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