,type,
    set_Pr2041158302at_nat: $tType ).

thf(produc1235635379_b_nat_type,type,
    produc1235635379_b_nat: $tType ).

thf(produc842455143at_nat_type,type,
    produc842455143at_nat: $tType ).

thf(produc1478835367term_b_type,type,
    produc1478835367term_b: $tType ).

thf(set_la1083530965_a_nat_type,type,
    set_la1083530965_a_nat: $tType ).

thf(labele935650037_a_nat_type,type,
    labele935650037_a_nat: $tType ).

thf(labele1835409643at_nat_type,type,
    labele1835409643at_nat: $tType ).

thf(set_Pr9961929at_nat_type,type,
    set_Pr9961929at_nat: $tType ).

thf(allego510293162tant_a_type,type,
    allego510293162tant_a: $tType ).

thf(allego1565409692at_nat_type,type,
    allego1565409692at_nat: $tType ).

thf(set_la1976028319_b_nat_type,type,
    set_la1976028319_b_nat: $tType ).

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

thf(set_Pr1986765409at_nat_type,type,
    set_Pr1986765409at_nat: $tType ).

thf(set_al1193902458term_b_type,type,
    set_al1193902458term_b: $tType ).

thf(labeled_graph_b_nat_type,type,
    labeled_graph_b_nat: $tType ).

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

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

thf(product_prod_nat_nat_type,type,
    product_prod_nat_nat: $tType ).

thf(allegorical_term_b_type,type,
    allegorical_term_b: $tType ).

thf(set_nat_type,type,
    set_nat: $tType ).

thf(itself_nat_type,type,
    itself_nat: $tType ).

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

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

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

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

thf(finite_finite_nat_type,type,
    finite_finite_nat: set_nat > $o ).

thf(finite1242387294at_nat_type,type,
    finite1242387294at_nat: set_Pr1647387645at_nat > $o ).

thf(finite772653738at_nat_type,type,
    finite772653738at_nat: set_Pr1986765409at_nat > $o ).

thf(finite48957584at_nat_type,type,
    finite48957584at_nat: set_Pr1490359111at_nat > $o ).

thf(finite1987068434at_nat_type,type,
    finite1987068434at_nat: set_Pr9961929at_nat > $o ).

thf(finite1015599120od_b_b_type,type,
    finite1015599120od_b_b: set_Product_prod_b_b > $o ).

thf(finite_finite_b_type,type,
    finite_finite_b: set_b > $o ).

thf(allego745587551tant_a_type,type,
    allego745587551tant_a: allego510293162tant_a > allego510293162tant_a > allego510293162tant_a ).

thf(allego266765201at_nat_type,type,
    allego266765201at_nat: allego1565409692at_nat > allego1565409692at_nat > allego1565409692at_nat ).

thf(allegorical_A_Int_b_type,type,
    allegorical_A_Int_b: allegorical_term_b > allegorical_term_b > allegorical_term_b ).

thf(semantics_b_nat_type,type,
    semantics_b_nat: labeled_graph_b_nat > allegorical_term_b > set_Pr1986765409at_nat ).

thf(graph_2130075512at_nat_type,type,
    graph_2130075512at_nat: labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o ).

thf(graph_2111906684at_nat_type,type,
    graph_2111906684at_nat: labele1835409643at_nat > labele1835409643at_nat > set_Pr1986765409at_nat > $o ).

thf(graph_529870330at_nat_type,type,
    graph_529870330at_nat: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).

thf(graph_union_b_nat_type,type,
    graph_union_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).

thf(labeled_LG_b_nat_type,type,
    labeled_LG_b_nat: set_Pr9961929at_nat > set_nat > labeled_graph_b_nat ).

thf(labele195203296_a_nat_type,type,
    labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).

thf(labele2032268018at_nat_type,type,
    labele2032268018at_nat: labele1835409643at_nat > set_Pr1490359111at_nat ).

thf(labeled_edges_b_nat_type,type,
    labeled_edges_b_nat: labeled_graph_b_nat > set_Pr9961929at_nat ).

thf(labele1810595089_a_nat_type,type,
    labele1810595089_a_nat: labele935650037_a_nat > set_nat ).

thf(labele560327297at_nat_type,type,
    labele560327297at_nat: labele1835409643at_nat > set_nat ).

thf(labele460410879_b_nat_type,type,
    labele460410879_b_nat: labeled_graph_b_nat > set_nat ).

thf(restri572569417_a_nat_type,type,
    restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).

thf(restri321299017at_nat_type,type,
    restri321299017at_nat: labele1835409643at_nat > labele1835409643at_nat ).

thf(restrict_b_nat_type,type,
    restrict_b_nat: labeled_graph_b_nat > labeled_graph_b_nat ).

thf(unival1191217828term_b_type,type,
    unival1191217828term_b: set_Pr1163220871term_b > $o ).

thf(unival1637751524_a_nat_type,type,
    unival1637751524_a_nat: set_Pr1987088711_a_nat > $o ).

thf(unival857119480_b_nat_type,type,
    unival857119480_b_nat: set_Pr551076371_b_nat > $o ).

thf(univalent_nat_nat_type,type,
    univalent_nat_nat: set_Pr1986765409at_nat > $o ).

thf(unival633212949at_nat_type,type,
    unival633212949at_nat: set_Pr2041158302at_nat > $o ).

thf(unival989235430at_nat_type,type,
    unival989235430at_nat: set_Pr9961929at_nat > $o ).

thf(bot_bo1024461546_nat_o_type,type,
    bot_bo1024461546_nat_o: produc1871334759_a_nat > $o ).

thf(bot_bot_nat_type,type,
    bot_bot_nat: nat ).

thf(bot_bot_set_nat_type,type,
    bot_bot_set_nat: set_nat ).

thf(bot_bo1836341171_a_nat_type,type,
    bot_bo1836341171_a_nat: set_Pr1987088711_a_nat ).

thf(bot_bo2130386637at_nat_type,type,
    bot_bo2130386637at_nat: set_Pr1986765409at_nat ).

thf(bot_bo1626616373at_nat_type,type,
    bot_bo1626616373at_nat: set_Pr9961929at_nat ).

thf(ord_less_eq_nat_type,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(ord_less_eq_set_nat_type,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(ord_le138473255term_b_type,type,
    ord_le138473255term_b: set_Pr1163220871term_b > set_Pr1163220871term_b > $o ).

thf(ord_le1718765799_a_nat_type,type,
    ord_le1718765799_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o ).

thf(ord_le13035955_b_nat_type,type,
    ord_le13035955_b_nat: set_Pr551076371_b_nat > set_Pr551076371_b_nat > $o ).

thf(ord_le841296385at_nat_type,type,
    ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).

thf(ord_le910748009at_nat_type,type,
    ord_le910748009at_nat: set_Pr9961929at_nat > set_Pr9961929at_nat > $o ).

thf(produc1990145943term_b_type,type,
    produc1990145943term_b: allegorical_term_b > allegorical_term_b > produc1478835367term_b ).

thf(produc1676969687_a_nat_type,type,
    produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).

thf(produc590202991at_nat_type,type,
    produc590202991at_nat: labele1835409643at_nat > labele1835409643at_nat > produc1391440311at_nat ).

thf(produc951298923_b_nat_type,type,
    produc951298923_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).

thf(product_Pair_nat_nat_type,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(produc859843415term_b_type,type,
    produc859843415term_b: produc1478835367term_b > produc1478835367term_b > produc1116408039term_b ).

thf(produc1754969175_b_nat_type,type,
    produc1754969175_b_nat: produc1235635379_b_nat > produc1235635379_b_nat > produc446386919_b_nat ).

thf(produc1168807639at_nat_type,type,
    produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat ).

thf(produc854192515term_b_type,type,
    produc854192515term_b: produc1478835367term_b > allegorical_term_b ).

thf(produc719117507_a_nat_type,type,
    produc719117507_a_nat: produc1871334759_a_nat > labele935650037_a_nat ).

thf(produc1995789403at_nat_type,type,
    produc1995789403at_nat: produc1391440311at_nat > labele1835409643at_nat ).

thf(produc1542243159_b_nat_type,type,
    produc1542243159_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).

thf(product_fst_nat_nat_type,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(produc1223098053term_b_type,type,
    produc1223098053term_b: produc1478835367term_b > allegorical_term_b ).

thf(produc880161797_a_nat_type,type,
    produc880161797_a_nat: produc1871334759_a_nat > labele935650037_a_nat ).

thf(produc1564126365at_nat_type,type,
    produc1564126365at_nat: produc1391440311at_nat > labele1835409643at_nat ).

thf(produc194497945_b_nat_type,type,
    produc194497945_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).

thf(product_snd_nat_nat_type,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(domain859272460term_b_type,type,
    domain859272460term_b: set_Pr1163220871term_b > set_al1193902458term_b ).

thf(domain767519072_b_nat_type,type,
    domain767519072_b_nat: set_Pr551076371_b_nat > set_la1976028319_b_nat ).

thf(domain_nat_nat_type,type,
    domain_nat_nat: set_Pr1986765409at_nat > set_nat ).

thf(domain1101989710at_nat_type,type,
    domain1101989710at_nat: set_Pr9961929at_nat > set_b ).

thf(id_on_1536886967term_b_type,type,
    id_on_1536886967term_b: set_al1193902458term_b > set_Pr1163220871term_b ).

thf(id_on_689842066_a_nat_type,type,
    id_on_689842066_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat ).

thf(id_on_583275916_b_nat_type,type,
    id_on_583275916_b_nat: set_la1976028319_b_nat > set_Pr551076371_b_nat ).

thf(id_on_nat_type,type,
    id_on_nat: set_nat > set_Pr1986765409at_nat ).

thf(id_on_1664915780term_b_type,type,
    id_on_1664915780term_b: set_Pr1163220871term_b > set_Pr1839611079term_b ).

thf(id_on_138931664_b_nat_type,type,
    id_on_138931664_b_nat: set_Pr551076371_b_nat > set_Pr1173424071_b_nat ).

thf(id_on_2144791838at_nat_type,type,
    id_on_2144791838at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat ).

thf(image_329221075term_b_type,type,
    image_329221075term_b: set_Pr1163220871term_b > set_al1193902458term_b > set_al1193902458term_b ).

thf(image_1971191571_a_nat_type,type,
    image_1971191571_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).

thf(image_1183964583_b_nat_type,type,
    image_1183964583_b_nat: set_Pr551076371_b_nat > set_la1976028319_b_nat > set_la1976028319_b_nat ).

thf(image_nat_nat_type,type,
    image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat ).

thf(image_1356842150at_nat_type,type,
    image_1356842150at_nat: set_Pr2041158302at_nat > set_Pr9961929at_nat > set_nat ).

thf(image_2112855445at_nat_type,type,
    image_2112855445at_nat: set_Pr9961929at_nat > set_b > set_Pr1986765409at_nat ).

thf(relcom1955155673term_b_type,type,
    relcom1955155673term_b: set_Pr1163220871term_b > set_Pr1163220871term_b > set_Pr1163220871term_b ).

thf(relcom1338300020_a_nat_type,type,
    relcom1338300020_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).

thf(relcom1426860350_b_nat_type,type,
    relcom1426860350_b_nat: set_Pr551076371_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat ).

thf(relcomp_nat_nat_nat_type,type,
    relcomp_nat_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).

thf(relcom195261566at_nat_type,type,
    relcom195261566at_nat: set_Pr9961929at_nat > set_Pr1490359111at_nat > set_Pr9961929at_nat ).

thf(relcom14055552at_nat_type,type,
    relcom14055552at_nat: set_Product_prod_b_b > set_Pr9961929at_nat > set_Pr9961929at_nat ).

thf(inv_translation_type,type,
    inv_translation: set_nat > $o ).

thf(transl1275713022tant_a_type,type,
    transl1275713022tant_a: allego510293162tant_a > labele935650037_a_nat ).

thf(transl490985778at_nat_type,type,
    transl490985778at_nat: allego1565409692at_nat > labele1835409643at_nat ).

thf(translation_b_type,type,
    translation_b: allegorical_term_b > labeled_graph_b_nat ).

thf(agree_on_b_nat_nat_type,type,
    agree_on_b_nat_nat: labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).

thf(chain_b_nat_type,type,
    chain_b_nat: ( nat > labeled_graph_b_nat ) > $o ).

thf(chain_sup_b_nat_type,type,
    chain_sup_b_nat: ( nat > labeled_graph_b_nat ) > labeled_graph_b_nat ).

thf(conseq1730780375at_nat_type,type,
    conseq1730780375at_nat: set_Pr551076371_b_nat > labeled_graph_b_nat > $o ).

thf(extensible_b_nat_nat_type,type,
    extensible_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).

thf(fair_chain_b_nat_nat_type,type,
    fair_chain_b_nat_nat: set_Pr551076371_b_nat > ( nat > labeled_graph_b_nat ) > $o ).

thf(fin_ma971967913at_nat_type,type,
    fin_ma971967913at_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o ).

thf(maintained_b_nat_nat_type,type,
    maintained_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o ).

thf(set_of1384085797_a_nat_type,type,
    set_of1384085797_a_nat: set_Pr1987088711_a_nat > $o ).

thf(set_of195930477at_nat_type,type,
    set_of195930477at_nat: set_Pr665622551at_nat > $o ).

thf(set_of41538795_b_nat_type,type,
    set_of41538795_b_nat: set_Pr551076371_b_nat > $o ).

thf(weak_u2026406106at_nat_type,type,
    weak_u2026406106at_nat: itself_nat > produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).

thf(collect_nat_type,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(collec135640594term_b_type,type,
    collec135640594term_b: ( produc1478835367term_b > $o ) > set_Pr1163220871term_b ).

thf(collec357096914_a_nat_type,type,
    collec357096914_a_nat: ( produc1871334759_a_nat > $o ) > set_Pr1987088711_a_nat ).

thf(collec1615000990_b_nat_type,type,
    collec1615000990_b_nat: ( produc1235635379_b_nat > $o ) > set_Pr551076371_b_nat ).

thf(collec7649004at_nat_type,type,
    collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).

thf(standa1897115818ules_a_type,type,
    standa1897115818ules_a: set_a > set_Pr1987088711_a_nat ).

thf(standa1568205540ules_a_type,type,
    standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).

thf(standa1410829644tant_a_type,type,
    standa1410829644tant_a: produc1871334759_a_nat ).

thf(standa214789732at_nat_type,type,
    standa214789732at_nat: produc1391440311at_nat ).

thf(standa879863266rule_b_type,type,
    standa879863266rule_b: produc1235635379_b_nat ).

thf(standa63370785tant_a_type,type,
    standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).

thf(standa2131591247at_nat_type,type,
    standa2131591247at_nat: product_prod_nat_nat > produc1391440311at_nat ).

thf(standa1329480013rule_b_type,type,
    standa1329480013rule_b: b > produc1235635379_b_nat ).

thf(standa305748545tant_a_type,type,
    standa305748545tant_a: standard_Constant_a > produc1871334759_a_nat ).

thf(standa153097263at_nat_type,type,
    standa153097263at_nat: product_prod_nat_nat > produc1391440311at_nat ).

thf(standa1360217389rule_b_type,type,
    standa1360217389rule_b: b > produc1235635379_b_nat ).

thf(member93680451term_b_type,type,
    member93680451term_b: allegorical_term_b > set_al1193902458term_b > $o ).

thf(member964390942_a_nat_type,type,
    member964390942_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > $o ).

thf(member1483953152_b_nat_type,type,
    member1483953152_b_nat: labeled_graph_b_nat > set_la1976028319_b_nat > $o ).

thf(member_nat_type,type,
    member_nat: nat > set_nat > $o ).

thf(member516522448term_b_type,type,
    member516522448term_b: produc1478835367term_b > set_Pr1163220871term_b > $o ).

thf(member832397200_a_nat_type,type,
    member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).

thf(member1129678944at_nat_type,type,
    member1129678944at_nat: produc1391440311at_nat > set_Pr665622551at_nat > $o ).

thf(member963855452_b_nat_type,type,
    member963855452_b_nat: produc1235635379_b_nat > set_Pr551076371_b_nat > $o ).

thf(member701585322at_nat_type,type,
    member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).

thf(member1449757456term_b_type,type,
    member1449757456term_b: produc1116408039term_b > set_Pr1839611079term_b > $o ).

thf(member889223696_b_nat_type,type,
    member889223696_b_nat: produc446386919_b_nat > set_Pr1173424071_b_nat > $o ).

thf(member2027625872at_nat_type,type,
    member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).

thf(c_type,type,
    c: set_a ).

thf(u_type,type,
    u: allegorical_term_b ).

thf(v_type,type,
    v: allegorical_term_b ).

thf(x_type,type,
    x: produc1871334759_a_nat ).

thf(200,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( graph_529870330at_nat @ A @ C @ D )
       => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A @ B ) @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_maintainedD) ).

thf(1024,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( graph_529870330at_nat @ A @ C @ D )
       => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A @ B ) @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(318,axiom,
    ! [A: set_Pr551076371_b_nat,B: labeled_graph_b_nat] :
      ( ! [C: produc1235635379_b_nat] :
          ( ( member963855452_b_nat @ C @ A )
         => ( maintained_b_nat_nat @ C @ B ) )
     => ( ! [C: produc1235635379_b_nat] :
            ( ( member963855452_b_nat @ C @ A )
           => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( produc194497945_b_nat @ C ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ C ) ) ) ) )
       => ( ( B
            = ( restrict_b_nat @ B ) )
         => ( conseq1730780375at_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_consequence__graphI) ).

thf(1454,plain,
    ! [A: set_Pr551076371_b_nat,B: labeled_graph_b_nat] :
      ( ! [C: produc1235635379_b_nat] :
          ( ( member963855452_b_nat @ C @ A )
         => ( maintained_b_nat_nat @ C @ B ) )
     => ( ! [C: produc1235635379_b_nat] :
            ( ( member963855452_b_nat @ C @ A )
           => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( produc194497945_b_nat @ C ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ C ) ) ) ) )
       => ( ( B
            = ( restrict_b_nat @ B ) )
         => ( conseq1730780375at_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(284,axiom,
    ! [A: standard_Constant_a] :
      ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ A ) ) @ ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ A ) ) ) ) )
      & ( ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) )
        = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) ) ) )
      & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) ) ) )
      & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_are__rules_I3_J) ).

thf(1315,plain,
    ! [A: standard_Constant_a] :
      ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ A ) ) @ ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ A ) ) ) ) )
      & ( ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) )
        = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) ) ) )
      & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) ) ) )
      & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(44,axiom,
    ! [A: produc1871334759_a_nat] :
      ( A
      = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ A ) @ ( produc880161797_a_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_surjective__pairing) ).

thf(468,plain,
    ! [A: produc1871334759_a_nat] :
      ( A
      = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ A ) @ ( produc880161797_a_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(15,axiom,
    ! [A: produc1871334759_a_nat,B: set_la1083530965_a_nat] :
      ( ( member832397200_a_nat @ A @ ( id_on_689842066_a_nat @ B ) )
     => ~ ! [C: labele935650037_a_nat] :
            ( ( member964390942_a_nat @ C @ B )
           => ( A
             != ( produc1676969687_a_nat @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Id__onE) ).

thf(365,plain,
    ! [A: produc1871334759_a_nat,B: set_la1083530965_a_nat] :
      ( ( member832397200_a_nat @ A @ ( id_on_689842066_a_nat @ B ) )
     => ~ ! [C: labele935650037_a_nat] :
            ( ( member964390942_a_nat @ C @ B )
           => ( A
             != ( produc1676969687_a_nat @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(249,axiom,
    ! [A: produc1478835367term_b > $o,B: produc1478835367term_b] :
      ( ! [C: allegorical_term_b,D: allegorical_term_b] : ( A @ ( produc1990145943term_b @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_old_Oprod_Oinducts) ).

thf(1190,plain,
    ! [A: produc1478835367term_b > $o,B: produc1478835367term_b] :
      ( ! [C: allegorical_term_b,D: allegorical_term_b] : ( A @ ( produc1990145943term_b @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(81,axiom,
    ! [A: nat > nat > $o,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_eq_nat @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: nat,E: nat] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_linorder__wlog) ).

thf(582,plain,
    ! [A: nat > nat > $o,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_eq_nat @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: nat,E: nat] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(194,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_2130075512at_nat @ A @ B @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) )
     => ( ( graph_2130075512at_nat @ C @ A @ D )
       => ( graph_2130075512at_nat @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_subgraph__preserves__hom) ).

thf(1005,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_2130075512at_nat @ A @ B @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) )
     => ( ( graph_2130075512at_nat @ C @ A @ D )
       => ( graph_2130075512at_nat @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(109,axiom,
    ! [A: nat > labeled_graph_b_nat] :
      ( ( chain_b_nat @ A )
     => ( ( chain_sup_b_nat @ A )
        = ( restrict_b_nat @ ( chain_sup_b_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_chain__sup__graph) ).

thf(683,plain,
    ! [A: nat > labeled_graph_b_nat] :
      ( ( chain_b_nat @ A )
     => ( ( chain_sup_b_nat @ A )
        = ( restrict_b_nat @ ( chain_sup_b_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(305,axiom,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: labeled_graph_b_nat,E: itself_nat,F: set_Pr1986765409at_nat] :
      ( ! [G: set_Pr1986765409at_nat,H: set_Pr1986765409at_nat,I: labeled_graph_b_nat] :
          ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ A ) @ I @ G )
         => ( ( graph_529870330at_nat @ B @ I @ H )
           => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ C @ H ) @ G )
             => ? [J: set_Pr1986765409at_nat] :
                  ( ( graph_529870330at_nat @ D @ I @ J )
                  & ( ord_le841296385at_nat @ H @ J ) ) ) ) )
     => ( weak_u2026406106at_nat @ E @ A @ B @ D @ C @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_weak__universalI) ).

thf(1401,plain,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: labeled_graph_b_nat,E: itself_nat,F: set_Pr1986765409at_nat] :
      ( ! [G: set_Pr1986765409at_nat,H: set_Pr1986765409at_nat,I: labeled_graph_b_nat] :
          ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ A ) @ I @ G )
         => ( ( graph_529870330at_nat @ B @ I @ H )
           => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ C @ H ) @ G )
             => ? [J: set_Pr1986765409at_nat] :
                  ( ( graph_529870330at_nat @ D @ I @ J )
                  & ( ord_le841296385at_nat @ H @ J ) ) ) ) )
     => ( weak_u2026406106at_nat @ E @ A @ B @ D @ C @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(214,axiom,
    ! [A: set_Pr1987088711_a_nat,B: produc1871334759_a_nat] :
      ( ( set_of1384085797_a_nat @ A )
     => ( ( member832397200_a_nat @ B @ A )
       => ( graph_2130075512at_nat @ ( produc719117507_a_nat @ B ) @ ( produc880161797_a_nat @ B ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_set__of__graph__rulesD_I3_J) ).

thf(1073,plain,
    ! [A: set_Pr1987088711_a_nat,B: produc1871334759_a_nat] :
      ( ( set_of1384085797_a_nat @ A )
     => ( ( member832397200_a_nat @ B @ A )
       => ( graph_2130075512at_nat @ ( produc719117507_a_nat @ B ) @ ( produc880161797_a_nat @ B ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(243,axiom,
    ( fin_ma971967913at_nat
    = ( ^ [A: produc1235635379_b_nat,B: labeled_graph_b_nat] :
        ! [C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
          ( ( ( C
              = ( restrict_b_nat @ C ) )
            & ( finite_finite_nat @ ( labele460410879_b_nat @ C ) )
            & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ C ) ) )
         => ( ( graph_529870330at_nat @ C @ ( produc1542243159_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ C ) ) )
           => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ C @ ( produc1542243159_b_nat @ A ) ) @ B @ D )
             => ( ( graph_529870330at_nat @ C @ B @ D )
               => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ C @ ( produc194497945_b_nat @ A ) ) @ B @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_fin__maintained__def) ).

thf(1173,plain,
    ( fin_ma971967913at_nat
    = ( ^ [A: produc1235635379_b_nat,B: labeled_graph_b_nat] :
        ! [C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
          ( ( ( C
              = ( restrict_b_nat @ C ) )
            & ( finite_finite_nat @ ( labele460410879_b_nat @ C ) )
            & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ C ) ) )
         => ( ( graph_529870330at_nat @ C @ ( produc1542243159_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ C ) ) )
           => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ C @ ( produc1542243159_b_nat @ A ) ) @ B @ D )
             => ( ( graph_529870330at_nat @ C @ B @ D )
               => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ C @ ( produc194497945_b_nat @ A ) ) @ B @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(123,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( ( produc1990145943term_b @ A @ B )
        = ( produc1990145943term_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_old_Oprod_Oinject) ).

thf(730,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( ( produc1990145943term_b @ A @ B )
        = ( produc1990145943term_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(277,axiom,
    ! [A: set_Pr551076371_b_nat,B: nat > labeled_graph_b_nat,C: produc1235635379_b_nat,D: nat,E: set_Pr1986765409at_nat] :
      ( ( fair_chain_b_nat_nat @ A @ B )
     => ( ( member963855452_b_nat @ C @ A )
       => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( B @ D ) @ E )
         => ? [F: nat] : ( extensible_b_nat_nat @ C @ ( B @ F ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_fair__chainD_I2_J) ).

thf(1290,plain,
    ! [A: set_Pr551076371_b_nat,B: nat > labeled_graph_b_nat,C: produc1235635379_b_nat,D: nat,E: set_Pr1986765409at_nat] :
      ( ( fair_chain_b_nat_nat @ A @ B )
     => ( ( member963855452_b_nat @ C @ A )
       => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( B @ D ) @ E )
         => ? [F: nat] : ( extensible_b_nat_nat @ C @ ( B @ F ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(165,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
      ( ( ( produc951298923_b_nat @ A @ B )
        = ( produc951298923_b_nat @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Pair__inject) ).

thf(878,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
      ( ( ( produc951298923_b_nat @ A @ B )
        = ( produc951298923_b_nat @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(37,axiom,
    ( ( (=) @ produc1871334759_a_nat )
    = ( ^ [A: produc1871334759_a_nat,B: produc1871334759_a_nat] :
          ( ( ( produc719117507_a_nat @ A )
            = ( produc719117507_a_nat @ B ) )
          & ( ( produc880161797_a_nat @ A )
            = ( produc880161797_a_nat @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_prod__eq__iff) ).

thf(440,plain,
    ( ( (=) @ produc1871334759_a_nat )
    = ( ^ [A: produc1871334759_a_nat,B: produc1871334759_a_nat] :
          ( ( ( produc719117507_a_nat @ A )
            = ( produc719117507_a_nat @ B ) )
          & ( ( produc880161797_a_nat @ A )
            = ( produc880161797_a_nat @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(99,axiom,
    ! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat] :
      ( ! [C: nat,D: nat] : ( A @ ( product_Pair_nat_nat @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_old_Oprod_Oinducts) ).

thf(655,plain,
    ! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat] :
      ( ! [C: nat,D: nat] : ( A @ ( product_Pair_nat_nat @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(21,axiom,
    ! [A: allego510293162tant_a] : ( inv_translation @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_verts__in__translation) ).

thf(385,plain,
    ! [A: allego510293162tant_a] : ( inv_translation @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(231,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_al1193902458term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ C )
     => ( ( member93680451term_b @ A @ D )
       => ( member93680451term_b @ B @ ( image_329221075term_b @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_ImageI) ).

thf(1137,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_al1193902458term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ C )
     => ( ( member93680451term_b @ A @ D )
       => ( member93680451term_b @ B @ ( image_329221075term_b @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(53,axiom,
    ! [A: produc1871334759_a_nat] :
    ? [B: labele935650037_a_nat,C: labele935650037_a_nat] :
      ( A
      = ( produc1676969687_a_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_surj__pair) ).

thf(500,plain,
    ! [A: produc1871334759_a_nat] :
    ? [B: labele935650037_a_nat,C: labele935650037_a_nat] :
      ( A
      = ( produc1676969687_a_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(144,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( relcom1955155673term_b @ C @ D ) )
     => ~ ! [E: allegorical_term_b] :
            ( ( member516522448term_b @ ( produc1990145943term_b @ A @ E ) @ C )
           => ~ ( member516522448term_b @ ( produc1990145943term_b @ E @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_relcompEpair) ).

thf(797,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( relcom1955155673term_b @ C @ D ) )
     => ~ ! [E: allegorical_term_b] :
            ( ( member516522448term_b @ ( produc1990145943term_b @ A @ E ) @ C )
           => ~ ( member516522448term_b @ ( produc1990145943term_b @ E @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(268,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_fst__conv) ).

thf(1260,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(173,axiom,
    ( fair_chain_b_nat_nat
    = ( ^ [A: set_Pr551076371_b_nat,B: nat > labeled_graph_b_nat] :
          ( ( chain_b_nat @ B )
          & ! [C: produc1235635379_b_nat,D: set_Pr1986765409at_nat,E: nat] :
              ( ( ( member963855452_b_nat @ C @ A )
                & ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( B @ E ) @ D ) )
             => ? [F: nat] : ( extensible_b_nat_nat @ C @ ( B @ F ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_fair__chain__def) ).

thf(913,plain,
    ( fair_chain_b_nat_nat
    = ( ^ [A: set_Pr551076371_b_nat,B: nat > labeled_graph_b_nat] :
          ( ( chain_b_nat @ B )
          & ! [C: produc1235635379_b_nat,D: set_Pr1986765409at_nat,E: nat] :
              ( ( ( member963855452_b_nat @ C @ A )
                & ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( B @ E ) @ D ) )
             => ? [F: nat] : ( extensible_b_nat_nat @ C @ ( B @ F ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(7,axiom,
    ! [A: produc1871334759_a_nat > $o,B: produc1871334759_a_nat > $o] :
      ( ! [C: produc1871334759_a_nat] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collec357096914_a_nat @ A )
        = ( collec357096914_a_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Collect__cong) ).

thf(340,plain,
    ! [A: produc1871334759_a_nat > $o,B: produc1871334759_a_nat > $o] :
      ( ! [C: produc1871334759_a_nat] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collec357096914_a_nat @ A )
        = ( collec357096914_a_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(104,axiom,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_eq__iff) ).

thf(670,plain,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(221,axiom,
    ! [A: labeled_graph_b_nat,B: nat,C: nat,D: allegorical_term_b] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( semantics_b_nat @ A @ D ) )
       => ( member_nat @ B @ ( labele460410879_b_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_semantics__in__vertices_I1_J) ).

thf(1095,plain,
    ! [A: labeled_graph_b_nat,B: nat,C: nat,D: allegorical_term_b] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( semantics_b_nat @ A @ D ) )
       => ( member_nat @ B @ ( labele460410879_b_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(263,axiom,
    ! [A: set_nat] :
      ( ( domain_nat_nat @ ( id_on_nat @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_Domain__Id__on) ).

thf(1243,plain,
    ! [A: set_nat] :
      ( ( domain_nat_nat @ ( id_on_nat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(302,axiom,
    ! [A: produc1478835367term_b,B: produc1478835367term_b] :
      ( ( ( produc854192515term_b @ A )
        = ( produc854192515term_b @ B ) )
     => ( ( ( produc1223098053term_b @ A )
          = ( produc1223098053term_b @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_prod__eqI) ).

thf(1391,plain,
    ! [A: produc1478835367term_b,B: produc1478835367term_b] :
      ( ( ( produc854192515term_b @ A )
        = ( produc854192515term_b @ B ) )
     => ( ( ( produc1223098053term_b @ A )
          = ( produc1223098053term_b @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(139,axiom,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
      = ( ? [C: allegorical_term_b,D: allegorical_term_b] :
            ( ( A = C )
            & ( member516522448term_b @ ( produc1990145943term_b @ C @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_Domain_Osimps) ).

thf(782,plain,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
      = ( ? [C: allegorical_term_b,D: allegorical_term_b] :
            ( ( A = C )
            & ( member516522448term_b @ ( produc1990145943term_b @ C @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(29,axiom,
    ! [A: set_Pr1987088711_a_nat] :
      ( ( collec357096914_a_nat
        @ ^ [B: produc1871334759_a_nat] : ( member832397200_a_nat @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Collect__mem__eq) ).

thf(417,plain,
    ! [A: set_Pr1987088711_a_nat] :
      ( ( collec357096914_a_nat
        @ ^ [B: produc1871334759_a_nat] : ( member832397200_a_nat @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(166,axiom,
    ! [A: produc1235635379_b_nat] :
      ( A
      = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_prod_Oexhaust__sel) ).

thf(885,plain,
    ! [A: produc1235635379_b_nat] :
      ( A
      = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(294,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A @ B ) @ C @ D )
     => ( ( B
          = ( restrict_b_nat @ B ) )
       => ( graph_529870330at_nat @ B @ C @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_graph__homo__union__id_I2_J) ).

thf(1359,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A @ B ) @ C @ D )
     => ( ( B
          = ( restrict_b_nat @ B ) )
       => ( graph_529870330at_nat @ B @ C @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(75,axiom,
    ! [A: allego510293162tant_a] : ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( transl1275713022tant_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_verts__in__translation__finite_I2_J) ).

thf(565,plain,
    ! [A: allego510293162tant_a] : ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( transl1275713022tant_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(35,axiom,
    ! [A: set_nat] :
      ( ( collect_nat
        @ ^ [B: nat] : ( member_nat @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Collect__mem__eq) ).

thf(436,plain,
    ! [A: set_nat] :
      ( ( collect_nat
        @ ^ [B: nat] : ( member_nat @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(259,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: labeled_graph_b_nat,E: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ D ) @ E )
       => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ D ) @ ( relcom1426860350_b_nat @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_relcomp_OrelcompI) ).

thf(1228,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: labeled_graph_b_nat,E: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ D ) @ E )
       => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ D ) @ ( relcom1426860350_b_nat @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(121,axiom,
    ! [A: labele935650037_a_nat] :
      ( ( graph_2130075512at_nat @ A @ ( restri572569417_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) )
      = ( A
        = ( restri572569417_a_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subgraph__restrict) ).

thf(724,plain,
    ! [A: labele935650037_a_nat] :
      ( ( graph_2130075512at_nat @ A @ ( restri572569417_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) )
      = ( A
        = ( restri572569417_a_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(77,axiom,
    ! [A: labele935650037_a_nat,B: set_Pr1987088711_a_nat,C: set_la1083530965_a_nat] :
      ( ( member964390942_a_nat @ A @ ( image_1971191571_a_nat @ B @ C ) )
      = ( ? [D: labele935650037_a_nat] :
            ( ( member964390942_a_nat @ D @ C )
            & ( member832397200_a_nat @ ( produc1676969687_a_nat @ D @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_Image__iff) ).

thf(570,plain,
    ! [A: labele935650037_a_nat,B: set_Pr1987088711_a_nat,C: set_la1083530965_a_nat] :
      ( ( member964390942_a_nat @ A @ ( image_1971191571_a_nat @ B @ C ) )
      = ( ? [D: labele935650037_a_nat] :
            ( ( member964390942_a_nat @ D @ C )
            & ( member832397200_a_nat @ ( produc1676969687_a_nat @ D @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(120,axiom,
    ! [A: labeled_graph_b_nat > labeled_graph_b_nat > $o,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: produc1235635379_b_nat] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc951298923_b_nat @ B @ C ) )
       => ( A @ ( produc1542243159_b_nat @ D ) @ ( produc194497945_b_nat @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_BNF__Greatest__Fixpoint_Osubst__Pair) ).

thf(719,plain,
    ! [A: labeled_graph_b_nat > labeled_graph_b_nat > $o,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: produc1235635379_b_nat] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc951298923_b_nat @ B @ C ) )
       => ( A @ ( produc1542243159_b_nat @ D ) @ ( produc194497945_b_nat @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(140,axiom,
    ( set_of1384085797_a_nat
    = ( ^ [A: set_Pr1987088711_a_nat] :
        ! [B: produc1871334759_a_nat] :
          ( ( member832397200_a_nat @ B @ A )
         => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ B ) @ ( produc880161797_a_nat @ B ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ B ) ) ) )
            & ( ( produc880161797_a_nat @ B )
              = ( restri572569417_a_nat @ ( produc880161797_a_nat @ B ) ) )
            & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ B ) ) )
            & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_set__of__graph__rules__def) ).

thf(785,plain,
    ( set_of1384085797_a_nat
    = ( ^ [A: set_Pr1987088711_a_nat] :
        ! [B: produc1871334759_a_nat] :
          ( ( member832397200_a_nat @ B @ A )
         => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ B ) @ ( produc880161797_a_nat @ B ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ B ) ) ) )
            & ( ( produc880161797_a_nat @ B )
              = ( restri572569417_a_nat @ ( produc880161797_a_nat @ B ) ) )
            & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ B ) ) )
            & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(17,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_ord__le__eq__trans) ).

thf(372,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(287,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( relcom1955155673term_b @ C @ D ) )
      = ( ? [E: allegorical_term_b,F: allegorical_term_b,G: allegorical_term_b] :
            ( ( A = E )
            & ( B = G )
            & ( member516522448term_b @ ( produc1990145943term_b @ E @ F ) @ C )
            & ( member516522448term_b @ ( produc1990145943term_b @ F @ G ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_relcomp_Osimps) ).

thf(1330,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( relcom1955155673term_b @ C @ D ) )
      = ( ? [E: allegorical_term_b,F: allegorical_term_b,G: allegorical_term_b] :
            ( ( A = E )
            & ( B = G )
            & ( member516522448term_b @ ( produc1990145943term_b @ E @ F ) @ C )
            & ( member516522448term_b @ ( produc1990145943term_b @ F @ G ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(273,axiom,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
     => ~ ! [C: allegorical_term_b] :
            ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_Domain_Ocases) ).

thf(1279,plain,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
     => ~ ! [C: allegorical_term_b] :
            ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(229,axiom,
    ( ( (=) @ produc1235635379_b_nat )
    = ( ^ [A: produc1235635379_b_nat,B: produc1235635379_b_nat] :
          ( ( ( produc1542243159_b_nat @ A )
            = ( produc1542243159_b_nat @ B ) )
          & ( ( produc194497945_b_nat @ A )
            = ( produc194497945_b_nat @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_prod__eq__iff) ).

thf(1132,plain,
    ( ( (=) @ produc1235635379_b_nat )
    = ( ^ [A: produc1235635379_b_nat,B: produc1235635379_b_nat] :
          ( ( ( produc1542243159_b_nat @ A )
            = ( produc1542243159_b_nat @ B ) )
          & ( ( produc194497945_b_nat @ A )
            = ( produc194497945_b_nat @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(218,axiom,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
      = ( ? [C: labeled_graph_b_nat] : ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_Domain__iff) ).

thf(1087,plain,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
      = ( ? [C: labeled_graph_b_nat] : ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(234,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ A ) @ ( labeled_edges_b_nat @ B ) )
     => ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ A ) @ ( labele460410879_b_nat @ B ) )
       => ( ( graph_union_b_nat @ A @ B )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_graph__unionI) ).

thf(1147,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ A ) @ ( labeled_edges_b_nat @ B ) )
     => ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ A ) @ ( labele460410879_b_nat @ B ) )
       => ( ( graph_union_b_nat @ A @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(323,axiom,
    ! [A: set_nat,B: nat] :
      ( ( finite_finite_nat @ A )
     => ( ( member_nat @ B @ A )
       => ? [C: nat] :
            ( ( member_nat @ C @ A )
            & ( ord_less_eq_nat @ B @ C )
            & ! [D: nat] :
                ( ( member_nat @ D @ A )
               => ( ( ord_less_eq_nat @ C @ D )
                 => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_finite__has__maximal2) ).

thf(1479,plain,
    ! [A: set_nat,B: nat] :
      ( ( finite_finite_nat @ A )
     => ( ( member_nat @ B @ A )
       => ? [C: nat] :
            ( ( member_nat @ C @ A )
            & ( ord_less_eq_nat @ B @ C )
            & ! [D: nat] :
                ( ( member_nat @ D @ A )
               => ( ( ord_less_eq_nat @ C @ D )
                 => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(291,axiom,
    ! [A: set_Pr1987088711_a_nat,B: produc1871334759_a_nat] :
      ( ( set_of1384085797_a_nat @ A )
     => ( ( member832397200_a_nat @ B @ A )
       => ( ( ( produc719117507_a_nat @ B )
            = ( restri572569417_a_nat @ ( produc719117507_a_nat @ B ) ) )
          & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ B ) ) )
          & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc719117507_a_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_set__of__graph__rulesD_I1_J) ).

thf(1347,plain,
    ! [A: set_Pr1987088711_a_nat,B: produc1871334759_a_nat] :
      ( ( set_of1384085797_a_nat @ A )
     => ( ( member832397200_a_nat @ B @ A )
       => ( ( ( produc719117507_a_nat @ B )
            = ( restri572569417_a_nat @ ( produc719117507_a_nat @ B ) ) )
          & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ B ) ) )
          & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc719117507_a_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(225,axiom,
    ! [A: set_nat,B: nat] :
      ( ( finite_finite_nat @ A )
     => ( ( member_nat @ B @ A )
       => ? [C: nat] :
            ( ( member_nat @ C @ A )
            & ( ord_less_eq_nat @ C @ B )
            & ! [D: nat] :
                ( ( member_nat @ D @ A )
               => ( ( ord_less_eq_nat @ D @ C )
                 => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_finite__has__minimal2) ).

thf(1115,plain,
    ! [A: set_nat,B: nat] :
      ( ( finite_finite_nat @ A )
     => ( ( member_nat @ B @ A )
       => ? [C: nat] :
            ( ( member_nat @ C @ A )
            & ( ord_less_eq_nat @ C @ B )
            & ! [D: nat] :
                ( ( member_nat @ D @ A )
               => ( ( ord_less_eq_nat @ D @ C )
                 => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(295,axiom,
    ! [A: set_nat] :
      ( ( finite_finite_nat @ A )
     => ( ( A != bot_bot_set_nat )
       => ? [B: nat] :
            ( ( member_nat @ B @ A )
            & ! [C: nat] :
                ( ( member_nat @ C @ A )
               => ( ( ord_less_eq_nat @ B @ C )
                 => ( B = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_finite__has__maximal) ).

thf(1362,plain,
    ! [A: set_nat] :
      ( ( finite_finite_nat @ A )
     => ( ( A != bot_bot_set_nat )
       => ? [B: nat] :
            ( ( member_nat @ B @ A )
            & ! [C: nat] :
                ( ( member_nat @ C @ A )
               => ( ( ord_less_eq_nat @ B @ C )
                 => ( B = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(326,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
      ( ( ( produc951298923_b_nat @ A @ B )
        = ( produc951298923_b_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_old_Oprod_Oinject) ).

thf(1489,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
      ( ( ( produc951298923_b_nat @ A @ B )
        = ( produc951298923_b_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(46,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_antisym__conv) ).

thf(475,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(317,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ A @ B ) )
        = C )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_fst__eqD) ).

thf(1450,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ A @ B ) )
        = C )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(95,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
       => ~ ( ord_less_eq_nat @ B @ C ) )
     => ( ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ A @ C ) )
       => ( ( ( ord_less_eq_nat @ A @ C )
           => ~ ( ord_less_eq_nat @ C @ B ) )
         => ( ( ( ord_less_eq_nat @ C @ B )
             => ~ ( ord_less_eq_nat @ B @ A ) )
           => ( ( ( ord_less_eq_nat @ B @ C )
               => ~ ( ord_less_eq_nat @ C @ A ) )
             => ~ ( ( ord_less_eq_nat @ C @ A )
                 => ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_le__cases3) ).

thf(623,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
       => ~ ( ord_less_eq_nat @ B @ C ) )
     => ( ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ A @ C ) )
       => ( ( ( ord_less_eq_nat @ A @ C )
           => ~ ( ord_less_eq_nat @ C @ B ) )
         => ( ( ( ord_less_eq_nat @ C @ B )
             => ~ ( ord_less_eq_nat @ B @ A ) )
           => ( ( ( ord_less_eq_nat @ B @ C )
               => ~ ( ord_less_eq_nat @ C @ A ) )
             => ~ ( ( ord_less_eq_nat @ C @ A )
                 => ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(87,axiom,
    ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat] :
      ( ( ( ( produc719117507_a_nat @ A )
          = ( produc719117507_a_nat @ B ) )
        & ( ( produc880161797_a_nat @ A )
          = ( produc880161797_a_nat @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_prod_Oexpand) ).

thf(602,plain,
    ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat] :
      ( ( ( ( produc719117507_a_nat @ A )
          = ( produc719117507_a_nat @ B ) )
        & ( ( produc880161797_a_nat @ A )
          = ( produc880161797_a_nat @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(242,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( ( produc1223098053term_b @ ( produc1990145943term_b @ A @ B ) )
        = C )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_snd__eqD) ).

thf(1169,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( ( produc1223098053term_b @ ( produc1990145943term_b @ A @ B ) )
        = C )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(255,axiom,
    ! [A: labeled_graph_b_nat] :
      ( ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ A ) @ ( labele460410879_b_nat @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_labeled__graph_Ocollapse) ).

thf(1215,plain,
    ! [A: labeled_graph_b_nat] :
      ( ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ A ) @ ( labele460410879_b_nat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(316,axiom,
    ! [A: allegorical_term_b,B: set_al1193902458term_b,C: allegorical_term_b,D: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ B )
     => ( ( member516522448term_b @ ( produc1990145943term_b @ A @ C ) @ D )
       => ( member93680451term_b @ C @ ( image_329221075term_b @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_rev__ImageI) ).

thf(1447,plain,
    ! [A: allegorical_term_b,B: set_al1193902458term_b,C: allegorical_term_b,D: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ B )
     => ( ( member516522448term_b @ ( produc1990145943term_b @ A @ C ) @ D )
       => ( member93680451term_b @ C @ ( image_329221075term_b @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(303,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( ( graph_union_b_nat @ A @ B )
        = B )
      = ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ A ) @ ( labeled_edges_b_nat @ B ) )
        & ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ A ) @ ( labele460410879_b_nat @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_graph__union__iff) ).

thf(1394,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( ( graph_union_b_nat @ A @ B )
        = B )
      = ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ A ) @ ( labeled_edges_b_nat @ B ) )
        & ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ A ) @ ( labele460410879_b_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(290,axiom,
    ! [A: labeled_graph_b_nat,B: set_la1976028319_b_nat] :
      ( ( member1483953152_b_nat @ A @ B )
     => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ A ) @ ( id_on_583275916_b_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Id__onI) ).

thf(1345,plain,
    ! [A: labeled_graph_b_nat,B: set_la1976028319_b_nat] :
      ( ( member1483953152_b_nat @ A @ B )
     => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ A ) @ ( id_on_583275916_b_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(158,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( ( produc1990145943term_b @ A @ B )
        = ( produc1990145943term_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_prod_Oinject) ).

thf(849,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( ( produc1990145943term_b @ A @ B )
        = ( produc1990145943term_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(63,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_eq__refl) ).

thf(527,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(19,axiom,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ B @ A )
          & ( ord_less_eq_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_dual__order_Oeq__iff) ).

thf(380,plain,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ B @ A )
          & ( ord_less_eq_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(107,axiom,
    ( set_of195930477at_nat
    = ( ^ [A: set_Pr665622551at_nat] :
        ! [B: produc1391440311at_nat] :
          ( ( member1129678944at_nat @ B @ A )
         => ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ B ) @ ( produc1564126365at_nat @ B ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ B ) ) ) )
            & ( ( produc1564126365at_nat @ B )
              = ( restri321299017at_nat @ ( produc1564126365at_nat @ B ) ) )
            & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ B ) ) )
            & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_set__of__graph__rules__def) ).

thf(678,plain,
    ( set_of195930477at_nat
    = ( ^ [A: set_Pr665622551at_nat] :
        ! [B: produc1391440311at_nat] :
          ( ( member1129678944at_nat @ B @ A )
         => ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ B ) @ ( produc1564126365at_nat @ B ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ B ) ) ) )
            & ( ( produc1564126365at_nat @ B )
              = ( restri321299017at_nat @ ( produc1564126365at_nat @ B ) ) )
            & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ B ) ) )
            & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(69,axiom,
    ! [A: produc1235635379_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ A @ B )
     => ( member889223696_b_nat @ ( produc1754969175_b_nat @ A @ A ) @ ( id_on_138931664_b_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Id__onI) ).

thf(546,plain,
    ! [A: produc1235635379_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ A @ B )
     => ( member889223696_b_nat @ ( produc1754969175_b_nat @ A @ A ) @ ( id_on_138931664_b_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(178,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_al1193902458term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( id_on_1536886967term_b @ C ) )
      = ( ( A = B )
        & ( member93680451term_b @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Id__on__iff) ).

thf(925,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_al1193902458term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( id_on_1536886967term_b @ C ) )
      = ( ( A = B )
        & ( member93680451term_b @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(149,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_al1193902458term_b] :
      ( ( A = B )
     => ( ( member93680451term_b @ A @ C )
       => ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( id_on_1536886967term_b @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Id__on__eqI) ).

thf(810,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_al1193902458term_b] :
      ( ( A = B )
     => ( ( member93680451term_b @ A @ C )
       => ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( id_on_1536886967term_b @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(65,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_order__class_Oorder_Oantisym) ).

thf(534,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(212,axiom,
    ! [A: produc1235635379_b_nat,B: produc1235635379_b_nat] :
      ( ( ( produc1542243159_b_nat @ A )
        = ( produc1542243159_b_nat @ B ) )
     => ( ( ( produc194497945_b_nat @ A )
          = ( produc194497945_b_nat @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_prod__eqI) ).

thf(1067,plain,
    ! [A: produc1235635379_b_nat,B: produc1235635379_b_nat] :
      ( ( ( produc1542243159_b_nat @ A )
        = ( produc1542243159_b_nat @ B ) )
     => ( ( ( produc194497945_b_nat @ A )
          = ( produc194497945_b_nat @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(211,axiom,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat] :
      ( ! [C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
          ( ( ( C
              = ( restrict_b_nat @ C ) )
            & ( finite_finite_nat @ ( labele460410879_b_nat @ C ) )
            & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ C ) ) )
         => ( ( graph_529870330at_nat @ C @ ( produc1542243159_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ C ) ) )
           => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ C @ ( produc1542243159_b_nat @ A ) ) @ B @ D )
             => ( ( graph_529870330at_nat @ C @ B @ D )
               => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ C @ ( produc194497945_b_nat @ A ) ) @ B @ D ) ) ) ) )
     => ( fin_ma971967913at_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_fin__maintainedI) ).

thf(1057,plain,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat] :
      ( ! [C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
          ( ( ( C
              = ( restrict_b_nat @ C ) )
            & ( finite_finite_nat @ ( labele460410879_b_nat @ C ) )
            & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ C ) ) )
         => ( ( graph_529870330at_nat @ C @ ( produc1542243159_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ C ) ) )
           => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ C @ ( produc1542243159_b_nat @ A ) ) @ B @ D )
             => ( ( graph_529870330at_nat @ C @ B @ D )
               => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ C @ ( produc194497945_b_nat @ A ) ) @ B @ D ) ) ) ) )
     => ( fin_ma971967913at_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(58,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( product_Pair_nat_nat @ A @ B )
        = ( product_Pair_nat_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_prod_Oinject) ).

thf(512,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( product_Pair_nat_nat @ A @ B )
        = ( product_Pair_nat_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(181,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ A @ B ) )
        = C )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_snd__eqD) ).

thf(942,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ A @ B ) )
        = C )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(36,axiom,
    member832397200_a_nat @ x @ ( standa1897115818ules_a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).

thf(439,plain,
    member832397200_a_nat @ x @ ( standa1897115818ules_a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(314,axiom,
    ! [A: set_Pr1163220871term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( unival1191217828term_b @ A )
     => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ C ) @ A )
       => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ D ) @ A )
         => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_univalentD) ).

thf(1438,plain,
    ! [A: set_Pr1163220871term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( unival1191217828term_b @ A )
     => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ C ) @ A )
       => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ D ) @ A )
         => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(101,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ A )
       => ( ord_less_eq_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_dual__order_Otrans) ).

thf(661,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ A )
       => ( ord_less_eq_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(236,axiom,
    ( ( id_on_nat @ bot_bot_set_nat )
    = bot_bo2130386637at_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_Id__on__empty) ).

thf(1153,plain,
    ( ( id_on_nat @ bot_bot_set_nat )
    = bot_bo2130386637at_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(134,axiom,
    ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) @ ( produc1564126365at_nat @ standa214789732at_nat ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) ) ) )
    & ( ( produc1564126365at_nat @ standa214789732at_nat )
      = ( restri321299017at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
    & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
    & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_are__rules_I1_J) ).

thf(761,plain,
    ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) @ ( produc1564126365at_nat @ standa214789732at_nat ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) ) ) )
    & ( ( produc1564126365at_nat @ standa214789732at_nat )
      = ( restri321299017at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
    & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
    & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(257,axiom,
    ! [A: labele935650037_a_nat] : ( graph_2130075512at_nat @ ( restri572569417_a_nat @ A ) @ ( restri572569417_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_graph__homomorphism__Id) ).

thf(1223,plain,
    ! [A: labele935650037_a_nat] : ( graph_2130075512at_nat @ ( restri572569417_a_nat @ A ) @ ( restri572569417_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(129,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( ( produc854192515term_b @ ( produc1990145943term_b @ A @ B ) )
        = C )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_fst__eqD) ).

thf(746,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( ( produc854192515term_b @ ( produc1990145943term_b @ A @ B ) )
        = C )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(199,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( relcom1426860350_b_nat @ C @ D ) )
     => ~ ! [E: labeled_graph_b_nat] :
            ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ E ) @ C )
           => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ E @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_relcomp_Ocases) ).

thf(1021,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( relcom1426860350_b_nat @ C @ D ) )
     => ~ ! [E: labeled_graph_b_nat] :
            ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ E ) @ C )
           => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ E @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(10,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_la1083530965_a_nat] :
      ( ( A = B )
     => ( ( member964390942_a_nat @ A @ C )
       => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( id_on_689842066_a_nat @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Id__on__eqI) ).

thf(349,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_la1083530965_a_nat] :
      ( ( A = B )
     => ( ( member964390942_a_nat @ A @ C )
       => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( id_on_689842066_a_nat @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(74,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
        = C )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_fst__eqD) ).

thf(561,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
        = C )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(113,axiom,
    ! [A: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ ( restrict_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
      = ( A
        = ( restrict_b_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_subgraph__restrict) ).

thf(693,plain,
    ! [A: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ ( restrict_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
      = ( A
        = ( restrict_b_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(297,axiom,
    ! [A: nat,B: set_nat] :
      ( ( member_nat @ A @ B )
     => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Id__onI) ).

thf(1370,plain,
    ! [A: nat,B: set_nat] :
      ( ( member_nat @ A @ B )
     => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(150,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( B
          = ( restrict_b_nat @ B ) )
       => ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
          = ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ A ) @ ( labele460410879_b_nat @ B ) )
            & ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ A ) @ ( labeled_edges_b_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_subgraph__def2) ).

thf(815,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( B
          = ( restrict_b_nat @ B ) )
       => ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
          = ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ A ) @ ( labele460410879_b_nat @ B ) )
            & ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ A ) @ ( labeled_edges_b_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(23,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_la1083530965_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ C )
     => ( ( member964390942_a_nat @ A @ D )
       => ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_ImageI) ).

thf(392,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_la1083530965_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ C )
     => ( ( member964390942_a_nat @ A @ D )
       => ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(325,axiom,
    ( translation_b
    = ( ^ [A: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_translation__graph) ).

thf(1487,plain,
    ( translation_b
    = ( ^ [A: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(157,axiom,
    ! [A: labeled_graph_b_nat > labeled_graph_b_nat > $o,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( A @ B @ C )
     => ( A @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ C @ B ) ) @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_exI__realizer) ).

thf(847,plain,
    ! [A: labeled_graph_b_nat > labeled_graph_b_nat > $o,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( A @ B @ C )
     => ( A @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ C @ B ) ) @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(203,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_snd__conv) ).

thf(1032,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(159,axiom,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( A
        = ( produc951298923_b_nat @ B @ C ) )
     => ( ( produc1542243159_b_nat @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_fstI) ).

thf(852,plain,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( A
        = ( produc951298923_b_nat @ B @ C ) )
     => ( ( produc1542243159_b_nat @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(245,axiom,
    ! [A: produc1235635379_b_nat > $o,B: produc1235635379_b_nat] :
      ( ! [C: labeled_graph_b_nat,D: labeled_graph_b_nat] : ( A @ ( produc951298923_b_nat @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_prod__cases) ).

thf(1178,plain,
    ! [A: produc1235635379_b_nat > $o,B: produc1235635379_b_nat] :
      ( ! [C: labeled_graph_b_nat,D: labeled_graph_b_nat] : ( A @ ( produc951298923_b_nat @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(61,axiom,
    ! [A: set_Pr1986765409at_nat] :
      ( ( collec7649004at_nat
        @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Collect__mem__eq) ).

thf(522,plain,
    ! [A: set_Pr1986765409at_nat] :
      ( ( collec7649004at_nat
        @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(251,axiom,
    ! [A: set_Pr9961929at_nat,B: set_nat] :
      ( ( labeled_edges_b_nat @ ( labeled_LG_b_nat @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_labeled__graph_Osel_I1_J) ).

thf(1195,plain,
    ! [A: set_Pr9961929at_nat,B: set_nat] :
      ( ( labeled_edges_b_nat @ ( labeled_LG_b_nat @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(71,axiom,
    ! [A: produc1871334759_a_nat] :
      ( A
      = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ A ) @ ( produc880161797_a_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_prod_Oexhaust__sel) ).

thf(551,plain,
    ! [A: produc1871334759_a_nat] :
      ( A
      = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ A ) @ ( produc880161797_a_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(188,axiom,
    ! [A: allego1565409692at_nat,B: allego1565409692at_nat] :
      ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) ) ) )
      & ( ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) )
        = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) ) )
      & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_graph__rule__translation) ).

thf(974,plain,
    ! [A: allego1565409692at_nat,B: allego1565409692at_nat] :
      ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) ) ) )
      & ( ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) )
        = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) ) )
      & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ A ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(216,axiom,
    ! [A: produc1478835367term_b,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A
        = ( produc1990145943term_b @ B @ C ) )
     => ( ( produc854192515term_b @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_fstI) ).

thf(1079,plain,
    ! [A: produc1478835367term_b,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A
        = ( produc1990145943term_b @ B @ C ) )
     => ( ( produc854192515term_b @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(201,axiom,
    ! [A: set_Pr9961929at_nat,B: set_Pr9961929at_nat] :
      ( ( ord_le910748009at_nat @ A @ B )
     => ( ~ ( finite1987068434at_nat @ A )
       => ~ ( finite1987068434at_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_infinite__super) ).

thf(1027,plain,
    ! [A: set_Pr9961929at_nat,B: set_Pr9961929at_nat] :
      ( ( ord_le910748009at_nat @ A @ B )
     => ( ~ ( finite1987068434at_nat @ A )
       => ~ ( finite1987068434at_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(60,axiom,
    ! [A: nat,B: nat] :
      ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_snd__conv) ).

thf(519,plain,
    ! [A: nat,B: nat] :
      ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(261,axiom,
    ! [A: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_verts__in__translation__finite_I2_J) ).

thf(1234,plain,
    ! [A: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(271,axiom,
    ! [A: set_Pr551076371_b_nat,B: produc1235635379_b_nat] :
      ( ( set_of41538795_b_nat @ A )
     => ( ( member963855452_b_nat @ B @ A )
       => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ B ) @ ( produc194497945_b_nat @ B ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_set__of__graph__rulesD_I3_J) ).

thf(1270,plain,
    ! [A: set_Pr551076371_b_nat,B: produc1235635379_b_nat] :
      ( ( set_of41538795_b_nat @ A )
     => ( ( member963855452_b_nat @ B @ A )
       => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ B ) @ ( produc194497945_b_nat @ B ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(183,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ( graph_529870330at_nat @ B @ C @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) )
       => ( graph_529870330at_nat @ A @ C @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_subgraph__trans) ).

thf(948,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ( graph_529870330at_nat @ B @ C @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) )
       => ( graph_529870330at_nat @ A @ C @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(286,axiom,
    ( ( (=) @ produc1478835367term_b )
    = ( ^ [A: produc1478835367term_b,B: produc1478835367term_b] :
          ( ( ( produc854192515term_b @ A )
            = ( produc854192515term_b @ B ) )
          & ( ( produc1223098053term_b @ A )
            = ( produc1223098053term_b @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_prod__eq__iff) ).

thf(1328,plain,
    ( ( (=) @ produc1478835367term_b )
    = ( ^ [A: produc1478835367term_b,B: produc1478835367term_b] :
          ( ( ( produc854192515term_b @ A )
            = ( produc854192515term_b @ B ) )
          & ( ( produc1223098053term_b @ A )
            = ( produc1223098053term_b @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(226,axiom,
    ! [A: labeled_graph_b_nat] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( maintained_b_nat_nat @ standa879863266rule_b @ A )
        = ( ( labele460410879_b_nat @ A )
         != bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_nonempty__rule) ).

thf(1121,plain,
    ! [A: labeled_graph_b_nat] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( maintained_b_nat_nat @ standa879863266rule_b @ A )
        = ( ( labele460410879_b_nat @ A )
         != bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(310,axiom,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat,C: labeled_graph_b_nat > $o] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
     => ( ! [D: labeled_graph_b_nat,E: labeled_graph_b_nat] :
            ( ( member963855452_b_nat @ ( produc951298923_b_nat @ D @ E ) @ B )
           => ( C @ D ) )
       => ( C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_Domain_Oinducts) ).

thf(1425,plain,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat,C: labeled_graph_b_nat > $o] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
     => ( ! [D: labeled_graph_b_nat,E: labeled_graph_b_nat] :
            ( ( member963855452_b_nat @ ( produc951298923_b_nat @ D @ E ) @ B )
           => ( C @ D ) )
       => ( C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(12,axiom,
    ! [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
      ( ( ord_le1718765799_a_nat @ A @ B )
     => ( ( member832397200_a_nat @ C @ A )
       => ( member832397200_a_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_in__mono) ).

thf(356,plain,
    ! [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
      ( ( ord_le1718765799_a_nat @ A @ B )
     => ( ( member832397200_a_nat @ C @ A )
       => ( member832397200_a_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(84,axiom,
    ! [A: labele935650037_a_nat] :
      ( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ A ) )
      = ( labele1810595089_a_nat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_vertices__restrict) ).

thf(593,plain,
    ! [A: labele935650037_a_nat] :
      ( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ A ) )
      = ( labele1810595089_a_nat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(162,axiom,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat,C: set_la1976028319_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( image_1183964583_b_nat @ B @ C ) )
      = ( ? [D: labeled_graph_b_nat] :
            ( ( member1483953152_b_nat @ D @ C )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ D @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_Image__iff) ).

thf(869,plain,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat,C: set_la1976028319_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( image_1183964583_b_nat @ B @ C ) )
      = ( ? [D: labeled_graph_b_nat] :
            ( ( member1483953152_b_nat @ D @ C )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ D @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(30,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat] :
      ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_snd__conv) ).

thf(420,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat] :
      ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(160,axiom,
    ! [A: allegorical_term_b > $o,B: allegorical_term_b,C: allegorical_term_b > $o,D: allegorical_term_b] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc854192515term_b @ ( produc1990145943term_b @ B @ D ) ) )
          & ( C @ ( produc1223098053term_b @ ( produc1990145943term_b @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_conjI__realizer) ).

thf(857,plain,
    ! [A: allegorical_term_b > $o,B: allegorical_term_b,C: allegorical_term_b > $o,D: allegorical_term_b] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc854192515term_b @ ( produc1990145943term_b @ B @ D ) ) )
          & ( C @ ( produc1223098053term_b @ ( produc1990145943term_b @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(304,axiom,
    ! [A: product_prod_nat_nat,B: set_nat] :
      ( ( member701585322at_nat @ A @ ( id_on_nat @ B ) )
     => ~ ! [C: nat] :
            ( ( member_nat @ C @ B )
           => ( A
             != ( product_Pair_nat_nat @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Id__onE) ).

thf(1397,plain,
    ! [A: product_prod_nat_nat,B: set_nat] :
      ( ( member701585322at_nat @ A @ ( id_on_nat @ B ) )
     => ~ ! [C: nat] :
            ( ( member_nat @ C @ B )
           => ( A
             != ( product_Pair_nat_nat @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(45,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat] :
      ( ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ A @ B ) )
        = C )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_snd__eqD) ).

thf(471,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat] :
      ( ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ A @ B ) )
        = C )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(72,axiom,
    ! [A: produc1871334759_a_nat] :
      ~ ! [B: labele935650037_a_nat,C: labele935650037_a_nat] :
          ( A
         != ( produc1676969687_a_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_old_Oprod_Oexhaust) ).

thf(554,plain,
    ! [A: produc1871334759_a_nat] :
      ~ ! [B: labele935650037_a_nat,C: labele935650037_a_nat] :
          ( A
         != ( produc1676969687_a_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(66,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_order__refl) ).

thf(537,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(110,axiom,
    ! [A: labeled_graph_b_nat] :
      ( A
      = ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ A ) @ ( labele460410879_b_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_labeled__graph_Oexhaust__sel) ).

thf(686,plain,
    ! [A: labeled_graph_b_nat] :
      ( A
      = ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ A ) @ ( labele460410879_b_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(97,axiom,
    ! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ A @ ( relcom1338300020_a_nat @ B @ C ) )
     => ~ ! [D: labele935650037_a_nat,E: labele935650037_a_nat,F: labele935650037_a_nat] :
            ( ( A
              = ( produc1676969687_a_nat @ D @ F ) )
           => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ D @ E ) @ B )
             => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ E @ F ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_relcompE) ).

thf(642,plain,
    ! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ A @ ( relcom1338300020_a_nat @ B @ C ) )
     => ~ ! [D: labele935650037_a_nat,E: labele935650037_a_nat,F: labele935650037_a_nat] :
            ( ( A
              = ( produc1676969687_a_nat @ D @ F ) )
           => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ D @ E ) @ B )
             => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ E @ F ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(96,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_ord__eq__le__trans) ).

thf(637,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(83,axiom,
    ! [A: produc1478835367term_b,B: produc1478835367term_b > $o] :
      ( ( member516522448term_b @ A @ ( collec135640594term_b @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_mem__Collect__eq) ).

thf(590,plain,
    ! [A: produc1478835367term_b,B: produc1478835367term_b > $o] :
      ( ( member516522448term_b @ A @ ( collec135640594term_b @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(205,axiom,
    ! [A: set_Pr9961929at_nat,B: set_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat,E: set_Pr9961929at_nat] :
      ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ A @ B ) @ C @ D )
     => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ ( labeled_LG_b_nat @ A @ B ) @ ( labeled_LG_b_nat @ E @ B ) ) @ C @ D )
        = ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E @ B ) @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_extensible__refl__concr) ).

thf(1039,plain,
    ! [A: set_Pr9961929at_nat,B: set_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat,E: set_Pr9961929at_nat] :
      ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ A @ B ) @ C @ D )
     => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ ( labeled_LG_b_nat @ A @ B ) @ ( labeled_LG_b_nat @ E @ B ) ) @ C @ D )
        = ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E @ B ) @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(237,axiom,
    finite1987068434at_nat @ bot_bo1626616373at_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_finite_OemptyI) ).

thf(1155,plain,
    finite1987068434at_nat @ bot_bo1626616373at_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(309,axiom,
    ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) @ ( produc880161797_a_nat @ standa1410829644tant_a ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) ) ) )
    & ( ( produc880161797_a_nat @ standa1410829644tant_a )
      = ( restri572569417_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
    & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
    & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_are__rules_I1_J) ).

thf(1419,plain,
    ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) @ ( produc880161797_a_nat @ standa1410829644tant_a ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) ) ) )
    & ( ( produc880161797_a_nat @ standa1410829644tant_a )
      = ( restri572569417_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
    & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
    & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(155,axiom,
    ! [A: set_Pr551076371_b_nat,B: produc1235635379_b_nat] :
      ( ( set_of41538795_b_nat @ A )
     => ( ( member963855452_b_nat @ B @ A )
       => ( ( ( produc1542243159_b_nat @ B )
            = ( restrict_b_nat @ ( produc1542243159_b_nat @ B ) ) )
          & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ B ) ) )
          & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc1542243159_b_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_set__of__graph__rulesD_I1_J) ).

thf(837,plain,
    ! [A: set_Pr551076371_b_nat,B: produc1235635379_b_nat] :
      ( ( set_of41538795_b_nat @ A )
     => ( ( member963855452_b_nat @ B @ A )
       => ( ( ( produc1542243159_b_nat @ B )
            = ( restrict_b_nat @ ( produc1542243159_b_nat @ B ) ) )
          & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ B ) ) )
          & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc1542243159_b_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(222,axiom,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
      = ( ? [C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
            ( ( A = C )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ C @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_Domain_Osimps) ).

thf(1099,plain,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
      = ( ? [C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
            ( ( A = C )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ C @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(279,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
      = ( ( A
          = ( restrict_b_nat @ A ) )
        & ( B
          = ( restrict_b_nat @ B ) )
        & ( ( graph_union_b_nat @ A @ B )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_subgraph__def) ).

thf(1297,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
      = ( ( A
          = ( restrict_b_nat @ A ) )
        & ( B
          = ( restrict_b_nat @ B ) )
        & ( ( graph_union_b_nat @ A @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(299,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: allegorical_term_b,E: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ C )
     => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ D ) @ E )
       => ( member516522448term_b @ ( produc1990145943term_b @ A @ D ) @ ( relcom1955155673term_b @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_relcomp_OrelcompI) ).

thf(1382,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: allegorical_term_b,E: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ C )
     => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ D ) @ E )
       => ( member516522448term_b @ ( produc1990145943term_b @ A @ D ) @ ( relcom1955155673term_b @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(189,axiom,
    ! [A: produc1235635379_b_nat] :
      ( ( produc951298923_b_nat @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_prod_Ocollapse) ).

thf(984,plain,
    ! [A: produc1235635379_b_nat] :
      ( ( produc951298923_b_nat @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(193,axiom,
    ! [A: allegorical_term_b > allegorical_term_b > $o,B: produc1478835367term_b] :
      ( ( A @ ( produc1223098053term_b @ B ) @ ( produc854192515term_b @ B ) )
     => ~ ! [C: allegorical_term_b,D: allegorical_term_b] :
            ~ ( A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_exE__realizer_H) ).

thf(1002,plain,
    ! [A: allegorical_term_b > allegorical_term_b > $o,B: produc1478835367term_b] :
      ( ( A @ ( produc1223098053term_b @ B ) @ ( produc854192515term_b @ B ) )
     => ~ ! [C: allegorical_term_b,D: allegorical_term_b] :
            ~ ( A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(311,axiom,
    ! [A: produc1235635379_b_nat] :
      ( A
      = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_surjective__pairing) ).

thf(1429,plain,
    ! [A: produc1235635379_b_nat] :
      ( A
      = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(264,axiom,
    ! [A: set_Pr1163220871term_b,B: set_Pr1163220871term_b] :
      ( ! [C: allegorical_term_b,D: allegorical_term_b] :
          ( ( member516522448term_b @ ( produc1990145943term_b @ C @ D ) @ A )
         => ( member516522448term_b @ ( produc1990145943term_b @ C @ D ) @ B ) )
     => ( ord_le138473255term_b @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_subrelI) ).

thf(1246,plain,
    ! [A: set_Pr1163220871term_b,B: set_Pr1163220871term_b] :
      ( ! [C: allegorical_term_b,D: allegorical_term_b] :
          ( ( member516522448term_b @ ( produc1990145943term_b @ C @ D ) @ A )
         => ( member516522448term_b @ ( produc1990145943term_b @ C @ D ) @ B ) )
     => ( ord_le138473255term_b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(138,axiom,
    ! [A: produc1235635379_b_nat > $o,B: produc1235635379_b_nat] :
      ( ! [C: labeled_graph_b_nat,D: labeled_graph_b_nat] : ( A @ ( produc951298923_b_nat @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_old_Oprod_Oinducts) ).

thf(779,plain,
    ! [A: produc1235635379_b_nat > $o,B: produc1235635379_b_nat] :
      ( ! [C: labeled_graph_b_nat,D: labeled_graph_b_nat] : ( A @ ( produc951298923_b_nat @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(98,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_ord__le__eq__subst) ).

thf(647,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(269,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( relcom1426860350_b_nat @ C @ D ) )
      = ( ? [E: labeled_graph_b_nat,F: labeled_graph_b_nat,G: labeled_graph_b_nat] :
            ( ( A = E )
            & ( B = G )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ E @ F ) @ C )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ F @ G ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_relcomp_Osimps) ).

thf(1263,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( relcom1426860350_b_nat @ C @ D ) )
      = ( ? [E: labeled_graph_b_nat,F: labeled_graph_b_nat,G: labeled_graph_b_nat] :
            ( ( A = E )
            & ( B = G )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ E @ F ) @ C )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ F @ G ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(191,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_la1976028319_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( member1483953152_b_nat @ A @ D )
       => ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_ImageI) ).

thf(997,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_la1976028319_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( member1483953152_b_nat @ A @ D )
       => ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(59,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_order__subst1) ).

thf(515,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(235,axiom,
    ! [A: set_Product_prod_b_b,B: set_Pr9961929at_nat] :
      ( ( finite1015599120od_b_b @ A )
     => ( ( finite1987068434at_nat @ B )
       => ( finite1987068434at_nat @ ( relcom14055552at_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_finite__relcomp) ).

thf(1150,plain,
    ! [A: set_Product_prod_b_b,B: set_Pr9961929at_nat] :
      ( ( finite1015599120od_b_b @ A )
     => ( ( finite1987068434at_nat @ B )
       => ( finite1987068434at_nat @ ( relcom14055552at_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(265,axiom,
    ! [A: allegorical_term_b,B: set_al1193902458term_b] :
      ( ( member93680451term_b @ A @ B )
     => ( member516522448term_b @ ( produc1990145943term_b @ A @ A ) @ ( id_on_1536886967term_b @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Id__onI) ).

thf(1249,plain,
    ! [A: allegorical_term_b,B: set_al1193902458term_b] :
      ( ( member93680451term_b @ A @ B )
     => ( member516522448term_b @ ( produc1990145943term_b @ A @ A ) @ ( id_on_1536886967term_b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(270,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( B
          = ( restrict_b_nat @ B ) )
       => ( ( graph_union_b_nat @ A @ B )
          = ( restrict_b_nat @ ( graph_union_b_nat @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_graph__union__preserves__restrict) ).

thf(1266,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( B
          = ( restrict_b_nat @ B ) )
       => ( ( graph_union_b_nat @ A @ B )
          = ( restrict_b_nat @ ( graph_union_b_nat @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(260,axiom,
    ! [A: labele935650037_a_nat] :
      ( ( graph_2130075512at_nat @ A @ A @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) )
      = ( A
        = ( restri572569417_a_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_subgraph__refl) ).

thf(1231,plain,
    ! [A: labele935650037_a_nat] :
      ( ( graph_2130075512at_nat @ A @ A @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) )
      = ( A
        = ( restri572569417_a_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(209,axiom,
    ! [A: set_nat] :
      ( ~ ( finite_finite_nat @ A )
     => ( A != bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_infinite__imp__nonempty) ).

thf(1050,plain,
    ! [A: set_nat] :
      ( ~ ( finite_finite_nat @ A )
     => ( A != bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(42,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_ord__eq__le__subst) ).

thf(457,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(54,axiom,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_order__class_Oorder_Oeq__iff) ).

thf(503,plain,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(88,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_linear) ).

thf(605,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(288,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_extensible__refl) ).

thf(1333,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(313,axiom,
    ! [A: labeled_graph_b_nat,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ B ) @ ( translation_b @ ( allegorical_A_Int_b @ B @ C ) ) ) @ A )
        = ( ( semantics_b_nat @ A @ ( produc854192515term_b @ ( produc1990145943term_b @ B @ ( allegorical_A_Int_b @ B @ C ) ) ) )
          = ( semantics_b_nat @ A @ ( produc1223098053term_b @ ( produc1990145943term_b @ B @ ( allegorical_A_Int_b @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_maintained__holds__iff) ).

thf(1434,plain,
    ! [A: labeled_graph_b_nat,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ B ) @ ( translation_b @ ( allegorical_A_Int_b @ B @ C ) ) ) @ A )
        = ( ( semantics_b_nat @ A @ ( produc854192515term_b @ ( produc1990145943term_b @ B @ ( allegorical_A_Int_b @ B @ C ) ) ) )
          = ( semantics_b_nat @ A @ ( produc1223098053term_b @ ( produc1990145943term_b @ B @ ( allegorical_A_Int_b @ B @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(8,axiom,
    ! [A: set_Pr1987088711_a_nat] :
      ( ! [B: produc1871334759_a_nat] :
          ~ ( member832397200_a_nat @ B @ A )
     => ( ord_le1718765799_a_nat @ A @ bot_bo1836341171_a_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_subset__emptyI) ).

thf(343,plain,
    ! [A: set_Pr1987088711_a_nat] :
      ( ! [B: produc1871334759_a_nat] :
          ~ ( member832397200_a_nat @ B @ A )
     => ( ord_le1718765799_a_nat @ A @ bot_bo1836341171_a_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(180,axiom,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( A
        = ( produc951298923_b_nat @ B @ C ) )
     => ( ( produc194497945_b_nat @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_sndI) ).

thf(938,plain,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ( A
        = ( produc951298923_b_nat @ B @ C ) )
     => ( ( produc194497945_b_nat @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(56,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_dual__order_Orefl) ).

thf(508,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(176,axiom,
    ! [A: set_Pr9961929at_nat] :
      ( ( finite1987068434at_nat @ A )
     => ( finite_finite_b @ ( domain1101989710at_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_finite__Domain) ).

thf(921,plain,
    ! [A: set_Pr9961929at_nat] :
      ( ( finite1987068434at_nat @ A )
     => ( finite_finite_b @ ( domain1101989710at_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(210,axiom,
    ! [A: set_nat] :
      ( ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ A )
      = ( restrict_b_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_graph__empty__e) ).

thf(1054,plain,
    ! [A: set_nat] :
      ( ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ A )
      = ( restrict_b_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(241,axiom,
    ( conseq1730780375at_nat
    = ( ^ [A: set_Pr551076371_b_nat,B: labeled_graph_b_nat] :
          ( ( B
            = ( restrict_b_nat @ B ) )
          & ! [C: produc1235635379_b_nat] :
              ( ( member963855452_b_nat @ C @ A )
             => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( produc194497945_b_nat @ C ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ C ) ) ) )
                & ( maintained_b_nat_nat @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_consequence__graph__def) ).

thf(1167,plain,
    ( conseq1730780375at_nat
    = ( ^ [A: set_Pr551076371_b_nat,B: labeled_graph_b_nat] :
          ( ( B
            = ( restrict_b_nat @ B ) )
          & ! [C: produc1235635379_b_nat] :
              ( ( member963855452_b_nat @ C @ A )
             => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( produc194497945_b_nat @ C ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ C ) ) ) )
                & ( maintained_b_nat_nat @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(143,axiom,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
      = ( ? [C: allegorical_term_b] : ( member516522448term_b @ ( produc1990145943term_b @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_Domain__iff) ).

thf(794,plain,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
      = ( ? [C: allegorical_term_b] : ( member516522448term_b @ ( produc1990145943term_b @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(167,axiom,
    ! [A: labeled_graph_b_nat] :
      ( ( labele460410879_b_nat @ ( restrict_b_nat @ A ) )
      = ( labele460410879_b_nat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_vertices__restrict) ).

thf(888,plain,
    ! [A: labeled_graph_b_nat] :
      ( ( labele460410879_b_nat @ ( restrict_b_nat @ A ) )
      = ( labele460410879_b_nat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(276,axiom,
    ! [A: labeled_graph_b_nat,B: nat,C: nat,D: allegorical_term_b] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( semantics_b_nat @ A @ D ) )
       => ( member_nat @ C @ ( labele460410879_b_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_semantics__in__vertices_I2_J) ).

thf(1286,plain,
    ! [A: labeled_graph_b_nat,B: nat,C: nat,D: allegorical_term_b] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( semantics_b_nat @ A @ D ) )
       => ( member_nat @ C @ ( labele460410879_b_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(25,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
      ( ( ( produc1676969687_a_nat @ A @ B )
        = ( produc1676969687_a_nat @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Pair__inject) ).

thf(398,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
      ( ( ( produc1676969687_a_nat @ A @ B )
        = ( produc1676969687_a_nat @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(204,axiom,
    ! [A: produc1235635379_b_nat] :
      ~ ! [B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
          ( A
         != ( produc951298923_b_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_old_Oprod_Oexhaust) ).

thf(1035,plain,
    ! [A: produc1235635379_b_nat] :
      ~ ! [B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
          ( A
         != ( produc951298923_b_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(320,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: allegorical_term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ C )
     => ( ( D = B )
       => ( member516522448term_b @ ( produc1990145943term_b @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_ssubst__Pair__rhs) ).

thf(1466,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: allegorical_term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ C )
     => ( ( D = B )
       => ( member516522448term_b @ ( produc1990145943term_b @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(73,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
     => ( A = bot_bot_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_bot_Oextremum__uniqueI) ).

thf(558,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
     => ( A = bot_bot_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(27,axiom,
    ! [A: labele935650037_a_nat,B: set_la1083530965_a_nat,C: labele935650037_a_nat,D: set_Pr1987088711_a_nat] :
      ( ( member964390942_a_nat @ A @ B )
     => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ C ) @ D )
       => ( member964390942_a_nat @ C @ ( image_1971191571_a_nat @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_rev__ImageI) ).

thf(412,plain,
    ! [A: labele935650037_a_nat,B: set_la1083530965_a_nat,C: labele935650037_a_nat,D: set_Pr1987088711_a_nat] :
      ( ( member964390942_a_nat @ A @ B )
     => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ C ) @ D )
       => ( member964390942_a_nat @ C @ ( image_1971191571_a_nat @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(130,axiom,
    ( maintained_b_nat_nat
    = ( ^ [A: produc1235635379_b_nat,B: labeled_graph_b_nat] :
        ! [C: set_Pr1986765409at_nat] :
          ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ A ) @ B @ C )
         => ( extensible_b_nat_nat @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_maintained__def) ).

thf(750,plain,
    ( maintained_b_nat_nat
    = ( ^ [A: produc1235635379_b_nat,B: labeled_graph_b_nat] :
        ! [C: set_Pr1986765409at_nat] :
          ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ A ) @ B @ C )
         => ( extensible_b_nat_nat @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(266,axiom,
    ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) @ ( produc194497945_b_nat @ standa879863266rule_b ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) ) ) )
    & ( ( produc194497945_b_nat @ standa879863266rule_b )
      = ( restrict_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
    & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
    & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_are__rules_I1_J) ).

thf(1251,plain,
    ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) @ ( produc194497945_b_nat @ standa879863266rule_b ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) ) ) )
    & ( ( produc194497945_b_nat @ standa879863266rule_b )
      = ( restrict_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
    & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
    & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(33,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( relcom1338300020_a_nat @ C @ D ) )
     => ~ ! [E: labele935650037_a_nat] :
            ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ E ) @ C )
           => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ E @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_relcomp_Ocases) ).

thf(430,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( relcom1338300020_a_nat @ C @ D ) )
     => ~ ! [E: labele935650037_a_nat] :
            ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ E ) @ C )
           => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ E @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(153,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ! [D: set_Pr1986765409at_nat] :
          ( ( graph_529870330at_nat @ A @ B @ D )
         => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A @ C ) @ B @ D ) )
     => ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_maintainedI) ).

thf(824,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( ! [D: set_Pr1986765409at_nat] :
          ( ( graph_529870330at_nat @ A @ B @ D )
         => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A @ C ) @ B @ D ) )
     => ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(272,axiom,
    ! [A: set_Pr551076371_b_nat,B: produc1235635379_b_nat] :
      ( ( set_of41538795_b_nat @ A )
     => ( ( member963855452_b_nat @ B @ A )
       => ( ( ( produc194497945_b_nat @ B )
            = ( restrict_b_nat @ ( produc194497945_b_nat @ B ) ) )
          & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ B ) ) )
          & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_set__of__graph__rulesD_I2_J) ).

thf(1273,plain,
    ! [A: set_Pr551076371_b_nat,B: produc1235635379_b_nat] :
      ( ( set_of41538795_b_nat @ A )
     => ( ( member963855452_b_nat @ B @ A )
       => ( ( ( produc194497945_b_nat @ B )
            = ( restrict_b_nat @ ( produc194497945_b_nat @ B ) ) )
          & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ B ) ) )
          & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(78,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_order__trans) ).

thf(573,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(111,axiom,
    ! [A: allegorical_term_b > allegorical_term_b > $o,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A @ B @ C )
     => ( A @ ( produc1223098053term_b @ ( produc1990145943term_b @ C @ B ) ) @ ( produc854192515term_b @ ( produc1990145943term_b @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_exI__realizer) ).

thf(689,plain,
    ! [A: allegorical_term_b > allegorical_term_b > $o,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A @ B @ C )
     => ( A @ ( produc1223098053term_b @ ( produc1990145943term_b @ C @ B ) ) @ ( produc854192515term_b @ ( produc1990145943term_b @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(124,axiom,
    ( unival857119480_b_nat
    = ( ^ [A: set_Pr551076371_b_nat] :
        ! [B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
          ( ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ C ) @ A )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ D ) @ A ) )
         => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_univalent__def) ).

thf(733,plain,
    ( unival857119480_b_nat
    = ( ^ [A: set_Pr551076371_b_nat] :
        ! [B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
          ( ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ C ) @ A )
            & ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ D ) @ A ) )
         => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(151,axiom,
    ! [A: labeled_graph_b_nat,B: produc1235635379_b_nat] :
      ( ( A
        = ( produc194497945_b_nat @ B ) )
      = ( ? [C: labeled_graph_b_nat] :
            ( B
            = ( produc951298923_b_nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_eq__snd__iff) ).

thf(819,plain,
    ! [A: labeled_graph_b_nat,B: produc1235635379_b_nat] :
      ( ( A
        = ( produc194497945_b_nat @ B ) )
      = ( ? [C: labeled_graph_b_nat] :
            ( B
            = ( produc951298923_b_nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(31,axiom,
    ! [A: product_prod_nat_nat] :
      ~ ! [B: nat,C: nat] :
          ( A
         != ( product_Pair_nat_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_old_Oprod_Oexhaust) ).

thf(423,plain,
    ! [A: product_prod_nat_nat] :
      ~ ! [B: nat,C: nat] :
          ( A
         != ( product_Pair_nat_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(156,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( univalent_nat_nat @ D )
       => ( ( agree_on_b_nat_nat @ A @ C @ D )
          = ( ord_le841296385at_nat @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_agree__iff__subset) ).

thf(843,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( univalent_nat_nat @ D )
       => ( ( agree_on_b_nat_nat @ A @ C @ D )
          = ( ord_le841296385at_nat @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(301,axiom,
    ! [A: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ A @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
      = ( A
        = ( restrict_b_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_subgraph__refl) ).

thf(1388,plain,
    ! [A: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ A @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
      = ( A
        = ( restrict_b_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(128,axiom,
    ! [A: set_Pr9961929at_nat,B: set_b] :
      ( ( finite1987068434at_nat @ A )
     => ( finite772653738at_nat @ ( image_2112855445at_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_finite__Image) ).

thf(743,plain,
    ! [A: set_Pr9961929at_nat,B: set_b] :
      ( ( finite1987068434at_nat @ A )
     => ( finite772653738at_nat @ ( image_2112855445at_nat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(164,axiom,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
     => ~ ! [C: labeled_graph_b_nat] :
            ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_DomainE) ).

thf(875,plain,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
     => ~ ! [C: labeled_graph_b_nat] :
            ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(80,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_bot_Oextremum__unique) ).

thf(579,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(227,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: labeled_graph_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( D = B )
       => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_ssubst__Pair__rhs) ).

thf(1124,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: labeled_graph_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( D = B )
       => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(39,axiom,
    ! [A: produc1478835367term_b,B: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ A @ B )
     => ( member1449757456term_b @ ( produc859843415term_b @ A @ A ) @ ( id_on_1664915780term_b @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Id__onI) ).

thf(445,plain,
    ! [A: produc1478835367term_b,B: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ A @ B )
     => ( member1449757456term_b @ ( produc859843415term_b @ A @ A ) @ ( id_on_1664915780term_b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(20,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_order_Otrans) ).

thf(382,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(283,axiom,
    ! [A: produc1478835367term_b,B: produc1478835367term_b] :
      ( ( ( ( produc854192515term_b @ A )
          = ( produc854192515term_b @ B ) )
        & ( ( produc1223098053term_b @ A )
          = ( produc1223098053term_b @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_prod_Oexpand) ).

thf(1312,plain,
    ! [A: produc1478835367term_b,B: produc1478835367term_b] :
      ( ( ( ( produc854192515term_b @ A )
          = ( produc854192515term_b @ B ) )
        & ( ( produc1223098053term_b @ A )
          = ( produc1223098053term_b @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(118,axiom,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
     => ~ ! [C: allegorical_term_b] :
            ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_DomainE) ).

thf(713,plain,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
     => ~ ! [C: allegorical_term_b] :
            ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(5,axiom,
    ! [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
      ( ! [C: produc1871334759_a_nat] :
          ( ( member832397200_a_nat @ C @ A )
         => ( member832397200_a_nat @ C @ B ) )
     => ( ord_le1718765799_a_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_subsetI) ).

thf(335,plain,
    ! [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
      ( ! [C: produc1871334759_a_nat] :
          ( ( member832397200_a_nat @ C @ A )
         => ( member832397200_a_nat @ C @ B ) )
     => ( ord_le1718765799_a_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(219,axiom,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat] :
      ( ( extensible_b_nat_nat @ A @ B @ C )
     => ~ ! [D: set_Pr1986765409at_nat] :
            ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ A ) @ B @ D )
           => ~ ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ A ) @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_extensibleD) ).

thf(1090,plain,
    ! [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat] :
      ( ( extensible_b_nat_nat @ A @ B @ C )
     => ~ ! [D: set_Pr1986765409at_nat] :
            ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ A ) @ B @ D )
           => ~ ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ A ) @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(147,axiom,
    ! [A: produc1235635379_b_nat] :
    ? [B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( A
      = ( produc951298923_b_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_surj__pair) ).

thf(804,plain,
    ! [A: produc1235635379_b_nat] :
    ? [B: labeled_graph_b_nat,C: labeled_graph_b_nat] :
      ( A
      = ( produc951298923_b_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(293,axiom,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b,C: set_al1193902458term_b] :
      ( ( member93680451term_b @ A @ ( image_329221075term_b @ B @ C ) )
      = ( ? [D: allegorical_term_b] :
            ( ( member93680451term_b @ D @ C )
            & ( member516522448term_b @ ( produc1990145943term_b @ D @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_Image__iff) ).

thf(1356,plain,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b,C: set_al1193902458term_b] :
      ( ( member93680451term_b @ A @ ( image_329221075term_b @ B @ C ) )
      = ( ? [D: allegorical_term_b] :
            ( ( member93680451term_b @ D @ C )
            & ( member516522448term_b @ ( produc1990145943term_b @ D @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(105,axiom,
    ! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat] :
      ( ! [C: nat,D: nat] : ( A @ ( product_Pair_nat_nat @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_prod__cases) ).

thf(672,plain,
    ! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat] :
      ( ! [C: nat,D: nat] : ( A @ ( product_Pair_nat_nat @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(91,axiom,
    ( bot_bo1024461546_nat_o
    = ( ^ [A: produc1871334759_a_nat] : ( member832397200_a_nat @ A @ bot_bo1836341171_a_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_bot__empty__eq) ).

thf(611,plain,
    ( bot_bo1024461546_nat_o
    = ( ^ [A: produc1871334759_a_nat] : ( member832397200_a_nat @ A @ bot_bo1836341171_a_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(141,axiom,
    ! [A: nat > labeled_graph_b_nat,B: nat] :
      ( ( chain_b_nat @ A )
     => ( ( A @ B )
        = ( restrict_b_nat @ ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_chain__then__restrict) ).

thf(787,plain,
    ! [A: nat > labeled_graph_b_nat,B: nat] :
      ( ( chain_b_nat @ A )
     => ( ( A @ B )
        = ( restrict_b_nat @ ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(274,axiom,
    ( set_of41538795_b_nat
    = ( ^ [A: set_Pr551076371_b_nat] :
        ! [B: produc1235635379_b_nat] :
          ( ( member963855452_b_nat @ B @ A )
         => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ B ) @ ( produc194497945_b_nat @ B ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ B ) ) ) )
            & ( ( produc194497945_b_nat @ B )
              = ( restrict_b_nat @ ( produc194497945_b_nat @ B ) ) )
            & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ B ) ) )
            & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_set__of__graph__rules__def) ).

thf(1282,plain,
    ( set_of41538795_b_nat
    = ( ^ [A: set_Pr551076371_b_nat] :
        ! [B: produc1235635379_b_nat] :
          ( ( member963855452_b_nat @ B @ A )
         => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ B ) @ ( produc194497945_b_nat @ B ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ B ) ) ) )
            & ( ( produc194497945_b_nat @ B )
              = ( restrict_b_nat @ ( produc194497945_b_nat @ B ) ) )
            & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ B ) ) )
            & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(196,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A @ B ) @ C @ D )
     => ( ( A
          = ( restrict_b_nat @ A ) )
       => ( graph_529870330at_nat @ A @ C @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_graph__homo__union__id_I1_J) ).

thf(1011,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A @ B ) @ C @ D )
     => ( ( A
          = ( restrict_b_nat @ A ) )
       => ( graph_529870330at_nat @ A @ C @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(208,axiom,
    ! [A: set_nat] : ( univalent_nat_nat @ ( id_on_nat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_id__univalent) ).

thf(1048,plain,
    ! [A: set_nat] : ( univalent_nat_nat @ ( id_on_nat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(18,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_antisym) ).

thf(377,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(233,axiom,
    ! [A: produc1478835367term_b] :
      ( A
      = ( produc1990145943term_b @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_prod_Oexhaust__sel) ).

thf(1144,plain,
    ! [A: produc1478835367term_b] :
      ( A
      = ( produc1990145943term_b @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(126,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ( graph_529870330at_nat @ C @ A @ D )
       => ( graph_529870330at_nat @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_subgraph__preserves__hom) ).

thf(737,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ( graph_529870330at_nat @ C @ A @ D )
       => ( graph_529870330at_nat @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(206,axiom,
    ( unival1191217828term_b
    = ( ^ [A: set_Pr1163220871term_b] :
        ! [B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
          ( ( ( member516522448term_b @ ( produc1990145943term_b @ B @ C ) @ A )
            & ( member516522448term_b @ ( produc1990145943term_b @ B @ D ) @ A ) )
         => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_univalent__def) ).

thf(1043,plain,
    ( unival1191217828term_b
    = ( ^ [A: set_Pr1163220871term_b] :
        ! [B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
          ( ( ( member516522448term_b @ ( produc1990145943term_b @ B @ C ) @ A )
            & ( member516522448term_b @ ( produc1990145943term_b @ B @ D ) @ A ) )
         => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(93,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_order__subst2) ).

thf(616,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(86,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_dual__order_Oantisym) ).

thf(599,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(244,axiom,
    ! [A: nat,B: nat,C: set_nat] :
      ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ C ) )
      = ( ( A = B )
        & ( member_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Id__on__iff) ).

thf(1175,plain,
    ! [A: nat,B: nat,C: set_nat] :
      ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ C ) )
      = ( ( A = B )
        & ( member_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(14,axiom,
    ! [A: product_prod_nat_nat] :
      ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_prod_Ocollapse) ).

thf(362,plain,
    ! [A: product_prod_nat_nat] :
      ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(76,axiom,
    ! [A: set_Pr551076371_b_nat] :
      ( ( collec1615000990_b_nat
        @ ^ [B: produc1235635379_b_nat] : ( member963855452_b_nat @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Collect__mem__eq) ).

thf(567,plain,
    ! [A: set_Pr551076371_b_nat] :
      ( ( collec1615000990_b_nat
        @ ^ [B: produc1235635379_b_nat] : ( member963855452_b_nat @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(22,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: labele935650037_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ C )
     => ( ( D = B )
       => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_ssubst__Pair__rhs) ).

thf(387,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: labele935650037_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ C )
     => ( ( D = B )
       => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(321,axiom,
    ! [A: nat,B: nat,C: set_nat] :
      ( ( A = B )
     => ( ( member_nat @ A @ C )
       => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_Id__on__eqI) ).

thf(1471,plain,
    ! [A: nat,B: nat,C: set_nat] :
      ( ( A = B )
     => ( ( member_nat @ A @ C )
       => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(51,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat] :
      ( ( ( ( labele195203296_a_nat @ A )
          = ( labele195203296_a_nat @ B ) )
        & ( ( labele1810595089_a_nat @ A )
          = ( labele1810595089_a_nat @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_labeled__graph_Oexpand) ).

thf(494,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat] :
      ( ( ( ( labele195203296_a_nat @ A )
          = ( labele195203296_a_nat @ B ) )
        & ( ( labele1810595089_a_nat @ A )
          = ( labele1810595089_a_nat @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(133,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_snd__conv) ).

thf(758,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(90,axiom,
    ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
      ( ( member701585322at_nat @ A @ B )
     => ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ A ) @ ( id_on_2144791838at_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Id__onI) ).

thf(609,plain,
    ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
      ( ( member701585322at_nat @ A @ B )
     => ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ A ) @ ( id_on_2144791838at_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(285,axiom,
    ! [A: produc1478835367term_b] :
    ? [B: allegorical_term_b,C: allegorical_term_b] :
      ( A
      = ( produc1990145943term_b @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_surj__pair) ).

thf(1325,plain,
    ! [A: produc1478835367term_b] :
    ? [B: allegorical_term_b,C: allegorical_term_b] :
      ( A
      = ( produc1990145943term_b @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(187,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b] :
      ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_graph__rule__translation) ).

thf(964,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b] :
      ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ A ) @ ( translation_b @ ( allegorical_A_Int_b @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(174,axiom,
    ! [A: labeled_graph_b_nat,B: set_la1976028319_b_nat,C: labeled_graph_b_nat,D: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ B )
     => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C ) @ D )
       => ( member1483953152_b_nat @ C @ ( image_1183964583_b_nat @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_rev__ImageI) ).

thf(915,plain,
    ! [A: labeled_graph_b_nat,B: set_la1976028319_b_nat,C: labeled_graph_b_nat,D: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ B )
     => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C ) @ D )
       => ( member1483953152_b_nat @ C @ ( image_1183964583_b_nat @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(278,axiom,
    ! [A: produc1235635379_b_nat,B: set_la1976028319_b_nat] :
      ( ( member963855452_b_nat @ A @ ( id_on_583275916_b_nat @ B ) )
     => ~ ! [C: labeled_graph_b_nat] :
            ( ( member1483953152_b_nat @ C @ B )
           => ( A
             != ( produc951298923_b_nat @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Id__onE) ).

thf(1293,plain,
    ! [A: produc1235635379_b_nat,B: set_la1976028319_b_nat] :
      ( ( member963855452_b_nat @ A @ ( id_on_583275916_b_nat @ B ) )
     => ~ ! [C: labeled_graph_b_nat] :
            ( ( member1483953152_b_nat @ C @ B )
           => ( A
             != ( produc951298923_b_nat @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(3,axiom,
    ( ord_le1718765799_a_nat
    = ( ^ [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
        ! [C: produc1871334759_a_nat] :
          ( ( member832397200_a_nat @ C @ A )
         => ( member832397200_a_nat @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_subset__iff) ).

thf(330,plain,
    ( ord_le1718765799_a_nat
    = ( ^ [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
        ! [C: produc1871334759_a_nat] :
          ( ( member832397200_a_nat @ C @ A )
         => ( member832397200_a_nat @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(224,axiom,
    ! [A: produc1478835367term_b] :
      ( A
      = ( produc1990145943term_b @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_surjective__pairing) ).

thf(1112,plain,
    ! [A: produc1478835367term_b] :
      ( A
      = ( produc1990145943term_b @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(202,axiom,
    ! [A: nat > labeled_graph_b_nat,B: set_Pr9961929at_nat,C: set_nat,D: set_Pr1986765409at_nat] :
      ( ( chain_b_nat @ A )
     => ( ( finite1987068434at_nat @ B )
       => ( ( finite_finite_nat @ C )
         => ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ B @ C ) @ ( chain_sup_b_nat @ A ) @ D )
           => ? [E: nat] : ( graph_529870330at_nat @ ( labeled_LG_b_nat @ B @ C ) @ ( A @ E ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_find__graph__occurence) ).

thf(1029,plain,
    ! [A: nat > labeled_graph_b_nat,B: set_Pr9961929at_nat,C: set_nat,D: set_Pr1986765409at_nat] :
      ( ( chain_b_nat @ A )
     => ( ( finite1987068434at_nat @ B )
       => ( ( finite_finite_nat @ C )
         => ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ B @ C ) @ ( chain_sup_b_nat @ A ) @ D )
           => ? [E: nat] : ( graph_529870330at_nat @ ( labeled_LG_b_nat @ B @ C ) @ ( A @ E ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(169,axiom,
    ! [A: itself_nat,B: produc1235635379_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat,E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat,G: labeled_graph_b_nat,H: set_Pr1986765409at_nat,I: set_Pr1986765409at_nat] :
      ( ( weak_u2026406106at_nat @ A @ B @ C @ D @ E @ F )
     => ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ B ) @ G @ H )
       => ( ( graph_529870330at_nat @ C @ G @ I )
         => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ E @ I ) @ H )
           => ? [J: set_Pr1986765409at_nat] :
                ( ( graph_529870330at_nat @ D @ G @ J )
                & ( ord_le841296385at_nat @ I @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_weak__universalD) ).

thf(895,plain,
    ! [A: itself_nat,B: produc1235635379_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat,E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat,G: labeled_graph_b_nat,H: set_Pr1986765409at_nat,I: set_Pr1986765409at_nat] :
      ( ( weak_u2026406106at_nat @ A @ B @ C @ D @ E @ F )
     => ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ B ) @ G @ H )
       => ( ( graph_529870330at_nat @ C @ G @ I )
         => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ E @ I ) @ H )
           => ? [J: set_Pr1986765409at_nat] :
                ( ( graph_529870330at_nat @ D @ G @ J )
                & ( ord_le841296385at_nat @ I @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(252,axiom,
    ! [A: allegorical_term_b > allegorical_term_b > $o,B: allegorical_term_b,C: allegorical_term_b,D: produc1478835367term_b] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc1990145943term_b @ B @ C ) )
       => ( A @ ( produc854192515term_b @ D ) @ ( produc1223098053term_b @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_BNF__Greatest__Fixpoint_Osubst__Pair) ).

thf(1198,plain,
    ! [A: allegorical_term_b > allegorical_term_b > $o,B: allegorical_term_b,C: allegorical_term_b,D: produc1478835367term_b] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc1990145943term_b @ B @ C ) )
       => ( A @ ( produc854192515term_b @ D ) @ ( produc1223098053term_b @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(192,axiom,
    ! [A: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_verts__in__translation__finite_I1_J) ).

thf(1000,plain,
    ! [A: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(223,axiom,
    ! [A: product_prod_nat_nat] :
      ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ A ) ) @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ A ) ) ) ) )
      & ( ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) )
        = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) ) ) )
      & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) ) ) )
      & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_are__rules_I3_J) ).

thf(1102,plain,
    ! [A: product_prod_nat_nat] :
      ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ A ) ) @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ A ) ) ) ) )
      & ( ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) )
        = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) ) ) )
      & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) ) ) )
      & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(55,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: labele935650037_a_nat,E: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ C )
     => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ D ) @ E )
       => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ D ) @ ( relcom1338300020_a_nat @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_relcomp_OrelcompI) ).

thf(505,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: labele935650037_a_nat,E: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ C )
     => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ D ) @ E )
       => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ D ) @ ( relcom1338300020_a_nat @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(100,axiom,
    ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat > $o] :
      ( ( member832397200_a_nat @ A @ ( collec357096914_a_nat @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_mem__Collect__eq) ).

thf(658,plain,
    ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat > $o] :
      ( ( member832397200_a_nat @ A @ ( collec357096914_a_nat @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(254,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ A ) @ ( labele460410879_b_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_subgraph__subset_I1_J) ).

thf(1213,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ A ) @ ( labele460410879_b_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(154,axiom,
    ! [A: standard_Constant_a] :
      ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ A ) ) @ ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ A ) ) ) ) )
      & ( ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) )
        = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) ) ) )
      & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) ) ) )
      & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_are__rules_I2_J) ).

thf(827,plain,
    ! [A: standard_Constant_a] :
      ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ A ) ) @ ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ A ) ) ) ) )
      & ( ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) )
        = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) ) ) )
      & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) ) ) )
      & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(106,axiom,
    ! [A: set_Pr1163220871term_b] :
      ( ( collec135640594term_b
        @ ^ [B: produc1478835367term_b] : ( member516522448term_b @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Collect__mem__eq) ).

thf(675,plain,
    ! [A: set_Pr1163220871term_b] :
      ( ( collec135640594term_b
        @ ^ [B: produc1478835367term_b] : ( member516522448term_b @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(281,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_la1976028319_b_nat] :
      ( ( A = B )
     => ( ( member1483953152_b_nat @ A @ C )
       => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( id_on_583275916_b_nat @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Id__on__eqI) ).

thf(1304,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_la1976028319_b_nat] :
      ( ( A = B )
     => ( ( member1483953152_b_nat @ A @ C )
       => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( id_on_583275916_b_nat @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(253,axiom,
    ! [A: product_prod_nat_nat] :
      ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ A ) ) @ ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ A ) ) ) ) )
      & ( ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) )
        = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) ) ) )
      & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) ) ) )
      & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_are__rules_I2_J) ).

thf(1203,plain,
    ! [A: product_prod_nat_nat] :
      ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ A ) ) @ ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ A ) ) ) ) )
      & ( ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) )
        = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) ) ) )
      & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) ) ) )
      & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(64,axiom,
    ! [A: produc1871334759_a_nat] :
      ( ( produc1676969687_a_nat @ ( produc719117507_a_nat @ A ) @ ( produc880161797_a_nat @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_prod_Ocollapse) ).

thf(531,plain,
    ! [A: produc1871334759_a_nat] :
      ( ( produc1676969687_a_nat @ ( produc719117507_a_nat @ A ) @ ( produc880161797_a_nat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(108,axiom,
    ! [A: produc1235635379_b_nat,B: produc1235635379_b_nat] :
      ( ( ( ( produc1542243159_b_nat @ A )
          = ( produc1542243159_b_nat @ B ) )
        & ( ( produc194497945_b_nat @ A )
          = ( produc194497945_b_nat @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_prod_Oexpand) ).

thf(680,plain,
    ! [A: produc1235635379_b_nat,B: produc1235635379_b_nat] :
      ( ( ( ( produc1542243159_b_nat @ A )
          = ( produc1542243159_b_nat @ B ) )
        & ( ( produc194497945_b_nat @ A )
          = ( produc194497945_b_nat @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(70,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
      ( ( ( produc1676969687_a_nat @ A @ B )
        = ( produc1676969687_a_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_old_Oprod_Oinject) ).

thf(548,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
      ( ( ( produc1676969687_a_nat @ A @ B )
        = ( produc1676969687_a_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(230,axiom,
    ! [A: nat > labeled_graph_b_nat,B: set_nat,C: set_Pr1986765409at_nat] :
      ( ( chain_b_nat @ A )
     => ( ( finite_finite_nat @ B )
       => ( ( univalent_nat_nat @ C )
         => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ C @ B ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ A ) ) )
           => ? [D: nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ C @ B ) @ ( labele460410879_b_nat @ ( A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_find__graph__occurence__vertices) ).

thf(1134,plain,
    ! [A: nat > labeled_graph_b_nat,B: set_nat,C: set_Pr1986765409at_nat] :
      ( ( chain_b_nat @ A )
     => ( ( finite_finite_nat @ B )
       => ( ( univalent_nat_nat @ C )
         => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ C @ B ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ A ) ) )
           => ? [D: nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ C @ B ) @ ( labele460410879_b_nat @ ( A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(198,axiom,
    ! [A: set_Pr9961929at_nat] :
      ( ( unival989235430at_nat @ A )
     => ( ( finite_finite_b @ ( domain1101989710at_nat @ A ) )
        = ( finite1987068434at_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_univalent__finite_I2_J) ).

thf(1018,plain,
    ! [A: set_Pr9961929at_nat] :
      ( ( unival989235430at_nat @ A )
     => ( ( finite_finite_b @ ( domain1101989710at_nat @ A ) )
        = ( finite1987068434at_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(246,axiom,
    ! [A: nat > labeled_graph_b_nat,B: nat,C: nat] :
      ( ( chain_b_nat @ A )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( graph_529870330at_nat @ ( A @ B ) @ ( A @ C ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_chain) ).

thf(1181,plain,
    ! [A: nat > labeled_graph_b_nat,B: nat,C: nat] :
      ( ( chain_b_nat @ A )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( graph_529870330at_nat @ ( A @ B ) @ ( A @ C ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(307,axiom,
    ! [A: produc1478835367term_b > $o,B: produc1478835367term_b] :
      ( ! [C: allegorical_term_b,D: allegorical_term_b] : ( A @ ( produc1990145943term_b @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_prod__cases) ).

thf(1413,plain,
    ! [A: produc1478835367term_b > $o,B: produc1478835367term_b] :
      ( ! [C: allegorical_term_b,D: allegorical_term_b] : ( A @ ( produc1990145943term_b @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(215,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( relcom1426860350_b_nat @ C @ D ) )
     => ~ ! [E: labeled_graph_b_nat] :
            ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ E ) @ C )
           => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ E @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_relcompEpair) ).

thf(1076,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( relcom1426860350_b_nat @ C @ D ) )
     => ~ ! [E: labeled_graph_b_nat] :
            ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ E ) @ C )
           => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ E @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(62,axiom,
    ( unival1637751524_a_nat
    = ( ^ [A: set_Pr1987088711_a_nat] :
        ! [B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
          ( ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ C ) @ A )
            & ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ D ) @ A ) )
         => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_univalent__def) ).

thf(525,plain,
    ( unival1637751524_a_nat
    = ( ^ [A: set_Pr1987088711_a_nat] :
        ! [B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
          ( ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ C ) @ A )
            & ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ D ) @ A ) )
         => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(258,axiom,
    ! [A: labeled_graph_b_nat > labeled_graph_b_nat > $o,B: produc1235635379_b_nat] :
      ( ( A @ ( produc194497945_b_nat @ B ) @ ( produc1542243159_b_nat @ B ) )
     => ~ ! [C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
            ~ ( A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_exE__realizer_H) ).

thf(1225,plain,
    ! [A: labeled_graph_b_nat > labeled_graph_b_nat > $o,B: produc1235635379_b_nat] :
      ( ( A @ ( produc194497945_b_nat @ B ) @ ( produc1542243159_b_nat @ B ) )
     => ~ ! [C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
            ~ ( A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1,conjecture,
    ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
    & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
      = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
    & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
    & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(327,plain,
    ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(185,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( ( produc1990145943term_b @ A @ B )
        = ( produc1990145943term_b @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Pair__inject) ).

thf(954,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( ( produc1990145943term_b @ A @ B )
        = ( produc1990145943term_b @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(213,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: nat,E: nat,F: allegorical_term_b,G: nat,H: nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( semantics_b_nat @ A @ F ) )
       => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ G ) @ C )
         => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ H ) @ C )
           => ( member701585322at_nat @ ( product_Pair_nat_nat @ G @ H ) @ ( semantics_b_nat @ B @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_graph__homomorphism__semantics) ).

thf(1070,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: nat,E: nat,F: allegorical_term_b,G: nat,H: nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( semantics_b_nat @ A @ F ) )
       => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ G ) @ C )
         => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ H ) @ C )
           => ( member701585322at_nat @ ( product_Pair_nat_nat @ G @ H ) @ ( semantics_b_nat @ B @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(163,axiom,
    ! [A: labeled_graph_b_nat] :
      ( ( restrict_b_nat @ ( restrict_b_nat @ A ) )
      = ( restrict_b_nat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_restrict__idemp) ).

thf(872,plain,
    ! [A: labeled_graph_b_nat] :
      ( ( restrict_b_nat @ ( restrict_b_nat @ A ) )
      = ( restrict_b_nat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(116,axiom,
    ! [A: labeled_graph_b_nat,B: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ bot_bot_set_nat ) @ A @ B )
      = ( ( B = bot_bo2130386637at_nat )
        & ( A
          = ( restrict_b_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_graph__homomorphism__empty) ).

thf(705,plain,
    ! [A: labeled_graph_b_nat,B: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ bot_bot_set_nat ) @ A @ B )
      = ( ( B = bot_bo2130386637at_nat )
        & ( A
          = ( restrict_b_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(238,axiom,
    ! [A: nat > labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( chain_b_nat @ A )
     => ( ! [C: produc1235635379_b_nat,D: set_Pr1986765409at_nat,E: nat] :
            ( ( member963855452_b_nat @ C @ B )
           => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( A @ E ) @ D )
             => ? [F: nat] : ( extensible_b_nat_nat @ C @ ( A @ F ) @ D ) ) )
       => ( fair_chain_b_nat_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_fair__chainI) ).

thf(1156,plain,
    ! [A: nat > labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( chain_b_nat @ A )
     => ( ! [C: produc1235635379_b_nat,D: set_Pr1986765409at_nat,E: nat] :
            ( ( member963855452_b_nat @ C @ B )
           => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ C ) @ ( A @ E ) @ D )
             => ? [F: nat] : ( extensible_b_nat_nat @ C @ ( A @ F ) @ D ) ) )
       => ( fair_chain_b_nat_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(312,axiom,
    ! [A: labeled_graph_b_nat] : ( graph_529870330at_nat @ ( restrict_b_nat @ A ) @ ( restrict_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_graph__homomorphism__Id) ).

thf(1432,plain,
    ! [A: labeled_graph_b_nat] : ( graph_529870330at_nat @ ( restrict_b_nat @ A ) @ ( restrict_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(280,axiom,
    ! [A: set_Pr9961929at_nat] :
      ( ~ ( finite1987068434at_nat @ A )
     => ( A != bot_bo1626616373at_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_infinite__imp__nonempty) ).

thf(1300,plain,
    ! [A: set_Pr9961929at_nat] :
      ( ~ ( finite1987068434at_nat @ A )
     => ( A != bot_bo1626616373at_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(142,axiom,
    ! [A: allegorical_term_b,B: produc1478835367term_b] :
      ( ( A
        = ( produc1223098053term_b @ B ) )
      = ( ? [C: allegorical_term_b] :
            ( B
            = ( produc1990145943term_b @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_eq__snd__iff) ).

thf(791,plain,
    ! [A: allegorical_term_b,B: produc1478835367term_b] :
      ( ( A
        = ( produc1223098053term_b @ B ) )
      = ( ? [C: allegorical_term_b] :
            ( B
            = ( produc1990145943term_b @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(248,axiom,
    ( chain_b_nat
    = ( ^ [A: nat > labeled_graph_b_nat] :
        ! [B: nat,C: nat] :
          ( ( ord_less_eq_nat @ B @ C )
         => ( graph_529870330at_nat @ ( A @ B ) @ ( A @ C ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_chain__def2) ).

thf(1188,plain,
    ( chain_b_nat
    = ( ^ [A: nat > labeled_graph_b_nat] :
        ! [B: nat,C: nat] :
          ( ( ord_less_eq_nat @ B @ C )
         => ( graph_529870330at_nat @ ( A @ B ) @ ( A @ C ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(6,axiom,
    ! [A: labele935650037_a_nat,B: set_la1083530965_a_nat] :
      ( ( member964390942_a_nat @ A @ B )
     => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ A ) @ ( id_on_689842066_a_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Id__onI) ).

thf(338,plain,
    ! [A: labele935650037_a_nat,B: set_la1083530965_a_nat] :
      ( ( member964390942_a_nat @ A @ B )
     => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ A ) @ ( id_on_689842066_a_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(79,axiom,
    ! [A: labele935650037_a_nat] :
      ( ( restri572569417_a_nat @ ( restri572569417_a_nat @ A ) )
      = ( restri572569417_a_nat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_restrict__idemp) ).

thf(576,plain,
    ! [A: labele935650037_a_nat] :
      ( ( restri572569417_a_nat @ ( restri572569417_a_nat @ A ) )
      = ( restri572569417_a_nat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(184,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( ( ( labeled_edges_b_nat @ A )
          = ( labeled_edges_b_nat @ B ) )
        & ( ( labele460410879_b_nat @ A )
          = ( labele460410879_b_nat @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_labeled__graph_Oexpand) ).

thf(951,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( ( ( labeled_edges_b_nat @ A )
          = ( labeled_edges_b_nat @ B ) )
        & ( ( labele460410879_b_nat @ A )
          = ( labele460410879_b_nat @ B ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(13,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_la1083530965_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( id_on_689842066_a_nat @ C ) )
      = ( ( A = B )
        & ( member964390942_a_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Id__on__iff) ).

thf(359,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_la1083530965_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( id_on_689842066_a_nat @ C ) )
      = ( ( A = B )
        & ( member964390942_a_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(256,axiom,
    ! [A: set_nat] :
      ( ( finite_finite_nat @ A )
     => ( ( A != bot_bot_set_nat )
       => ? [B: nat] :
            ( ( member_nat @ B @ A )
            & ! [C: nat] :
                ( ( member_nat @ C @ A )
               => ( ( ord_less_eq_nat @ C @ B )
                 => ( B = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_finite__has__minimal) ).

thf(1218,plain,
    ! [A: set_nat] :
      ( ( finite_finite_nat @ A )
     => ( ( A != bot_bot_set_nat )
       => ? [B: nat] :
            ( ( member_nat @ B @ A )
            & ! [C: nat] :
                ( ( member_nat @ C @ A )
               => ( ( ord_less_eq_nat @ C @ B )
                 => ( B = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(267,axiom,
    ! [A: labeled_graph_b_nat] :
      ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ A ) @ ( labeled_edges_b_nat @ ( restrict_b_nat @ A ) ) )
     => ( A
        = ( restrict_b_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_restrict__subsD) ).

thf(1257,plain,
    ! [A: labeled_graph_b_nat] :
      ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ A ) @ ( labeled_edges_b_nat @ ( restrict_b_nat @ A ) ) )
     => ( A
        = ( restrict_b_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(92,axiom,
    ! [A: produc1871334759_a_nat > $o,B: produc1871334759_a_nat] :
      ( ! [C: labele935650037_a_nat,D: labele935650037_a_nat] : ( A @ ( produc1676969687_a_nat @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_prod__cases) ).

thf(613,plain,
    ! [A: produc1871334759_a_nat > $o,B: produc1871334759_a_nat] :
      ( ! [C: labele935650037_a_nat,D: labele935650037_a_nat] : ( A @ ( produc1676969687_a_nat @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(275,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ B )
     => ( ( finite_finite_nat @ B )
       => ( finite_finite_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_finite__subset) ).

thf(1284,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ B )
     => ( ( finite_finite_nat @ B )
       => ( finite_finite_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(292,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: labeled_graph_b_nat,E: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( graph_529870330at_nat @ B @ D @ E )
       => ( graph_529870330at_nat @ A @ D @ ( relcomp_nat_nat_nat @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_graph__homomorphism__composes) ).

thf(1353,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: labeled_graph_b_nat,E: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( graph_529870330at_nat @ B @ D @ E )
       => ( graph_529870330at_nat @ A @ D @ ( relcomp_nat_nat_nat @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(324,axiom,
    ( weak_u2026406106at_nat
    = ( ^ [A: itself_nat,B: produc1235635379_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat,E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
        ! [G: set_Pr1986765409at_nat,H: set_Pr1986765409at_nat,I: labeled_graph_b_nat] :
          ( ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ B ) @ I @ G )
            & ( graph_529870330at_nat @ C @ I @ H )
            & ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ E @ H ) @ G ) )
         => ? [J: set_Pr1986765409at_nat] :
              ( ( graph_529870330at_nat @ D @ I @ J )
              & ( ord_le841296385at_nat @ H @ J ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_weak__universal__def) ).

thf(1485,plain,
    ( weak_u2026406106at_nat
    = ( ^ [A: itself_nat,B: produc1235635379_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat,E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
        ! [G: set_Pr1986765409at_nat,H: set_Pr1986765409at_nat,I: labeled_graph_b_nat] :
          ( ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ B ) @ I @ G )
            & ( graph_529870330at_nat @ C @ I @ H )
            & ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ E @ H ) @ G ) )
         => ? [J: set_Pr1986765409at_nat] :
              ( ( graph_529870330at_nat @ D @ I @ J )
              & ( ord_le841296385at_nat @ H @ J ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(122,axiom,
    ! [A: allegorical_term_b,B: produc1478835367term_b] :
      ( ( A
        = ( produc854192515term_b @ B ) )
      = ( ? [C: allegorical_term_b] :
            ( B
            = ( produc1990145943term_b @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_eq__fst__iff) ).

thf(727,plain,
    ! [A: allegorical_term_b,B: produc1478835367term_b] :
      ( ( A
        = ( produc854192515term_b @ B ) )
      = ( ? [C: allegorical_term_b] :
            ( B
            = ( produc1990145943term_b @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(232,axiom,
    ! [A: set_Pr551076371_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
      ( ( unival857119480_b_nat @ A )
     => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ C ) @ A )
       => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ D ) @ A )
         => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_univalentD) ).

thf(1140,plain,
    ! [A: set_Pr551076371_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
      ( ( unival857119480_b_nat @ A )
     => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ C ) @ A )
       => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ D ) @ A )
         => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(195,axiom,
    ! [A: set_Pr9961929at_nat,B: set_nat] :
      ( ( labele460410879_b_nat @ ( labeled_LG_b_nat @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_labeled__graph_Osel_I2_J) ).

thf(1008,plain,
    ! [A: set_Pr9961929at_nat,B: set_nat] :
      ( ( labele460410879_b_nat @ ( labeled_LG_b_nat @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(298,axiom,
    ! [A: b] :
      ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ A ) ) @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ A ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_are__rules_I2_J) ).

thf(1372,plain,
    ! [A: b] :
      ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ A ) ) @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ A ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(52,axiom,
    ! [A: product_prod_nat_nat,B: product_prod_nat_nat > $o] :
      ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_mem__Collect__eq) ).

thf(497,plain,
    ! [A: product_prod_nat_nat,B: product_prod_nat_nat > $o] :
      ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(43,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
      ( ( ( produc1676969687_a_nat @ A @ B )
        = ( produc1676969687_a_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_prod_Oinject) ).

thf(465,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
      ( ( ( produc1676969687_a_nat @ A @ B )
        = ( produc1676969687_a_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(217,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_fst__conv) ).

thf(1084,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(67,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
        = C )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_snd__eqD) ).

thf(539,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
        = C )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(48,axiom,
    ! [A: set_Pr1987088711_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
      ( ( unival1637751524_a_nat @ A )
     => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ C ) @ A )
       => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ D ) @ A )
         => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_univalentD) ).

thf(482,plain,
    ! [A: set_Pr1987088711_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat,D: labele935650037_a_nat] :
      ( ( unival1637751524_a_nat @ A )
     => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ C ) @ A )
       => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ D ) @ A )
         => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(171,axiom,
    ! [A: produc1478835367term_b,B: set_Pr1163220871term_b,C: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ A @ ( relcom1955155673term_b @ B @ C ) )
     => ~ ! [D: allegorical_term_b,E: allegorical_term_b,F: allegorical_term_b] :
            ( ( A
              = ( produc1990145943term_b @ D @ F ) )
           => ( ( member516522448term_b @ ( produc1990145943term_b @ D @ E ) @ B )
             => ~ ( member516522448term_b @ ( produc1990145943term_b @ E @ F ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_relcompE) ).

thf(903,plain,
    ! [A: produc1478835367term_b,B: set_Pr1163220871term_b,C: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ A @ ( relcom1955155673term_b @ B @ C ) )
     => ~ ! [D: allegorical_term_b,E: allegorical_term_b,F: allegorical_term_b] :
            ( ( A
              = ( produc1990145943term_b @ D @ F ) )
           => ( ( member516522448term_b @ ( produc1990145943term_b @ D @ E ) @ B )
             => ~ ( member516522448term_b @ ( produc1990145943term_b @ E @ F ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(168,axiom,
    ! [A: produc1478835367term_b,B: set_al1193902458term_b] :
      ( ( member516522448term_b @ A @ ( id_on_1536886967term_b @ B ) )
     => ~ ! [C: allegorical_term_b] :
            ( ( member93680451term_b @ C @ B )
           => ( A
             != ( produc1990145943term_b @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Id__onE) ).

thf(891,plain,
    ! [A: produc1478835367term_b,B: set_al1193902458term_b] :
      ( ( member516522448term_b @ A @ ( id_on_1536886967term_b @ B ) )
     => ~ ! [C: allegorical_term_b] :
            ( ( member93680451term_b @ C @ B )
           => ( A
             != ( produc1990145943term_b @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(136,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: allegorical_term_b] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( ( semantics_b_nat @ A @ D )
         != bot_bo2130386637at_nat )
       => ( ( semantics_b_nat @ B @ D )
         != bot_bo2130386637at_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_graph__homomorphism__nonempty) ).

thf(771,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: allegorical_term_b] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( ( semantics_b_nat @ A @ D )
         != bot_bo2130386637at_nat )
       => ( ( semantics_b_nat @ B @ D )
         != bot_bo2130386637at_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(322,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: nat,E: nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ C )
       => ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_Id__on__vertices__identity_I1_J) ).

thf(1476,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: nat,E: nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ C )
       => ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(182,axiom,
    ! [A: allegorical_term_b] : ( inv_translation @ ( labele460410879_b_nat @ ( translation_b @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_verts__in__translation) ).

thf(946,plain,
    ! [A: allegorical_term_b] : ( inv_translation @ ( labele460410879_b_nat @ ( translation_b @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(82,axiom,
    ( transl1275713022tant_a
    = ( ^ [A: allego510293162tant_a] : ( restri572569417_a_nat @ ( transl1275713022tant_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_translation__graph) ).

thf(588,plain,
    ( transl1275713022tant_a
    = ( ^ [A: allego510293162tant_a] : ( restri572569417_a_nat @ ( transl1275713022tant_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(115,axiom,
    ! [A: set_Pr1987088711_a_nat,B: produc1871334759_a_nat] :
      ( ( set_of1384085797_a_nat @ A )
     => ( ( member832397200_a_nat @ B @ A )
       => ( ( ( produc880161797_a_nat @ B )
            = ( restri572569417_a_nat @ ( produc880161797_a_nat @ B ) ) )
          & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ B ) ) )
          & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_set__of__graph__rulesD_I2_J) ).

thf(699,plain,
    ! [A: set_Pr1987088711_a_nat,B: produc1871334759_a_nat] :
      ( ( set_of1384085797_a_nat @ A )
     => ( ( member832397200_a_nat @ B @ A )
       => ( ( ( produc880161797_a_nat @ B )
            = ( restri572569417_a_nat @ ( produc880161797_a_nat @ B ) ) )
          & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ B ) ) )
          & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(186,axiom,
    ! [A: set_Pr551076371_b_nat,B: set_Pr551076371_b_nat] :
      ( ! [C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
          ( ( member963855452_b_nat @ ( produc951298923_b_nat @ C @ D ) @ A )
         => ( member963855452_b_nat @ ( produc951298923_b_nat @ C @ D ) @ B ) )
     => ( ord_le13035955_b_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_subrelI) ).

thf(961,plain,
    ! [A: set_Pr551076371_b_nat,B: set_Pr551076371_b_nat] :
      ( ! [C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
          ( ( member963855452_b_nat @ ( produc951298923_b_nat @ C @ D ) @ A )
         => ( member963855452_b_nat @ ( produc951298923_b_nat @ C @ D ) @ B ) )
     => ( ord_le13035955_b_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(300,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( finite_finite_nat @ A )
     => ( ( ord_less_eq_set_nat @ B @ A )
       => ( finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_rev__finite__subset) ).

thf(1385,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( finite_finite_nat @ A )
     => ( ( ord_less_eq_set_nat @ B @ A )
       => ( finite_finite_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(103,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat] :
      ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_fst__conv) ).

thf(667,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat] :
      ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(250,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ ( restrict_b_nat @ A ) ) @ ( labeled_edges_b_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_subgraph__subset_I2_J) ).

thf(1193,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ ( restrict_b_nat @ A ) ) @ ( labeled_edges_b_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(47,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat] :
      ( ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ A @ B ) )
        = C )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_fst__eqD) ).

thf(478,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat] :
      ( ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ A @ B ) )
        = C )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(170,axiom,
    ! [A: produc1478835367term_b,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A
        = ( produc1990145943term_b @ B @ C ) )
     => ( ( produc1223098053term_b @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_sndI) ).

thf(899,plain,
    ! [A: produc1478835367term_b,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A
        = ( produc1990145943term_b @ B @ C ) )
     => ( ( produc1223098053term_b @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(315,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_Pr551076371_b_nat,E: labeled_graph_b_nat > labeled_graph_b_nat > $o] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( relcom1426860350_b_nat @ C @ D ) )
     => ( ! [F: labeled_graph_b_nat,G: labeled_graph_b_nat,H: labeled_graph_b_nat] :
            ( ( member963855452_b_nat @ ( produc951298923_b_nat @ F @ G ) @ C )
           => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ G @ H ) @ D )
             => ( E @ F @ H ) ) )
       => ( E @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_relcomp_Oinducts) ).

thf(1442,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat,D: set_Pr551076371_b_nat,E: labeled_graph_b_nat > labeled_graph_b_nat > $o] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( relcom1426860350_b_nat @ C @ D ) )
     => ( ! [F: labeled_graph_b_nat,G: labeled_graph_b_nat,H: labeled_graph_b_nat] :
            ( ( member963855452_b_nat @ ( produc951298923_b_nat @ F @ G ) @ C )
           => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ G @ H ) @ D )
             => ( E @ F @ H ) ) )
       => ( E @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(207,axiom,
    ! [A: set_Pr9961929at_nat,B: set_Pr9961929at_nat] :
      ( ( finite1987068434at_nat @ A )
     => ( ( ord_le910748009at_nat @ B @ A )
       => ( finite1987068434at_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_rev__finite__subset) ).

thf(1045,plain,
    ! [A: set_Pr9961929at_nat,B: set_Pr9961929at_nat] :
      ( ( finite1987068434at_nat @ A )
     => ( ( ord_le910748009at_nat @ B @ A )
       => ( finite1987068434at_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(34,axiom,
    ! [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
      ( ! [C: labele935650037_a_nat,D: labele935650037_a_nat] :
          ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ C @ D ) @ A )
         => ( member832397200_a_nat @ ( produc1676969687_a_nat @ C @ D ) @ B ) )
     => ( ord_le1718765799_a_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_subrelI) ).

thf(433,plain,
    ! [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
      ( ! [C: labele935650037_a_nat,D: labele935650037_a_nat] :
          ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ C @ D ) @ A )
         => ( member832397200_a_nat @ ( produc1676969687_a_nat @ C @ D ) @ B ) )
     => ( ord_le1718765799_a_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(57,axiom,
    ! [A: allego1565409692at_nat] : ( finite48957584at_nat @ ( labele2032268018at_nat @ ( transl490985778at_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_verts__in__translation__finite_I2_J) ).

thf(510,plain,
    ! [A: allego1565409692at_nat] : ( finite48957584at_nat @ ( labele2032268018at_nat @ ( transl490985778at_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(9,axiom,
    ! [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
      ( ( ord_le1718765799_a_nat @ A @ B )
     => ( ( member832397200_a_nat @ C @ A )
       => ( member832397200_a_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_subsetD) ).

thf(346,plain,
    ! [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
      ( ( ord_le1718765799_a_nat @ A @ B )
     => ( ( member832397200_a_nat @ C @ A )
       => ( member832397200_a_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(282,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: nat,E: nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ C )
       => ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( relcomp_nat_nat_nat @ C @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_Id__on__vertices__identity_I2_J) ).

thf(1309,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: nat,E: nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ C )
       => ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( relcomp_nat_nat_nat @ C @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(119,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: labeled_graph_b_nat,E: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( agree_on_b_nat_nat @ D @ E @ C )
       => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_extensibleI) ).

thf(716,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat,D: labeled_graph_b_nat,E: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ A @ B @ C )
     => ( ( agree_on_b_nat_nat @ D @ E @ C )
       => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(239,axiom,
    ! [A: labeled_graph_b_nat,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ B @ ( allegorical_A_Int_b @ B @ C ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ B @ ( allegorical_A_Int_b @ B @ C ) ) ) ) ) @ A )
        = ( ord_le841296385at_nat @ ( semantics_b_nat @ A @ B ) @ ( semantics_b_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_maintained__holds__subset__iff) ).

thf(1161,plain,
    ! [A: labeled_graph_b_nat,B: allegorical_term_b,C: allegorical_term_b] :
      ( ( A
        = ( restrict_b_nat @ A ) )
     => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ B @ ( allegorical_A_Int_b @ B @ C ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ B @ ( allegorical_A_Int_b @ B @ C ) ) ) ) ) @ A )
        = ( ord_le841296385at_nat @ ( semantics_b_nat @ A @ B ) @ ( semantics_b_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(145,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat] :
      ( ( graph_2130075512at_nat @ A @ B @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) )
     => ( ( graph_2130075512at_nat @ B @ C @ ( id_on_nat @ ( labele1810595089_a_nat @ B ) ) )
       => ( graph_2130075512at_nat @ A @ C @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_subgraph__trans) ).

thf(800,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: labele935650037_a_nat] :
      ( ( graph_2130075512at_nat @ A @ B @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) )
     => ( ( graph_2130075512at_nat @ B @ C @ ( id_on_nat @ ( labele1810595089_a_nat @ B ) ) )
       => ( graph_2130075512at_nat @ A @ C @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(94,axiom,
    ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat] :
      ( ( ( produc719117507_a_nat @ A )
        = ( produc719117507_a_nat @ B ) )
     => ( ( ( produc880161797_a_nat @ A )
          = ( produc880161797_a_nat @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_prod__eqI) ).

thf(620,plain,
    ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat] :
      ( ( ( produc719117507_a_nat @ A )
        = ( produc719117507_a_nat @ B ) )
     => ( ( ( produc880161797_a_nat @ A )
          = ( produc880161797_a_nat @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(131,axiom,
    ! [A: set_Pr9961929at_nat,B: set_Pr1490359111at_nat] :
      ( ( finite1987068434at_nat @ A )
     => ( ( finite48957584at_nat @ B )
       => ( finite1987068434at_nat @ ( relcom195261566at_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_finite__relcomp) ).

thf(752,plain,
    ! [A: set_Pr9961929at_nat,B: set_Pr1490359111at_nat] :
      ( ( finite1987068434at_nat @ A )
     => ( ( finite48957584at_nat @ B )
       => ( finite1987068434at_nat @ ( relcom195261566at_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(40,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( product_Pair_nat_nat @ A @ B )
        = ( product_Pair_nat_nat @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Pair__inject) ).

thf(447,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( product_Pair_nat_nat @ A @ B )
        = ( product_Pair_nat_nat @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(26,axiom,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq_nat @ D @ C ) )
       => ~ ! [D: nat] :
              ( ( A @ D )
             => ~ ! [E: nat] :
                    ( ( A @ E )
                   => ( ord_less_eq_nat @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_bounded__Max__nat) ).

thf(405,plain,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq_nat @ D @ C ) )
       => ~ ! [D: nat] :
              ( ( A @ D )
             => ~ ! [E: nat] :
                    ( ( A @ E )
                   => ( ord_less_eq_nat @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(161,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ C )
     => ( member93680451term_b @ A @ ( domain859272460term_b @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_Domain_ODomainI) ).

thf(867,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ C )
     => ( member93680451term_b @ A @ ( domain859272460term_b @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(125,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_Domain_ODomainI) ).

thf(735,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(175,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( relcom1955155673term_b @ C @ D ) )
     => ~ ! [E: allegorical_term_b] :
            ( ( member516522448term_b @ ( produc1990145943term_b @ A @ E ) @ C )
           => ~ ( member516522448term_b @ ( produc1990145943term_b @ E @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_relcomp_Ocases) ).

thf(918,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_Pr1163220871term_b] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( relcom1955155673term_b @ C @ D ) )
     => ~ ! [E: allegorical_term_b] :
            ( ( member516522448term_b @ ( produc1990145943term_b @ A @ E ) @ C )
           => ~ ( member516522448term_b @ ( produc1990145943term_b @ E @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(148,axiom,
    ! [A: labeled_graph_b_nat,B: produc1235635379_b_nat] :
      ( ( A
        = ( produc1542243159_b_nat @ B ) )
      = ( ? [C: labeled_graph_b_nat] :
            ( B
            = ( produc951298923_b_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_eq__fst__iff) ).

thf(807,plain,
    ! [A: labeled_graph_b_nat,B: produc1235635379_b_nat] :
      ( ( A
        = ( produc1542243159_b_nat @ B ) )
      = ( ? [C: labeled_graph_b_nat] :
            ( B
            = ( produc951298923_b_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(289,axiom,
    ! [A: allego510293162tant_a,B: allego510293162tant_a] :
      ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) ) ) )
      & ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) )
        = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) ) )
      & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_graph__rule__translation) ).

thf(1335,plain,
    ! [A: allego510293162tant_a,B: allego510293162tant_a] :
      ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) ) ) )
      & ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) )
        = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) ) )
      & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ A ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(102,axiom,
    ! [A: nat,B: nat] :
      ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_fst__conv) ).

thf(664,plain,
    ! [A: nat,B: nat] :
      ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(114,axiom,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
     => ~ ! [C: labeled_graph_b_nat] :
            ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_Domain_Ocases) ).

thf(696,plain,
    ! [A: labeled_graph_b_nat,B: set_Pr551076371_b_nat] :
      ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ B ) )
     => ~ ! [C: labeled_graph_b_nat] :
            ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(240,axiom,
    ( finite_finite_nat
    = ( ^ [A: set_nat] :
        ? [B: nat] :
        ! [C: nat] :
          ( ( member_nat @ C @ A )
         => ( ord_less_eq_nat @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_finite__nat__set__iff__bounded__le) ).

thf(1165,plain,
    ( finite_finite_nat
    = ( ^ [A: set_nat] :
        ? [B: nat] :
        ! [C: nat] :
          ( ( member_nat @ C @ A )
         => ( ord_less_eq_nat @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(306,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( ( allegorical_A_Int_b @ A @ B )
        = ( allegorical_A_Int_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_allegorical__term_Oinject_I1_J) ).

thf(1410,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: allegorical_term_b,D: allegorical_term_b] :
      ( ( ( allegorical_A_Int_b @ A @ B )
        = ( allegorical_A_Int_b @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(135,axiom,
    ! [A: allegorical_term_b,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ ( translation_b @ A ) @ B @ C )
     => ( ( semantics_b_nat @ B @ A )
       != bot_bo2130386637at_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_translation__homomorphism_I2_J) ).

thf(767,plain,
    ! [A: allegorical_term_b,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat] :
      ( ( graph_529870330at_nat @ ( translation_b @ A ) @ B @ C )
     => ( ( semantics_b_nat @ B @ A )
       != bot_bo2130386637at_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(179,axiom,
    ! [A: labeled_graph_b_nat > $o,B: labeled_graph_b_nat,C: labeled_graph_b_nat > $o,D: labeled_graph_b_nat] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ B @ D ) ) )
          & ( C @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_conjI__realizer) ).

thf(928,plain,
    ! [A: labeled_graph_b_nat > $o,B: labeled_graph_b_nat,C: labeled_graph_b_nat > $o,D: labeled_graph_b_nat] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ B @ D ) ) )
          & ( C @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(28,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_le__cases) ).

thf(415,plain,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(127,axiom,
    ! [A: nat > labeled_graph_b_nat,B: nat] :
      ( ( chain_b_nat @ A )
     => ( graph_529870330at_nat @ ( A @ B ) @ ( chain_sup_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_chain__sup__subgraph) ).

thf(740,plain,
    ! [A: nat > labeled_graph_b_nat,B: nat] :
      ( ( chain_b_nat @ A )
     => ( graph_529870330at_nat @ ( A @ B ) @ ( chain_sup_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(32,axiom,
    ! [A: produc1235635379_b_nat,B: produc1235635379_b_nat > $o] :
      ( ( member963855452_b_nat @ A @ ( collec1615000990_b_nat @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_mem__Collect__eq) ).

thf(427,plain,
    ! [A: produc1235635379_b_nat,B: produc1235635379_b_nat > $o] :
      ( ( member963855452_b_nat @ A @ ( collec1615000990_b_nat @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(85,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( product_Pair_nat_nat @ A @ B )
        = ( product_Pair_nat_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_old_Oprod_Oinject) ).

thf(596,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( product_Pair_nat_nat @ A @ B )
        = ( product_Pair_nat_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(172,axiom,
    ! [A: produc1235635379_b_nat,B: set_Pr551076371_b_nat,C: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ A @ ( relcom1426860350_b_nat @ B @ C ) )
     => ~ ! [D: labeled_graph_b_nat,E: labeled_graph_b_nat,F: labeled_graph_b_nat] :
            ( ( A
              = ( produc951298923_b_nat @ D @ F ) )
           => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ D @ E ) @ B )
             => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ E @ F ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_relcompE) ).

thf(908,plain,
    ! [A: produc1235635379_b_nat,B: set_Pr551076371_b_nat,C: set_Pr551076371_b_nat] :
      ( ( member963855452_b_nat @ A @ ( relcom1426860350_b_nat @ B @ C ) )
     => ~ ! [D: labeled_graph_b_nat,E: labeled_graph_b_nat,F: labeled_graph_b_nat] :
            ( ( A
              = ( produc951298923_b_nat @ D @ F ) )
           => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ D @ E ) @ B )
             => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ E @ F ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(152,axiom,
    ! [A: allego510293162tant_a] : ( finite_finite_nat @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_verts__in__translation__finite_I1_J) ).

thf(822,plain,
    ! [A: allego510293162tant_a] : ( finite_finite_nat @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(112,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ B )
     => ( ~ ( finite_finite_nat @ A )
       => ~ ( finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_infinite__super) ).

thf(691,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ B )
     => ( ~ ( finite_finite_nat @ A )
       => ~ ( finite_finite_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(38,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( relcom1338300020_a_nat @ C @ D ) )
      = ( ? [E: labele935650037_a_nat,F: labele935650037_a_nat,G: labele935650037_a_nat] :
            ( ( A = E )
            & ( B = G )
            & ( member832397200_a_nat @ ( produc1676969687_a_nat @ E @ F ) @ C )
            & ( member832397200_a_nat @ ( produc1676969687_a_nat @ F @ G ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_relcomp_Osimps) ).

thf(442,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( relcom1338300020_a_nat @ C @ D ) )
      = ( ? [E: labele935650037_a_nat,F: labele935650037_a_nat,G: labele935650037_a_nat] :
            ( ( A = E )
            & ( B = G )
            & ( member832397200_a_nat @ ( produc1676969687_a_nat @ E @ F ) @ C )
            & ( member832397200_a_nat @ ( produc1676969687_a_nat @ F @ G ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(220,axiom,
    ! [A: set_Pr9961929at_nat,B: set_Pr9961929at_nat] :
      ( ( ord_le910748009at_nat @ A @ B )
     => ( ( finite1987068434at_nat @ B )
       => ( finite1987068434at_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_finite__subset) ).

thf(1093,plain,
    ! [A: set_Pr9961929at_nat,B: set_Pr9961929at_nat] :
      ( ( ord_le910748009at_nat @ A @ B )
     => ( ( finite1987068434at_nat @ B )
       => ( finite1987068434at_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(24,axiom,
    ! [A: produc1871334759_a_nat > $o,B: produc1871334759_a_nat] :
      ( ! [C: labele935650037_a_nat,D: labele935650037_a_nat] : ( A @ ( produc1676969687_a_nat @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_old_Oprod_Oinducts) ).

thf(395,plain,
    ! [A: produc1871334759_a_nat > $o,B: produc1871334759_a_nat] :
      ( ! [C: labele935650037_a_nat,D: labele935650037_a_nat] : ( A @ ( produc1676969687_a_nat @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(262,axiom,
    ! [A: produc1871334759_a_nat,B: set_St761939237tant_a] :
      ( ( member832397200_a_nat @ A @ ( standa1568205540ules_a @ B ) )
     => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ A ) @ ( produc880161797_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ A ) ) ) )
        & ( ( produc880161797_a_nat @ A )
          = ( restri572569417_a_nat @ ( produc880161797_a_nat @ A ) ) )
        & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ A ) ) )
        & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_identity__rules__graph__rule) ).

thf(1236,plain,
    ! [A: produc1871334759_a_nat,B: set_St761939237tant_a] :
      ( ( member832397200_a_nat @ A @ ( standa1568205540ules_a @ B ) )
     => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ A ) @ ( produc880161797_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ A ) ) ) )
        & ( ( produc880161797_a_nat @ A )
          = ( restri572569417_a_nat @ ( produc880161797_a_nat @ A ) ) )
        & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ A ) ) )
        & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(190,axiom,
    ! [A: b] :
      ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ A ) ) @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ A ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_are__rules_I3_J) ).

thf(987,plain,
    ! [A: b] :
      ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ A ) ) @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ A ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(4,axiom,
    ! [A: product_prod_nat_nat] :
      ( A
      = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_prod_Oexhaust__sel) ).

thf(332,plain,
    ! [A: product_prod_nat_nat] :
      ( A
      = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(228,axiom,
    ! [A: nat > labeled_graph_b_nat,B: set_Pr9961929at_nat,C: set_Pr2041158302at_nat] :
      ( ( chain_b_nat @ A )
     => ( ( finite1987068434at_nat @ B )
       => ( ( unival633212949at_nat @ C )
         => ( ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ C @ B ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ A ) ) )
           => ? [D: nat] : ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ C @ B ) @ ( labele460410879_b_nat @ ( A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_find__graph__occurence__vertices) ).

thf(1129,plain,
    ! [A: nat > labeled_graph_b_nat,B: set_Pr9961929at_nat,C: set_Pr2041158302at_nat] :
      ( ( chain_b_nat @ A )
     => ( ( finite1987068434at_nat @ B )
       => ( ( unival633212949at_nat @ C )
         => ( ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ C @ B ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ A ) ) )
           => ? [D: nat] : ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ C @ B ) @ ( labele460410879_b_nat @ ( A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(16,axiom,
    ! [A: product_prod_nat_nat] :
      ( A
      = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_surjective__pairing) ).

thf(369,plain,
    ! [A: product_prod_nat_nat] :
      ( A
      = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(89,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_bot_Oextremum) ).

thf(607,plain,
    ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(49,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_Pr1987088711_a_nat,E: labele935650037_a_nat > labele935650037_a_nat > $o] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( relcom1338300020_a_nat @ C @ D ) )
     => ( ! [F: labele935650037_a_nat,G: labele935650037_a_nat,H: labele935650037_a_nat] :
            ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ F @ G ) @ C )
           => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ G @ H ) @ D )
             => ( E @ F @ H ) ) )
       => ( E @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_relcomp_Oinducts) ).

thf(486,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_Pr1987088711_a_nat,E: labele935650037_a_nat > labele935650037_a_nat > $o] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( relcom1338300020_a_nat @ C @ D ) )
     => ( ! [F: labele935650037_a_nat,G: labele935650037_a_nat,H: labele935650037_a_nat] :
            ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ F @ G ) @ C )
           => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ G @ H ) @ D )
             => ( E @ F @ H ) ) )
       => ( E @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(146,axiom,
    finite_finite_nat @ bot_bot_set_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_finite_OemptyI) ).

thf(803,plain,
    finite_finite_nat @ bot_bot_set_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(296,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_la1976028319_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( id_on_583275916_b_nat @ C ) )
      = ( ( A = B )
        & ( member1483953152_b_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Id__on__iff) ).

thf(1367,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: set_la1976028319_b_nat] :
      ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( id_on_583275916_b_nat @ C ) )
      = ( ( A = B )
        & ( member1483953152_b_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(11,axiom,
    ( ord_le1718765799_a_nat
    = ( ^ [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
        ! [C: produc1871334759_a_nat] :
          ( ( member832397200_a_nat @ C @ A )
         => ( member832397200_a_nat @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_subset__eq) ).

thf(354,plain,
    ( ord_le1718765799_a_nat
    = ( ^ [A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
        ! [C: produc1871334759_a_nat] :
          ( ( member832397200_a_nat @ C @ A )
         => ( member832397200_a_nat @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(177,axiom,
    ( extensible_b_nat_nat
    = ( ^ [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat] :
        ? [D: set_Pr1986765409at_nat] :
          ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ A ) @ B @ D )
          & ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ A ) @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_extensible__def) ).

thf(923,plain,
    ( extensible_b_nat_nat
    = ( ^ [A: produc1235635379_b_nat,B: labeled_graph_b_nat,C: set_Pr1986765409at_nat] :
        ? [D: set_Pr1986765409at_nat] :
          ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ A ) @ B @ D )
          & ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ A ) @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(247,axiom,
    ! [A: produc1478835367term_b] :
      ~ ! [B: allegorical_term_b,C: allegorical_term_b] :
          ( A
         != ( produc1990145943term_b @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_old_Oprod_Oexhaust) ).

thf(1184,plain,
    ! [A: produc1478835367term_b] :
      ~ ! [B: allegorical_term_b,C: allegorical_term_b] :
          ( A
         != ( produc1990145943term_b @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(319,axiom,
    ! [A: produc1478835367term_b] :
      ( ( produc1990145943term_b @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_prod_Ocollapse) ).

thf(1463,plain,
    ! [A: produc1478835367term_b] :
      ( ( produc1990145943term_b @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(68,axiom,
    ! [A: nat,B: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_mem__Collect__eq) ).

thf(543,plain,
    ! [A: nat,B: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(137,axiom,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b,C: allegorical_term_b > $o] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
     => ( ! [D: allegorical_term_b,E: allegorical_term_b] :
            ( ( member516522448term_b @ ( produc1990145943term_b @ D @ E ) @ B )
           => ( C @ D ) )
       => ( C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_Domain_Oinducts) ).

thf(775,plain,
    ! [A: allegorical_term_b,B: set_Pr1163220871term_b,C: allegorical_term_b > $o] :
      ( ( member93680451term_b @ A @ ( domain859272460term_b @ B ) )
     => ( ! [D: allegorical_term_b,E: allegorical_term_b] :
            ( ( member516522448term_b @ ( produc1990145943term_b @ D @ E ) @ B )
           => ( C @ D ) )
       => ( C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(308,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
      ( ( ( produc951298923_b_nat @ A @ B )
        = ( produc951298923_b_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_prod_Oinject) ).

thf(1416,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: labeled_graph_b_nat] :
      ( ( ( produc951298923_b_nat @ A @ B )
        = ( produc951298923_b_nat @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(132,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: nat,D: nat,E: allegorical_term_b] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ ( semantics_b_nat @ A @ E ) )
       => ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ ( semantics_b_nat @ B @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_subgraph__semantics) ).

thf(755,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: nat,D: nat,E: allegorical_term_b] :
      ( ( graph_529870330at_nat @ A @ B @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) )
     => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ ( semantics_b_nat @ A @ E ) )
       => ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ ( semantics_b_nat @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(50,axiom,
    ! [A: product_prod_nat_nat] :
    ? [B: nat,C: nat] :
      ( A
      = ( product_Pair_nat_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_surj__pair) ).

thf(491,plain,
    ! [A: product_prod_nat_nat] :
    ? [B: nat,C: nat] :
      ( A
      = ( product_Pair_nat_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(41,axiom,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( relcom1338300020_a_nat @ C @ D ) )
     => ~ ! [E: labele935650037_a_nat] :
            ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ E ) @ C )
           => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ E @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_relcompEpair) ).

thf(454,plain,
    ! [A: labele935650037_a_nat,B: labele935650037_a_nat,C: set_Pr1987088711_a_nat,D: set_Pr1987088711_a_nat] :
      ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( relcom1338300020_a_nat @ C @ D ) )
     => ~ ! [E: labele935650037_a_nat] :
            ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ E ) @ C )
           => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ E @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(117,axiom,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_Pr1163220871term_b,E: allegorical_term_b > allegorical_term_b > $o] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( relcom1955155673term_b @ C @ D ) )
     => ( ! [F: allegorical_term_b,G: allegorical_term_b,H: allegorical_term_b] :
            ( ( member516522448term_b @ ( produc1990145943term_b @ F @ G ) @ C )
           => ( ( member516522448term_b @ ( produc1990145943term_b @ G @ H ) @ D )
             => ( E @ F @ H ) ) )
       => ( E @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_relcomp_Oinducts) ).

thf(708,plain,
    ! [A: allegorical_term_b,B: allegorical_term_b,C: set_Pr1163220871term_b,D: set_Pr1163220871term_b,E: allegorical_term_b > allegorical_term_b > $o] :
      ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( relcom1955155673term_b @ C @ D ) )
     => ( ! [F: allegorical_term_b,G: allegorical_term_b,H: allegorical_term_b] :
            ( ( member516522448term_b @ ( produc1990145943term_b @ F @ G ) @ C )
           => ( ( member516522448term_b @ ( produc1990145943term_b @ G @ H ) @ D )
             => ( E @ F @ H ) ) )
       => ( E @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(197,axiom,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( graph_529870330at_nat @ A @ C @ D )
       => ~ ! [E: set_Pr1986765409at_nat] :
              ( ( graph_529870330at_nat @ B @ C @ E )
             => ~ ( ord_le841296385at_nat @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_maintainedD2) ).

thf(1014,plain,
    ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,C: labeled_graph_b_nat,D: set_Pr1986765409at_nat] :
      ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A @ B ) @ C )
     => ( ( graph_529870330at_nat @ A @ C @ D )
       => ~ ! [E: set_Pr1986765409at_nat] :
              ( ( graph_529870330at_nat @ B @ C @ E )
             => ~ ( ord_le841296385at_nat @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(1492,plain,
    $false,
    inference(e,[status(thm)],[1024,1454,1315,468,365,1190,582,1005,683,1401,1073,1173,730,1290,878,440,655,385,1137,500,797,1260,913,340,670,1095,1243,1391,782,417,885,1359,565,436,1228,724,570,719,785,372,1330,1279,1132,1087,1147,1479,1347,1115,1362,1489,475,1450,623,602,1169,1215,1447,1394,1345,849,527,380,678,546,925,810,534,1067,1057,512,942,439,1438,661,1153,761,1223,746,1021,349,561,693,1370,815,392,1487,847,1032,852,1178,522,1195,551,974,1079,1027,519,1234,1270,948,1328,1121,1425,356,593,869,420,857,1397,471,554,537,686,642,637,590,1039,1155,1419,837,1099,1297,1382,984,1002,1429,1246,779,647,1263,997,515,1150,1249,1266,1231,1050,457,503,605,1333,1434,343,938,508,921,1054,1167,794,888,1286,398,1035,1466,558,412,750,1251,430,824,1273,573,689,733,819,423,843,1388,743,875,579,1124,445,382,1312,713,335,1090,804,1356,672,611,787,1282,1011,1048,377,1144,737,1043,616,599,1175,362,567,387,1471,494,758,609,1325,964,915,1293,330,1112,1029,895,1198,1000,1102,505,658,1213,827,675,1304,1203,531,680,548,1134,1018,1181,1413,1076,525,1225,327,954,1070,872,705,1156,1432,1300,791,1188,338,576,951,359,1218,1257,613,1284,1353,1485,727,1140,1008,1372,497,465,1084,539,482,903,891,771,1476,946,588,699,961,1385,667,1193,478,899,1442,1045,433,510,346,1309,716,1161,800,620,752,447,405,867,735,918,807,1335,664,696,1165,1410,767,928,415,740,427,596,908,822,691,442,1093,395,1236,987,332,1129,369,607,486,803,1367,354,923,1184,1463,543,775,1416,755,491,454,708,1014]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ITP178^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n005.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 18:23:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.07/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.31/1.32  % [INFO] 	 Parsing done (362ms). 
% 2.31/1.33  % [INFO] 	 Running in sequential loop mode. 
% 2.99/1.58  % [INFO] 	 eprover registered as external prover. 
% 2.99/1.58  % [INFO] 	 cvc4 registered as external prover. 
% 2.99/1.59  % [INFO] 	 Scanning for conjecture ... 
% 3.42/1.71  % [INFO] 	 Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ... 
% 3.95/1.84  % [INFO] 	 Axiom selection finished. Selected 324 axioms (removed 31 axioms). 
% 4.66/2.03  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.66/2.04  % [INFO] 	 Type checking passed. 
% 4.66/2.05  % [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 ... 
% 23.70/7.56  % External prover 'e' found a proof!
% 23.70/7.56  % [INFO] 	 Killing All external provers ... 
% 23.70/7.56  % Time passed: 7034ms (effective reasoning time: 6231ms)
% 23.70/7.56  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 23.70/7.56  % Axioms used in derivation (324): fact_281_relcomp_Ocases, fact_30_translation__graph, fact_329_finite__Image, fact_118_Id__onI, fact_90_snd__eqD, fact_19_verts__in__translation__finite_I1_J, fact_316_univalentD, fact_54_old_Oprod_Oexhaust, fact_87_snd__eqD, fact_284_relcompEpair, fact_147_conjI__realizer, fact_303_graph__homo__union__id_I2_J, fact_17_are__rules_I2_J, fact_21_are__rules_I3_J, fact_343_Domain__iff, fact_64_prod__cases, fact_223_maintainedD2, fact_321_find__graph__occurence__vertices, fact_140_Collect__mem__eq, fact_177_fair__chainD_I2_J, fact_230_linorder__wlog, fact_126_set__of__graph__rules__def, fact_129_mem__Collect__eq, fact_150_allegorical__term_Oinject_I1_J, fact_60_Pair__inject, fact_99_prod__eqI, fact_14_are__rules_I1_J, fact_301_weak__universalD, fact_219_restrict__subsD, fact_307_subset__emptyI, fact_96_prod_Oexpand, fact_234_ord__le__eq__trans, fact_312_agree__iff__subset, fact_143_verts__in__translation, fact_259_graph__union__preserves__restrict, fact_204_labeled__graph_Ocollapse, fact_261_graph__union__iff, fact_255_graph__unionI, fact_311_ssubst__Pair__rhs, fact_6_subgraph__restrict, fact_33_old_Oprod_Oinject, fact_49_old_Oprod_Oinducts, fact_48_old_Oprod_Oinducts, fact_157_set__of__graph__rulesD_I3_J, fact_156_extensible__refl, fact_117_Id__onI, fact_124_Id__onI, fact_328_finite__Domain, fact_313_id__univalent, fact_50_old_Oprod_Oexhaust, fact_249_subset__iff, fact_172_Id__on__iff, fact_308_bot__empty__eq, fact_40_prod_Oinject, fact_69_surj__pair, fact_347_DomainE, fact_92_prod__eq__iff, fact_79_fst__eqD, fact_165_Id__onE, fact_326_Domain__Id__on, fact_102_labeled__graph_Oexpand, fact_295_finite__has__maximal, fact_327_univalent__finite_I2_J, fact_47_old_Oprod_Oinducts, fact_290_finite_OemptyI, fact_201_eq__snd__iff, fact_260_subgraph__def, fact_120_Id__onI, fact_91_snd__eqD, fact_352_Image__iff, fact_334_Domain_ODomainI, fact_121_Id__onI, fact_94_prod__eq__iff, fact_346_DomainE, fact_285_relcompEpair, fact_291_finite_OemptyI, fact_116_subgraph__trans, fact_2_graph__rule__translation, fact_251_subsetD, fact_283_relcomp_Ocases, fact_309_ssubst__Pair__rhs, fact_182_consequence__graphI, fact_141_Collect__cong, fact_128_set__of__graph__rules__def, fact_86_snd__conv, fact_113_subgraph__preserves__hom, fact_95_prod_Oexpand, fact_123_Id__onI, fact_10_verts__in__translation__finite_I2_J, fact_164_Id__onE, fact_337_Domain_Osimps, fact_132_mem__Collect__eq, fact_271_bot_Oextremum__uniqueI, fact_239_order_Otrans, fact_264_weak__universalI, fact_162_Id__onE, fact_310_ssubst__Pair__rhs, fact_184_maintained__def, fact_81_fst__eqD, fact_144_BNF__Greatest__Fixpoint_Osubst__Pair, fact_288_relcompE, fact_3_graph__rule__translation, fact_294_finite__has__minimal, fact_36_old_Oprod_Oinject, fact_344_Domain__iff, fact_8_graph__homomorphism__Id, fact_100_prod__eqI, fact_27_prod_Ocollapse, fact_28_prod_Ocollapse, fact_194_graph__homomorphism__semantics, fact_282_relcomp_Ocases, fact_176_fin__maintained__def, fact_278_relcomp_Osimps, fact_341_Domain_Ocases, fact_53_old_Oprod_Oexhaust, fact_85_snd__conv, fact_179_maintainedI, fact_153_set__of__graph__rulesD_I1_J, fact_11_verts__in__translation__finite_I2_J, fact_325_ImageI, fact_266_graph__homomorphism__composes, fact_107_surjective__pairing, fact_155_set__of__graph__rulesD_I2_J, fact_101_labeled__graph_Oexpand, fact_134_mem__Collect__eq, fact_306_finite__relcomp, fact_4_subgraph__refl, fact_15_are__rules_I1_J, fact_166_Id__on__eqI, fact_173_Id__on__iff, fact_105_surjective__pairing, fact_138_Collect__mem__eq, fact_193_chain__then__restrict, fact_114_subgraph__preserves__hom, fact_263_nonempty__rule, fact_338_Domain_Osimps, fact_195_semantics__in__vertices_I2_J, fact_168_Id__on__eqI, fact_43_restrict__idemp, fact_98_prod__eqI, fact_38_prod_Oinject, fact_275_relcomp_Oinducts, fact_253_chain, fact_45_old_Oprod_Oinducts, fact_174_Id__on__iff, fact_37_old_Oprod_Oinject, fact_142_verts__in__translation, fact_279_relcomp_Osimps, fact_42_prod_Oinject, fact_222_subgraph__subset_I1_J, fact_350_rev__ImageI, fact_354_Image__iff, fact_270_bot_Oextremum__unique, fact_297_bounded__Max__nat, fact_299_Id__on__vertices__identity_I1_J, fact_175_Id__on__iff, fact_224_subgraph__subset_I2_J, fact_111_prod_Oexhaust__sel, fact_348_rev__ImageI, fact_287_relcompE, fact_215_rev__finite__subset, fact_257_extensible__def, fact_208_subrelI, fact_189_maintained__holds__iff, fact_57_Pair__inject, fact_351_rev__ImageI, fact_20_verts__in__translation__finite_I1_J, fact_235_ord__eq__le__trans, fact_23_are__rules_I3_J, fact_268_graph__homomorphism__empty, fact_209_finite__has__maximal2, fact_52_old_Oprod_Oexhaust, fact_197_subgraph__semantics, fact_145_BNF__Greatest__Fixpoint_Osubst__Pair, fact_29_translation__graph, fact_181_sndI, fact_41_prod_Oinject, fact_139_Collect__mem__eq, fact_192_chain__sup__subgraph, fact_74_fst__conv, fact_335_Domain_ODomainI, fact_319_univalent__def, fact_24_prod_Ocollapse, fact_220_subgraph__def2, fact_188_fair__chainI, fact_61_Pair__inject, fact_35_old_Oprod_Oinject, fact_108_prod_Oexhaust__sel, fact_240_le__cases, fact_247_order__subst2, fact_16_are__rules_I2_J, fact_84_snd__conv, fact_196_semantics__in__vertices_I1_J, fact_187_fstI, fact_286_relcompEpair, fact_190_fair__chain__def, fact_302_weak__universal__def, fact_180_sndI, fact_238_le__cases3, fact_186_fstI, fact_205_extensible__refl__concr, fact_106_surjective__pairing, fact_213_infinite__super, fact_250_subset__eq, fact_214_infinite__super, fact_202_eq__fst__iff, fact_298_Id__on__vertices__identity_I2_J, fact_318_univalent__def, fact_210_finite__has__minimal2, fact_269_bot_Oextremum, fact_300_translation__homomorphism_I2_J, fact_148_exI__realizer, fact_89_snd__eqD, fact_331_Domain_Oinducts, fact_163_Id__onE, fact_237_antisym__conv, fact_276_relcomp_Oinducts, fact_293_infinite__imp__nonempty, fact_241_eq__refl, fact_273_relcomp_OrelcompI, fact_65_prod__cases, fact_289_relcompE, fact_66_prod__cases, fact_82_snd__conv, fact_130_mem__Collect__eq, fact_206_subrelI, fact_242_linear, fact_317_univalent__def, fact_9_graph__homomorphism__Id, fact_115_subgraph__trans, fact_127_set__of__graph__rules__def, fact_103_surjective__pairing, fact_22_are__rules_I3_J, fact_262_finite__nat__set__iff__bounded__le, fact_59_Pair__inject, fact_267_graph__empty__e, fact_231_dual__order_Orefl, fact_280_relcomp_Osimps, fact_198_maintained__holds__subset__iff, fact_200_eq__snd__iff, fact_93_prod__eq__iff, fact_26_prod_Ocollapse, fact_274_relcomp_OrelcompI, fact_229_dual__order_Otrans, fact_211_finite__subset, fact_304_graph__homo__union__id_I1_J, fact_243_antisym, fact_110_prod_Oexhaust__sel, fact_236_order__class_Oorder_Oeq__iff, fact_353_Image__iff, fact_170_Id__on__eqI, fact_62_prod__cases, fact_160_exE__realizer_H, fact_31_vertices__restrict, fact_332_Domain_Oinducts, fact_244_eq__iff, fact_77_fst__eqD, fact_340_Domain_Ocases, fact_44_restrict__idemp, fact_112_prod_Oexhaust__sel, fact_159_exE__realizer_H, fact_323_ImageI, fact_183_consequence__graph__def, fact_232_order__trans, fact_7_subgraph__restrict, fact_13_are__rules_I1_J, fact_80_fst__eqD, fact_272_relcomp_OrelcompI, fact_5_subgraph__refl, fact_158_set__of__graph__rulesD_I3_J, fact_258_extensibleI, fact_18_are__rules_I2_J, fact_252_in__mono, fact_277_relcomp_Oinducts, fact_233_order__class_Oorder_Oantisym, fact_32_vertices__restrict, fact_185_maintainedD, fact_212_finite__subset, fact_296_graph__homomorphism__nonempty, fact_305_finite__relcomp, fact_226_order__refl, fact_265_Id__on__empty, fact_324_ImageI, fact_315_univalentD, fact_217_labeled__graph_Osel_I2_J, fact_178_identity__rules__graph__rule, fact_227_dual__order_Oantisym, fact_216_rev__finite__subset, fact_320_find__graph__occurence__vertices, fact_67_surj__pair, fact_207_subrelI, fact_12_verts__in__translation__finite_I2_J, fact_154_set__of__graph__rulesD_I2_J, fact_0_assms, fact_191_chain__sup__graph, fact_246_ord__eq__le__subst, fact_314_univalentD, fact_76_fst__conv, fact_225_subsetI, fact_125_Id__onI, fact_152_set__of__graph__rulesD_I1_J, fact_256_extensibleD, fact_245_ord__le__eq__subst, fact_292_infinite__imp__nonempty, fact_203_eq__fst__iff, fact_228_dual__order_Oeq__iff, fact_71_surj__pair, fact_218_labeled__graph_Osel_I1_J, fact_199_find__graph__occurence, fact_151_fin__maintainedI, fact_149_exI__realizer, fact_72_fst__conv, fact_146_conjI__realizer, fact_254_chain__def2, fact_135_Collect__mem__eq, fact_70_surj__pair, fact_221_labeled__graph_Oexhaust__sel, fact_136_Collect__mem__eq, fact_248_order__subst1, fact_1_graph__rule__translation, fact_97_prod_Oexpand, fact_133_mem__Collect__eq, fact_169_Id__on__eqI, fact_75_fst__conv
% 23.70/7.56  % No. of inferences in proof: 652
% 23.70/7.57  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7034 ms resp. 6231 ms w/o parsing
% 24.97/7.79  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.97/7.79  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------