%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP177^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:04 AM UTC 2026
% Result : Theorem 26.18s 7.89s
% Output : Refutation 28.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 307
% Syntax : Number of formulae : 616 ( 299 unt; 0 typ; 0 def)
% Number of atoms : 1631 ( 602 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 5690 ( 234 ~; 17 |; 104 &;4731 @)
% ( 0 <=>; 604 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 53 ( 52 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 124 ( 121 usr; 17 con; 0-3 aty)
% Number of variables : 1703 ( 48 ^;1613 !; 42 ?;1703 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr197580003_a_nat_type,type,
set_Pr197580003_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_Pr1954438265od_b_b_type,type,
set_Pr1954438265od_b_b: $tType ).
thf(produc1169496899od_b_b_type,type,
produc1169496899od_b_b: $tType ).
thf(set_Pr1190604087od_b_b_type,type,
set_Pr1190604087od_b_b: $tType ).
thf(produc1084374401od_b_b_type,type,
produc1084374401od_b_b: $tType ).
thf(labele1322729112_a_nat_type,type,
labele1322729112_a_nat: $tType ).
thf(set_Pr667377223od_b_b_type,type,
set_Pr667377223od_b_b: $tType ).
thf(produc1485083751od_b_b_type,type,
produc1485083751od_b_b: $tType ).
thf(set_Pr2109276827od_b_b_type,type,
set_Pr2109276827od_b_b: $tType ).
thf(set_Pr1646010159_a_nat_type,type,
set_Pr1646010159_a_nat: $tType ).
thf(set_Pr812188767_nat_b_type,type,
set_Pr812188767_nat_b: $tType ).
thf(produc970027067od_b_b_type,type,
produc970027067od_b_b: $tType ).
thf(produc845793663_nat_b_type,type,
produc845793663_nat_b: $tType ).
thf(set_Pr1987088711_a_nat_type,type,
set_Pr1987088711_a_nat: $tType ).
thf(produc1871334759_a_nat_type,type,
produc1871334759_a_nat: $tType ).
thf(produc1398946881nt_a_b_type,type,
produc1398946881nt_a_b: $tType ).
thf(labele1644675410od_b_b_type,type,
labele1644675410od_b_b: $tType ).
thf(set_Pr1071216121od_b_b_type,type,
set_Pr1071216121od_b_b: $tType ).
thf(set_Pr2134561957od_b_b_type,type,
set_Pr2134561957od_b_b: $tType ).
thf(set_Pr1021918435od_b_b_type,type,
set_Pr1021918435od_b_b: $tType ).
thf(produc1052326083od_b_b_type,type,
produc1052326083od_b_b: $tType ).
thf(produc1990339951od_b_b_type,type,
produc1990339951od_b_b: $tType ).
thf(produc644633773od_b_b_type,type,
produc644633773od_b_b: $tType ).
thf(set_Pr2060523537od_b_b_type,type,
set_Pr2060523537od_b_b: $tType ).
thf(set_Pr1906739389_b_b_b_type,type,
set_Pr1906739389_b_b_b: $tType ).
thf(produc1605346267od_b_b_type,type,
produc1605346267od_b_b: $tType ).
thf(produc276146823_b_b_b_type,type,
produc276146823_b_b_b: $tType ).
thf(set_Pr154086431tant_a_type,type,
set_Pr154086431tant_a: $tType ).
thf(set_Pr1324126435od_b_b_type,type,
set_Pr1324126435od_b_b: $tType ).
thf(produc90515391tant_a_type,type,
produc90515391tant_a: $tType ).
thf(labele1835558936od_b_b_type,type,
labele1835558936od_b_b: $tType ).
thf(set_Pr2007082183od_b_b_type,type,
set_Pr2007082183od_b_b: $tType ).
thf(produc1213276845od_b_b_type,type,
produc1213276845od_b_b: $tType ).
thf(set_la1083530965_a_nat_type,type,
set_la1083530965_a_nat: $tType ).
thf(produc1168037607od_b_b_type,type,
produc1168037607od_b_b: $tType ).
thf(labele935650037_a_nat_type,type,
labele935650037_a_nat: $tType ).
thf(set_Pr1649131859tant_a_type,type,
set_Pr1649131859tant_a: $tType ).
thf(allego510293162tant_a_type,type,
allego510293162tant_a: $tType ).
thf(labele1159362096nt_a_b_type,type,
labele1159362096nt_a_b: $tType ).
thf(set_Pr621705391od_b_b_type,type,
set_Pr621705391od_b_b: $tType ).
thf(set_Pr357419743_b_b_b_type,type,
set_Pr357419743_b_b_b: $tType ).
thf(produc255402447od_b_b_type,type,
produc255402447od_b_b: $tType ).
thf(produc2112523263_b_b_b_type,type,
produc2112523263_b_b_b: $tType ).
thf(set_St761939237tant_a_type,type,
set_St761939237tant_a: $tType ).
thf(set_Pr2106913242_nat_b_type,type,
set_Pr2106913242_nat_b: $tType ).
thf(set_Product_prod_b_b_type,type,
set_Product_prod_b_b: $tType ).
thf(standard_Constant_a_type,type,
standard_Constant_a: $tType ).
thf(product_prod_b_b_type,type,
product_prod_b_b: $tType ).
thf(set_b_type,type,
set_b: $tType ).
thf(b_type,type,
b: $tType ).
thf(bNF_Gr1272216980od_b_b_decl,type,
bNF_Gr1272216980od_b_b: set_St761939237tant_a > ( standard_Constant_a > product_prod_b_b ) > set_Pr1324126435od_b_b ).
thf(bNF_Gr492676974_b_b_b_decl,type,
bNF_Gr492676974_b_b_b: set_Pr1324126435od_b_b > ( produc1213276845od_b_b > b ) > set_Pr1906739389_b_b_b ).
thf(bNF_Gr521784954_b_b_b_decl,type,
bNF_Gr521784954_b_b_b: set_Product_prod_b_b > ( product_prod_b_b > b ) > set_Pr357419743_b_b_b ).
thf(bNF_Gr230160332tant_a_decl,type,
bNF_Gr230160332tant_a: set_b > ( b > standard_Constant_a ) > set_Pr1649131859tant_a ).
thf(bNF_Gr_b_b_decl,type,
bNF_Gr_b_b: set_b > ( b > b ) > set_Product_prod_b_b ).
thf(equiv_1821124534_set_b_decl,type,
equiv_1821124534_set_b: set_Product_prod_b_b > ( b > set_b ) > $o ).
thf(equiv_291114781_a_nat_decl,type,
equiv_291114781_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat > $o ).
thf(equiv_equiv_b_decl,type,
equiv_equiv_b: set_b > set_Product_prod_b_b > $o ).
thf(hilbert_Eps_b_decl,type,
hilbert_Eps_b: ( b > $o ) > b ).
thf(if_b_decl,type,
if_b: $o > b > b > b ).
thf(standard_S_Idt_a_decl,type,
standard_S_Idt_a: standard_Constant_a ).
thf(getRel904497637nt_a_b_decl,type,
getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b ).
thf(semant55076487nt_a_b_decl,type,
semant55076487nt_a_b: labele1159362096nt_a_b > allego510293162tant_a > set_Product_prod_b_b ).
thf(edge_p1817988046tant_a_decl,type,
edge_p1817988046tant_a: set_Pr1906739389_b_b_b > set_Pr1190604087od_b_b > set_Pr1324126435od_b_b > $o ).
thf(edge_p1969196346tant_a_decl,type,
edge_p1969196346tant_a: set_Pr357419743_b_b_b > set_Pr1021918435od_b_b > set_Pr1324126435od_b_b > $o ).
thf(edge_p1384198690tant_a_decl,type,
edge_p1384198690tant_a: set_Product_prod_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).
thf(graph_726202286_nat_b_decl,type,
graph_726202286_nat_b: labele1322729112_a_nat > labele1159362096nt_a_b > set_Pr812188767_nat_b > $o ).
thf(graph_222606102_a_b_b_decl,type,
graph_222606102_a_b_b: labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).
thf(graph_1309249505nt_a_b_decl,type,
graph_1309249505nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b > labele1159362096nt_a_b ).
thf(labele27098724_a_nat_decl,type,
labele27098724_a_nat: set_Pr197580003_a_nat > set_Pr1987088711_a_nat > labele1322729112_a_nat ).
thf(labele1230159100nt_a_b_decl,type,
labele1230159100nt_a_b: set_Pr1324126435od_b_b > set_b > labele1159362096nt_a_b ).
thf(labele2032816061od_b_b_decl,type,
labele2032816061od_b_b: labele1644675410od_b_b > set_Pr1190604087od_b_b ).
thf(labele372159959od_b_b_decl,type,
labele372159959od_b_b: labele1835558936od_b_b > set_Pr1021918435od_b_b ).
thf(labele1741081071nt_a_b_decl,type,
labele1741081071nt_a_b: labele1159362096nt_a_b > set_Pr1324126435od_b_b ).
thf(labele595103470od_b_b_decl,type,
labele595103470od_b_b: labele1644675410od_b_b > set_Pr1324126435od_b_b ).
thf(labele442485990od_b_b_decl,type,
labele442485990od_b_b: labele1835558936od_b_b > set_Product_prod_b_b ).
thf(labele1424214014nt_a_b_decl,type,
labele1424214014nt_a_b: labele1159362096nt_a_b > set_b ).
thf(map_gr926947118tant_a_decl,type,
map_gr926947118tant_a: set_Product_prod_b_b > labele1159362096nt_a_b > labele1159362096nt_a_b ).
thf(restri446606278nt_a_b_decl,type,
restri446606278nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b ).
thf(bot_bo1160111033tant_a_decl,type,
bot_bo1160111033tant_a: set_St761939237tant_a ).
thf(bot_bo2122869057_a_nat_decl,type,
bot_bo2122869057_a_nat: set_la1083530965_a_nat ).
thf(bot_bo1653310327_a_nat_decl,type,
bot_bo1653310327_a_nat: set_Pr197580003_a_nat ).
thf(bot_bo1664927607od_b_b_decl,type,
bot_bo1664927607od_b_b: set_Pr1324126435od_b_b ).
thf(bot_bo1836341171_a_nat_decl,type,
bot_bo1836341171_a_nat: set_Pr1987088711_a_nat ).
thf(bot_bo1973379891_a_nat_decl,type,
bot_bo1973379891_a_nat: set_Pr924198087_a_nat ).
thf(bot_bo1113554635_nat_b_decl,type,
bot_bo1113554635_nat_b: set_Pr812188767_nat_b ).
thf(bot_bo1343651123od_b_b_decl,type,
bot_bo1343651123od_b_b: set_Product_prod_b_b ).
thf(bot_bot_set_b_decl,type,
bot_bot_set_b: set_b ).
thf(ord_le123089219od_b_b_decl,type,
ord_le123089219od_b_b: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).
thf(ord_le1718765799_a_nat_decl,type,
ord_le1718765799_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o ).
thf(ord_le107617383_a_nat_decl,type,
ord_le107617383_a_nat: set_Pr924198087_a_nat > set_Pr924198087_a_nat > $o ).
thf(ord_le1036320359od_b_b_decl,type,
ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(ord_less_eq_set_b_decl,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(produc1788032435od_b_b_decl,type,
produc1788032435od_b_b: standard_Constant_a > produc970027067od_b_b > produc1084374401od_b_b ).
thf(produc618266719od_b_b_decl,type,
produc618266719od_b_b: standard_Constant_a > produc1168037607od_b_b > produc644633773od_b_b ).
thf(produc1432590431od_b_b_decl,type,
produc1432590431od_b_b: standard_Constant_a > product_prod_b_b > produc1213276845od_b_b ).
thf(produc1676969687_a_nat_decl,type,
produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).
thf(produc1569511545nt_a_b_decl,type,
produc1569511545nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b > produc1398946881nt_a_b ).
thf(produc449289715od_b_b_decl,type,
produc449289715od_b_b: produc1213276845od_b_b > produc1213276845od_b_b > produc970027067od_b_b ).
thf(produc1580777273_b_b_b_decl,type,
produc1580777273_b_b_b: produc1213276845od_b_b > b > produc276146823_b_b_b ).
thf(produc401731773od_b_b_decl,type,
produc401731773od_b_b: produc1871334759_a_nat > produc1213276845od_b_b > produc1169496899od_b_b ).
thf(produc1677124439_a_nat_decl,type,
produc1677124439_a_nat: produc1871334759_a_nat > produc1871334759_a_nat > produc398057191_a_nat ).
thf(produc590959831od_b_b_decl,type,
produc590959831od_b_b: produc1871334759_a_nat > product_prod_b_b > produc1485083751od_b_b ).
thf(produc2059954415_nat_b_decl,type,
produc2059954415_nat_b: produc1871334759_a_nat > b > produc845793663_nat_b ).
thf(produc546497367od_b_b_decl,type,
produc546497367od_b_b: product_prod_b_b > product_prod_b_b > produc1168037607od_b_b ).
thf(produc1001682799_b_b_b_decl,type,
produc1001682799_b_b_b: product_prod_b_b > b > produc2112523263_b_b_b ).
thf(produc800495189od_b_b_decl,type,
produc800495189od_b_b: b > produc1213276845od_b_b > produc1605346267od_b_b ).
thf(produc1257047359od_b_b_decl,type,
produc1257047359od_b_b: b > product_prod_b_b > produc255402447od_b_b ).
thf(product_Pair_b_b_decl,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(id_on_689842066_a_nat_decl,type,
id_on_689842066_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat ).
thf(id_on_1651096324_a_nat_decl,type,
id_on_1651096324_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat ).
thf(id_on_b_decl,type,
id_on_b: set_b > set_Product_prod_b_b ).
thf(image_1916422435od_b_b_decl,type,
image_1916422435od_b_b: set_Pr1324126435od_b_b > set_St761939237tant_a > set_Product_prod_b_b ).
thf(image_1971191571_a_nat_decl,type,
image_1971191571_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).
thf(image_1764625405_b_b_b_decl,type,
image_1764625405_b_b_b: set_Pr1906739389_b_b_b > set_Pr1324126435od_b_b > set_b ).
thf(image_480774529od_b_b_decl,type,
image_480774529od_b_b: set_Pr1954438265od_b_b > set_Pr1987088711_a_nat > set_Pr1324126435od_b_b ).
thf(image_1168831379_a_nat_decl,type,
image_1168831379_a_nat: set_Pr924198087_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(image_1214223635od_b_b_decl,type,
image_1214223635od_b_b: set_Pr667377223od_b_b > set_Pr1987088711_a_nat > set_Product_prod_b_b ).
thf(image_924992811_nat_b_decl,type,
image_924992811_nat_b: set_Pr812188767_nat_b > set_Pr1987088711_a_nat > set_b ).
thf(image_921732011_b_b_b_decl,type,
image_921732011_b_b_b: set_Pr357419743_b_b_b > set_Product_prod_b_b > set_b ).
thf(image_984343321od_b_b_decl,type,
image_984343321od_b_b: set_Pr2060523537od_b_b > set_b > set_Pr1324126435od_b_b ).
thf(image_1749766139_a_nat_decl,type,
image_1749766139_a_nat: set_Pr1646010159_a_nat > set_b > set_Pr1987088711_a_nat ).
thf(image_1177096571od_b_b_decl,type,
image_1177096571od_b_b: set_Pr621705391od_b_b > set_b > set_Product_prod_b_b ).
thf(image_b_b_decl,type,
image_b_b: set_Product_prod_b_b > set_b > set_b ).
thf(refl_o1213627494_a_nat_decl,type,
refl_o1213627494_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat > $o ).
thf(refl_on_b_decl,type,
refl_on_b: set_b > set_Product_prod_b_b > $o ).
thf(relcom1338300020_a_nat_decl,type,
relcom1338300020_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(relcom112561144od_b_b_decl,type,
relcom112561144od_b_b: set_Pr1649131859tant_a > set_Pr1324126435od_b_b > set_Pr621705391od_b_b ).
thf(relcomp_b_b_b_decl,type,
relcomp_b_b_b: set_Product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(agree_221379389_a_b_b_decl,type,
agree_221379389_a_b_b: labele1159362096nt_a_b > set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(conseq956760372_nat_b_decl,type,
conseq956760372_nat_b: set_Pr1987088711_a_nat > labele1159362096nt_a_b > $o ).
thf(extens1779443913_a_b_b_decl,type,
extens1779443913_a_b_b: produc1398946881nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).
thf(mainta1604381365_nat_b_decl,type,
mainta1604381365_nat_b: produc1871334759_a_nat > labele1159362096nt_a_b > $o ).
thf(mainta374363448_a_b_b_decl,type,
mainta374363448_a_b_b: produc1398946881nt_a_b > labele1159362096nt_a_b > $o ).
thf(collec279084418od_b_b_decl,type,
collec279084418od_b_b: ( produc1213276845od_b_b > $o ) > set_Pr1324126435od_b_b ).
thf(collec357096914_a_nat_decl,type,
collec357096914_a_nat: ( produc1871334759_a_nat > $o ) > set_Pr1987088711_a_nat ).
thf(collec1481886546od_b_b_decl,type,
collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
thf(collect_b_decl,type,
collect_b: ( b > $o ) > set_b ).
thf(image_1683732397od_b_b_decl,type,
image_1683732397od_b_b: ( b > product_prod_b_b ) > set_b > set_Product_prod_b_b ).
thf(insert1909710879tant_a_decl,type,
insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).
thf(insert2037698781od_b_b_decl,type,
insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
thf(insert1574423351_a_nat_decl,type,
insert1574423351_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(insert1810136247_a_nat_decl,type,
insert1810136247_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > set_Pr924198087_a_nat ).
thf(insert1952693431od_b_b_decl,type,
insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(insert_b_decl,type,
insert_b: b > set_b > set_b ).
thf(standa1568205540ules_a_decl,type,
standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).
thf(standa63370785tant_a_decl,type,
standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(standa997693288tant_a_decl,type,
standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(standa1795879409tant_a_decl,type,
standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(member1632892294tant_a_decl,type,
member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
thf(member147868824od_b_b_decl,type,
member147868824od_b_b: produc1084374401od_b_b > set_Pr1190604087od_b_b > $o ).
thf(member1744485444od_b_b_decl,type,
member1744485444od_b_b: produc644633773od_b_b > set_Pr1021918435od_b_b > $o ).
thf(member1516365892od_b_b_decl,type,
member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o ).
thf(member832397200_a_nat_decl,type,
member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).
thf(member1417789726_b_b_b_decl,type,
member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o ).
thf(member1533761242od_b_b_decl,type,
member1533761242od_b_b: produc1169496899od_b_b > set_Pr1954438265od_b_b > $o ).
thf(member584645392_a_nat_decl,type,
member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
thf(member301892752od_b_b_decl,type,
member301892752od_b_b: produc1485083751od_b_b > set_Pr667377223od_b_b > $o ).
thf(member1544800936_nat_b_decl,type,
member1544800936_nat_b: produc845793663_nat_b > set_Pr812188767_nat_b > $o ).
thf(member351494440_b_b_b_decl,type,
member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o ).
thf(member599505522od_b_b_decl,type,
member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o ).
thf(member641857272od_b_b_decl,type,
member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o ).
thf(member1285940496od_b_b_decl,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(member_b_decl,type,
member_b: b > set_b > $o ).
thf(g_decl,type,
g: labele1159362096nt_a_b ).
thf(l_decl,type,
l: set_St761939237tant_a ).
thf(p_decl,type,
p: b > b > $o ).
thf(f_decl,type,
f: b > b ).
thf(l2_decl,type,
l2: standard_Constant_a ).
thf(x_decl,type,
x: b ).
thf(y_decl,type,
y: b ).
thf(140,axiom,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: b,E: b] : ( A @ ( produc1432590431od_b_b @ C @ ( product_Pair_b_b @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_prod__induct3) ).
thf(760,plain,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: b,E: b] : ( A @ ( produc1432590431od_b_b @ C @ ( product_Pair_b_b @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(243,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member_b @ B @ ( image_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_ImageI) ).
thf(1105,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member_b @ B @ ( image_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(288,axiom,
! [A: set_b] :
( ( ! [B: b] :
~ ( member_b @ B @ A ) )
= ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_all__not__in__conv) ).
thf(1237,plain,
! [A: set_b] :
( ( ! [B: b] :
~ ( member_b @ B @ A ) )
= ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(51,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b] :
( ! [D: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ D )
=> ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ C ) @ B @ D ) )
=> ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_maintainedI) ).
thf(468,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b] :
( ! [D: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ D )
=> ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ C ) @ B @ D ) )
=> ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(307,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( B
= ( restri446606278nt_a_b @ B ) )
=> ( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
= ( ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ A ) @ ( labele1424214014nt_a_b @ B ) )
& ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1741081071nt_a_b @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_subgraph__def2) ).
thf(1295,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( B
= ( restri446606278nt_a_b @ B ) )
=> ( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
= ( ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ A ) @ ( labele1424214014nt_a_b @ B ) )
& ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1741081071nt_a_b @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(218,axiom,
! [A: set_b] :
( ( collect_b
@ ^ [B: b] : ( member_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(1031,plain,
! [A: set_b] :
( ( collect_b
@ ^ [B: b] : ( member_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(10,axiom,
! [A: set_Product_prod_b_b] :
( ( ! [B: product_prod_b_b] :
~ ( member1285940496od_b_b @ B @ A ) )
= ( A = bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_all__not__in__conv) ).
thf(333,plain,
! [A: set_Product_prod_b_b] :
( ( ! [B: product_prod_b_b] :
~ ( member1285940496od_b_b @ B @ A ) )
= ( A = bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(102,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_prod_Oinject) ).
thf(628,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(278,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ ( graph_1309249505nt_a_b @ A @ B ) @ C @ D )
=> ( ( B
= ( restri446606278nt_a_b @ B ) )
=> ( graph_222606102_a_b_b @ B @ C @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ B ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_graph__homo__union__id_I2_J) ).
thf(1200,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ ( graph_1309249505nt_a_b @ A @ B ) @ C @ D )
=> ( ( B
= ( restri446606278nt_a_b @ B ) )
=> ( graph_222606102_a_b_b @ B @ C @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ B ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(32,axiom,
! [A: set_Pr1987088711_a_nat,B: set_Pr924198087_a_nat,C: produc1871334759_a_nat,D: produc1871334759_a_nat] :
( ( equiv_291114781_a_nat @ A @ B )
=> ( ( ord_le1718765799_a_nat @ ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) @ ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) )
=> ( ( member832397200_a_nat @ C @ A )
=> ( member584645392_a_nat @ ( produc1677124439_a_nat @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_subset__equiv__class) ).
thf(408,plain,
! [A: set_Pr1987088711_a_nat,B: set_Pr924198087_a_nat,C: produc1871334759_a_nat,D: produc1871334759_a_nat] :
( ( equiv_291114781_a_nat @ A @ B )
=> ( ( ord_le1718765799_a_nat @ ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) @ ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) )
=> ( ( member832397200_a_nat @ C @ A )
=> ( member584645392_a_nat @ ( produc1677124439_a_nat @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(86,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b] :
( ( image_b_b @ ( relcomp_b_b_b @ A @ B ) @ C )
= ( image_b_b @ B @ ( image_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_relcomp__Image) ).
thf(582,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b] :
( ( image_b_b @ ( relcomp_b_b_b @ A @ B ) @ C )
= ( image_b_b @ B @ ( image_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(132,axiom,
( ( id_on_689842066_a_nat @ bot_bo2122869057_a_nat )
= bot_bo1836341171_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Id__on__empty) ).
thf(730,plain,
( ( id_on_689842066_a_nat @ bot_bo2122869057_a_nat )
= bot_bo1836341171_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(232,axiom,
member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_fv_I1_J) ).
thf(1073,plain,
member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(45,axiom,
! [A: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_empty__iff) ).
thf(449,plain,
! [A: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(98,axiom,
! [A: product_prod_b_b] :
~ ! [B: b,C: b] :
( A
!= ( product_Pair_b_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Oprod_Oexhaust) ).
thf(614,plain,
! [A: product_prod_b_b] :
~ ! [B: b,C: b] :
( A
!= ( product_Pair_b_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(92,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) )
=> ( ord_le123089219od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_subsetI) ).
thf(597,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) )
=> ( ord_le123089219od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(268,axiom,
equiv_equiv_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_equiv) ).
thf(1173,plain,
equiv_equiv_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(175,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Pair__inject) ).
thf(878,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(65,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_doubleton__eq__iff) ).
thf(511,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(26,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ~ ( member1285940496od_b_b @ A @ C )
=> ( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_insert__ident) ).
thf(384,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ~ ( member1285940496od_b_b @ A @ C )
=> ( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(72,axiom,
! [A: produc1871334759_a_nat > $o] :
( ( ( collec357096914_a_nat @ A )
= bot_bo1836341171_a_nat )
= ( ! [B: produc1871334759_a_nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Collect__empty__eq) ).
thf(533,plain,
! [A: produc1871334759_a_nat > $o] :
( ( ( collec357096914_a_nat @ A )
= bot_bo1836341171_a_nat )
= ( ! [B: produc1871334759_a_nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(77,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_1309249505nt_a_b @ A @ ( graph_1309249505nt_a_b @ A @ B ) )
= ( graph_1309249505nt_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_graph__union__idemp_I2_J) ).
thf(550,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_1309249505nt_a_b @ A @ ( graph_1309249505nt_a_b @ A @ B ) )
= ( graph_1309249505nt_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(52,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: standard_Constant_a > product_prod_b_b,D: product_prod_b_b] :
( ( ~ ( member1632892294tant_a @ A @ B )
| ( ( C @ A )
!= D ) )
=> ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ D ) @ ( bNF_Gr1272216980od_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Gr__not__in) ).
thf(472,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: standard_Constant_a > product_prod_b_b,D: product_prod_b_b] :
( ( ~ ( member1632892294tant_a @ A @ B )
| ( ( C @ A )
!= D ) )
=> ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ D ) @ ( bNF_Gr1272216980od_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(157,axiom,
! [A: b > b] :
( ( bNF_Gr_b_b @ bot_bot_set_b @ A )
= bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Gr__empty) ).
thf(814,plain,
! [A: b > b] :
( ( bNF_Gr_b_b @ bot_bot_set_b @ A )
= bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(183,axiom,
! [A: set_Pr924198087_a_nat,B: set_Pr924198087_a_nat,C: set_Pr1987088711_a_nat,D: produc1871334759_a_nat] :
( ( ord_le107617383_a_nat @ A @ B )
=> ( ( equiv_291114781_a_nat @ C @ A )
=> ( ( equiv_291114781_a_nat @ C @ B )
=> ( ( image_1168831379_a_nat @ B @ ( image_1168831379_a_nat @ A @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) )
= ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_refines__equiv__class__eq2) ).
thf(913,plain,
! [A: set_Pr924198087_a_nat,B: set_Pr924198087_a_nat,C: set_Pr1987088711_a_nat,D: produc1871334759_a_nat] :
( ( ord_le107617383_a_nat @ A @ B )
=> ( ( equiv_291114781_a_nat @ C @ A )
=> ( ( equiv_291114781_a_nat @ C @ B )
=> ( ( image_1168831379_a_nat @ B @ ( image_1168831379_a_nat @ A @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) )
= ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(114,axiom,
! [A: b > $o] :
( ( bot_bot_set_b
= ( collect_b @ A ) )
= ( ! [B: b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_empty__Collect__eq) ).
thf(670,plain,
! [A: b > $o] :
( ( bot_bot_set_b
= ( collect_b @ A ) )
= ( ! [B: b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(240,axiom,
! [A: labele1159362096nt_a_b,B: b,C: b,D: allego510293162tant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( semant55076487nt_a_b @ A @ D ) )
=> ( member_b @ B @ ( labele1424214014nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_semantics__in__vertices_I1_J) ).
thf(1095,plain,
! [A: labele1159362096nt_a_b,B: b,C: b,D: allego510293162tant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( semant55076487nt_a_b @ A @ D ) )
=> ( member_b @ B @ ( labele1424214014nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(222,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ( graph_222606102_a_b_b @ B @ C @ ( id_on_b @ ( labele1424214014nt_a_b @ B ) ) )
=> ( graph_222606102_a_b_b @ A @ C @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_subgraph__trans) ).
thf(1046,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ( graph_222606102_a_b_b @ B @ C @ ( id_on_b @ ( labele1424214014nt_a_b @ B ) ) )
=> ( graph_222606102_a_b_b @ A @ C @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(297,axiom,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_subsetD) ).
thf(1265,plain,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(293,axiom,
! [A: b,B: b,C: standard_Constant_a,D: labele1159362096nt_a_b,E: labele1159362096nt_a_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ D ) )
=> ( ( graph_222606102_a_b_b @ D @ E @ ( id_on_b @ ( labele1424214014nt_a_b @ D ) ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_getRel__subgraph) ).
thf(1254,plain,
! [A: b,B: b,C: standard_Constant_a,D: labele1159362096nt_a_b,E: labele1159362096nt_a_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ D ) )
=> ( ( graph_222606102_a_b_b @ D @ E @ ( id_on_b @ ( labele1424214014nt_a_b @ D ) ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(108,axiom,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: produc1871334759_a_nat,D: produc1871334759_a_nat] :
( ( ( insert1574423351_a_nat @ A @ ( insert1574423351_a_nat @ B @ bot_bo1836341171_a_nat ) )
= ( insert1574423351_a_nat @ C @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_doubleton__eq__iff) ).
thf(651,plain,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: produc1871334759_a_nat,D: produc1871334759_a_nat] :
( ( ( insert1574423351_a_nat @ A @ ( insert1574423351_a_nat @ B @ bot_bo1836341171_a_nat ) )
= ( insert1574423351_a_nat @ C @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(225,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
= ( ( A
= ( restri446606278nt_a_b @ A ) )
& ( B
= ( restri446606278nt_a_b @ B ) )
& ( ( graph_1309249505nt_a_b @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_subgraph__def) ).
thf(1055,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
= ( ( A
= ( restri446606278nt_a_b @ A ) )
& ( B
= ( restri446606278nt_a_b @ B ) )
& ( ( graph_1309249505nt_a_b @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(184,axiom,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_prod__cases) ).
thf(917,plain,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(153,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: set_Pr1987088711_a_nat] :
( ~ ( member832397200_a_nat @ A @ B )
=> ( ~ ( member832397200_a_nat @ A @ C )
=> ( ( ( insert1574423351_a_nat @ A @ B )
= ( insert1574423351_a_nat @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_insert__ident) ).
thf(802,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: set_Pr1987088711_a_nat] :
( ~ ( member832397200_a_nat @ A @ B )
=> ( ~ ( member832397200_a_nat @ A @ C )
=> ( ( ( insert1574423351_a_nat @ A @ B )
= ( insert1574423351_a_nat @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(302,axiom,
! [A: b,B: set_Product_prod_b_b,C: b] :
( ( member_b @ A @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Image__singleton__iff) ).
thf(1279,plain,
! [A: b,B: set_Product_prod_b_b,C: b] :
( ( member_b @ A @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(16,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b,D: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ~ ( member1516365892od_b_b @ C @ D )
=> ( ( ( insert2037698781od_b_b @ A @ B )
= ( insert2037698781od_b_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ C @ E ) )
& ~ ( member1516365892od_b_b @ C @ E )
& ( D
= ( insert2037698781od_b_b @ A @ E ) )
& ~ ( member1516365892od_b_b @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_insert__eq__iff) ).
thf(357,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b,D: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ~ ( member1516365892od_b_b @ C @ D )
=> ( ( ( insert2037698781od_b_b @ A @ B )
= ( insert2037698781od_b_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ C @ E ) )
& ~ ( member1516365892od_b_b @ C @ E )
& ( D
= ( insert2037698781od_b_b @ A @ E ) )
& ~ ( member1516365892od_b_b @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(227,axiom,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
= ( ( A = B )
| ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_insert__iff) ).
thf(1059,plain,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
= ( ( A = B )
| ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(75,axiom,
! [A: produc1213276845od_b_b] :
~ ! [B: standard_Constant_a,C: product_prod_b_b] :
( A
!= ( produc1432590431od_b_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_old_Oprod_Oexhaust) ).
thf(542,plain,
! [A: produc1213276845od_b_b] :
~ ! [B: standard_Constant_a,C: product_prod_b_b] :
( A
!= ( produc1432590431od_b_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(158,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ord_le123089219od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_in__mono) ).
thf(817,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ord_le123089219od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(79,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: allego510293162tant_a] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( ( semant55076487nt_a_b @ A @ D )
!= bot_bo1343651123od_b_b )
=> ( ( semant55076487nt_a_b @ B @ D )
!= bot_bo1343651123od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_graph__homomorphism__nonempty) ).
thf(559,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: allego510293162tant_a] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( ( semant55076487nt_a_b @ A @ D )
!= bot_bo1343651123od_b_b )
=> ( ( semant55076487nt_a_b @ B @ D )
!= bot_bo1343651123od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(291,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: b,E: b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Id__on__vertices__identity_I1_J) ).
thf(1247,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: b,E: b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(213,axiom,
! [A: b,B: set_b,C: b,D: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_b] :
( ( B
= ( insert_b @ C @ E ) )
& ~ ( member_b @ C @ E )
& ( D
= ( insert_b @ A @ E ) )
& ~ ( member_b @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_insert__eq__iff) ).
thf(1013,plain,
! [A: b,B: set_b,C: b,D: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_b] :
( ( B
= ( insert_b @ C @ E ) )
& ~ ( member_b @ C @ E )
& ( D
= ( insert_b @ A @ E ) )
& ~ ( member_b @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(8,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( ( insert2037698781od_b_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__absorb) ).
thf(325,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( ( insert2037698781od_b_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(201,axiom,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_in__mono) ).
thf(969,plain,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(95,axiom,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b > $o] :
( ( member1516365892od_b_b @ A @ ( collec279084418od_b_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_mem__Collect__eq) ).
thf(606,plain,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b > $o] :
( ( member1516365892od_b_b @ A @ ( collec279084418od_b_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(90,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( insert1574423351_a_nat @ A @ ( insert1574423351_a_nat @ A @ B ) )
= ( insert1574423351_a_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_insert__absorb2) ).
thf(591,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( insert1574423351_a_nat @ A @ ( insert1574423351_a_nat @ A @ B ) )
= ( insert1574423351_a_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(43,axiom,
! [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_singletonI) ).
thf(443,plain,
! [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(255,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: b,D: set_Pr1906739389_b_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_1764625405_b_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_rev__ImageI) ).
thf(1136,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: b,D: set_Pr1906739389_b_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_1764625405_b_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(66,axiom,
! [A: produc1871334759_a_nat] : ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_singletonI) ).
thf(514,plain,
! [A: produc1871334759_a_nat] : ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(260,axiom,
! [A: product_prod_b_b,B: b,C: set_Pr357419743_b_b_b,D: set_Product_prod_b_b] :
( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ B ) @ C )
=> ( ( member1285940496od_b_b @ A @ D )
=> ( member_b @ B @ ( image_921732011_b_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_ImageI) ).
thf(1151,plain,
! [A: product_prod_b_b,B: b,C: set_Pr357419743_b_b_b,D: set_Product_prod_b_b] :
( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ B ) @ C )
=> ( ( member1285940496od_b_b @ A @ D )
=> ( member_b @ B @ ( image_921732011_b_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(215,axiom,
! [A: b,B: b,C: set_b] :
( ( A = B )
=> ( ( member_b @ A @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( id_on_b @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Id__on__eqI) ).
thf(1020,plain,
! [A: b,B: b,C: set_b] :
( ( A = B )
=> ( ( member_b @ A @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( id_on_b @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(154,axiom,
( ord_le123089219od_b_b
= ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_subset__iff) ).
thf(806,plain,
( ord_le123089219od_b_b
= ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(272,axiom,
! [A: produc1871334759_a_nat] :
( ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ ( standa63370785tant_a @ standard_S_Idt_a ) @ ( insert1574423351_a_nat @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ ( insert1574423351_a_nat @ ( standa997693288tant_a @ standard_S_Idt_a ) @ bot_bo1836341171_a_nat ) ) ) )
=> ( mainta1604381365_nat_b @ A @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_ma) ).
thf(1183,plain,
! [A: produc1871334759_a_nat] :
( ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ ( standa63370785tant_a @ standard_S_Idt_a ) @ ( insert1574423351_a_nat @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ ( insert1574423351_a_nat @ ( standa997693288tant_a @ standard_S_Idt_a ) @ bot_bo1836341171_a_nat ) ) ) )
=> ( mainta1604381365_nat_b @ A @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(54,axiom,
! [A: set_Pr1324126435od_b_b] :
( ( ? [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
= ( A != bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_ex__in__conv) ).
thf(480,plain,
! [A: set_Pr1324126435od_b_b] :
( ( ? [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
= ( A != bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(245,axiom,
! [A: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ ( restri446606278nt_a_b @ A ) @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
= ( A
= ( restri446606278nt_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_subgraph__restrict) ).
thf(1109,plain,
! [A: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ ( restri446606278nt_a_b @ A ) @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
= ( A
= ( restri446606278nt_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(7,axiom,
! [A: set_Pr1324126435od_b_b] :
( ! [B: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ B @ A )
=> ( A = bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_equals0I) ).
thf(321,plain,
! [A: set_Pr1324126435od_b_b] :
( ! [B: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ B @ A )
=> ( A = bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(119,axiom,
! [A: set_b] :
( ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A )
= ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_graph__empty__e) ).
thf(687,plain,
! [A: set_b] :
( ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A )
= ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(104,axiom,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( ! [B: b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Collect__empty__eq) ).
thf(634,plain,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( ! [B: b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(248,axiom,
refl_on_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_local_Orefl) ).
thf(1119,plain,
refl_on_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(33,axiom,
! [A: set_Product_prod_b_b] :
( ! [B: product_prod_b_b] :
~ ( member1285940496od_b_b @ B @ A )
=> ( A = bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_equals0I) ).
thf(411,plain,
! [A: set_Product_prod_b_b] :
( ! [B: product_prod_b_b] :
~ ( member1285940496od_b_b @ B @ A )
=> ( A = bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(233,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: b,E: b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ ( relcomp_b_b_b @ C @ ( id_on_b @ ( labele1424214014nt_a_b @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Id__on__vertices__identity_I2_J) ).
thf(1074,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: b,E: b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ ( relcomp_b_b_b @ C @ ( id_on_b @ ( labele1424214014nt_a_b @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(191,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ ( restri446606278nt_a_b @ A ) ) @ ( labele1741081071nt_a_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_subgraph__subset_I2_J) ).
thf(942,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ ( restri446606278nt_a_b @ A ) ) @ ( labele1741081071nt_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(111,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_prod_Oinject) ).
thf(661,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(186,axiom,
! [A: b,B: b,C: set_b,D: b > b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( bNF_Gr_b_b @ C @ D ) )
=> ( ( D @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_GrD2) ).
thf(925,plain,
! [A: b,B: b,C: set_b,D: b > b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( bNF_Gr_b_b @ C @ D ) )
=> ( ( D @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(25,axiom,
! [A: set_Pr1324126435od_b_b] :
( ( ! [B: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ B @ A ) )
= ( A = bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_all__not__in__conv) ).
thf(381,plain,
! [A: set_Pr1324126435od_b_b] :
( ( ! [B: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ B @ A ) )
= ( A = bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(230,axiom,
! [A: set_Pr1324126435od_b_b,B: set_b] :
( ( labele1424214014nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_labeled__graph_Osel_I2_J) ).
thf(1067,plain,
! [A: set_Pr1324126435od_b_b,B: set_b] :
( ( labele1424214014nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(265,axiom,
! [A: b,B: b,C: standard_Constant_a,D: labele1159362096nt_a_b,E: b > b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ D ) )
=> ( ( member_b @ A @ ( labele1424214014nt_a_b @ D ) )
=> ( ( member_b @ B @ ( labele1424214014nt_a_b @ D ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ ( E @ A ) @ ( E @ B ) ) @ ( getRel904497637nt_a_b @ C @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ D ) @ E ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_getRel__hom) ).
thf(1163,plain,
! [A: b,B: b,C: standard_Constant_a,D: labele1159362096nt_a_b,E: b > b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ D ) )
=> ( ( member_b @ A @ ( labele1424214014nt_a_b @ D ) )
=> ( ( member_b @ B @ ( labele1424214014nt_a_b @ D ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ ( E @ A ) @ ( E @ B ) ) @ ( getRel904497637nt_a_b @ C @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ D ) @ E ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(280,axiom,
! [A: labele1159362096nt_a_b,B: b,C: b,D: allego510293162tant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( semant55076487nt_a_b @ A @ D ) )
=> ( member_b @ C @ ( labele1424214014nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_semantics__in__vertices_I2_J) ).
thf(1206,plain,
! [A: labele1159362096nt_a_b,B: b,C: b,D: allego510293162tant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( semant55076487nt_a_b @ A @ D ) )
=> ( member_b @ C @ ( labele1424214014nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(46,axiom,
! [A: product_prod_b_b] :
~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_empty__iff) ).
thf(452,plain,
! [A: product_prod_b_b] :
~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(76,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( relcomp_b_b_b @ C @ D ) )
=> ~ ! [E: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ E ) @ C )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_relcomp_Ocases) ).
thf(546,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( relcomp_b_b_b @ C @ D ) )
=> ~ ! [E: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ E ) @ C )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(150,axiom,
! [A: product_prod_b_b] :
? [B: b,C: b] :
( A
= ( product_Pair_b_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_surj__pair) ).
thf(793,plain,
! [A: product_prod_b_b] :
? [B: b,C: b] :
( A
= ( product_Pair_b_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(182,axiom,
! [A: b,B: b,C: standard_Constant_a,D: labele1159362096nt_a_b,E: b,F: set_Product_prod_b_b,G: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ D ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ E ) @ F )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ G ) @ F )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ G ) @ ( getRel904497637nt_a_b @ C @ ( map_gr926947118tant_a @ F @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_getRel__homR) ).
thf(910,plain,
! [A: b,B: b,C: standard_Constant_a,D: labele1159362096nt_a_b,E: b,F: set_Product_prod_b_b,G: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ D ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ E ) @ F )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ G ) @ F )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ G ) @ ( getRel904497637nt_a_b @ C @ ( map_gr926947118tant_a @ F @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(136,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ B )
=> ( ( insert1574423351_a_nat @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_insert__absorb) ).
thf(746,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ B )
=> ( ( insert1574423351_a_nat @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(145,axiom,
! [A: produc1871334759_a_nat] :
~ ( member832397200_a_nat @ A @ bot_bo1836341171_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_empty__iff) ).
thf(778,plain,
! [A: produc1871334759_a_nat] :
~ ( member832397200_a_nat @ A @ bot_bo1836341171_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(221,axiom,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_ImageE) ).
thf(1042,plain,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(269,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( ( graph_1309249505nt_a_b @ A @ B )
= B )
= ( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1741081071nt_a_b @ B ) )
& ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ A ) @ ( labele1424214014nt_a_b @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_graph__union__iff) ).
thf(1174,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( ( graph_1309249505nt_a_b @ A @ B )
= B )
= ( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1741081071nt_a_b @ B ) )
& ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ A ) @ ( labele1424214014nt_a_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(159,axiom,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Image__singleton__iff) ).
thf(820,plain,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(121,axiom,
! [A: set_Product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b,D: b,E: b,F: b,G: b,H: standard_Constant_a] :
( ( edge_p1384198690tant_a @ A @ B @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ A )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ F @ G ) @ A )
=> ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ H @ ( product_Pair_b_b @ D @ F ) ) @ B )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ H @ ( product_Pair_b_b @ E @ G ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_edge__preserving__atomic) ).
thf(693,plain,
! [A: set_Product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b,D: b,E: b,F: b,G: b,H: standard_Constant_a] :
( ( edge_p1384198690tant_a @ A @ B @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ A )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ F @ G ) @ A )
=> ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ H @ ( product_Pair_b_b @ D @ F ) ) @ B )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ H @ ( product_Pair_b_b @ E @ G ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(39,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_in__mono) ).
thf(429,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(284,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( ( ( labele1741081071nt_a_b @ A )
= ( labele1741081071nt_a_b @ B ) )
& ( ( labele1424214014nt_a_b @ A )
= ( labele1424214014nt_a_b @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_labeled__graph_Oexpand) ).
thf(1223,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( ( ( labele1741081071nt_a_b @ A )
= ( labele1741081071nt_a_b @ B ) )
& ( ( labele1424214014nt_a_b @ A )
= ( labele1424214014nt_a_b @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(178,axiom,
! [A: labele1159362096nt_a_b,B: set_Pr812188767_nat_b] :
( ( graph_726202286_nat_b @ ( labele27098724_a_nat @ bot_bo1653310327_a_nat @ bot_bo1836341171_a_nat ) @ A @ B )
= ( ( B = bot_bo1113554635_nat_b )
& ( A
= ( restri446606278nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_graph__homomorphism__empty) ).
thf(894,plain,
! [A: labele1159362096nt_a_b,B: set_Pr812188767_nat_b] :
( ( graph_726202286_nat_b @ ( labele27098724_a_nat @ bot_bo1653310327_a_nat @ bot_bo1836341171_a_nat ) @ A @ B )
= ( ( B = bot_bo1113554635_nat_b )
& ( A
= ( restri446606278nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(250,axiom,
! [A: produc1871334759_a_nat] :
( ( member832397200_a_nat @ A @ ( standa1568205540ules_a @ l ) )
=> ( mainta1604381365_nat_b @ A @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_assms_I2_J) ).
thf(1123,plain,
! [A: produc1871334759_a_nat] :
( ( member832397200_a_nat @ A @ ( standa1568205540ules_a @ l ) )
=> ( mainta1604381365_nat_b @ A @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(170,axiom,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: set_Pr1987088711_a_nat] :
( ( insert1574423351_a_nat @ A @ ( insert1574423351_a_nat @ B @ C ) )
= ( insert1574423351_a_nat @ B @ ( insert1574423351_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_insert__commute) ).
thf(862,plain,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: set_Pr1987088711_a_nat] :
( ( insert1574423351_a_nat @ A @ ( insert1574423351_a_nat @ B @ C ) )
= ( insert1574423351_a_nat @ B @ ( insert1574423351_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(81,axiom,
! [A: set_Pr924198087_a_nat] :
( ( image_1168831379_a_nat @ A @ bot_bo1836341171_a_nat )
= bot_bo1836341171_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Image__empty2) ).
thf(566,plain,
! [A: set_Pr924198087_a_nat] :
( ( image_1168831379_a_nat @ A @ bot_bo1836341171_a_nat )
= bot_bo1836341171_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(17,axiom,
! [A: set_Pr1987088711_a_nat] :
( ( ord_le1718765799_a_nat @ A @ bot_bo1836341171_a_nat )
= ( A = bot_bo1836341171_a_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_subset__empty) ).
thf(361,plain,
! [A: set_Pr1987088711_a_nat] :
( ( ord_le1718765799_a_nat @ A @ bot_bo1836341171_a_nat )
= ( A = bot_bo1836341171_a_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(139,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: labele1159362096nt_a_b,E: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( graph_222606102_a_b_b @ B @ D @ E )
=> ( graph_222606102_a_b_b @ A @ D @ ( relcomp_b_b_b @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_graph__homomorphism__composes) ).
thf(757,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: labele1159362096nt_a_b,E: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( graph_222606102_a_b_b @ B @ D @ E )
=> ( graph_222606102_a_b_b @ A @ D @ ( relcomp_b_b_b @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(276,axiom,
! [A: labele1159362096nt_a_b] :
( ( labele1424214014nt_a_b @ ( restri446606278nt_a_b @ A ) )
= ( labele1424214014nt_a_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_vertices__restrict) ).
thf(1195,plain,
! [A: labele1159362096nt_a_b] :
( ( labele1424214014nt_a_b @ ( restri446606278nt_a_b @ A ) )
= ( labele1424214014nt_a_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(252,axiom,
! [A: labele1159362096nt_a_b] :
( ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_labeled__graph_Ocollapse) ).
thf(1128,plain,
! [A: labele1159362096nt_a_b] :
( ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(126,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_old_Oprod_Oinject) ).
thf(710,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(164,axiom,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ B @ C ) )
=> ( ( A != B )
=> ( member832397200_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_insertE) ).
thf(842,plain,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ B @ C ) )
=> ( ( A != B )
=> ( member832397200_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(203,axiom,
! [A: set_b,B: b] :
( ( A = bot_bot_set_b )
=> ~ ( member_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_equals0D) ).
thf(974,plain,
! [A: set_b,B: b] :
( ( A = bot_bot_set_b )
=> ~ ( member_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(69,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ord_le123089219od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_subsetD) ).
thf(522,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ord_le123089219od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(162,axiom,
! [A: b] : ( refl_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_refl__on__singleton) ).
thf(830,plain,
! [A: b] : ( refl_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(263,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: b,D: set_Pr357419743_b_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_921732011_b_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_rev__ImageI) ).
thf(1159,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: b,D: set_Pr357419743_b_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_921732011_b_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(49,axiom,
! [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_singletonI) ).
thf(461,plain,
! [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(58,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] : ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_insertI1) ).
thf(493,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] : ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(281,axiom,
! [A: labele1159362096nt_a_b,B: b > b,C: b > b] :
( ! [D: b] :
( ( member_b @ D @ ( labele1424214014nt_a_b @ A ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ A )
= ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_map__graph__fn__eqI) ).
thf(1210,plain,
! [A: labele1159362096nt_a_b,B: b > b,C: b > b] :
( ! [D: b] :
( ( member_b @ D @ ( labele1424214014nt_a_b @ A ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ A )
= ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(174,axiom,
! [A: labele1159362096nt_a_b,B: set_Product_prod_b_b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( map_gr926947118tant_a @ B @ A )
= ( restri446606278nt_a_b @ ( map_gr926947118tant_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_map__graph__preserves__restricted) ).
thf(874,plain,
! [A: labele1159362096nt_a_b,B: set_Product_prod_b_b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( map_gr926947118tant_a @ B @ A )
= ( restri446606278nt_a_b @ ( map_gr926947118tant_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(299,axiom,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
= ( p @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_r1) ).
thf(1270,plain,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
= ( p @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(194,axiom,
! [A: set_Product_prod_b_b,B: labele1159362096nt_a_b] :
( ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ A @ B ) )
= ( image_b_b @ A @ ( labele1424214014nt_a_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_map__graph__selectors_I1_J) ).
thf(948,plain,
! [A: set_Product_prod_b_b,B: labele1159362096nt_a_b] :
( ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ A @ B ) )
= ( image_b_b @ A @ ( labele1424214014nt_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(214,axiom,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_empty__iff) ).
thf(1017,plain,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(27,axiom,
! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b] :
( ( A = bot_bo1664927607od_b_b )
=> ~ ( member1516365892od_b_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_equals0D) ).
thf(388,plain,
! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b] :
( ( A = bot_bo1664927607od_b_b )
=> ~ ( member1516365892od_b_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [A: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_emptyE) ).
thf(420,plain,
! [A: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(68,axiom,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ B @ C ) )
= ( ( A = B )
| ( member832397200_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_insert__iff) ).
thf(519,plain,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ B @ C ) )
= ( ( A = B )
| ( member832397200_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(135,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( B
= ( restri446606278nt_a_b @ B ) )
=> ( ( graph_1309249505nt_a_b @ A @ B )
= ( restri446606278nt_a_b @ ( graph_1309249505nt_a_b @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_graph__union__preserves__restrict) ).
thf(742,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( B
= ( restri446606278nt_a_b @ B ) )
=> ( ( graph_1309249505nt_a_b @ A @ B )
= ( restri446606278nt_a_b @ ( graph_1309249505nt_a_b @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(238,axiom,
! [A: set_b] :
( ( ? [B: b] : ( member_b @ B @ A ) )
= ( A != bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_ex__in__conv) ).
thf(1089,plain,
! [A: set_b] :
( ( ? [B: b] : ( member_b @ B @ A ) )
= ( A != bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(287,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b] :
( ( refl_on_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_refl__onD) ).
thf(1234,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b] :
( ( refl_on_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(9,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ~ ! [C: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ A @ C ) )
=> ( member1285940496od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_Set_Oset__insert) ).
thf(328,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ~ ! [C: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ A @ C ) )
=> ( member1285940496od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(217,axiom,
! [A: b,B: b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ standard_S_Idt_a @ ( product_Pair_b_b @ A @ B ) ) @ ( labele1741081071nt_a_b @ g ) )
=> ( ( hilbert_Eps_b @ ( p @ A ) )
= ( hilbert_Eps_b @ ( p @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_idt__eq) ).
thf(1028,plain,
! [A: b,B: b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ standard_S_Idt_a @ ( product_Pair_b_b @ A @ B ) ) @ ( labele1741081071nt_a_b @ g ) )
=> ( ( hilbert_Eps_b @ ( p @ A ) )
= ( hilbert_Eps_b @ ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(180,axiom,
! [A: set_b] :
( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
= ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_subset__empty) ).
thf(901,plain,
! [A: set_b] :
( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
= ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(105,axiom,
! [A: labele1835558936od_b_b,B: product_prod_b_b > b,C: set_Pr1324126435od_b_b] :
( ! [D: standard_Constant_a,E: product_prod_b_b,F: product_prod_b_b] :
( ( member1744485444od_b_b @ ( produc618266719od_b_b @ D @ ( produc546497367od_b_b @ E @ F ) ) @ ( labele372159959od_b_b @ A ) )
=> ( ( member1285940496od_b_b @ E @ ( labele442485990od_b_b @ A ) )
=> ( ( member1285940496od_b_b @ F @ ( labele442485990od_b_b @ A ) )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ ( product_Pair_b_b @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
=> ( edge_p1969196346tant_a @ ( bNF_Gr521784954_b_b_b @ ( labele442485990od_b_b @ A ) @ B ) @ ( labele372159959od_b_b @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_edge__preserving__on__graphI) ).
thf(637,plain,
! [A: labele1835558936od_b_b,B: product_prod_b_b > b,C: set_Pr1324126435od_b_b] :
( ! [D: standard_Constant_a,E: product_prod_b_b,F: product_prod_b_b] :
( ( member1744485444od_b_b @ ( produc618266719od_b_b @ D @ ( produc546497367od_b_b @ E @ F ) ) @ ( labele372159959od_b_b @ A ) )
=> ( ( member1285940496od_b_b @ E @ ( labele442485990od_b_b @ A ) )
=> ( ( member1285940496od_b_b @ F @ ( labele442485990od_b_b @ A ) )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ ( product_Pair_b_b @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
=> ( edge_p1969196346tant_a @ ( bNF_Gr521784954_b_b_b @ ( labele442485990od_b_b @ A ) @ B ) @ ( labele372159959od_b_b @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(89,axiom,
refl_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_refl__on__empty) ).
thf(590,plain,
refl_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(220,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( member_b @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_refl__onD1) ).
thf(1039,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( member_b @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(306,axiom,
! [A: b,B: b,C: set_b,D: b > b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( bNF_Gr_b_b @ C @ D ) )
= ( ( member_b @ A @ C )
& ( ( D @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_in__Gr) ).
thf(1292,plain,
! [A: b,B: b,C: set_b,D: b > b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( bNF_Gr_b_b @ C @ D ) )
= ( ( member_b @ A @ C )
& ( ( D @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(188,axiom,
! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_singletonI) ).
thf(933,plain,
! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(28,axiom,
! [A: set_Pr1987088711_a_nat] : ( ord_le1718765799_a_nat @ bot_bo1836341171_a_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_empty__subsetI) ).
thf(393,plain,
! [A: set_Pr1987088711_a_nat] : ( ord_le1718765799_a_nat @ bot_bo1836341171_a_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(123,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ! [C: b,D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) )
=> ( ord_le1036320359od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subrelI) ).
thf(701,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ! [C: b,D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) )
=> ( ord_le1036320359od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(275,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: b > b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( graph_222606102_a_b_b @ A @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ D ) @ B ) @ ( relcomp_b_b_b @ C @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_graph__homomorphism__on__graph) ).
thf(1192,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: b > b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( graph_222606102_a_b_b @ A @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ D ) @ B ) @ ( relcomp_b_b_b @ C @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(130,axiom,
! [A: labele1644675410od_b_b,B: produc1213276845od_b_b > b,C: set_Pr1324126435od_b_b] :
( ! [D: standard_Constant_a,E: produc1213276845od_b_b,F: produc1213276845od_b_b] :
( ( member147868824od_b_b @ ( produc1788032435od_b_b @ D @ ( produc449289715od_b_b @ E @ F ) ) @ ( labele2032816061od_b_b @ A ) )
=> ( ( member1516365892od_b_b @ E @ ( labele595103470od_b_b @ A ) )
=> ( ( member1516365892od_b_b @ F @ ( labele595103470od_b_b @ A ) )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ ( product_Pair_b_b @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
=> ( edge_p1817988046tant_a @ ( bNF_Gr492676974_b_b_b @ ( labele595103470od_b_b @ A ) @ B ) @ ( labele2032816061od_b_b @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_edge__preserving__on__graphI) ).
thf(721,plain,
! [A: labele1644675410od_b_b,B: produc1213276845od_b_b > b,C: set_Pr1324126435od_b_b] :
( ! [D: standard_Constant_a,E: produc1213276845od_b_b,F: produc1213276845od_b_b] :
( ( member147868824od_b_b @ ( produc1788032435od_b_b @ D @ ( produc449289715od_b_b @ E @ F ) ) @ ( labele2032816061od_b_b @ A ) )
=> ( ( member1516365892od_b_b @ E @ ( labele595103470od_b_b @ A ) )
=> ( ( member1516365892od_b_b @ F @ ( labele595103470od_b_b @ A ) )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ ( product_Pair_b_b @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
=> ( edge_p1817988046tant_a @ ( bNF_Gr492676974_b_b_b @ ( labele595103470od_b_b @ A ) @ B ) @ ( labele2032816061od_b_b @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(210,axiom,
! [A: b,B: set_b,C: b] :
( ( ~ ( member_b @ A @ B )
=> ( A = C ) )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_insertCI) ).
thf(1002,plain,
! [A: b,B: set_b,C: b] :
( ( ~ ( member_b @ A @ B )
=> ( A = C ) )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(82,axiom,
! [A: set_Product_prod_b_b] :
( ( image_b_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Image__empty2) ).
thf(569,plain,
! [A: set_Product_prod_b_b] :
( ( image_b_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(62,axiom,
! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_empty__subsetI) ).
thf(503,plain,
! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(107,axiom,
! [A: set_Pr1987088711_a_nat] :
( ! [B: produc1871334759_a_nat] :
~ ( member832397200_a_nat @ B @ A )
=> ( A = bot_bo1836341171_a_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_equals0I) ).
thf(647,plain,
! [A: set_Pr1987088711_a_nat] :
( ! [B: produc1871334759_a_nat] :
~ ( member832397200_a_nat @ B @ A )
=> ( A = bot_bo1836341171_a_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(296,axiom,
( ( graph_1309249505nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) @ g )
= g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__092_060open_062graph__union_A_Imap__graph__fn_AG_Af_J_AG_A_061_AG_092_060close_062) ).
thf(1263,plain,
( ( graph_1309249505nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) @ g )
= g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(241,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ ( graph_1309249505nt_a_b @ A @ B ) @ C @ D )
=> ( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( graph_222606102_a_b_b @ A @ C @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_graph__homo__union__id_I1_J) ).
thf(1099,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ ( graph_1309249505nt_a_b @ A @ B ) @ C @ D )
=> ( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( graph_222606102_a_b_b @ A @ C @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(205,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ~ ! [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_Set_Oset__insert) ).
thf(985,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ~ ! [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(253,axiom,
! [A: b,B: b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
=> ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
@ ^ [D: b] : ( image_b_b @ ( getRel904497637nt_a_b @ C @ g ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_congr_I1_J) ).
thf(1131,plain,
! [A: b,B: b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
=> ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
@ ^ [D: b] : ( image_b_b @ ( getRel904497637nt_a_b @ C @ g ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(109,axiom,
! [A: set_b] :
( ( image_b_b @ bot_bo1343651123od_b_b @ A )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Image__empty1) ).
thf(654,plain,
! [A: set_b] :
( ( image_b_b @ bot_bo1343651123od_b_b @ A )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(237,axiom,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_emptyE) ).
thf(1086,plain,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(64,axiom,
! [A: set_Pr1324126435od_b_b,B: set_b] :
( ( labele1741081071nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_labeled__graph_Osel_I1_J) ).
thf(508,plain,
! [A: set_Pr1324126435od_b_b,B: set_b] :
( ( labele1741081071nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(110,axiom,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
=> ~ ! [D: standard_Constant_a] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B )
=> ~ ( member1632892294tant_a @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_ImageE) ).
thf(657,plain,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
=> ~ ! [D: standard_Constant_a] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B )
=> ~ ( member1632892294tant_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(141,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b,D: b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( equiv_equiv_b @ C @ A )
=> ( ( equiv_equiv_b @ C @ B )
=> ( ( image_b_b @ B @ ( image_b_b @ A @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_refines__equiv__class__eq2) ).
thf(765,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b,D: b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( equiv_equiv_b @ C @ A )
=> ( ( equiv_equiv_b @ C @ B )
=> ( ( image_b_b @ B @ ( image_b_b @ A @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(196,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ A ) @ ( labele1424214014nt_a_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_subgraph__subset_I1_J) ).
thf(953,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ A ) @ ( labele1424214014nt_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(273,axiom,
! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
=> ( member_b @ B @ ( labele1424214014nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_getRel__dom_I1_J) ).
thf(1185,plain,
! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
=> ( member_b @ B @ ( labele1424214014nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(129,axiom,
! [A: set_Pr812188767_nat_b] :
( ( image_924992811_nat_b @ A @ bot_bo1836341171_a_nat )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Image__empty2) ).
thf(718,plain,
! [A: set_Pr812188767_nat_b] :
( ( image_924992811_nat_b @ A @ bot_bo1836341171_a_nat )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(176,axiom,
! [A: labele1159362096nt_a_b] :
( ( restri446606278nt_a_b @ ( restri446606278nt_a_b @ A ) )
= ( restri446606278nt_a_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_restrict__idemp) ).
thf(888,plain,
! [A: labele1159362096nt_a_b] :
( ( restri446606278nt_a_b @ ( restri446606278nt_a_b @ A ) )
= ( restri446606278nt_a_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(99,axiom,
! [A: set_la1083530965_a_nat] :
( ( image_1971191571_a_nat @ bot_bo1836341171_a_nat @ A )
= bot_bo2122869057_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Image__empty1) ).
thf(618,plain,
! [A: set_la1083530965_a_nat] :
( ( image_1971191571_a_nat @ bot_bo1836341171_a_nat @ A )
= bot_bo2122869057_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(258,axiom,
! [A: b] :
( ( member_b @ ( f @ A ) @ ( labele1424214014nt_a_b @ g ) )
=> ( member_b @ A @ ( labele1424214014nt_a_b @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).
thf(1146,plain,
! [A: b] :
( ( member_b @ ( f @ A ) @ ( labele1424214014nt_a_b @ g ) )
=> ( member_b @ A @ ( labele1424214014nt_a_b @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(283,axiom,
! [A: labele1159362096nt_a_b,B: b,C: b,D: allego510293162tant_a,E: b > b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( semant55076487nt_a_b @ A @ D ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ ( E @ B ) @ ( E @ C ) ) @ ( semant55076487nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ E ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_map__graph__in) ).
thf(1219,plain,
! [A: labele1159362096nt_a_b,B: b,C: b,D: allego510293162tant_a,E: b > b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( semant55076487nt_a_b @ A @ D ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ ( E @ B ) @ ( E @ C ) ) @ ( semant55076487nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ E ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(300,axiom,
! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: set_b] :
( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member599505522od_b_b @ ( produc800495189od_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_ImageE) ).
thf(1273,plain,
! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: set_b] :
( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member599505522od_b_b @ ( produc800495189od_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(168,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( relcomp_b_b_b @ C @ D ) )
= ( ? [E: b,F: b,G: b] :
( ( A = E )
& ( B = G )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ F ) @ C )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ F @ G ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_relcomp_Osimps) ).
thf(856,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( relcomp_b_b_b @ C @ D ) )
= ( ? [E: b,F: b,G: b] :
( ( A = E )
& ( B = G )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ F ) @ C )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ F @ G ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(22,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_insertI1) ).
thf(375,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,axiom,
! [A: produc1871334759_a_nat > $o] :
( ( bot_bo1836341171_a_nat
= ( collec357096914_a_nat @ A ) )
= ( ! [B: produc1871334759_a_nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_empty__Collect__eq) ).
thf(601,plain,
! [A: produc1871334759_a_nat > $o] :
( ( bot_bo1836341171_a_nat
= ( collec357096914_a_nat @ A ) )
= ( ! [B: produc1871334759_a_nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(261,axiom,
! [A: standard_Constant_a,B: b,C: b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ ( labele1741081071nt_a_b @ g ) )
=> ( ( member_b @ B @ ( labele1424214014nt_a_b @ g ) )
=> ( ( member_b @ C @ ( labele1424214014nt_a_b @ g ) )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ ( f @ B ) @ ( f @ C ) ) ) @ ( labele1741081071nt_a_b @ g ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_gu1) ).
thf(1154,plain,
! [A: standard_Constant_a,B: b,C: b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ ( labele1741081071nt_a_b @ g ) )
=> ( ( member_b @ B @ ( labele1424214014nt_a_b @ g ) )
=> ( ( member_b @ C @ ( labele1424214014nt_a_b @ g ) )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ ( f @ B ) @ ( f @ C ) ) ) @ ( labele1741081071nt_a_b @ g ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(181,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_Product_prod_b_b,E: b > b > $o] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( relcomp_b_b_b @ C @ D ) )
=> ( ! [F: b,G: b,H: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ F @ G ) @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ G @ H ) @ D )
=> ( E @ F @ H ) ) )
=> ( E @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_relcomp_Oinducts) ).
thf(904,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_Product_prod_b_b,E: b > b > $o] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( relcomp_b_b_b @ C @ D ) )
=> ( ! [F: b,G: b,H: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ F @ G ) @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ G @ H ) @ D )
=> ( E @ F @ H ) ) )
=> ( E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(37,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_St761939237tant_a,D: standard_Constant_a > product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ ( bNF_Gr1272216980od_b_b @ C @ D ) )
=> ( member1632892294tant_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_GrD1) ).
thf(423,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_St761939237tant_a,D: standard_Constant_a > product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ ( bNF_Gr1272216980od_b_b @ C @ D ) )
=> ( member1632892294tant_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(133,axiom,
! [A: b,B: set_b] :
( ( insert_b @ A @ B )
!= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_insert__not__empty) ).
thf(732,plain,
! [A: b,B: set_b] :
( ( insert_b @ A @ B )
!= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(251,axiom,
! [A: b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
!= bot_bot_set_b )
=> ( ( hilbert_Eps_b @ ( p @ ( hilbert_Eps_b @ ( p @ A ) ) ) )
= ( hilbert_Eps_b @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_P__eq) ).
thf(1125,plain,
! [A: b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
!= bot_bot_set_b )
=> ( ( hilbert_Eps_b @ ( p @ ( hilbert_Eps_b @ ( p @ A ) ) ) )
= ( hilbert_Eps_b @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(143,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( relcomp_b_b_b @ C @ D ) )
=> ~ ! [E: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ E ) @ C )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_relcompEpair) ).
thf(772,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( relcomp_b_b_b @ C @ D ) )
=> ~ ! [E: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ E ) @ C )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(85,axiom,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: set_Pr1987088711_a_nat] :
( ( ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat )
= ( insert1574423351_a_nat @ B @ C ) )
= ( ( B = A )
& ( ord_le1718765799_a_nat @ C @ ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_singleton__insert__inj__eq) ).
thf(579,plain,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,C: set_Pr1987088711_a_nat] :
( ( ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat )
= ( insert1574423351_a_nat @ B @ C ) )
= ( ( B = A )
& ( ord_le1718765799_a_nat @ C @ ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(198,axiom,
! [A: b,B: set_b,C: produc1213276845od_b_b,D: set_Pr2060523537od_b_b] :
( ( member_b @ A @ B )
=> ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ C ) @ D )
=> ( member1516365892od_b_b @ C @ ( image_984343321od_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_rev__ImageI) ).
thf(958,plain,
! [A: b,B: set_b,C: produc1213276845od_b_b,D: set_Pr2060523537od_b_b] :
( ( member_b @ A @ B )
=> ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ C ) @ D )
=> ( member1516365892od_b_b @ C @ ( image_984343321od_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(285,axiom,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
= ( ? [D: b] :
( ( member_b @ D @ C )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Image__iff) ).
thf(1226,plain,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
= ( ? [D: b] :
( ( member_b @ D @ C )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(256,axiom,
( ( getRel904497637nt_a_b @ standard_S_Idt_a @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) )
= ( image_1683732397od_b_b
@ ^ [A: b] : ( product_Pair_b_b @ A @ A )
@ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_ident) ).
thf(1139,plain,
( ( getRel904497637nt_a_b @ standard_S_Idt_a @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) )
= ( image_1683732397od_b_b
@ ^ [A: b] : ( product_Pair_b_b @ A @ A )
@ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(44,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b,D: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ~ ( member1285940496od_b_b @ C @ D )
=> ( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ C @ E ) )
& ~ ( member1285940496od_b_b @ C @ E )
& ( D
= ( insert1952693431od_b_b @ A @ E ) )
& ~ ( member1285940496od_b_b @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_insert__eq__iff) ).
thf(445,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b,D: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ~ ( member1285940496od_b_b @ C @ D )
=> ( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ C @ E ) )
& ~ ( member1285940496od_b_b @ C @ E )
& ( D
= ( insert1952693431od_b_b @ A @ E ) )
& ~ ( member1285940496od_b_b @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(83,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: product_prod_b_b,D: set_Pr1324126435od_b_b] :
( ( member1632892294tant_a @ A @ B )
=> ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ C ) @ D )
=> ( member1285940496od_b_b @ C @ ( image_1916422435od_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_rev__ImageI) ).
thf(572,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: product_prod_b_b,D: set_Pr1324126435od_b_b] :
( ( member1632892294tant_a @ A @ B )
=> ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ C ) @ D )
=> ( member1285940496od_b_b @ C @ ( image_1916422435od_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(4,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ A ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_extensible__refl) ).
thf(313,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(148,axiom,
! [A: set_Pr1987088711_a_nat] :
( ( ? [B: produc1871334759_a_nat] : ( member832397200_a_nat @ B @ A ) )
= ( A != bot_bo1836341171_a_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_ex__in__conv) ).
thf(787,plain,
! [A: set_Pr1987088711_a_nat] :
( ( ? [B: produc1871334759_a_nat] : ( member832397200_a_nat @ B @ A ) )
= ( A != bot_bo1836341171_a_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(226,axiom,
member1516365892od_b_b @ ( produc1432590431od_b_b @ l2 @ ( product_Pair_b_b @ ( f @ x ) @ ( f @ y ) ) ) @ ( labele1741081071nt_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_a) ).
thf(1058,plain,
member1516365892od_b_b @ ( produc1432590431od_b_b @ l2 @ ( product_Pair_b_b @ ( f @ x ) @ ( f @ y ) ) ) @ ( labele1741081071nt_a_b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(239,axiom,
! [A: labele1159362096nt_a_b] :
( ( map_gr926947118tant_a @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) @ A )
= ( restri446606278nt_a_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_map__graph__fn__id_I2_J) ).
thf(1092,plain,
! [A: labele1159362096nt_a_b] :
( ( map_gr926947118tant_a @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) @ A )
= ( restri446606278nt_a_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(193,axiom,
member_b @ ( f @ y ) @ ( labele1424214014nt_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_fv_I2_J) ).
thf(947,plain,
member_b @ ( f @ y ) @ ( labele1424214014nt_a_b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(127,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_St761939237tant_a,D: standard_Constant_a > product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ ( bNF_Gr1272216980od_b_b @ C @ D ) )
=> ( ( D @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_GrD2) ).
thf(713,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_St761939237tant_a,D: standard_Constant_a > product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ ( bNF_Gr1272216980od_b_b @ C @ D ) )
=> ( ( D @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(60,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: b,E: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ D ) @ E )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ ( relcomp_b_b_b @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_relcomp_OrelcompI) ).
thf(498,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: b,E: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ D ) @ E )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ ( relcomp_b_b_b @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(117,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: set_Pr1987088711_a_nat] :
( ( ord_le1718765799_a_nat @ ( insert1574423351_a_nat @ A @ B ) @ C )
= ( ( member832397200_a_nat @ A @ C )
& ( ord_le1718765799_a_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_insert__subset) ).
thf(681,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: set_Pr1987088711_a_nat] :
( ( ord_le1718765799_a_nat @ ( insert1574423351_a_nat @ A @ B ) @ C )
= ( ( member832397200_a_nat @ A @ C )
& ( ord_le1718765799_a_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(303,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( member_b @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_refl__onD2) ).
thf(1282,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( member_b @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(147,axiom,
! [A: set_Pr1987088711_a_nat] :
( ( relcom1338300020_a_nat @ bot_bo1836341171_a_nat @ A )
= bot_bo1836341171_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_relcomp__empty1) ).
thf(784,plain,
! [A: set_Pr1987088711_a_nat] :
( ( relcom1338300020_a_nat @ bot_bo1836341171_a_nat @ A )
= bot_bo1836341171_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(134,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
( ( ~ ( member832397200_a_nat @ A @ B )
=> ( A = C ) )
=> ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insertCI) ).
thf(736,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
( ( ~ ( member832397200_a_nat @ A @ B )
=> ( A = C ) )
=> ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(6,axiom,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
= ( ( A = B )
| ( member1285940496od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_insert__iff) ).
thf(318,plain,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
= ( ( A = B )
| ( member1285940496od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(204,axiom,
! [A: labele1159362096nt_a_b,B: b > b,C: set_Pr1324126435od_b_b] :
( ! [D: standard_Constant_a,E: b,F: b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ ( product_Pair_b_b @ E @ F ) ) @ ( labele1741081071nt_a_b @ A ) )
=> ( ( member_b @ E @ ( labele1424214014nt_a_b @ A ) )
=> ( ( member_b @ F @ ( labele1424214014nt_a_b @ A ) )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ ( product_Pair_b_b @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
=> ( edge_p1384198690tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ ( labele1741081071nt_a_b @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_edge__preserving__on__graphI) ).
thf(979,plain,
! [A: labele1159362096nt_a_b,B: b > b,C: set_Pr1324126435od_b_b] :
( ! [D: standard_Constant_a,E: b,F: b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ ( product_Pair_b_b @ E @ F ) ) @ ( labele1741081071nt_a_b @ A ) )
=> ( ( member_b @ E @ ( labele1424214014nt_a_b @ A ) )
=> ( ( member_b @ F @ ( labele1424214014nt_a_b @ A ) )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ ( product_Pair_b_b @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
=> ( edge_p1384198690tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ ( labele1741081071nt_a_b @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(94,axiom,
( ord_le123089219od_b_b
= ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_subset__eq) ).
thf(604,plain,
( ord_le123089219od_b_b
= ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(23,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001tf__b_T) ).
thf(377,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(206,axiom,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ ( hilbert_Eps_b @ ( p @ A ) ) ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_vert__P) ).
thf(990,plain,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ ( hilbert_Eps_b @ ( p @ A ) ) ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(208,axiom,
! [A: b,B: set_Pr812188767_nat_b,C: produc1871334759_a_nat] :
( ( member_b @ A @ ( image_924992811_nat_b @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) )
= ( member1544800936_nat_b @ ( produc2059954415_nat_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Image__singleton__iff) ).
thf(996,plain,
! [A: b,B: set_Pr812188767_nat_b,C: produc1871334759_a_nat] :
( ( member_b @ A @ ( image_924992811_nat_b @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) )
= ( member1544800936_nat_b @ ( produc2059954415_nat_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(53,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_insertI2) ).
thf(477,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(156,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1954438265od_b_b,C: produc1871334759_a_nat] :
( ( member1516365892od_b_b @ A @ ( image_480774529od_b_b @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) )
= ( member1533761242od_b_b @ ( produc401731773od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Image__singleton__iff) ).
thf(811,plain,
! [A: produc1213276845od_b_b,B: set_Pr1954438265od_b_b,C: produc1871334759_a_nat] :
( ( member1516365892od_b_b @ A @ ( image_480774529od_b_b @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) )
= ( member1533761242od_b_b @ ( produc401731773od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(103,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
( ( member832397200_a_nat @ A @ B )
=> ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_insertI2) ).
thf(631,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
( ( member832397200_a_nat @ A @ B )
=> ( member832397200_a_nat @ A @ ( insert1574423351_a_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(19,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_subsetD) ).
thf(367,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,axiom,
! [A: labele1159362096nt_a_b] :
( ( graph_1309249505nt_a_b @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_graph__union__idemp_I1_J) ).
thf(609,plain,
! [A: labele1159362096nt_a_b] :
( ( graph_1309249505nt_a_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(91,axiom,
! [A: b,B: b] :
( ( if_b @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001tf__b_T) ).
thf(594,plain,
! [A: b,B: b] :
( ( if_b @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(100,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_1309249505nt_a_b @ A @ ( graph_1309249505nt_a_b @ B @ A ) )
= ( graph_1309249505nt_a_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_graph__union__idemp_I3_J) ).
thf(621,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( graph_1309249505nt_a_b @ A @ ( graph_1309249505nt_a_b @ B @ A ) )
= ( graph_1309249505nt_a_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(55,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: standard_Constant_a > product_prod_b_b] :
( ( bNF_Gr1272216980od_b_b @ ( insert1909710879tant_a @ A @ B ) @ C )
= ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( C @ A ) ) @ ( bNF_Gr1272216980od_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Gr__insert) ).
thf(483,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: standard_Constant_a > product_prod_b_b] :
( ( bNF_Gr1272216980od_b_b @ ( insert1909710879tant_a @ A @ B ) @ C )
= ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( C @ A ) ) @ ( bNF_Gr1272216980od_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(166,axiom,
! [A: produc1213276845od_b_b] :
? [B: standard_Constant_a,C: product_prod_b_b] :
( A
= ( produc1432590431od_b_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_surj__pair) ).
thf(848,plain,
! [A: produc1213276845od_b_b] :
? [B: standard_Constant_a,C: product_prod_b_b] :
( A
= ( produc1432590431od_b_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(200,axiom,
! [A: product_prod_b_b,B: set_b] :
( ( member1285940496od_b_b @ A @ ( id_on_b @ B ) )
=> ~ ! [C: b] :
( ( member_b @ C @ B )
=> ( A
!= ( product_Pair_b_b @ C @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Id__onE) ).
thf(964,plain,
! [A: product_prod_b_b,B: set_b] :
( ( member1285940496od_b_b @ A @ ( id_on_b @ B ) )
=> ~ ! [C: b] :
( ( member_b @ C @ B )
=> ( A
!= ( product_Pair_b_b @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(142,axiom,
! [A: set_Pr1987088711_a_nat] :
( ( ! [B: produc1871334759_a_nat] :
~ ( member832397200_a_nat @ B @ A ) )
= ( A = bot_bo1836341171_a_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_all__not__in__conv) ).
thf(769,plain,
! [A: set_Pr1987088711_a_nat] :
( ( ! [B: produc1871334759_a_nat] :
~ ( member832397200_a_nat @ B @ A ) )
= ( A = bot_bo1836341171_a_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(270,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ( graph_222606102_a_b_b @ C @ A @ D )
=> ( graph_222606102_a_b_b @ C @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_subgraph__preserves__hom) ).
thf(1177,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ( graph_222606102_a_b_b @ C @ A @ D )
=> ( graph_222606102_a_b_b @ C @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(246,axiom,
! [A: b,B: set_Pr357419743_b_b_b,C: set_Product_prod_b_b] :
( ( member_b @ A @ ( image_921732011_b_b_b @ B @ C ) )
=> ~ ! [D: product_prod_b_b] :
( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ D @ A ) @ B )
=> ~ ( member1285940496od_b_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_ImageE) ).
thf(1112,plain,
! [A: b,B: set_Pr357419743_b_b_b,C: set_Product_prod_b_b] :
( ( member_b @ A @ ( image_921732011_b_b_b @ B @ C ) )
=> ~ ! [D: product_prod_b_b] :
( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ D @ A ) @ B )
=> ~ ( member1285940496od_b_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(152,axiom,
! [A: b,B: set_b,C: b > b] :
( ( bNF_Gr_b_b @ ( insert_b @ A @ B ) @ C )
= ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ ( C @ A ) ) @ ( bNF_Gr_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Gr__insert) ).
thf(799,plain,
! [A: b,B: set_b,C: b > b] :
( ( bNF_Gr_b_b @ ( insert_b @ A @ B ) @ C )
= ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ ( C @ A ) ) @ ( bNF_Gr_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(264,axiom,
member1285940496od_b_b @ ( product_Pair_b_b @ ( f @ x ) @ ( f @ y ) ) @ ( getRel904497637nt_a_b @ l2 @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_gr) ).
thf(1162,plain,
member1285940496od_b_b @ ( product_Pair_b_b @ ( f @ x ) @ ( f @ y ) ) @ ( getRel904497637nt_a_b @ l2 @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(267,axiom,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_subset__eq) ).
thf(1171,plain,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(277,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( id_on_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Id__onI) ).
thf(1198,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( id_on_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(161,axiom,
! [A: set_Pr1987088711_a_nat] :
( ( relcom1338300020_a_nat @ A @ bot_bo1836341171_a_nat )
= bot_bo1836341171_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_relcomp__empty2) ).
thf(827,plain,
! [A: set_Pr1987088711_a_nat] :
( ( relcom1338300020_a_nat @ A @ bot_bo1836341171_a_nat )
= bot_bo1836341171_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(172,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_Pr1324126435od_b_b,D: set_St761939237tant_a] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ C )
=> ( ( member1632892294tant_a @ A @ D )
=> ( member1285940496od_b_b @ B @ ( image_1916422435od_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_ImageI) ).
thf(868,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_Pr1324126435od_b_b,D: set_St761939237tant_a] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ C )
=> ( ( member1632892294tant_a @ A @ D )
=> ( member1285940496od_b_b @ B @ ( image_1916422435od_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(47,axiom,
! [A: product_prod_b_b] :
~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_emptyE) ).
thf(455,plain,
! [A: product_prod_b_b] :
~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(80,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ( ord_le123089219od_b_b @ ( insert2037698781od_b_b @ A @ B ) @ C )
= ( ( member1516365892od_b_b @ A @ C )
& ( ord_le123089219od_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_insert__subset) ).
thf(563,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ( ord_le123089219od_b_b @ ( insert2037698781od_b_b @ A @ B ) @ C )
= ( ( member1516365892od_b_b @ A @ C )
& ( ord_le123089219od_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(292,axiom,
! [A: labele1159362096nt_a_b,B: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( mainta1604381365_nat_b @ ( standa63370785tant_a @ B ) @ A )
=> ( refl_on_b @ ( labele1424214014nt_a_b @ A ) @ ( getRel904497637nt_a_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_reflexivity__rule) ).
thf(1250,plain,
! [A: labele1159362096nt_a_b,B: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( mainta1604381365_nat_b @ ( standa63370785tant_a @ B ) @ A )
=> ( refl_on_b @ ( labele1424214014nt_a_b @ A ) @ ( getRel904497637nt_a_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(185,axiom,
! [A: set_Pr1324126435od_b_b] :
( ( collec279084418od_b_b
@ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Collect__mem__eq) ).
thf(922,plain,
! [A: set_Pr1324126435od_b_b] :
( ( collec279084418od_b_b
@ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(167,axiom,
! [A: set_Pr1987088711_a_nat,B: produc1871334759_a_nat] :
( ( A = bot_bo1836341171_a_nat )
=> ~ ( member832397200_a_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_equals0D) ).
thf(851,plain,
! [A: set_Pr1987088711_a_nat,B: produc1871334759_a_nat] :
( ( A = bot_bo1836341171_a_nat )
=> ~ ( member832397200_a_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(242,axiom,
! [A: b,B: product_prod_b_b,C: set_Pr621705391od_b_b,D: set_b] :
( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member1285940496od_b_b @ B @ ( image_1177096571od_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_ImageI) ).
thf(1102,plain,
! [A: b,B: product_prod_b_b,C: set_Pr621705391od_b_b,D: set_b] :
( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member1285940496od_b_b @ B @ ( image_1177096571od_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(63,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: labele1159362096nt_a_b,E: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( agree_221379389_a_b_b @ D @ E @ C )
=> ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ D @ A ) @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_extensibleI) ).
thf(505,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: labele1159362096nt_a_b,E: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( agree_221379389_a_b_b @ D @ E @ C )
=> ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ D @ A ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(42,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ~ ! [C: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ A @ C ) )
=> ( member1516365892od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_Set_Oset__insert) ).
thf(438,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ~ ! [C: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ A @ C ) )
=> ( member1516365892od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(219,axiom,
! [A: b,B: set_b,C: b > b,D: b] :
( ( ~ ( member_b @ A @ B )
| ( ( C @ A )
!= D ) )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ ( bNF_Gr_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Gr__not__in) ).
thf(1034,plain,
! [A: b,B: set_b,C: b > b,D: b] :
( ( ~ ( member_b @ A @ B )
| ( ( C @ A )
!= D ) )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ ( bNF_Gr_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(57,axiom,
! [A: b,B: b,C: set_b] :
( ( insert_b @ A @ ( insert_b @ B @ C ) )
= ( insert_b @ B @ ( insert_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_insert__commute) ).
thf(490,plain,
! [A: b,B: b,C: set_b] :
( ( insert_b @ A @ ( insert_b @ B @ C ) )
= ( insert_b @ B @ ( insert_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(279,axiom,
! [A: labele1159362096nt_a_b,B: b > b] :
( ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ A )
= ( restri446606278nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_map__graph__fn__graphI) ).
thf(1203,plain,
! [A: labele1159362096nt_a_b,B: b > b] :
( ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ A )
= ( restri446606278nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(192,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: b,D: b,E: allego510293162tant_a] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ ( semant55076487nt_a_b @ A @ E ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ ( semant55076487nt_a_b @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_subgraph__semantics) ).
thf(944,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: b,D: b,E: allego510293162tant_a] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ ( semant55076487nt_a_b @ A @ E ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ ( semant55076487nt_a_b @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(301,axiom,
! [A: labele1159362096nt_a_b] : ( graph_222606102_a_b_b @ ( restri446606278nt_a_b @ A ) @ ( restri446606278nt_a_b @ A ) @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_graph__homomorphism__Id) ).
thf(1277,plain,
! [A: labele1159362096nt_a_b] : ( graph_222606102_a_b_b @ ( restri446606278nt_a_b @ A ) @ ( restri446606278nt_a_b @ A ) @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(67,axiom,
! [A: produc1871334759_a_nat] :
~ ( member832397200_a_nat @ A @ bot_bo1836341171_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_emptyE) ).
thf(516,plain,
! [A: produc1871334759_a_nat] :
~ ( member832397200_a_nat @ A @ bot_bo1836341171_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(190,axiom,
! [A: b,B: b,C: set_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( id_on_b @ C ) )
= ( ( A = B )
& ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Id__on__iff) ).
thf(939,plain,
! [A: b,B: b,C: set_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( id_on_b @ C ) )
= ( ( A = B )
& ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(138,axiom,
! [A: b,B: b,C: set_b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_b @ C @ ( insert_b @ A @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_singleton__insert__inj__eq) ).
thf(754,plain,
! [A: b,B: b,C: set_b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_b @ C @ ( insert_b @ A @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(78,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( relcomp_b_b_b @ B @ C ) )
=> ~ ! [D: b,E: b,F: b] :
( ( A
= ( product_Pair_b_b @ D @ F ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ B )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ F ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_relcompE) ).
thf(553,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( relcomp_b_b_b @ B @ C ) )
=> ~ ! [D: b,E: b,F: b] :
( ( A
= ( product_Pair_b_b @ D @ F ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ B )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ F ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(223,axiom,
! [A: set_b,B: set_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) )
=> ( ord_less_eq_set_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_subsetI) ).
thf(1049,plain,
! [A: set_b,B: set_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) )
=> ( ord_less_eq_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(38,axiom,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
=> ( ( A != B )
=> ( member1516365892od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_insertE) ).
thf(426,plain,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
=> ( ( A != B )
=> ( member1516365892od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(266,axiom,
! [A: b,B: labele1159362096nt_a_b,C: b,D: standard_Constant_a,E: b > b,F: b,G: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ B ) )
=> ( ( member_b @ C @ ( labele1424214014nt_a_b @ B ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ ( getRel904497637nt_a_b @ D @ B ) )
=> ( ( ( E @ A )
= F )
=> ( ( ( E @ C )
= G )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ F @ G ) @ ( getRel904497637nt_a_b @ D @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_getRel__map__fn) ).
thf(1166,plain,
! [A: b,B: labele1159362096nt_a_b,C: b,D: standard_Constant_a,E: b > b,F: b,G: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ B ) )
=> ( ( member_b @ C @ ( labele1424214014nt_a_b @ B ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ ( getRel904497637nt_a_b @ D @ B ) )
=> ( ( ( E @ A )
= F )
=> ( ( ( E @ C )
= G )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ F @ G ) @ ( getRel904497637nt_a_b @ D @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(235,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( graph_222606102_a_b_b @ ( map_gr926947118tant_a @ C @ A ) @ ( map_gr926947118tant_a @ C @ B ) @ ( id_on_b @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_map__graph__preserves__subgraph) ).
thf(1081,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
=> ( graph_222606102_a_b_b @ ( map_gr926947118tant_a @ C @ A ) @ ( map_gr926947118tant_a @ C @ B ) @ ( id_on_b @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(137,axiom,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_prod__cases) ).
thf(749,plain,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(48,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_St761939237tant_a,D: standard_Constant_a > product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ ( bNF_Gr1272216980od_b_b @ C @ D ) )
= ( ( member1632892294tant_a @ A @ C )
& ( ( D @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_in__Gr) ).
thf(458,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_St761939237tant_a,D: standard_Constant_a > product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ ( bNF_Gr1272216980od_b_b @ C @ D ) )
= ( ( member1632892294tant_a @ A @ C )
& ( ( D @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(160,axiom,
! [A: produc1213276845od_b_b] :
~ ! [B: standard_Constant_a,C: b,D: b] :
( A
!= ( produc1432590431od_b_b @ B @ ( product_Pair_b_b @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_prod__cases3) ).
thf(823,plain,
! [A: produc1213276845od_b_b] :
~ ! [B: standard_Constant_a,C: b,D: b] :
( A
!= ( produc1432590431od_b_b @ B @ ( product_Pair_b_b @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(144,axiom,
! [A: labele935650037_a_nat,B: labele1159362096nt_a_b] : ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ A @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_maintained__refl) ).
thf(776,plain,
! [A: labele935650037_a_nat,B: labele1159362096nt_a_b] : ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ A @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(70,axiom,
! [A: b,B: b] :
( ( if_b @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001tf__b_T) ).
thf(525,plain,
! [A: b,B: b] :
( ( if_b @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(120,axiom,
! [A: b,B: set_b,C: b] :
( ( ( insert_b @ A @ B )
= ( insert_b @ C @ bot_bot_set_b ) )
= ( ( A = C )
& ( ord_less_eq_set_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_singleton__insert__inj__eq_H) ).
thf(690,plain,
! [A: b,B: set_b,C: b] :
( ( ( insert_b @ A @ B )
= ( insert_b @ C @ bot_bot_set_b ) )
= ( ( A = C )
& ( ord_less_eq_set_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(216,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_insert__absorb) ).
thf(1025,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(231,axiom,
! [A: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ A @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
= ( A
= ( restri446606278nt_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_subgraph__refl) ).
thf(1070,plain,
! [A: labele1159362096nt_a_b] :
( ( graph_222606102_a_b_b @ A @ A @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
= ( A
= ( restri446606278nt_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(125,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b,D: set_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( ord_less_eq_set_b @ C @ D )
=> ( ord_less_eq_set_b @ ( image_b_b @ A @ C ) @ ( image_b_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_Image__mono) ).
thf(707,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b,D: set_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( ord_less_eq_set_b @ C @ D )
=> ( ord_less_eq_set_b @ ( image_b_b @ A @ C ) @ ( image_b_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(3,axiom,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
=> ( ( A != B )
=> ( member1285940496od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_insertE) ).
thf(310,plain,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
=> ( ( A != B )
=> ( member1285940496od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(124,axiom,
! [A: set_b] : ( refl_on_b @ A @ ( id_on_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_refl__on__Id__on) ).
thf(705,plain,
! [A: set_b] : ( refl_on_b @ A @ ( id_on_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(262,axiom,
! [A: b,B: b > $o] :
( ( member_b @ A @ ( collect_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mem__Collect__eq) ).
thf(1156,plain,
! [A: b,B: b > $o] :
( ( member_b @ A @ ( collect_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(224,axiom,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member_b @ ( f @ A ) @ ( labele1424214014nt_a_b @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_gu2) ).
thf(1053,plain,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member_b @ ( f @ A ) @ ( labele1424214014nt_a_b @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(115,axiom,
! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: b] :
( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member641857272od_b_b @ ( produc1257047359od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Image__singleton__iff) ).
thf(673,plain,
! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: b] :
( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member641857272od_b_b @ ( produc1257047359od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(50,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ? [C: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ A @ C ) )
& ~ ( member1285940496od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_mk__disjoint__insert) ).
thf(463,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ? [C: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ A @ C ) )
& ~ ( member1285940496od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(12,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ C )
=> ( ( graph_222606102_a_b_b @ A @ C @ D )
=> ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_maintainedD) ).
thf(338,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ C )
=> ( ( graph_222606102_a_b_b @ A @ C @ D )
=> ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(304,axiom,
! [A: b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ ( insert_b @ A @ B ) @ C )
= ( ( member_b @ A @ C )
& ( ord_less_eq_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_insert__subset) ).
thf(1285,plain,
! [A: b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ ( insert_b @ A @ B ) @ C )
= ( ( member_b @ A @ C )
& ( ord_less_eq_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(106,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( insert1574423351_a_nat @ A @ B )
!= bot_bo1836341171_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_insert__not__empty) ).
thf(643,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( insert1574423351_a_nat @ A @ B )
!= bot_bo1836341171_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(87,axiom,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
= ( ? [D: standard_Constant_a] :
( ( member1632892294tant_a @ D @ C )
& ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_Image__iff) ).
thf(585,plain,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
= ( ? [D: standard_Constant_a] :
( ( member1632892294tant_a @ D @ C )
& ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(20,axiom,
! [A: set_Pr1987088711_a_nat,B: set_Pr924198087_a_nat,C: produc1871334759_a_nat,D: produc1871334759_a_nat] :
( ( equiv_291114781_a_nat @ A @ B )
=> ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ C @ D ) @ B )
=> ( ord_le1718765799_a_nat @ ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) @ ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_equiv__class__subset) ).
thf(370,plain,
! [A: set_Pr1987088711_a_nat,B: set_Pr924198087_a_nat,C: produc1871334759_a_nat,D: produc1871334759_a_nat] :
( ( equiv_291114781_a_nat @ A @ B )
=> ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ C @ D ) @ B )
=> ( ord_le1718765799_a_nat @ ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) @ ( image_1168831379_a_nat @ B @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(195,axiom,
( p
= ( ^ [A: b,B: b] : ( member_b @ B @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_P) ).
thf(951,plain,
( p
= ( ^ [A: b,B: b] : ( member_b @ B @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(155,axiom,
! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: b] :
( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member599505522od_b_b @ ( produc800495189od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Image__singleton__iff) ).
thf(808,plain,
! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: b] :
( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member599505522od_b_b @ ( produc800495189od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(11,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_insertI1) ).
thf(336,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(294,axiom,
! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
=> ( member_b @ C @ ( labele1424214014nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_getRel__dom_I2_J) ).
thf(1257,plain,
! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
=> ( member_b @ C @ ( labele1424214014nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(257,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ( member_b @ C @ A )
& ( member_b @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_refl__on__domain) ).
thf(1141,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ( member_b @ C @ A )
& ( member_b @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(131,axiom,
! [A: labele1159362096nt_a_b] :
( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1741081071nt_a_b @ ( restri446606278nt_a_b @ A ) ) )
=> ( A
= ( restri446606278nt_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_restrict__subsD) ).
thf(727,plain,
! [A: labele1159362096nt_a_b] :
( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1741081071nt_a_b @ ( restri446606278nt_a_b @ A ) ) )
=> ( A
= ( restri446606278nt_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(211,axiom,
( g
= ( restri446606278nt_a_b @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(1008,plain,
( g
= ( restri446606278nt_a_b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(97,axiom,
! [A: set_Product_prod_b_b,B: labele1159362096nt_a_b] : ( edge_p1384198690tant_a @ A @ ( labele1741081071nt_a_b @ B ) @ ( labele1741081071nt_a_b @ ( map_gr926947118tant_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_map__graph__edge__preserving) ).
thf(612,plain,
! [A: set_Product_prod_b_b,B: labele1159362096nt_a_b] : ( edge_p1384198690tant_a @ A @ ( labele1741081071nt_a_b @ B ) @ ( labele1741081071nt_a_b @ ( map_gr926947118tant_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(169,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
( ( ( insert1574423351_a_nat @ A @ B )
= ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) )
= ( ( A = C )
& ( ord_le1718765799_a_nat @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_singleton__insert__inj__eq_H) ).
thf(859,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat] :
( ( ( insert1574423351_a_nat @ A @ B )
= ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) )
= ( ( A = C )
& ( ord_le1718765799_a_nat @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(289,axiom,
! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: set_b] :
( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member641857272od_b_b @ ( produc1257047359od_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_ImageE) ).
thf(1240,plain,
! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: set_b] :
( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member641857272od_b_b @ ( produc1257047359od_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(165,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_old_Oprod_Oinject) ).
thf(845,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(236,axiom,
( agree_221379389_a_b_b
= ( ^ [A: labele1159362096nt_a_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
! [D: b] :
( ( member_b @ D @ ( labele1424214014nt_a_b @ A ) )
=> ( ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) )
= ( image_b_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_agree__on__def) ).
thf(1084,plain,
( agree_221379389_a_b_b
= ( ^ [A: labele1159362096nt_a_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
! [D: b] :
( ( member_b @ D @ ( labele1424214014nt_a_b @ A ) )
=> ( ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) )
= ( image_b_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(271,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1741081071nt_a_b @ B ) )
=> ( ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ A ) @ ( labele1424214014nt_a_b @ B ) )
=> ( ( graph_1309249505nt_a_b @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_graph__unionI) ).
thf(1180,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1741081071nt_a_b @ B ) )
=> ( ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ A ) @ ( labele1424214014nt_a_b @ B ) )
=> ( ( graph_1309249505nt_a_b @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(74,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: b,E: b,F: allego510293162tant_a,G: b,H: b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ ( semant55076487nt_a_b @ A @ F ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ G ) @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ H ) @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ G @ H ) @ ( semant55076487nt_a_b @ B @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_graph__homomorphism__semantics) ).
thf(539,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: set_Product_prod_b_b,D: b,E: b,F: allego510293162tant_a,G: b,H: b] :
( ( graph_222606102_a_b_b @ A @ B @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ ( semant55076487nt_a_b @ A @ F ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ G ) @ C )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ H ) @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ G @ H ) @ ( semant55076487nt_a_b @ B @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(59,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ord_less_eq_set_b @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) @ ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_equiv__class__subset) ).
thf(495,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ord_less_eq_set_b @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) @ ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(274,axiom,
! [A: b,B: b,C: set_b,D: b > b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( bNF_Gr_b_b @ C @ D ) )
=> ( member_b @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_GrD1) ).
thf(1189,plain,
! [A: b,B: b,C: set_b,D: b > b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( bNF_Gr_b_b @ C @ D ) )
=> ( member_b @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(212,axiom,
! [A: labele1159362096nt_a_b] :
( A
= ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_labeled__graph_Oexhaust__sel) ).
thf(1010,plain,
! [A: labele1159362096nt_a_b] :
( A
= ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(244,axiom,
graph_222606102_a_b_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) @ g @ ( id_on_b @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_subg) ).
thf(1108,plain,
graph_222606102_a_b_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) @ g @ ( id_on_b @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(282,axiom,
! [A: b,B: produc1213276845od_b_b,C: set_Pr2060523537od_b_b,D: set_b] :
( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member1516365892od_b_b @ B @ ( image_984343321od_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_ImageI) ).
thf(1216,plain,
! [A: b,B: produc1213276845od_b_b,C: set_Pr2060523537od_b_b,D: set_b] :
( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member1516365892od_b_b @ B @ ( image_984343321od_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(177,axiom,
! [A: set_Product_prod_b_b] :
( ( collec1481886546od_b_b
@ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Collect__mem__eq) ).
thf(891,plain,
! [A: set_Product_prod_b_b] :
( ( collec1481886546od_b_b
@ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(88,axiom,
( ( id_on_1651096324_a_nat @ bot_bo1836341171_a_nat )
= bot_bo1973379891_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Id__on__empty) ).
thf(588,plain,
( ( id_on_1651096324_a_nat @ bot_bo1836341171_a_nat )
= bot_bo1973379891_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(199,axiom,
! [A: b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
= ( ~ ( member_b @ A @ ( labele1424214014nt_a_b @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_r2) ).
thf(961,plain,
! [A: b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
= ( ~ ( member_b @ A @ ( labele1424214014nt_a_b @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(228,axiom,
! [A: produc1213276845od_b_b,B: b,C: set_Pr1906739389_b_b_b,D: set_Pr1324126435od_b_b] :
( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ B ) @ C )
=> ( ( member1516365892od_b_b @ A @ D )
=> ( member_b @ B @ ( image_1764625405_b_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_ImageI) ).
thf(1062,plain,
! [A: produc1213276845od_b_b,B: b,C: set_Pr1906739389_b_b_b,D: set_Pr1324126435od_b_b] :
( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ B ) @ C )
=> ( ( member1516365892od_b_b @ A @ D )
=> ( member_b @ B @ ( image_1764625405_b_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(15,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ~ ( member1285940496od_b_b @ A @ B )
=> ( A = C ) )
=> ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_insertCI) ).
thf(351,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ~ ( member1285940496od_b_b @ A @ B )
=> ( A = C ) )
=> ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(30,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) )
=> ( ord_le1036320359od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_subsetI) ).
thf(401,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) )
=> ( ord_le1036320359od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(290,axiom,
! [A: b,B: set_b,C: b,D: set_Product_prod_b_b] :
( ( member_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_rev__ImageI) ).
thf(1244,plain,
! [A: b,B: set_b,C: b,D: set_Product_prod_b_b] :
( ( member_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(35,axiom,
( ord_le1036320359od_b_b
= ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_subset__eq) ).
thf(418,plain,
( ord_le1036320359od_b_b
= ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(146,axiom,
! [A: b,B: set_b] :
( ( insert_b @ A @ ( insert_b @ A @ B ) )
= ( insert_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_insert__absorb2) ).
thf(781,plain,
! [A: b,B: set_b] :
( ( insert_b @ A @ ( insert_b @ A @ B ) )
= ( insert_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(24,axiom,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
= ( ( A = B )
| ( member1516365892od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_insert__iff) ).
thf(378,plain,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
= ( ( A = B )
| ( member1516365892od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(113,axiom,
! [A: set_Pr1646010159_a_nat] :
( ( image_1749766139_a_nat @ A @ bot_bot_set_b )
= bot_bo1836341171_a_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Image__empty2) ).
thf(667,plain,
! [A: set_Pr1646010159_a_nat] :
( ( image_1749766139_a_nat @ A @ bot_bot_set_b )
= bot_bo1836341171_a_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(234,axiom,
! [A: b,B: set_Pr1906739389_b_b_b,C: set_Pr1324126435od_b_b] :
( ( member_b @ A @ ( image_1764625405_b_b_b @ B @ C ) )
=> ~ ! [D: produc1213276845od_b_b] :
( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ D @ A ) @ B )
=> ~ ( member1516365892od_b_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_ImageE) ).
thf(1077,plain,
! [A: b,B: set_Pr1906739389_b_b_b,C: set_Pr1324126435od_b_b] :
( ( member_b @ A @ ( image_1764625405_b_b_b @ B @ C ) )
=> ~ ! [D: produc1213276845od_b_b] :
( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ D @ A ) @ B )
=> ~ ( member1516365892od_b_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(14,axiom,
! [A: set_Product_prod_b_b,B: product_prod_b_b] :
( ( A = bot_bo1343651123od_b_b )
=> ~ ( member1285940496od_b_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_equals0D) ).
thf(346,plain,
! [A: set_Product_prod_b_b,B: product_prod_b_b] :
( ( A = bot_bo1343651123od_b_b )
=> ~ ( member1285940496od_b_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,axiom,
! [A: b,B: b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_singleton__inject) ).
thf(536,plain,
! [A: b,B: b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(128,axiom,
( ( id_on_b @ bot_bot_set_b )
= bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Id__on__empty) ).
thf(716,plain,
( ( id_on_b @ bot_bot_set_b )
= bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(163,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Pair__inject) ).
thf(832,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(118,axiom,
! [A: product_prod_b_b,B: product_prod_b_b > $o] :
( ( member1285940496od_b_b @ A @ ( collec1481886546od_b_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_mem__Collect__eq) ).
thf(684,plain,
! [A: product_prod_b_b,B: product_prod_b_b > $o] :
( ( member1285940496od_b_b @ A @ ( collec1481886546od_b_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(247,axiom,
! [A: b,B: set_b,C: product_prod_b_b,D: set_Pr621705391od_b_b] :
( ( member_b @ A @ B )
=> ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ C ) @ D )
=> ( member1285940496od_b_b @ C @ ( image_1177096571od_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_rev__ImageI) ).
thf(1116,plain,
! [A: b,B: set_b,C: product_prod_b_b,D: set_Pr621705391od_b_b] :
( ( member_b @ A @ B )
=> ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ C ) @ D )
=> ( member1285940496od_b_b @ C @ ( image_1177096571od_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(254,axiom,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_insertI2) ).
thf(1133,plain,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(209,axiom,
! [A: b,B: labele1159362096nt_a_b,C: b > standard_Constant_a,D: product_prod_b_b,E: set_Pr1324126435od_b_b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ B ) )
=> ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ ( C @ A ) @ D ) @ E )
=> ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ D ) @ ( relcom112561144od_b_b @ ( bNF_Gr230160332tant_a @ ( labele1424214014nt_a_b @ B ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_in__on__graph) ).
thf(999,plain,
! [A: b,B: labele1159362096nt_a_b,C: b > standard_Constant_a,D: product_prod_b_b,E: set_Pr1324126435od_b_b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ B ) )
=> ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ ( C @ A ) @ D ) @ E )
=> ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ D ) @ ( relcom112561144od_b_b @ ( bNF_Gr230160332tant_a @ ( labele1424214014nt_a_b @ B ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(5,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_insertI2) ).
thf(315,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ C )
=> ( ( graph_222606102_a_b_b @ A @ C @ D )
=> ~ ! [E: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ B @ C @ E )
=> ~ ( ord_le1036320359od_b_b @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_maintainedD2) ).
thf(432,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b] :
( ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ C )
=> ( ( graph_222606102_a_b_b @ A @ C @ D )
=> ~ ! [E: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ B @ C @ E )
=> ~ ( ord_le1036320359od_b_b @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(286,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ? [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
& ~ ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_mk__disjoint__insert) ).
thf(1229,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ? [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
& ~ ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(31,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ ( insert1952693431od_b_b @ A @ B ) @ C )
= ( ( member1285940496od_b_b @ A @ C )
& ( ord_le1036320359od_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_insert__subset) ).
thf(405,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ ( insert1952693431od_b_b @ A @ B ) @ C )
= ( ( member1285940496od_b_b @ A @ C )
& ( ord_le1036320359od_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(259,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( ord_less_eq_set_b @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) @ ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
=> ( ( member_b @ C @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_subset__equiv__class) ).
thf(1148,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( ord_less_eq_set_b @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) @ ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
=> ( ( member_b @ C @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(149,axiom,
! [A: labele1159362096nt_a_b,B: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ bot_bot_set_b ) @ A @ B )
= ( ( B = bot_bo1343651123od_b_b )
& ( A
= ( restri446606278nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_graph__homomorphism__empty) ).
thf(790,plain,
! [A: labele1159362096nt_a_b,B: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ bot_bot_set_b ) @ A @ B )
= ( ( B = bot_bo1343651123od_b_b )
& ( A
= ( restri446606278nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(171,axiom,
! [A: standard_Constant_a,B: b,C: b] :
( ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_graph__single) ).
thf(865,plain,
! [A: standard_Constant_a,B: b,C: b] :
( ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(21,axiom,
( ord_le1036320359od_b_b
= ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_subset__iff) ).
thf(373,plain,
( ord_le1036320359od_b_b
= ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ? [C: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ A @ C ) )
& ~ ( member1516365892od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_mk__disjoint__insert) ).
thf(341,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ? [C: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ A @ C ) )
& ~ ( member1516365892od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(41,axiom,
refl_o1213627494_a_nat @ bot_bo1836341171_a_nat @ bot_bo1973379891_a_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_refl__on__empty) ).
thf(437,plain,
refl_o1213627494_a_nat @ bot_bo1836341171_a_nat @ bot_bo1973379891_a_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(179,axiom,
! [A: set_Pr1324126435od_b_b,B: set_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b,E: set_Pr1324126435od_b_b] :
( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ A @ B ) @ C @ D )
=> ( ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) @ ( labele1230159100nt_a_b @ E @ B ) ) @ C @ D )
= ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ E @ B ) @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_extensible__refl__concr) ).
thf(897,plain,
! [A: set_Pr1324126435od_b_b,B: set_b,C: labele1159362096nt_a_b,D: set_Product_prod_b_b,E: set_Pr1324126435od_b_b] :
( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ A @ B ) @ C @ D )
=> ( ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) @ ( labele1230159100nt_a_b @ E @ B ) ) @ C @ D )
= ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ E @ B ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(112,axiom,
! [A: product_prod_b_b,B: set_Pr667377223od_b_b,C: produc1871334759_a_nat] :
( ( member1285940496od_b_b @ A @ ( image_1214223635od_b_b @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) )
= ( member301892752od_b_b @ ( produc590959831od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Image__singleton__iff) ).
thf(664,plain,
! [A: product_prod_b_b,B: set_Pr667377223od_b_b,C: produc1871334759_a_nat] :
( ( member1285940496od_b_b @ A @ ( image_1214223635od_b_b @ B @ ( insert1574423351_a_nat @ C @ bot_bo1836341171_a_nat ) ) )
= ( member301892752od_b_b @ ( produc590959831od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(305,axiom,
! [A: set_b] :
( ! [B: b] :
~ ( member_b @ B @ A )
=> ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_equals0I) ).
thf(1288,plain,
! [A: set_b] :
( ! [B: b] :
~ ( member_b @ B @ A )
=> ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(229,axiom,
( f
= ( ^ [A: b] :
( if_b
@ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
@ A
@ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062) ).
thf(1065,plain,
( f
= ( ^ [A: b] :
( if_b
@ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
@ A
@ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(122,axiom,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_old_Oprod_Oinducts) ).
thf(696,plain,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(197,axiom,
! [A: b,B: labele1159362096nt_a_b,C: b > b,D: b,E: set_Product_prod_b_b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ B ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ ( C @ A ) @ D ) @ E )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ ( relcomp_b_b_b @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_in__on__graph) ).
thf(955,plain,
! [A: b,B: labele1159362096nt_a_b,C: b > b,D: b,E: set_Product_prod_b_b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ B ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ ( C @ A ) @ D ) @ E )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ D ) @ ( relcomp_b_b_b @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(151,axiom,
! [A: set_Pr1987088711_a_nat,B: labele1159362096nt_a_b,C: produc1871334759_a_nat] :
( ( conseq956760372_nat_b @ A @ B )
=> ( ( member832397200_a_nat @ C @ A )
=> ( mainta1604381365_nat_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_consequence__graphD_I1_J) ).
thf(796,plain,
! [A: set_Pr1987088711_a_nat,B: labele1159362096nt_a_b,C: produc1871334759_a_nat] :
( ( conseq956760372_nat_b @ A @ B )
=> ( ( member832397200_a_nat @ C @ A )
=> ( mainta1604381365_nat_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(187,axiom,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_old_Oprod_Oinducts) ).
thf(928,plain,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(34,axiom,
! [A: set_Product_prod_b_b] :
( ( ? [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
= ( A != bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_ex__in__conv) ).
thf(415,plain,
! [A: set_Product_prod_b_b] :
( ( ? [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
= ( A != bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(295,axiom,
( f
= ( ^ [A: b] :
( if_b
@ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
@ A
@ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_f) ).
thf(1261,plain,
( f
= ( ^ [A: b] :
( if_b
@ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
@ A
@ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(71,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ B )
=> ? [C: set_Pr1987088711_a_nat] :
( ( B
= ( insert1574423351_a_nat @ A @ C ) )
& ~ ( member832397200_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_mk__disjoint__insert) ).
thf(528,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ B )
=> ? [C: set_Pr1987088711_a_nat] :
( ( B
= ( insert1574423351_a_nat @ A @ C ) )
& ~ ( member832397200_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(207,axiom,
! [A: labele1159362096nt_a_b,B: b > b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( graph_222606102_a_b_b @ A @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ A ) @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_graph__homo) ).
thf(992,plain,
! [A: labele1159362096nt_a_b,B: b > b] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( graph_222606102_a_b_b @ A @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) @ A ) @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(308,axiom,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062) ).
thf(1299,plain,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(173,axiom,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat] :
( ( ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat )
= ( insert1574423351_a_nat @ B @ bot_bo1836341171_a_nat ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_singleton__inject) ).
thf(871,plain,
! [A: produc1871334759_a_nat,B: produc1871334759_a_nat] :
( ( ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat )
= ( insert1574423351_a_nat @ B @ bot_bo1836341171_a_nat ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(249,axiom,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
=> ( ( A != B )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_insertE) ).
thf(1120,plain,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
=> ( ( A != B )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(61,axiom,
! [A: produc1871334759_a_nat] : ( refl_o1213627494_a_nat @ ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat ) @ ( insert1810136247_a_nat @ ( produc1677124439_a_nat @ A @ A ) @ bot_bo1973379891_a_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_refl__on__singleton) ).
thf(501,plain,
! [A: produc1871334759_a_nat] : ( refl_o1213627494_a_nat @ ( insert1574423351_a_nat @ A @ bot_bo1836341171_a_nat ) @ ( insert1810136247_a_nat @ ( produc1677124439_a_nat @ A @ A ) @ bot_bo1973379891_a_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(29,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ~ ( member1516365892od_b_b @ A @ B )
=> ( A = C ) )
=> ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_insertCI) ).
thf(395,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ~ ( member1516365892od_b_b @ A @ B )
=> ( A = C ) )
=> ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(101,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) )
=> ( ord_le123089219od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subrelI) ).
thf(624,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) )
=> ( ord_le123089219od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(298,axiom,
! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_insertI1) ).
thf(1268,plain,
! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(84,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat,D: set_Pr1987088711_a_nat] :
( ~ ( member832397200_a_nat @ A @ B )
=> ( ~ ( member832397200_a_nat @ C @ D )
=> ( ( ( insert1574423351_a_nat @ A @ B )
= ( insert1574423351_a_nat @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Pr1987088711_a_nat] :
( ( B
= ( insert1574423351_a_nat @ C @ E ) )
& ~ ( member832397200_a_nat @ C @ E )
& ( D
= ( insert1574423351_a_nat @ A @ E ) )
& ~ ( member832397200_a_nat @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_insert__eq__iff) ).
thf(575,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,C: produc1871334759_a_nat,D: set_Pr1987088711_a_nat] :
( ~ ( member832397200_a_nat @ A @ B )
=> ( ~ ( member832397200_a_nat @ C @ D )
=> ( ( ( insert1574423351_a_nat @ A @ B )
= ( insert1574423351_a_nat @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Pr1987088711_a_nat] :
( ( B
= ( insert1574423351_a_nat @ C @ E ) )
& ~ ( member832397200_a_nat @ C @ E )
& ( D
= ( insert1574423351_a_nat @ A @ E ) )
& ~ ( member832397200_a_nat @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(56,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ~ ( member1516365892od_b_b @ A @ C )
=> ( ( ( insert2037698781od_b_b @ A @ B )
= ( insert2037698781od_b_b @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_insert__ident) ).
thf(486,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ~ ( member1516365892od_b_b @ A @ C )
=> ( ( ( insert2037698781od_b_b @ A @ B )
= ( insert2037698781od_b_b @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(189,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_insert__ident) ).
thf(935,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1,conjecture,
member_b @ x @ ( labele1424214014nt_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(309,plain,
~ ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(116,axiom,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ B )
=> ~ ! [C: set_Pr1987088711_a_nat] :
( ( B
= ( insert1574423351_a_nat @ A @ C ) )
=> ( member832397200_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_Set_Oset__insert) ).
thf(676,plain,
! [A: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
( ( member832397200_a_nat @ A @ B )
=> ~ ! [C: set_Pr1987088711_a_nat] :
( ( B
= ( insert1574423351_a_nat @ A @ C ) )
=> ( member832397200_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(18,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( insert1952693431od_b_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_insert__absorb) ).
thf(364,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( insert1952693431od_b_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(202,axiom,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_subset__iff) ).
thf(972,plain,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1311,plain,
$false,
inference(e,[status(thm)],[760,1105,1237,468,1295,1031,333,628,1200,408,582,730,1073,449,614,597,1173,878,511,384,533,550,472,814,913,670,1095,1046,1265,1254,651,1055,917,802,1279,357,1059,542,817,559,1247,1013,325,969,606,591,443,1136,514,1151,1020,806,1183,480,1109,321,687,634,1119,411,1074,942,661,925,381,1067,1163,1206,452,546,793,910,746,778,1042,1174,820,693,429,1223,894,1123,862,566,361,757,1195,1128,710,842,974,522,830,1159,461,493,1210,874,1270,948,1017,388,420,519,742,1089,1234,328,1028,901,637,590,1039,1292,933,393,701,1192,721,1002,569,503,647,1263,1099,985,1131,654,1086,508,657,765,953,1185,718,888,618,1146,1219,1273,856,375,601,1154,904,423,732,1125,772,579,958,1226,1139,445,572,313,787,1058,1092,947,713,498,681,1282,784,736,318,979,604,377,990,996,477,811,631,367,609,594,621,483,848,964,769,1177,1112,799,1162,1171,1198,827,868,455,563,1250,922,851,1102,505,438,1034,490,1203,944,1277,516,939,754,553,1049,426,1166,1081,749,458,823,776,525,690,1025,1070,707,310,705,1156,1053,673,463,338,1285,643,585,370,951,808,336,1257,1141,727,1008,612,859,1240,845,1084,1180,539,495,1189,1010,1108,1216,891,588,961,1062,351,401,1244,418,781,378,667,1077,346,536,716,832,684,1116,1133,999,315,432,1229,405,1148,790,865,373,341,437,897,664,1288,1065,696,955,796,928,415,1261,528,992,1299,871,1120,501,395,624,1268,575,486,935,309,676,364,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP177^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n003.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 20:08:29 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.15/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.96/1.49 % [INFO] Parsing done (579ms).
% 3.44/1.51 % [INFO] Running in sequential loop mode.
% 5.26/2.09 % [INFO] eprover registered as external prover.
% 5.26/2.10 % [INFO] Scanning for conjecture ...
% 5.76/2.37 % [INFO] Found a conjecture (or negated_conjecture) and 359 axioms. Running axiom selection ...
% 6.66/2.67 % [INFO] Axiom selection finished. Selected 306 axioms (removed 53 axioms).
% 8.28/3.12 % [INFO] Problem is higher-order (TPTP THF).
% 8.60/3.16 % [INFO] Type checking passed.
% 8.60/3.17 % [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 ...
% 26.18/7.88 % External prover 'e' found a proof!
% 26.18/7.88 % [INFO] Killing All external provers ...
% 26.18/7.88 % Time passed: 7526ms (effective reasoning time: 6360ms)
% 26.18/7.88 % 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)>
% 26.18/7.89 % Axioms used in derivation (306): fact_298_emptyE, fact_337_insertI1, fact_246_all__not__in__conv, fact_281_graph__empty__e, fact_354_congr_I1_J, fact_150_graph__homomorphism__composes, fact_45_vert__P, fact_221_graph__union__iff, fact_4_assms_I1_J, fact_256_subsetI, fact_350_doubleton__eq__iff, fact_165_graph__homomorphism__empty, fact_258_insert__absorb2, fact_329_Set_Oset__insert, fact_279_relcomp__empty1, fact_286_ex__in__conv, fact_353_P, fact_31_labeled__graph_Osel_I1_J, fact_108_old_Oprod_Oinducts, fact_161_Image__singleton__iff, fact_224_subgraph__subset_I1_J, fact_32_subgraph__def, fact_96_GrD1, fact_293_equals0D, fact_343_insertE, fact_310_in__mono, fact_187_ImageE, fact_272_singletonI, fact_64_Id__on__iff, fact_201_relcomp_Osimps, fact_147_Id__on__empty, fact_341_insertE, fact_97_GrD1, fact_217_refl__on__empty, fact_299_subset__iff, fact_168_graph__single, fact_255_subsetI, fact_116_extensible__refl, fact_227_Id__on__vertices__identity_I2_J, fact_335_insertI2, fact_346_singleton__inject, fact_248_all__not__in__conv, fact_229_graph__homomorphism__on__graph, fact_277_insert__subset, fact_130_ImageI, fact_60_getRel__dom_I2_J, fact_35_subgraph__preserves__hom, fact_11__092_060open_062graph__union_A_Imap__graph__fn_AG_Af_J_AG_A_061_AG_092_060close_062, fact_349_doubleton__eq__iff, fact_185_ImageE, fact_80_refl__on__Id__on, fact_145_Id__on__empty, fact_118_consequence__graphD_I1_J, fact_124_extensibleI, fact_291_equals0D, fact_311_mk__disjoint__insert, fact_112_map__graph__in, fact_348_insert__not__empty, fact_89_prod_Oinject, fact_331_Set_Oset__insert, fact_10_equiv, fact_37_labeled__graph_Oexpand, fact_313_mk__disjoint__insert, fact_129_ImageI, fact_324_insert__absorb, fact_7_gr, fact_295_emptyE, fact_245_Collect__empty__eq, fact_262_insert__iff, fact_158_Image__singleton__iff, fact_115_extensible__refl__concr, fact_345_singleton__inject, fact_111_prod__induct3, fact_144_Image__empty1, fact_178_rev__ImageI, fact_226_maintainedD2, fact_183_Image__iff, fact_338_insertI1, fact_127_graph__homo__union__id_I2_J, fact_120_semantics__in__vertices_I2_J, fact_242_empty__Collect__eq, fact_138_ImageI, fact_186_ImageE, fact_241_refines__equiv__class__eq2, fact_269_subset__empty, fact_2_fv_I1_J, fact_344_insertE, fact_289_equals0I, fact_81_getRel__homR, fact_213_relcomp__Image, fact_318_insert__eq__iff, fact_252_empty__iff, fact_238_subset__equiv__class, fact_1_fv_I2_J, fact_284_ex__in__conv, fact_157_Image__singleton__iff, fact_351_ma, fact_268_empty__subsetI, fact_332_Set_Oset__insert, fact_156_Image__singleton__iff, fact_266_insertCI, fact_160_Image__singleton__iff, fact_215_agree__on__def, fact_87_old_Oprod_Oinject, fact_93_refl__on__domain, fact_159_Image__singleton__iff, fact_119_semantics__in__vertices_I1_J, fact_316_insert__commute, fact_294_equals0D, help_If_1_1_If_001tf__b_T, fact_140_Image__empty2, fact_100_surj__pair, fact_305_subsetD, fact_290_equals0I, fact_261_insert__iff, fact_134_ImageI, fact_321_insert__absorb, fact_175_rev__ImageI, fact_340_insertI1, fact_235_equiv__class__subset, fact_24_subgraph__refl, fact_347_insert__not__empty, fact_125_subgraph__subset_I2_J, fact_139_Image__empty2, fact_274_singletonI, fact_342_insertE, fact_155_map__graph__selectors_I1_J, fact_172_refl__on__singleton, fact_102_prod__cases, fact_334_insertI2, fact_327_insert__ident, fact_251_empty__iff, fact_302_subset__eq, fact_43_getRel__map__fn, fact_169_r2, fact_315_insert__commute, fact_319_insert__eq__iff, fact_273_singletonI, fact_297_emptyE, fact_15_subg, fact_154_Gr__insert, fact_247_all__not__in__conv, fact_232_singleton__insert__inj__eq_H, fact_198_relcomp_Oinducts, fact_280_relcomp__empty2, fact_194_ImageE, fact_263_insertCI, fact_323_insert__absorb, fact_328_insert__ident, fact_46_mem__Collect__eq, fact_14_labeled__graph_Osel_I2_J, fact_30_graph__homo, fact_164_in__on__graph, fact_52_getRel__subgraph, fact_56_Gr__not__in, fact_5_r1, fact_40_getRel__hom, fact_234_equiv__class__subset, fact_193_ImageE, fact_301_subset__iff, fact_34_map__graph__fn__eqI, fact_230_singleton__insert__inj__eq, fact_223_subgraph__def2, fact_254_subsetI, fact_94_GrD2, fact_320_insert__eq__iff, fact_204_relcomp_Ocases, fact_36_labeled__graph_Oexhaust__sel, fact_303_subset__eq, fact_288_equals0I, fact_16_vertices__restrict, fact_109_old_Oprod_Oinducts, fact_278_insert__subset, fact_173_rev__ImageI, fact_312_mk__disjoint__insert, fact_336_insertI2, fact_239_subset__equiv__class, fact_76_refl__onD1, fact_103_prod__cases, fact_207_relcompEpair, fact_18_graph__union__idemp_I3_J, fact_249_all__not__in__conv, fact_85_edge__preserving__on__graphI, fact_308_in__mono, fact_260_insert__iff, fact_8_a, fact_218_refl__on__empty, fact_67_Id__on__eqI, fact_53_in__Gr, fact_250_empty__iff, fact_220_subrelI, fact_181_rev__ImageI, fact_326_insert__ident, fact_333_insertI2, fact_267_empty__subsetI, fact_142_Image__empty2, fact_20_graph__union__idemp_I1_J, fact_83_edge__preserving__on__graphI, fact_70_Id__onE, fact_355_ident, fact_73_refl__onD2, fact_210_relcompE, fact_86_reflexivity__rule, fact_98_map__graph__edge__preserving, fact_131_ImageI, fact_128__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062, fact_307_subsetD, fact_174_rev__ImageI, fact_296_emptyE, fact_44_idt__eq, fact_50_Collect__mem__eq, fact_214_Image__mono, fact_105_Pair__inject, fact_253_empty__iff, fact_271_singletonI, fact_292_equals0D, fact_282_graph__homomorphism__nonempty, fact_48_mem__Collect__eq, fact_6_assms_I2_J, fact_167_graph__unionI, fact_84_edge__preserving__on__graphI, fact_54_in__Gr, fact_244_Collect__empty__eq, fact_49_Collect__mem__eq, fact_300_subset__iff, fact_99_edge__preserving__atomic, fact_149_Gr__empty, fact_259_insert__iff, fact_306_subsetD, fact_184_Image__iff, fact_243_empty__Collect__eq, fact_171_refl__on__singleton, fact_325_insert__ident, fact_276_insert__subset, fact_123_maintainedD, fact_12_gu1, fact_61_getRel__dom_I1_J, fact_270_subset__empty, fact_106_old_Oprod_Oexhaust, fact_228_Id__on__vertices__identity_I1_J, fact_265_insertCI, fact_153_Gr__insert, fact_322_insert__absorb, fact_33_subgraph__trans, fact_304_subset__eq, fact_137_ImageI, fact_196_relcomp_OrelcompI, fact_114_maintainedI, fact_126_graph__homo__union__id_I1_J, fact_55_Gr__not__in, fact_79_refl__onD, fact_25_subgraph__restrict, fact_19_graph__union__idemp_I2_J, fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062, fact_121_subgraph__semantics, fact_283_ex__in__conv, fact_28_map__graph__fn__id_I2_J, fact_90_prod_Oinject, fact_9_local_Orefl, fact_107_old_Oprod_Oexhaust, fact_352_f, fact_27_map__graph__preserves__subgraph, fact_309_in__mono, fact_287_equals0I, fact_151_P__eq, fact_285_ex__in__conv, fact_219_subrelI, fact_47_mem__Collect__eq, fact_101_surj__pair, fact_222_restrict__subsD, fact_339_insertI1, fact_141_Image__empty2, fact_23_labeled__graph_Ocollapse, fact_22_graph__union__preserves__restrict, fact_26_graph__homomorphism__Id, fact_330_Set_Oset__insert, fact_240_refines__equiv__class__eq2, fact_21_map__graph__preserves__restricted, fact_143_Image__empty1, fact_182_rev__ImageI, fact_117_graph__homomorphism__semantics, fact_317_insert__eq__iff, fact_13__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062, fact_166_graph__homomorphism__empty, fact_314_mk__disjoint__insert, fact_257_insert__absorb2, fact_264_insertCI, fact_163_in__on__graph, fact_162_Image__singleton__iff, help_If_2_1_If_001tf__b_T, fact_275_insert__subset, fact_82_maintained__refl, fact_95_GrD2, fact_29_map__graph__fn__graphI, fact_231_singleton__insert__inj__eq, fact_110_prod__cases3, fact_190_ImageE, fact_233_singleton__insert__inj__eq_H, help_If_3_1_If_001tf__b_T, fact_51_Collect__mem__eq, fact_17_restrict__idemp, fact_59_Id__onI, fact_104_Pair__inject, fact_3_gu2, fact_88_old_Oprod_Oinject, fact_146_Id__on__empty
% 26.18/7.89 % No. of inferences in proof: 616
% 26.18/7.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7526 ms resp. 6360 ms w/o parsing
% 28.03/8.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 28.03/8.28 % [INFO] Killing All external provers ...
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