%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP179^1 : 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 : n012.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 10.09s 2.84s
% Output : Refutation 10.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 341
% Syntax : Number of formulae : 684 ( 463 unt; 0 typ; 0 def)
% Number of atoms : 1629 ( 693 equ; 2 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 4715 ( 210 ~; 18 |; 117 &;3972 @)
% ( 0 <=>; 398 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 55 ( 54 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 138 ( 135 usr; 29 con; 0-3 aty)
% Number of variables : 1570 ( 36 ^;1480 !; 54 ?;1570 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1355257963at_nat_type,type,
set_Pr1355257963at_nat: $tType ).
thf(set_Pr1429673827um_a_b_type,type,
set_Pr1429673827um_a_b: $tType ).
thf(set_Pr2065572323um_a_b_type,type,
set_Pr2065572323um_a_b: $tType ).
thf(set_Pr1558970842um_a_b_type,type,
set_Pr1558970842um_a_b: $tType ).
thf(set_Pr1121389018um_a_b_type,type,
set_Pr1121389018um_a_b: $tType ).
thf(produc1733247354um_a_b_type,type,
produc1733247354um_a_b: $tType ).
thf(produc1681803642um_a_b_type,type,
produc1681803642um_a_b: $tType ).
thf(produc1871334759_a_nat_type,type,
produc1871334759_a_nat: $tType ).
thf(labele498606060at_nat_type,type,
labele498606060at_nat: $tType ).
thf(set_Pr304595758um_a_b_type,type,
set_Pr304595758um_a_b: $tType ).
thf(set_Pr409224873um_a_b_type,type,
set_Pr409224873um_a_b: $tType ).
thf(set_Pr45173959um_a_b_type,type,
set_Pr45173959um_a_b: $tType ).
thf(set_Pr689416536at_nat_type,type,
set_Pr689416536at_nat: $tType ).
thf(set_Pr1134469976at_nat_type,type,
set_Pr1134469976at_nat: $tType ).
thf(labele1191284958um_a_b_type,type,
labele1191284958um_a_b: $tType ).
thf(produc1963079155um_a_b_type,type,
produc1963079155um_a_b: $tType ).
thf(produc1918750183um_a_b_type,type,
produc1918750183um_a_b: $tType ).
thf(set_Pr55236280um_a_b_type,type,
set_Pr55236280um_a_b: $tType ).
thf(set_Pr326391507um_a_b_type,type,
set_Pr326391507um_a_b: $tType ).
thf(set_Pr386468381um_a_b_type,type,
set_Pr386468381um_a_b: $tType ).
thf(labele261019144um_a_b_type,type,
labele261019144um_a_b: $tType ).
thf(produc1003469085um_a_b_type,type,
produc1003469085um_a_b: $tType ).
thf(produc1546082365um_a_b_type,type,
produc1546082365um_a_b: $tType ).
thf(set_Pr1783309276um_a_b_type,type,
set_Pr1783309276um_a_b: $tType ).
thf(set_Pr507214050_b_nat_type,type,
set_Pr507214050_b_nat: $tType ).
thf(set_Pr653770722um_a_b_type,type,
set_Pr653770722um_a_b: $tType ).
thf(set_Pr1155046920um_a_b_type,type,
set_Pr1155046920um_a_b: $tType ).
thf(set_Pr1647387645at_nat_type,type,
set_Pr1647387645at_nat: $tType ).
thf(produc323101606um_a_b_type,type,
produc323101606um_a_b: $tType ).
thf(produc585753260um_a_b_type,type,
produc585753260um_a_b: $tType ).
thf(produc1032616263at_nat_type,type,
produc1032616263at_nat: $tType ).
thf(set_Pr1994339542um_a_b_type,type,
set_Pr1994339542um_a_b: $tType ).
thf(set_Pr1902304780_b_nat_type,type,
set_Pr1902304780_b_nat: $tType ).
thf(set_Pr195945996um_a_b_type,type,
set_Pr195945996um_a_b: $tType ).
thf(set_Pr1618094130um_a_b_type,type,
set_Pr1618094130um_a_b: $tType ).
thf(labele431970251um_a_b_type,type,
labele431970251um_a_b: $tType ).
thf(produc1394389750um_a_b_type,type,
produc1394389750um_a_b: $tType ).
thf(produc1798470614um_a_b_type,type,
produc1798470614um_a_b: $tType ).
thf(produc204140796um_a_b_type,type,
produc204140796um_a_b: $tType ).
thf(set_Pr1916610317um_a_b_type,type,
set_Pr1916610317um_a_b: $tType ).
thf(labele935650037_a_nat_type,type,
labele935650037_a_nat: $tType ).
thf(produc1548871597um_a_b_type,type,
produc1548871597um_a_b: $tType ).
thf(set_Pr375490359_b_nat_type,type,
set_Pr375490359_b_nat: $tType ).
thf(set_Pr1174980151um_a_b_type,type,
set_Pr1174980151um_a_b: $tType ).
thf(produc1978941143_b_nat_type,type,
produc1978941143_b_nat: $tType ).
thf(produc1124793815um_a_b_type,type,
produc1124793815um_a_b: $tType ).
thf(set_St761939237tant_a_type,type,
set_St761939237tant_a: $tType ).
thf(set_Pr1986765409at_nat_type,type,
set_Pr1986765409at_nat: $tType ).
thf(standard_Constant_a_type,type,
standard_Constant_a: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(set_Sum_sum_a_b_type,type,
set_Sum_sum_a_b: $tType ).
thf(sum_sum_a_b_type,type,
sum_sum_a_b: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(standard_S_Bot_a_decl,type,
standard_S_Bot_a: standard_Constant_a ).
thf(standard_S_Idt_a_decl,type,
standard_S_Idt_a: standard_Constant_a ).
thf(getRel1465196352um_a_b_decl,type,
getRel1465196352um_a_b: standard_Constant_a > labele431970251um_a_b > set_Pr1916610317um_a_b ).
thf(edge_p170421892tant_a_decl,type,
edge_p170421892tant_a: set_Pr1986765409at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o ).
thf(edge_p1382426714tant_a_decl,type,
edge_p1382426714tant_a: set_Pr1174980151um_a_b > set_Pr1647387645at_nat > set_Pr409224873um_a_b > $o ).
thf(edge_p749155930tant_a_decl,type,
edge_p749155930tant_a: set_Pr375490359_b_nat > set_Pr409224873um_a_b > set_Pr1647387645at_nat > $o ).
thf(edge_p1871801392tant_a_decl,type,
edge_p1871801392tant_a: set_Pr1916610317um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o ).
thf(graph_2130075512at_nat_decl,type,
graph_2130075512at_nat: labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o ).
thf(graph_1452133198um_a_b_decl,type,
graph_1452133198um_a_b: labele935650037_a_nat > labele431970251um_a_b > set_Pr1174980151um_a_b > $o ).
thf(graph_149544303at_nat_decl,type,
graph_149544303at_nat: labele498606060at_nat > labele935650037_a_nat > set_Pr689416536at_nat > $o ).
thf(graph_166346565um_a_b_decl,type,
graph_166346565um_a_b: labele498606060at_nat > labele431970251um_a_b > set_Pr304595758um_a_b > $o ).
thf(graph_1203757137_b_nat_decl,type,
graph_1203757137_b_nat: labele261019144um_a_b > labele935650037_a_nat > set_Pr1902304780_b_nat > $o ).
thf(graph_502887975um_a_b_decl,type,
graph_502887975um_a_b: labele261019144um_a_b > labele431970251um_a_b > set_Pr653770722um_a_b > $o ).
thf(graph_1815313447_b_nat_decl,type,
graph_1815313447_b_nat: labele1191284958um_a_b > labele935650037_a_nat > set_Pr507214050_b_nat > $o ).
thf(graph_1763806717um_a_b_decl,type,
graph_1763806717um_a_b: labele1191284958um_a_b > labele431970251um_a_b > set_Pr55236280um_a_b > $o ).
thf(graph_165730638_b_nat_decl,type,
graph_165730638_b_nat: labele431970251um_a_b > labele935650037_a_nat > set_Pr375490359_b_nat > $o ).
thf(graph_611893540um_a_b_decl,type,
graph_611893540um_a_b: labele431970251um_a_b > labele431970251um_a_b > set_Pr1916610317um_a_b > $o ).
thf(labele16114835_a_nat_decl,type,
labele16114835_a_nat: set_Pr1647387645at_nat > set_nat > labele935650037_a_nat ).
thf(labele1813985418at_nat_decl,type,
labele1813985418at_nat: set_Pr1355257963at_nat > set_Pr1647387645at_nat > labele498606060at_nat ).
thf(labele2034032468um_a_b_decl,type,
labele2034032468um_a_b: set_Pr2065572323um_a_b > set_Pr1174980151um_a_b > labele261019144um_a_b ).
thf(labele989994um_a_b_decl,type,
labele989994um_a_b: set_Pr1429673827um_a_b > set_Pr1916610317um_a_b > labele1191284958um_a_b ).
thf(labele1729654377um_a_b_decl,type,
labele1729654377um_a_b: set_Pr409224873um_a_b > set_Sum_sum_a_b > labele431970251um_a_b ).
thf(labele195203296_a_nat_decl,type,
labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).
thf(labele1939049654um_a_b_decl,type,
labele1939049654um_a_b: labele431970251um_a_b > set_Pr409224873um_a_b ).
thf(labele1810595089_a_nat_decl,type,
labele1810595089_a_nat: labele935650037_a_nat > set_nat ).
thf(labele577278695um_a_b_decl,type,
labele577278695um_a_b: labele431970251um_a_b > set_Sum_sum_a_b ).
thf(restri572569417_a_nat_decl,type,
restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).
thf(restri1162247455um_a_b_decl,type,
restri1162247455um_a_b: labele431970251um_a_b > labele431970251um_a_b ).
thf(unival860567212at_nat_decl,type,
unival860567212at_nat: set_Pr1647387645at_nat > $o ).
thf(unival1487587672um_a_b_decl,type,
unival1487587672um_a_b: set_Pr409224873um_a_b > $o ).
thf(unival2092813468um_a_b_decl,type,
unival2092813468um_a_b: set_Pr1174980151um_a_b > $o ).
thf(unival118648434um_a_b_decl,type,
unival118648434um_a_b: set_Pr1916610317um_a_b > $o ).
thf(bot_bot_nat_decl,type,
bot_bot_nat: nat ).
thf(bot_bo1160111033tant_a_decl,type,
bot_bo1160111033tant_a: set_St761939237tant_a ).
thf(bot_bot_set_nat_decl,type,
bot_bot_set_nat: set_nat ).
thf(bot_bo810816657at_nat_decl,type,
bot_bo810816657at_nat: set_Pr1647387645at_nat ).
thf(bot_bo1524397311at_nat_decl,type,
bot_bo1524397311at_nat: set_Pr1355257963at_nat ).
thf(bot_bo1208513655um_a_b_decl,type,
bot_bo1208513655um_a_b: set_Pr2065572323um_a_b ).
thf(bot_bo1262778871um_a_b_decl,type,
bot_bo1262778871um_a_b: set_Pr1429673827um_a_b ).
thf(bot_bo1262634813um_a_b_decl,type,
bot_bo1262634813um_a_b: set_Pr409224873um_a_b ).
thf(bot_bo2130386637at_nat_decl,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(bot_bo575978147um_a_b_decl,type,
bot_bo575978147um_a_b: set_Pr1174980151um_a_b ).
thf(bot_bo1582968772at_nat_decl,type,
bot_bo1582968772at_nat: set_Pr689416536at_nat ).
thf(bot_bo627753370um_a_b_decl,type,
bot_bo627753370um_a_b: set_Pr304595758um_a_b ).
thf(bot_bo949957280_b_nat_decl,type,
bot_bo949957280_b_nat: set_Pr1902304780_b_nat ).
thf(bot_bo1892785270um_a_b_decl,type,
bot_bo1892785270um_a_b: set_Pr653770722um_a_b ).
thf(bot_bo1746228598_b_nat_decl,type,
bot_bo1746228598_b_nat: set_Pr507214050_b_nat ).
thf(bot_bo1217542988um_a_b_decl,type,
bot_bo1217542988um_a_b: set_Pr55236280um_a_b ).
thf(bot_bo1923972003_b_nat_decl,type,
bot_bo1923972003_b_nat: set_Pr375490359_b_nat ).
thf(bot_bo225809273um_a_b_decl,type,
bot_bo225809273um_a_b: set_Pr1916610317um_a_b ).
thf(bot_bo1491243248um_a_b_decl,type,
bot_bo1491243248um_a_b: set_Sum_sum_a_b ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_le1739761029tant_a_decl,type,
ord_le1739761029tant_a: set_St761939237tant_a > set_St761939237tant_a > $o ).
thf(ord_less_eq_set_nat_decl,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(ord_le1909159005at_nat_decl,type,
ord_le1909159005at_nat: set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o ).
thf(ord_le615126793um_a_b_decl,type,
ord_le615126793um_a_b: set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o ).
thf(ord_le841296385at_nat_decl,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(ord_le823954903um_a_b_decl,type,
ord_le823954903um_a_b: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > $o ).
thf(ord_le1059794605um_a_b_decl,type,
ord_le1059794605um_a_b: set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > $o ).
thf(ord_le192794300um_a_b_decl,type,
ord_le192794300um_a_b: set_Sum_sum_a_b > set_Sum_sum_a_b > $o ).
thf(produc407553657at_nat_decl,type,
produc407553657at_nat: standard_Constant_a > product_prod_nat_nat > produc1032616263at_nat ).
thf(produc414524239um_a_b_decl,type,
produc414524239um_a_b: standard_Constant_a > produc1124793815um_a_b > produc1003469085um_a_b ).
thf(produc1697725733um_a_b_decl,type,
produc1697725733um_a_b: standard_Constant_a > produc1548871597um_a_b > produc1963079155um_a_b ).
thf(produc584843310um_a_b_decl,type,
produc584843310um_a_b: standard_Constant_a > sum_sum_a_b > produc1394389750um_a_b ).
thf(produc1676969687_a_nat_decl,type,
produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).
thf(product_Pair_nat_nat_decl,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(produc1346373166um_a_b_decl,type,
produc1346373166um_a_b: nat > produc1124793815um_a_b > produc204140796um_a_b ).
thf(produc1808556047um_a_b_decl,type,
produc1808556047um_a_b: nat > sum_sum_a_b > produc1124793815um_a_b ).
thf(produc335036333um_a_b_decl,type,
produc335036333um_a_b: product_prod_nat_nat > produc1124793815um_a_b > produc1546082365um_a_b ).
thf(produc1872245072um_a_b_decl,type,
produc1872245072um_a_b: product_prod_nat_nat > sum_sum_a_b > produc1798470614um_a_b ).
thf(produc831476262um_a_b_decl,type,
produc831476262um_a_b: produc1124793815um_a_b > sum_sum_a_b > produc585753260um_a_b ).
thf(produc522153487_b_nat_decl,type,
produc522153487_b_nat: sum_sum_a_b > nat > produc1978941143_b_nat ).
thf(produc176426981um_a_b_decl,type,
produc176426981um_a_b: sum_sum_a_b > sum_sum_a_b > produc1548871597um_a_b ).
thf(domain1060562500at_nat_decl,type,
domain1060562500at_nat: set_Pr1647387645at_nat > set_St761939237tant_a ).
thf(domain1362581744um_a_b_decl,type,
domain1362581744um_a_b: set_Pr409224873um_a_b > set_St761939237tant_a ).
thf(domain_nat_nat_decl,type,
domain_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(domain1368163076um_a_b_decl,type,
domain1368163076um_a_b: set_Pr1174980151um_a_b > set_nat ).
thf(domain2069673178um_a_b_decl,type,
domain2069673178um_a_b: set_Pr1916610317um_a_b > set_Sum_sum_a_b ).
thf(id_on_Sum_sum_a_b_decl,type,
id_on_Sum_sum_a_b: set_Sum_sum_a_b > set_Pr1916610317um_a_b ).
thf(image_127502653at_nat_decl,type,
image_127502653at_nat: set_Pr1647387645at_nat > set_St761939237tant_a > set_Pr1986765409at_nat ).
thf(image_1179143699um_a_b_decl,type,
image_1179143699um_a_b: set_Pr326391507um_a_b > set_St761939237tant_a > set_Pr1174980151um_a_b ).
thf(image_2023280617um_a_b_decl,type,
image_2023280617um_a_b: set_Pr409224873um_a_b > set_St761939237tant_a > set_Pr1916610317um_a_b ).
thf(image_2129435242um_a_b_decl,type,
image_2129435242um_a_b: set_Pr1994339542um_a_b > set_St761939237tant_a > set_Sum_sum_a_b ).
thf(image_nat_nat_decl,type,
image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat ).
thf(image_489788268at_nat_decl,type,
image_489788268at_nat: set_Pr1134469976at_nat > set_nat > set_Pr1647387645at_nat ).
thf(image_1228479730um_a_b_decl,type,
image_1228479730um_a_b: set_Pr1618094130um_a_b > set_nat > set_Pr1174980151um_a_b ).
thf(image_166667464um_a_b_decl,type,
image_166667464um_a_b: set_Pr1155046920um_a_b > set_nat > set_Pr1916610317um_a_b ).
thf(image_256773707um_a_b_decl,type,
image_256773707um_a_b: set_Pr1174980151um_a_b > set_nat > set_Sum_sum_a_b ).
thf(image_452296684at_nat_decl,type,
image_452296684at_nat: set_Pr689416536at_nat > set_Pr1647387645at_nat > set_nat ).
thf(image_320480233um_a_b_decl,type,
image_320480233um_a_b: set_Pr386468381um_a_b > set_Pr1986765409at_nat > set_Pr1174980151um_a_b ).
thf(image_1754351636um_a_b_decl,type,
image_1754351636um_a_b: set_Pr195945996um_a_b > set_Pr1986765409at_nat > set_Sum_sum_a_b ).
thf(image_128716052_b_nat_decl,type,
image_128716052_b_nat: set_Pr1902304780_b_nat > set_Pr1174980151um_a_b > set_nat ).
thf(image_869585130um_a_b_decl,type,
image_869585130um_a_b: set_Pr653770722um_a_b > set_Pr1174980151um_a_b > set_Sum_sum_a_b ).
thf(image_1117854795_b_nat_decl,type,
image_1117854795_b_nat: set_Pr375490359_b_nat > set_Sum_sum_a_b > set_nat ).
thf(image_1918588449um_a_b_decl,type,
image_1918588449um_a_b: set_Pr1916610317um_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b ).
thf(mainta522127984um_a_b_decl,type,
mainta522127984um_a_b: produc1871334759_a_nat > labele431970251um_a_b > $o ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(collec52779676at_nat_decl,type,
collec52779676at_nat: ( produc1032616263at_nat > $o ) > set_Pr1647387645at_nat ).
thf(collec1254333256um_a_b_decl,type,
collec1254333256um_a_b: ( produc1963079155um_a_b > $o ) > set_Pr409224873um_a_b ).
thf(collec492052930um_a_b_decl,type,
collec492052930um_a_b: ( produc1124793815um_a_b > $o ) > set_Pr1174980151um_a_b ).
thf(collec1769032088um_a_b_decl,type,
collec1769032088um_a_b: ( produc1548871597um_a_b > $o ) > set_Pr1916610317um_a_b ).
thf(collect_Sum_sum_a_b_decl,type,
collect_Sum_sum_a_b: ( sum_sum_a_b > $o ) > set_Sum_sum_a_b ).
thf(insert1909710879tant_a_decl,type,
insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).
thf(insert_nat_decl,type,
insert_nat: nat > set_nat > set_nat ).
thf(insert1625259895at_nat_decl,type,
insert1625259895at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat ).
thf(insert323157027um_a_b_decl,type,
insert323157027um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b ).
thf(insert271595217at_nat_decl,type,
insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(insert983991207um_a_b_decl,type,
insert983991207um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).
thf(insert1435405693um_a_b_decl,type,
insert1435405693um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > set_Pr1916610317um_a_b ).
thf(insert_Sum_sum_a_b_decl,type,
insert_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b ).
thf(standa1343274079tant_a_decl,type,
standa1343274079tant_a: standard_Constant_a > standard_Constant_a > produc1871334759_a_nat ).
thf(standa1410829644tant_a_decl,type,
standa1410829644tant_a: produc1871334759_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(member_nat_decl,type,
member_nat: nat > set_nat > $o ).
thf(member1696759390at_nat_decl,type,
member1696759390at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > $o ).
thf(member1502344244um_a_b_decl,type,
member1502344244um_a_b: produc1003469085um_a_b > set_Pr326391507um_a_b > $o ).
thf(member1998628618um_a_b_decl,type,
member1998628618um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > $o ).
thf(member1641046175um_a_b_decl,type,
member1641046175um_a_b: produc1394389750um_a_b > set_Pr1994339542um_a_b > $o ).
thf(member701585322at_nat_decl,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(member1139034387um_a_b_decl,type,
member1139034387um_a_b: produc204140796um_a_b > set_Pr1618094130um_a_b > $o ).
thf(member1294585472um_a_b_decl,type,
member1294585472um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > $o ).
thf(member834135910um_a_b_decl,type,
member834135910um_a_b: produc1546082365um_a_b > set_Pr386468381um_a_b > $o ).
thf(member585880557um_a_b_decl,type,
member585880557um_a_b: produc1798470614um_a_b > set_Pr195945996um_a_b > $o ).
thf(member748122307um_a_b_decl,type,
member748122307um_a_b: produc585753260um_a_b > set_Pr653770722um_a_b > $o ).
thf(member1249152_b_nat_decl,type,
member1249152_b_nat: produc1978941143_b_nat > set_Pr375490359_b_nat > $o ).
thf(member947389014um_a_b_decl,type,
member947389014um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > $o ).
thf(member_Sum_sum_a_b_decl,type,
member_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > $o ).
thf(g_decl,type,
g: labele431970251um_a_b ).
thf(f_decl,type,
f: set_Pr1174980151um_a_b ).
thf(l_decl,type,
l: standard_Constant_a ).
thf(v_decl,type,
v: sum_sum_a_b ).
thf(176,axiom,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
=> ~ ! [C: nat] :
~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_Domain_Ocases) ).
thf(892,plain,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
=> ~ ! [C: nat] :
~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(94,axiom,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Pr1916610317um_a_b] :
( ( domain2069673178um_a_b @ ( insert1435405693um_a_b @ ( produc176426981um_a_b @ A @ B ) @ C ) )
= ( insert_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Domain__insert) ).
thf(629,plain,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Pr1916610317um_a_b] :
( ( domain2069673178um_a_b @ ( insert1435405693um_a_b @ ( produc176426981um_a_b @ A @ B ) @ C ) )
= ( insert_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(268,axiom,
! [A: standard_Constant_a,B: sum_sum_a_b,C: sum_sum_a_b] :
( ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) )
= ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_graph__single) ).
thf(1168,plain,
! [A: standard_Constant_a,B: sum_sum_a_b,C: sum_sum_a_b] :
( ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) )
= ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(246,axiom,
! [A: set_Pr689416536at_nat] :
( ( image_452296684at_nat @ A @ bot_bo810816657at_nat )
= bot_bot_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Image__empty2) ).
thf(1105,plain,
! [A: set_Pr689416536at_nat] :
( ( image_452296684at_nat @ A @ bot_bo810816657at_nat )
= bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(161,axiom,
! [A: set_Pr1174980151um_a_b] :
( ( ! [B: produc1124793815um_a_b] :
~ ( member1294585472um_a_b @ B @ A ) )
= ( A = bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_all__not__in__conv) ).
thf(846,plain,
! [A: set_Pr1174980151um_a_b] :
( ( ! [B: produc1124793815um_a_b] :
~ ( member1294585472um_a_b @ B @ A ) )
= ( A = bot_bo575978147um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(200,axiom,
! [A: nat,B: nat,C: set_nat] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
=> ( ( A != B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_insertE) ).
thf(962,plain,
! [A: nat,B: nat,C: set_nat] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
=> ( ( A != B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(192,axiom,
! [A: set_Pr1647387645at_nat] : ( ord_le1909159005at_nat @ bot_bo810816657at_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_empty__subsetI) ).
thf(941,plain,
! [A: set_Pr1647387645at_nat] : ( ord_le1909159005at_nat @ bot_bo810816657at_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(137,axiom,
! [A: produc1124793815um_a_b,B: set_Pr326391507um_a_b,C: standard_Constant_a] :
( ( member1294585472um_a_b @ A @ ( image_1179143699um_a_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1502344244um_a_b @ ( produc414524239um_a_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Image__singleton__iff) ).
thf(777,plain,
! [A: produc1124793815um_a_b,B: set_Pr326391507um_a_b,C: standard_Constant_a] :
( ( member1294585472um_a_b @ A @ ( image_1179143699um_a_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1502344244um_a_b @ ( produc414524239um_a_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(4,axiom,
! [A: set_Pr1916610317um_a_b,B: produc1548871597um_a_b] :
( ( A = bot_bo225809273um_a_b )
=> ~ ( member947389014um_a_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_equals0D) ).
thf(352,plain,
! [A: set_Pr1916610317um_a_b,B: produc1548871597um_a_b] :
( ( A = bot_bo225809273um_a_b )
=> ~ ( member947389014um_a_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(182,axiom,
! [A: labele935650037_a_nat] :
( ( restri572569417_a_nat @ ( restri572569417_a_nat @ A ) )
= ( restri572569417_a_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_restrict__idemp) ).
thf(909,plain,
! [A: labele935650037_a_nat] :
( ( restri572569417_a_nat @ ( restri572569417_a_nat @ A ) )
= ( restri572569417_a_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(223,axiom,
! [A: labele431970251um_a_b] :
( ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ A ) @ ( labele577278695um_a_b @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_labeled__graph_Ocollapse) ).
thf(1031,plain,
! [A: labele431970251um_a_b] :
( ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ A ) @ ( labele577278695um_a_b @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(102,axiom,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b,D: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ B )
=> ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ C ) @ D )
=> ( member_Sum_sum_a_b @ C @ ( image_1918588449um_a_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_rev__ImageI) ).
thf(666,plain,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b,D: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ B )
=> ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ C ) @ D )
=> ( member_Sum_sum_a_b @ C @ ( image_1918588449um_a_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(311,axiom,
! [A: set_Pr1647387645at_nat] :
( ( ( domain1060562500at_nat @ A )
= bot_bo1160111033tant_a )
= ( A = bot_bo810816657at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Domain__empty__iff) ).
thf(1295,plain,
! [A: set_Pr1647387645at_nat] :
( ( ( domain1060562500at_nat @ A )
= bot_bo1160111033tant_a )
= ( A = bot_bo810816657at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(58,axiom,
! [A: standard_Constant_a] : ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_singletonI) ).
thf(523,plain,
! [A: standard_Constant_a] : ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(122,axiom,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
( ( ( insert323157027um_a_b @ A @ B )
= ( insert323157027um_a_b @ C @ bot_bo1262634813um_a_b ) )
= ( ( A = C )
& ( ord_le615126793um_a_b @ B @ ( insert323157027um_a_b @ C @ bot_bo1262634813um_a_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_singleton__insert__inj__eq_H) ).
thf(730,plain,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
( ( ( insert323157027um_a_b @ A @ B )
= ( insert323157027um_a_b @ C @ bot_bo1262634813um_a_b ) )
= ( ( A = C )
& ( ord_le615126793um_a_b @ B @ ( insert323157027um_a_b @ C @ bot_bo1262634813um_a_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(259,axiom,
! [A: product_prod_nat_nat,B: set_Pr1647387645at_nat,C: set_St761939237tant_a] :
( ( member701585322at_nat @ A @ ( image_127502653at_nat @ B @ C ) )
=> ~ ! [D: standard_Constant_a] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ D @ A ) @ B )
=> ~ ( member1632892294tant_a @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_ImageE) ).
thf(1142,plain,
! [A: product_prod_nat_nat,B: set_Pr1647387645at_nat,C: set_St761939237tant_a] :
( ( member701585322at_nat @ A @ ( image_127502653at_nat @ B @ C ) )
=> ~ ! [D: standard_Constant_a] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ D @ A ) @ B )
=> ~ ( member1632892294tant_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(281,axiom,
( ( getRel1465196352um_a_b @ standard_S_Bot_a @ g )
= bot_bo225809273um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_gr_I2_J) ).
thf(1205,plain,
( ( getRel1465196352um_a_b @ standard_S_Bot_a @ g )
= bot_bo225809273um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(36,axiom,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
= ( ? [C: produc1548871597um_a_b] : ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Domain__iff) ).
thf(449,plain,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
= ( ? [C: produc1548871597um_a_b] : ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(257,axiom,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
( ! [C: nat,D: sum_sum_a_b] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ C @ D ) @ A )
=> ( member1294585472um_a_b @ ( produc1808556047um_a_b @ C @ D ) @ B ) )
=> ( ord_le823954903um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_subrelI) ).
thf(1137,plain,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
( ! [C: nat,D: sum_sum_a_b] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ C @ D ) @ A )
=> ( member1294585472um_a_b @ ( produc1808556047um_a_b @ C @ D ) @ B ) )
=> ( ord_le823954903um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(62,axiom,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
=> ~ ! [C: sum_sum_a_b] :
~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_DomainE) ).
thf(533,plain,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
=> ~ ! [C: sum_sum_a_b] :
~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(290,axiom,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
( ( ~ ( member1294585472um_a_b @ A @ B )
=> ( A = C ) )
=> ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_insertCI) ).
thf(1233,plain,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
( ( ~ ( member1294585472um_a_b @ A @ B )
=> ( A = C ) )
=> ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(326,axiom,
! [A: nat > $o] :
( ( bot_bot_set_nat
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_empty__Collect__eq) ).
thf(1342,plain,
! [A: nat > $o] :
( ( bot_bot_set_nat
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(189,axiom,
! [A: produc1124793815um_a_b,B: set_Pr1618094130um_a_b,C: nat] :
( ( member1294585472um_a_b @ A @ ( image_1228479730um_a_b @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
= ( member1139034387um_a_b @ ( produc1346373166um_a_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Image__singleton__iff) ).
thf(930,plain,
! [A: produc1124793815um_a_b,B: set_Pr1618094130um_a_b,C: nat] :
( ( member1294585472um_a_b @ A @ ( image_1228479730um_a_b @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
= ( member1139034387um_a_b @ ( produc1346373166um_a_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(104,axiom,
! [A: produc1963079155um_a_b] :
~ ( member1998628618um_a_b @ A @ bot_bo1262634813um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_emptyE) ).
thf(670,plain,
! [A: produc1963079155um_a_b] :
~ ( member1998628618um_a_b @ A @ bot_bo1262634813um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(150,axiom,
! [A: set_Pr1647387645at_nat] :
( ( ? [B: produc1032616263at_nat] : ( member1696759390at_nat @ B @ A ) )
= ( A != bot_bo810816657at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_ex__in__conv) ).
thf(814,plain,
! [A: set_Pr1647387645at_nat] :
( ( ? [B: produc1032616263at_nat] : ( member1696759390at_nat @ B @ A ) )
= ( A != bot_bo810816657at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(321,axiom,
member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ v @ v ) ) @ ( labele1939049654um_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43__092_060open_062_IS__Idt_M_Av_M_Av_J_A_092_060in_062_Aedges_AG_092_060close_062) ).
thf(1327,plain,
member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ v @ v ) ) @ ( labele1939049654um_a_b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(21,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
( ( insert271595217at_nat @ A @ ( insert271595217at_nat @ A @ B ) )
= ( insert271595217at_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_insert__absorb2) ).
thf(404,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
( ( insert271595217at_nat @ A @ ( insert271595217at_nat @ A @ B ) )
= ( insert271595217at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(278,axiom,
! [A: produc1032616263at_nat,B: produc1032616263at_nat,C: set_Pr1647387645at_nat] :
( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ C ) )
= ( ( A = B )
| ( member1696759390at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_insert__iff) ).
thf(1196,plain,
! [A: produc1032616263at_nat,B: produc1032616263at_nat,C: set_Pr1647387645at_nat] :
( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ C ) )
= ( ( A = B )
| ( member1696759390at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(213,axiom,
! [A: nat,B: set_Pr1986765409at_nat,C: nat] :
( ( member_nat @ A @ ( image_nat_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
= ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Image__singleton__iff) ).
thf(1001,plain,
! [A: nat,B: set_Pr1986765409at_nat,C: nat] :
( ( member_nat @ A @ ( image_nat_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
= ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(174,axiom,
! [A: set_Pr1174980151um_a_b] :
( ! [B: produc1124793815um_a_b] :
~ ( member1294585472um_a_b @ B @ A )
=> ( A = bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_equals0I) ).
thf(885,plain,
! [A: set_Pr1174980151um_a_b] :
( ! [B: produc1124793815um_a_b] :
~ ( member1294585472um_a_b @ B @ A )
=> ( A = bot_bo575978147um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(332,axiom,
! [A: nat,B: set_nat] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_insert__absorb2) ).
thf(1359,plain,
! [A: nat,B: set_nat] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(297,axiom,
! [A: nat,B: nat,C: set_nat] :
( ( ( insert_nat @ A @ bot_bot_set_nat )
= ( insert_nat @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_nat @ C @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_singleton__insert__inj__eq) ).
thf(1254,plain,
! [A: nat,B: nat,C: set_nat] :
( ( ( insert_nat @ A @ bot_bot_set_nat )
= ( insert_nat @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_nat @ C @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(293,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_bot__nat__0_Oextremum) ).
thf(1243,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(253,axiom,
unival2092813468um_a_b @ f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_u) ).
thf(1127,plain,
unival2092813468um_a_b @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(16,axiom,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
= ( ? [C: sum_sum_a_b] : ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Domain__iff) ).
thf(389,plain,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
= ( ? [C: sum_sum_a_b] : ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(307,axiom,
ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_r) ).
thf(1287,plain,
ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(312,axiom,
! [A: produc1032616263at_nat > $o] :
( ( ( collec52779676at_nat @ A )
= bot_bo810816657at_nat )
= ( ! [B: produc1032616263at_nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Collect__empty__eq) ).
thf(1298,plain,
! [A: produc1032616263at_nat > $o] :
( ( ( collec52779676at_nat @ A )
= bot_bo810816657at_nat )
= ( ! [B: produc1032616263at_nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(10,axiom,
! [A: set_Pr1916610317um_a_b] :
( ( ? [B: produc1548871597um_a_b] : ( member947389014um_a_b @ B @ A ) )
= ( A != bot_bo225809273um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_ex__in__conv) ).
thf(372,plain,
! [A: set_Pr1916610317um_a_b] :
( ( ? [B: produc1548871597um_a_b] : ( member947389014um_a_b @ B @ A ) )
= ( A != bot_bo225809273um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,axiom,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Pr1916610317um_a_b,D: set_Sum_sum_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ C )
=> ( ( member_Sum_sum_a_b @ A @ D )
=> ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_ImageI) ).
thf(504,plain,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Pr1916610317um_a_b,D: set_Sum_sum_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ C )
=> ( ( member_Sum_sum_a_b @ A @ D )
=> ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(300,axiom,
! [A: sum_sum_a_b,B: set_Pr1174980151um_a_b,C: set_nat] :
( ( member_Sum_sum_a_b @ A @ ( image_256773707um_a_b @ B @ C ) )
=> ~ ! [D: nat] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ D @ A ) @ B )
=> ~ ( member_nat @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ImageE) ).
thf(1264,plain,
! [A: sum_sum_a_b,B: set_Pr1174980151um_a_b,C: set_nat] :
( ( member_Sum_sum_a_b @ A @ ( image_256773707um_a_b @ B @ C ) )
=> ~ ! [D: nat] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ D @ A ) @ B )
=> ~ ( member_nat @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(231,axiom,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ord_less_eq_set_nat @ ( domain1368163076um_a_b @ A ) @ ( domain1368163076um_a_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Domain__mono) ).
thf(1059,plain,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ord_less_eq_set_nat @ ( domain1368163076um_a_b @ A ) @ ( domain1368163076um_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(195,axiom,
( ( domain1368163076um_a_b @ f )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_d) ).
thf(949,plain,
( ( domain1368163076um_a_b @ f )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(65,axiom,
( ( domain2069673178um_a_b @ bot_bo225809273um_a_b )
= bot_bo1491243248um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Domain__empty) ).
thf(542,plain,
( ( domain2069673178um_a_b @ bot_bo225809273um_a_b )
= bot_bo1491243248um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(185,axiom,
! [A: product_prod_nat_nat,B: set_Pr1647387645at_nat,C: standard_Constant_a] :
( ( member701585322at_nat @ A @ ( image_127502653at_nat @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1696759390at_nat @ ( produc407553657at_nat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Image__singleton__iff) ).
thf(917,plain,
! [A: product_prod_nat_nat,B: set_Pr1647387645at_nat,C: standard_Constant_a] :
( ( member701585322at_nat @ A @ ( image_127502653at_nat @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1696759390at_nat @ ( produc407553657at_nat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(115,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
( ( ~ ( member701585322at_nat @ A @ B )
=> ( A = C ) )
=> ( member701585322at_nat @ A @ ( insert271595217at_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_insertCI) ).
thf(702,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
( ( ~ ( member701585322at_nat @ A @ B )
=> ( A = C ) )
=> ( member701585322at_nat @ A @ ( insert271595217at_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(5,axiom,
! [A: produc1548871597um_a_b,B: set_Pr1916610317um_a_b,C: set_Pr1916610317um_a_b] :
( ( ord_le1059794605um_a_b @ ( insert1435405693um_a_b @ A @ B ) @ C )
= ( ( member947389014um_a_b @ A @ C )
& ( ord_le1059794605um_a_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_insert__subset) ).
thf(357,plain,
! [A: produc1548871597um_a_b,B: set_Pr1916610317um_a_b,C: set_Pr1916610317um_a_b] :
( ( ord_le1059794605um_a_b @ ( insert1435405693um_a_b @ A @ B ) @ C )
= ( ( member947389014um_a_b @ A @ C )
& ( ord_le1059794605um_a_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(276,axiom,
! [A: set_Pr1174980151um_a_b] :
( ( ord_le823954903um_a_b @ A @ bot_bo575978147um_a_b )
= ( A = bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_subset__empty) ).
thf(1191,plain,
! [A: set_Pr1174980151um_a_b] :
( ( ord_le823954903um_a_b @ A @ bot_bo575978147um_a_b )
= ( A = bot_bo575978147um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(71,axiom,
! [A: produc1963079155um_a_b] :
~ ( member1998628618um_a_b @ A @ bot_bo1262634813um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_empty__iff) ).
thf(559,plain,
! [A: produc1963079155um_a_b] :
~ ( member1998628618um_a_b @ A @ bot_bo1262634813um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(339,axiom,
! [A: labele935650037_a_nat] :
( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ A ) )
= ( labele1810595089_a_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_vertices__restrict) ).
thf(1379,plain,
! [A: labele935650037_a_nat] :
( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ A ) )
= ( labele1810595089_a_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(27,axiom,
! [A: set_Sum_sum_a_b,B: sum_sum_a_b] :
( ( A = bot_bo1491243248um_a_b )
=> ~ ( member_Sum_sum_a_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_equals0D) ).
thf(421,plain,
! [A: set_Sum_sum_a_b,B: sum_sum_a_b] :
( ( A = bot_bo1491243248um_a_b )
=> ~ ( member_Sum_sum_a_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(217,axiom,
! [A: sum_sum_a_b > $o,B: sum_sum_a_b > $o] :
( ! [C: sum_sum_a_b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ A ) @ ( collect_Sum_sum_a_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_Collect__mono) ).
thf(1013,plain,
! [A: sum_sum_a_b > $o,B: sum_sum_a_b > $o] :
( ! [C: sum_sum_a_b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ A ) @ ( collect_Sum_sum_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(25,axiom,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Pr1916610317um_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ C )
=> ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_Domain_ODomainI) ).
thf(416,plain,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Pr1916610317um_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ C )
=> ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(333,axiom,
! [A: labele935650037_a_nat,B: set_Pr507214050_b_nat] :
( ( graph_1815313447_b_nat @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ A @ B )
= ( ( B = bot_bo1746228598_b_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_graph__homomorphism__empty) ).
thf(1362,plain,
! [A: labele935650037_a_nat,B: set_Pr507214050_b_nat] :
( ( graph_1815313447_b_nat @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ A @ B )
= ( ( B = bot_bo1746228598_b_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(151,axiom,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
=> ( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_in__mono) ).
thf(817,plain,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
=> ( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(179,axiom,
( ( domain1060562500at_nat @ bot_bo810816657at_nat )
= bot_bo1160111033tant_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Domain__empty) ).
thf(902,plain,
( ( domain1060562500at_nat @ bot_bo810816657at_nat )
= bot_bo1160111033tant_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(131,axiom,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b,C: sum_sum_a_b > $o] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
=> ( ! [D: sum_sum_a_b,E: sum_sum_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Domain_Oinducts) ).
thf(756,plain,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b,C: sum_sum_a_b > $o] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
=> ( ! [D: sum_sum_a_b,E: sum_sum_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(141,axiom,
~ ! [A: sum_sum_a_b] :
~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ A ) @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(789,plain,
~ ! [A: sum_sum_a_b] :
~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ A ) @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(337,axiom,
! [A: set_Sum_sum_a_b] :
( ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ A )
= ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_graph__empty__e) ).
thf(1373,plain,
! [A: set_Sum_sum_a_b] :
( ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ A )
= ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(92,axiom,
! [A: produc1548871597um_a_b > $o] :
( ( ( collec1769032088um_a_b @ A )
= bot_bo225809273um_a_b )
= ( ! [B: produc1548871597um_a_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Collect__empty__eq) ).
thf(623,plain,
! [A: produc1548871597um_a_b > $o] :
( ( ( collec1769032088um_a_b @ A )
= bot_bo225809273um_a_b )
= ( ! [B: produc1548871597um_a_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(157,axiom,
! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,C: set_Pr1174980151um_a_b] :
( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ C ) )
=> ( ( A != B )
=> ( member1294585472um_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_insertE) ).
thf(834,plain,
! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,C: set_Pr1174980151um_a_b] :
( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ C ) )
=> ( ( A != B )
=> ( member1294585472um_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(262,axiom,
! [A: nat,B: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
= ( ? [C: sum_sum_a_b] : ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Domain__iff) ).
thf(1151,plain,
! [A: nat,B: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
= ( ? [C: sum_sum_a_b] : ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(219,axiom,
( ord_le192794300um_a_b
= ( ^ [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
! [C: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_subset__iff) ).
thf(1020,plain,
( ord_le192794300um_a_b
= ( ^ [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
! [C: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(147,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_empty__subsetI) ).
thf(806,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(273,axiom,
! [A: set_Pr1174980151um_a_b] :
( ( ? [B: produc1124793815um_a_b] : ( member1294585472um_a_b @ B @ A ) )
= ( A != bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_ex__in__conv) ).
thf(1183,plain,
! [A: set_Pr1174980151um_a_b] :
( ( ? [B: produc1124793815um_a_b] : ( member1294585472um_a_b @ B @ A ) )
= ( A != bot_bo575978147um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(44,axiom,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b] :
( ( ~ ( member_Sum_sum_a_b @ A @ B )
=> ( A = C ) )
=> ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_insertCI) ).
thf(480,plain,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b] :
( ( ~ ( member_Sum_sum_a_b @ A @ B )
=> ( A = C ) )
=> ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(206,axiom,
! [A: set_Pr1174980151um_a_b] :
( ( ( domain1368163076um_a_b @ A )
= bot_bot_set_nat )
= ( A = bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Domain__empty__iff) ).
thf(981,plain,
! [A: set_Pr1174980151um_a_b] :
( ( ( domain1368163076um_a_b @ A )
= bot_bot_set_nat )
= ( A = bot_bo575978147um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(96,axiom,
! [A: sum_sum_a_b,B: set_Pr195945996um_a_b,C: product_prod_nat_nat] :
( ( member_Sum_sum_a_b @ A @ ( image_1754351636um_a_b @ B @ ( insert271595217at_nat @ C @ bot_bo2130386637at_nat ) ) )
= ( member585880557um_a_b @ ( produc1872245072um_a_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Image__singleton__iff) ).
thf(634,plain,
! [A: sum_sum_a_b,B: set_Pr195945996um_a_b,C: product_prod_nat_nat] :
( ( member_Sum_sum_a_b @ A @ ( image_1754351636um_a_b @ B @ ( insert271595217at_nat @ C @ bot_bo2130386637at_nat ) ) )
= ( member585880557um_a_b @ ( produc1872245072um_a_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(168,axiom,
! [A: set_nat] :
( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
= ( A = bot_bot_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_subset__empty) ).
thf(866,plain,
! [A: set_nat] :
( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
= ( A = bot_bot_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(100,axiom,
! [A: standard_Constant_a,B: standard_Constant_a,C: set_St761939237tant_a] :
( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ C ) )
=> ( ( A != B )
=> ( member1632892294tant_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_insertE) ).
thf(660,plain,
! [A: standard_Constant_a,B: standard_Constant_a,C: set_St761939237tant_a] :
( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ C ) )
=> ( ( A != B )
=> ( member1632892294tant_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(212,axiom,
! [A: sum_sum_a_b,B: set_Pr653770722um_a_b,C: produc1124793815um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_869585130um_a_b @ B @ ( insert983991207um_a_b @ C @ bot_bo575978147um_a_b ) ) )
= ( member748122307um_a_b @ ( produc831476262um_a_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Image__singleton__iff) ).
thf(998,plain,
! [A: sum_sum_a_b,B: set_Pr653770722um_a_b,C: produc1124793815um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_869585130um_a_b @ B @ ( insert983991207um_a_b @ C @ bot_bo575978147um_a_b ) ) )
= ( member748122307um_a_b @ ( produc831476262um_a_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(327,axiom,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
= ( ? [C: nat,D: nat] :
( ( A = C )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_Domain_Osimps) ).
thf(1345,plain,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
= ( ? [C: nat,D: nat] :
( ( A = C )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_le__trans) ).
thf(428,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(162,axiom,
! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,C: set_Pr1174980151um_a_b] :
( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ C ) )
= ( ( A = B )
| ( member1294585472um_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_insert__iff) ).
thf(849,plain,
! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,C: set_Pr1174980151um_a_b] :
( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ C ) )
= ( ( A = B )
| ( member1294585472um_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_nat__le__linear) ).
thf(507,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(252,axiom,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( A = B )
=> ~ ( ( ord_le192794300um_a_b @ A @ B )
=> ~ ( ord_le192794300um_a_b @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_equalityE) ).
thf(1119,plain,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( A = B )
=> ~ ( ( ord_le192794300um_a_b @ A @ B )
=> ~ ( ord_le192794300um_a_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(136,axiom,
! [A: set_Sum_sum_a_b] :
( ( image_1918588449um_a_b @ bot_bo225809273um_a_b @ A )
= bot_bo1491243248um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Image__empty1) ).
thf(774,plain,
! [A: set_Sum_sum_a_b] :
( ( image_1918588449um_a_b @ bot_bo225809273um_a_b @ A )
= bot_bo1491243248um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(236,axiom,
( ( getRel1465196352um_a_b @ standard_S_Idt_a @ g )
= ( id_on_Sum_sum_a_b @ ( labele577278695um_a_b @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_gr_I1_J) ).
thf(1074,plain,
( ( getRel1465196352um_a_b @ standard_S_Idt_a @ g )
= ( id_on_Sum_sum_a_b @ ( labele577278695um_a_b @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(37,axiom,
! [A: produc1548871597um_a_b > $o] :
( ( bot_bo225809273um_a_b
= ( collec1769032088um_a_b @ A ) )
= ( ! [B: produc1548871597um_a_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_empty__Collect__eq) ).
thf(452,plain,
! [A: produc1548871597um_a_b > $o] :
( ( bot_bo225809273um_a_b
= ( collec1769032088um_a_b @ A ) )
= ( ! [B: produc1548871597um_a_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(186,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_le__0__eq) ).
thf(920,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(13,axiom,
! [A: produc1548871597um_a_b] :
~ ( member947389014um_a_b @ A @ bot_bo225809273um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_emptyE) ).
thf(380,plain,
! [A: produc1548871597um_a_b] :
~ ( member947389014um_a_b @ A @ bot_bo225809273um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(142,axiom,
! [A: standard_Constant_a,B: nat,C: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_graph__single) ).
thf(793,plain,
! [A: standard_Constant_a,B: nat,C: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(315,axiom,
! [A: nat,B: set_nat,C: sum_sum_a_b,D: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ B )
=> ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ C ) @ D )
=> ( member_Sum_sum_a_b @ C @ ( image_256773707um_a_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rev__ImageI) ).
thf(1306,plain,
! [A: nat,B: set_nat,C: sum_sum_a_b,D: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ B )
=> ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ C ) @ D )
=> ( member_Sum_sum_a_b @ C @ ( image_256773707um_a_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(279,axiom,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_empty__iff) ).
thf(1199,plain,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(8,axiom,
! [A: set_Pr1916610317um_a_b] :
( ( ! [B: produc1548871597um_a_b] :
~ ( member947389014um_a_b @ B @ A ) )
= ( A = bot_bo225809273um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_all__not__in__conv) ).
thf(366,plain,
! [A: set_Pr1916610317um_a_b] :
( ( ! [B: produc1548871597um_a_b] :
~ ( member947389014um_a_b @ B @ A ) )
= ( A = bot_bo225809273um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(317,axiom,
! [A: set_Pr1916610317um_a_b,B: set_Pr1916610317um_a_b,C: set_Sum_sum_a_b,D: set_Sum_sum_a_b] :
( ( ord_le1059794605um_a_b @ A @ B )
=> ( ( ord_le192794300um_a_b @ C @ D )
=> ( ord_le192794300um_a_b @ ( image_1918588449um_a_b @ A @ C ) @ ( image_1918588449um_a_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Image__mono) ).
thf(1311,plain,
! [A: set_Pr1916610317um_a_b,B: set_Pr1916610317um_a_b,C: set_Sum_sum_a_b,D: set_Sum_sum_a_b] :
( ( ord_le1059794605um_a_b @ A @ B )
=> ( ( ord_le192794300um_a_b @ C @ D )
=> ( ord_le192794300um_a_b @ ( image_1918588449um_a_b @ A @ C ) @ ( image_1918588449um_a_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(228,axiom,
( ( domain_nat_nat @ bot_bo2130386637at_nat )
= bot_bot_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Domain__empty) ).
thf(1047,plain,
( ( domain_nat_nat @ bot_bo2130386637at_nat )
= bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(54,axiom,
! [A: standard_Constant_a,B: produc1548871597um_a_b,C: set_Pr409224873um_a_b] :
( ( domain1362581744um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ C ) )
= ( insert1909710879tant_a @ A @ ( domain1362581744um_a_b @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Domain__insert) ).
thf(512,plain,
! [A: standard_Constant_a,B: produc1548871597um_a_b,C: set_Pr409224873um_a_b] :
( ( domain1362581744um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ C ) )
= ( insert1909710879tant_a @ A @ ( domain1362581744um_a_b @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(33,axiom,
! [A: sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_singletonI) ).
thf(439,plain,
! [A: sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(198,axiom,
! [A: produc1032616263at_nat,B: produc1032616263at_nat,C: set_Pr1647387645at_nat] :
( ( ( insert1625259895at_nat @ A @ bot_bo810816657at_nat )
= ( insert1625259895at_nat @ B @ C ) )
= ( ( B = A )
& ( ord_le1909159005at_nat @ C @ ( insert1625259895at_nat @ A @ bot_bo810816657at_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_singleton__insert__inj__eq) ).
thf(957,plain,
! [A: produc1032616263at_nat,B: produc1032616263at_nat,C: set_Pr1647387645at_nat] :
( ( ( insert1625259895at_nat @ A @ bot_bo810816657at_nat )
= ( insert1625259895at_nat @ B @ C ) )
= ( ( B = A )
& ( ord_le1909159005at_nat @ C @ ( insert1625259895at_nat @ A @ bot_bo810816657at_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(127,axiom,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b,C: set_Sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_1918588449um_a_b @ B @ C ) )
= ( ? [D: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ D @ C )
& ( member947389014um_a_b @ ( produc176426981um_a_b @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Image__iff) ).
thf(746,plain,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b,C: set_Sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_1918588449um_a_b @ B @ C ) )
= ( ? [D: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ D @ C )
& ( member947389014um_a_b @ ( produc176426981um_a_b @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(226,axiom,
( f
= ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_f) ).
thf(1042,plain,
( f
= ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(167,axiom,
! [A: set_Pr1647387645at_nat] :
( ! [B: produc1032616263at_nat] :
~ ( member1696759390at_nat @ B @ A )
=> ( A = bot_bo810816657at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_equals0I) ).
thf(862,plain,
! [A: set_Pr1647387645at_nat] :
( ! [B: produc1032616263at_nat] :
~ ( member1696759390at_nat @ B @ A )
=> ( A = bot_bo810816657at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(270,axiom,
! [A: labele935650037_a_nat] :
( ( labele16114835_a_nat @ ( labele195203296_a_nat @ A ) @ ( labele1810595089_a_nat @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_labeled__graph_Ocollapse) ).
thf(1174,plain,
! [A: labele935650037_a_nat] :
( ( labele16114835_a_nat @ ( labele195203296_a_nat @ A ) @ ( labele1810595089_a_nat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(152,axiom,
! [A: set_Pr1647387645at_nat] :
( ( ! [B: produc1032616263at_nat] :
~ ( member1696759390at_nat @ B @ A ) )
= ( A = bot_bo810816657at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_all__not__in__conv) ).
thf(820,plain,
! [A: set_Pr1647387645at_nat] :
( ( ! [B: produc1032616263at_nat] :
~ ( member1696759390at_nat @ B @ A ) )
= ( A = bot_bo810816657at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(17,axiom,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
( ( ord_le615126793um_a_b @ A @ B )
=> ( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_subsetD) ).
thf(392,plain,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
( ( ord_le615126793um_a_b @ A @ B )
=> ( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(22,axiom,
! [A: produc1548871597um_a_b,B: set_Pr1916610317um_a_b,C: produc1548871597um_a_b] :
( ( ( insert1435405693um_a_b @ A @ B )
= ( insert1435405693um_a_b @ C @ bot_bo225809273um_a_b ) )
= ( ( A = C )
& ( ord_le1059794605um_a_b @ B @ ( insert1435405693um_a_b @ C @ bot_bo225809273um_a_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_singleton__insert__inj__eq_H) ).
thf(407,plain,
! [A: produc1548871597um_a_b,B: set_Pr1916610317um_a_b,C: produc1548871597um_a_b] :
( ( ( insert1435405693um_a_b @ A @ B )
= ( insert1435405693um_a_b @ C @ bot_bo225809273um_a_b ) )
= ( ( A = C )
& ( ord_le1059794605um_a_b @ B @ ( insert1435405693um_a_b @ C @ bot_bo225809273um_a_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(336,axiom,
! [A: produc1032616263at_nat,B: set_Pr1647387645at_nat] :
( ( insert1625259895at_nat @ A @ ( insert1625259895at_nat @ A @ B ) )
= ( insert1625259895at_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_insert__absorb2) ).
thf(1370,plain,
! [A: produc1032616263at_nat,B: set_Pr1647387645at_nat] :
( ( insert1625259895at_nat @ A @ ( insert1625259895at_nat @ A @ B ) )
= ( insert1625259895at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(285,axiom,
! [A: nat,B: sum_sum_a_b,C: set_Pr1174980151um_a_b,D: set_nat] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ C )
=> ( ( member_nat @ A @ D )
=> ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_ImageI) ).
thf(1217,plain,
! [A: nat,B: sum_sum_a_b,C: set_Pr1174980151um_a_b,D: set_nat] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ C )
=> ( ( member_nat @ A @ D )
=> ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(85,axiom,
! [A: standard_Constant_a,B: produc1548871597um_a_b,C: set_Pr409224873um_a_b,D: set_St761939237tant_a] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ C )
=> ( ( member1632892294tant_a @ A @ D )
=> ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_ImageI) ).
thf(598,plain,
! [A: standard_Constant_a,B: produc1548871597um_a_b,C: set_Pr409224873um_a_b,D: set_St761939237tant_a] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ C )
=> ( ( member1632892294tant_a @ A @ D )
=> ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(334,axiom,
! [A: produc1032616263at_nat] : ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ A @ bot_bo810816657at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_singletonI) ).
thf(1365,plain,
! [A: produc1032616263at_nat] : ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ A @ bot_bo810816657at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(172,axiom,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ ( insert_Sum_sum_a_b @ A @ B ) @ C )
= ( ( member_Sum_sum_a_b @ A @ C )
& ( ord_le192794300um_a_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_insert__subset) ).
thf(879,plain,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ ( insert_Sum_sum_a_b @ A @ B ) @ C )
= ( ( member_Sum_sum_a_b @ A @ C )
& ( ord_le192794300um_a_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(163,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_le__zero__eq) ).
thf(852,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(175,axiom,
! [A: produc1032616263at_nat,B: set_Pr1647387645at_nat,C: produc1032616263at_nat] :
( ( ( insert1625259895at_nat @ A @ B )
= ( insert1625259895at_nat @ C @ bot_bo810816657at_nat ) )
= ( ( A = C )
& ( ord_le1909159005at_nat @ B @ ( insert1625259895at_nat @ C @ bot_bo810816657at_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_singleton__insert__inj__eq_H) ).
thf(889,plain,
! [A: produc1032616263at_nat,B: set_Pr1647387645at_nat,C: produc1032616263at_nat] :
( ( ( insert1625259895at_nat @ A @ B )
= ( insert1625259895at_nat @ C @ bot_bo810816657at_nat ) )
= ( ( A = C )
& ( ord_le1909159005at_nat @ B @ ( insert1625259895at_nat @ C @ bot_bo810816657at_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(265,axiom,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b] :
( ( insert983991207um_a_b @ A @ ( insert983991207um_a_b @ A @ B ) )
= ( insert983991207um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_insert__absorb2) ).
thf(1159,plain,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b] :
( ( insert983991207um_a_b @ A @ ( insert983991207um_a_b @ A @ B ) )
= ( insert983991207um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(238,axiom,
! [A: nat,B: set_nat,C: nat,D: set_Pr1986765409at_nat] :
( ( member_nat @ A @ B )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ D )
=> ( member_nat @ C @ ( image_nat_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rev__ImageI) ).
thf(1079,plain,
! [A: nat,B: set_nat,C: nat,D: set_Pr1986765409at_nat] :
( ( member_nat @ A @ B )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ D )
=> ( member_nat @ C @ ( image_nat_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_le__antisym) ).
thf(682,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(305,axiom,
! [A: produc1032616263at_nat,B: produc1032616263at_nat,C: set_Pr1647387645at_nat] :
( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ C ) )
=> ( ( A != B )
=> ( member1696759390at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_insertE) ).
thf(1281,plain,
! [A: produc1032616263at_nat,B: produc1032616263at_nat,C: set_Pr1647387645at_nat] :
( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ C ) )
=> ( ( A != B )
=> ( member1696759390at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(80,axiom,
! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,C: set_Pr409224873um_a_b] :
( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ C ) )
= ( ( A = B )
| ( member1998628618um_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_insert__iff) ).
thf(583,plain,
! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,C: set_Pr409224873um_a_b] :
( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ C ) )
= ( ( A = B )
| ( member1998628618um_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(155,axiom,
! [A: set_Pr1174980151um_a_b,B: set_Pr1647387645at_nat,C: set_Pr409224873um_a_b,D: nat,E: sum_sum_a_b,F: nat,G: sum_sum_a_b,H: standard_Constant_a] :
( ( edge_p1382426714tant_a @ A @ B @ C )
=> ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ D @ E ) @ A )
=> ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ F @ G ) @ A )
=> ( ( member1696759390at_nat @ ( produc407553657at_nat @ H @ ( product_Pair_nat_nat @ D @ F ) ) @ B )
=> ( member1998628618um_a_b @ ( produc1697725733um_a_b @ H @ ( produc176426981um_a_b @ E @ G ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_edge__preserving__atomic) ).
thf(830,plain,
! [A: set_Pr1174980151um_a_b,B: set_Pr1647387645at_nat,C: set_Pr409224873um_a_b,D: nat,E: sum_sum_a_b,F: nat,G: sum_sum_a_b,H: standard_Constant_a] :
( ( edge_p1382426714tant_a @ A @ B @ C )
=> ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ D @ E ) @ A )
=> ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ F @ G ) @ A )
=> ( ( member1696759390at_nat @ ( produc407553657at_nat @ H @ ( product_Pair_nat_nat @ D @ F ) ) @ B )
=> ( member1998628618um_a_b @ ( produc1697725733um_a_b @ H @ ( produc176426981um_a_b @ E @ G ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(47,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a] :
( ( insert1909710879tant_a @ A @ ( insert1909710879tant_a @ A @ B ) )
= ( insert1909710879tant_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_insert__absorb2) ).
thf(493,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a] :
( ( insert1909710879tant_a @ A @ ( insert1909710879tant_a @ A @ B ) )
= ( insert1909710879tant_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(283,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ! [C: nat,D: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ A )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ B ) )
=> ( ord_le841296385at_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_subrelI) ).
thf(1210,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ! [C: nat,D: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ A )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ B ) )
=> ( ord_le841296385at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(69,axiom,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
( ( ~ ( member1998628618um_a_b @ A @ B )
=> ( A = C ) )
=> ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_insertCI) ).
thf(551,plain,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
( ( ~ ( member1998628618um_a_b @ A @ B )
=> ( A = C ) )
=> ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(254,axiom,
! [A: produc1124793815um_a_b] :
~ ( member1294585472um_a_b @ A @ bot_bo575978147um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_empty__iff) ).
thf(1128,plain,
! [A: produc1124793815um_a_b] :
~ ( member1294585472um_a_b @ A @ bot_bo575978147um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(329,axiom,
! [A: labele935650037_a_nat] :
( ( ord_le1909159005at_nat @ ( labele195203296_a_nat @ A ) @ ( labele195203296_a_nat @ ( restri572569417_a_nat @ A ) ) )
=> ( A
= ( restri572569417_a_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_restrict__subsD) ).
thf(1350,plain,
! [A: labele935650037_a_nat] :
( ( ord_le1909159005at_nat @ ( labele195203296_a_nat @ A ) @ ( labele195203296_a_nat @ ( restri572569417_a_nat @ A ) ) )
=> ( A
= ( restri572569417_a_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(78,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_less_eq_set_nat @ ( domain_nat_nat @ A ) @ ( domain_nat_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Domain__mono) ).
thf(578,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_less_eq_set_nat @ ( domain_nat_nat @ A ) @ ( domain_nat_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(113,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_insertI1) ).
thf(697,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(218,axiom,
! [A: set_nat] :
( ( ! [B: nat] :
~ ( member_nat @ B @ A ) )
= ( A = bot_bot_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_all__not__in__conv) ).
thf(1017,plain,
! [A: set_nat] :
( ( ! [B: nat] :
~ ( member_nat @ B @ A ) )
= ( A = bot_bot_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(322,axiom,
! [A: nat,B: nat,C: set_nat] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
= ( ( A = B )
| ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_insert__iff) ).
thf(1328,plain,
! [A: nat,B: nat,C: set_nat] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
= ( ( A = B )
| ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(233,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_less__eq__nat_Osimps_I1_J) ).
thf(1064,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(243,axiom,
! [A: set_Pr375490359_b_nat] :
( ( image_1117854795_b_nat @ A @ bot_bo1491243248um_a_b )
= bot_bot_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Image__empty2) ).
thf(1096,plain,
! [A: set_Pr375490359_b_nat] :
( ( image_1117854795_b_nat @ A @ bot_bo1491243248um_a_b )
= bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(169,axiom,
( ( domain1368163076um_a_b @ bot_bo575978147um_a_b )
= bot_bot_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Domain__empty) ).
thf(869,plain,
( ( domain1368163076um_a_b @ bot_bo575978147um_a_b )
= bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(248,axiom,
! [A: set_Pr653770722um_a_b] :
( ( image_869585130um_a_b @ A @ bot_bo575978147um_a_b )
= bot_bo1491243248um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Image__empty2) ).
thf(1111,plain,
! [A: set_Pr653770722um_a_b] :
( ( image_869585130um_a_b @ A @ bot_bo575978147um_a_b )
= bot_bo1491243248um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(288,axiom,
! [A: produc1032616263at_nat > $o] :
( ( bot_bo810816657at_nat
= ( collec52779676at_nat @ A ) )
= ( ! [B: produc1032616263at_nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_empty__Collect__eq) ).
thf(1227,plain,
! [A: produc1032616263at_nat > $o] :
( ( bot_bo810816657at_nat
= ( collec52779676at_nat @ A ) )
= ( ! [B: produc1032616263at_nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(139,axiom,
! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,C: set_Pr1916610317um_a_b] :
( ( ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b )
= ( insert1435405693um_a_b @ B @ C ) )
= ( ( B = A )
& ( ord_le1059794605um_a_b @ C @ ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_singleton__insert__inj__eq) ).
thf(783,plain,
! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,C: set_Pr1916610317um_a_b] :
( ( ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b )
= ( insert1435405693um_a_b @ B @ C ) )
= ( ( B = A )
& ( ord_le1059794605um_a_b @ C @ ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(251,axiom,
mainta522127984um_a_b @ ( standa1343274079tant_a @ standard_S_Idt_a @ l ) @ g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351__092_060open_062maintained_A_Icongruence__rule_AS__Idt_Al_J_AG_092_060close_062) ).
thf(1118,plain,
mainta522127984um_a_b @ ( standa1343274079tant_a @ standard_S_Idt_a @ l ) @ g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(103,axiom,
unival1487587672um_a_b @ bot_bo1262634813um_a_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_univalent__empty) ).
thf(669,plain,
unival1487587672um_a_b @ bot_bo1262634813um_a_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(43,axiom,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
( ! [C: produc1963079155um_a_b] :
( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) )
=> ( ord_le615126793um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_subsetI) ).
thf(476,plain,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
( ! [C: produc1963079155um_a_b] :
( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) )
=> ( ord_le615126793um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(97,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_Nat_Oex__has__greatest__nat) ).
thf(637,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(46,axiom,
! [A: set_Pr409224873um_a_b] :
( ! [B: produc1963079155um_a_b] :
~ ( member1998628618um_a_b @ B @ A )
=> ( A = bot_bo1262634813um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_equals0I) ).
thf(489,plain,
! [A: set_Pr409224873um_a_b] :
( ! [B: produc1963079155um_a_b] :
~ ( member1998628618um_a_b @ B @ A )
=> ( A = bot_bo1262634813um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(284,axiom,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
( ( ( insert983991207um_a_b @ A @ B )
= ( insert983991207um_a_b @ C @ bot_bo575978147um_a_b ) )
= ( ( A = C )
& ( ord_le823954903um_a_b @ B @ ( insert983991207um_a_b @ C @ bot_bo575978147um_a_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_singleton__insert__inj__eq_H) ).
thf(1214,plain,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
( ( ( insert983991207um_a_b @ A @ B )
= ( insert983991207um_a_b @ C @ bot_bo575978147um_a_b ) )
= ( ( A = C )
& ( ord_le823954903um_a_b @ B @ ( insert983991207um_a_b @ C @ bot_bo575978147um_a_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(282,axiom,
! [A: produc1032616263at_nat] :
~ ( member1696759390at_nat @ A @ bot_bo810816657at_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_emptyE) ).
thf(1207,plain,
! [A: produc1032616263at_nat] :
~ ( member1696759390at_nat @ A @ bot_bo810816657at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(107,axiom,
! [A: produc1963079155um_a_b > $o] :
( ( bot_bo1262634813um_a_b
= ( collec1254333256um_a_b @ A ) )
= ( ! [B: produc1963079155um_a_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_empty__Collect__eq) ).
thf(679,plain,
! [A: produc1963079155um_a_b > $o] :
( ( bot_bo1262634813um_a_b
= ( collec1254333256um_a_b @ A ) )
= ( ! [B: produc1963079155um_a_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(67,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_le__refl) ).
thf(547,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(222,axiom,
! [A: produc1032616263at_nat,B: set_Pr1647387645at_nat,C: set_Pr1647387645at_nat] :
( ( ord_le1909159005at_nat @ ( insert1625259895at_nat @ A @ B ) @ C )
= ( ( member1696759390at_nat @ A @ C )
& ( ord_le1909159005at_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_insert__subset) ).
thf(1028,plain,
! [A: produc1032616263at_nat,B: set_Pr1647387645at_nat,C: set_Pr1647387645at_nat] :
( ( ord_le1909159005at_nat @ ( insert1625259895at_nat @ A @ B ) @ C )
= ( ( member1696759390at_nat @ A @ C )
& ( ord_le1909159005at_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(239,axiom,
! [A: produc1032616263at_nat,B: set_Pr1647387645at_nat,C: produc1032616263at_nat] :
( ( ~ ( member1696759390at_nat @ A @ B )
=> ( A = C ) )
=> ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_insertCI) ).
thf(1082,plain,
! [A: produc1032616263at_nat,B: set_Pr1647387645at_nat,C: produc1032616263at_nat] :
( ( ~ ( member1696759390at_nat @ A @ B )
=> ( A = C ) )
=> ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(310,axiom,
! [A: labele431970251um_a_b] :
( ( labele577278695um_a_b @ ( restri1162247455um_a_b @ A ) )
= ( labele577278695um_a_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_vertices__restrict) ).
thf(1292,plain,
! [A: labele431970251um_a_b] :
( ( labele577278695um_a_b @ ( restri1162247455um_a_b @ A ) )
= ( labele577278695um_a_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(190,axiom,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b )
= ( insert_Sum_sum_a_b @ B @ C ) )
= ( ( B = A )
& ( ord_le192794300um_a_b @ C @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_singleton__insert__inj__eq) ).
thf(933,plain,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b )
= ( insert_Sum_sum_a_b @ B @ C ) )
= ( ( B = A )
& ( ord_le192794300um_a_b @ C @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(158,axiom,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
=> ~ ! [C: product_prod_nat_nat] :
~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_DomainE) ).
thf(837,plain,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
=> ~ ! [C: product_prod_nat_nat] :
~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(244,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_bot__nat__0_Oextremum__uniqueI) ).
thf(1099,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(55,axiom,
( ord_le823954903um_a_b
= ( ^ [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
! [C: produc1124793815um_a_b] :
( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_subset__iff) ).
thf(515,plain,
( ord_le823954903um_a_b
= ( ^ [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
! [C: produc1124793815um_a_b] :
( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(340,axiom,
! [A: set_Pr1134469976at_nat] :
( ( image_489788268at_nat @ A @ bot_bot_set_nat )
= bot_bo810816657at_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Image__empty2) ).
thf(1382,plain,
! [A: set_Pr1134469976at_nat] :
( ( image_489788268at_nat @ A @ bot_bot_set_nat )
= bot_bo810816657at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(255,axiom,
! [A: labele431970251um_a_b,B: labele431970251um_a_b] :
( ( ( ( labele1939049654um_a_b @ A )
= ( labele1939049654um_a_b @ B ) )
& ( ( labele577278695um_a_b @ A )
= ( labele577278695um_a_b @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_labeled__graph_Oexpand) ).
thf(1131,plain,
! [A: labele431970251um_a_b,B: labele431970251um_a_b] :
( ( ( ( labele1939049654um_a_b @ A )
= ( labele1939049654um_a_b @ B ) )
& ( ( labele577278695um_a_b @ A )
= ( labele577278695um_a_b @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(207,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_zero__reorient) ).
thf(984,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(75,axiom,
! [A: produc1963079155um_a_b,B: produc1963079155um_a_b > $o] :
( ( member1998628618um_a_b @ A @ ( collec1254333256um_a_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_mem__Collect__eq) ).
thf(569,plain,
! [A: produc1963079155um_a_b,B: produc1963079155um_a_b > $o] :
( ( member1998628618um_a_b @ A @ ( collec1254333256um_a_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(320,axiom,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
= ( ? [C: standard_Constant_a,D: product_prod_nat_nat] :
( ( A = C )
& ( member1696759390at_nat @ ( produc407553657at_nat @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Domain_Osimps) ).
thf(1324,plain,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
= ( ? [C: standard_Constant_a,D: product_prod_nat_nat] :
( ( A = C )
& ( member1696759390at_nat @ ( produc407553657at_nat @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(249,axiom,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
=> ~ ! [C: nat] :
~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_DomainE) ).
thf(1114,plain,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
=> ~ ! [C: nat] :
~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(324,axiom,
! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_singletonI) ).
thf(1333,plain,
! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1,conjecture,
( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
& ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
& ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
& ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
& ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(343,plain,
~ ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
& ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
& ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(280,axiom,
! [A: set_Pr409224873um_a_b,B: set_Sum_sum_a_b] :
( ( labele1939049654um_a_b @ ( labele1729654377um_a_b @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_labeled__graph_Osel_I1_J) ).
thf(1202,plain,
! [A: set_Pr409224873um_a_b,B: set_Sum_sum_a_b] :
( ( labele1939049654um_a_b @ ( labele1729654377um_a_b @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(6,axiom,
! [A: set_Pr1916610317um_a_b] :
( ! [B: produc1548871597um_a_b] :
~ ( member947389014um_a_b @ B @ A )
=> ( A = bot_bo225809273um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_equals0I) ).
thf(360,plain,
! [A: set_Pr1916610317um_a_b] :
( ! [B: produc1548871597um_a_b] :
~ ( member947389014um_a_b @ B @ A )
=> ( A = bot_bo225809273um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: sum_sum_a_b > $o] :
( ( ( collect_Sum_sum_a_b @ A )
= bot_bo1491243248um_a_b )
= ( ! [B: sum_sum_a_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Collect__empty__eq) ).
thf(398,plain,
! [A: sum_sum_a_b > $o] :
( ( ( collect_Sum_sum_a_b @ A )
= bot_bo1491243248um_a_b )
= ( ! [B: sum_sum_a_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(235,axiom,
! [A: labele935650037_a_nat,B: set_Pr689416536at_nat] :
( ( graph_149544303at_nat @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ A @ B )
= ( ( B = bot_bo1582968772at_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_graph__homomorphism__empty) ).
thf(1071,plain,
! [A: labele935650037_a_nat,B: set_Pr689416536at_nat] :
( ( graph_149544303at_nat @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ A @ B )
= ( ( B = bot_bo1582968772at_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(61,axiom,
! [A: set_Sum_sum_a_b] :
( ( ! [B: sum_sum_a_b] :
~ ( member_Sum_sum_a_b @ B @ A ) )
= ( A = bot_bo1491243248um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_all__not__in__conv) ).
thf(530,plain,
! [A: set_Sum_sum_a_b] :
( ( ! [B: sum_sum_a_b] :
~ ( member_Sum_sum_a_b @ B @ A ) )
= ( A = bot_bo1491243248um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(81,axiom,
! [A: set_Sum_sum_a_b] :
( ( collect_Sum_sum_a_b
@ ^ [B: sum_sum_a_b] : ( member_Sum_sum_a_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Collect__mem__eq) ).
thf(586,plain,
! [A: set_Sum_sum_a_b] :
( ( collect_Sum_sum_a_b
@ ^ [B: sum_sum_a_b] : ( member_Sum_sum_a_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(201,axiom,
! [A: set_Pr1618094130um_a_b] :
( ( image_1228479730um_a_b @ A @ bot_bot_set_nat )
= bot_bo575978147um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Image__empty2) ).
thf(965,plain,
! [A: set_Pr1618094130um_a_b] :
( ( image_1228479730um_a_b @ A @ bot_bot_set_nat )
= bot_bo575978147um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(296,axiom,
! [A: labele935650037_a_nat,B: set_Pr1902304780_b_nat] :
( ( graph_1203757137_b_nat @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ A @ B )
= ( ( B = bot_bo949957280_b_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_graph__homomorphism__empty) ).
thf(1251,plain,
! [A: labele935650037_a_nat,B: set_Pr1902304780_b_nat] :
( ( graph_1203757137_b_nat @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ A @ B )
= ( ( B = bot_bo949957280_b_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(260,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ C )
=> ( member_nat @ A @ ( domain_nat_nat @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Domain_ODomainI) ).
thf(1146,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ C )
=> ( member_nat @ A @ ( domain_nat_nat @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(165,axiom,
! [A: set_Pr1986765409at_nat] :
( ( ( domain_nat_nat @ A )
= bot_bot_set_nat )
= ( A = bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Domain__empty__iff) ).
thf(856,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( domain_nat_nat @ A )
= bot_bot_set_nat )
= ( A = bot_bo2130386637at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(313,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_le0) ).
thf(1301,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(86,axiom,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b,C: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_1918588449um_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) )
= ( member947389014um_a_b @ ( produc176426981um_a_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Image__singleton__iff) ).
thf(601,plain,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b,C: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_1918588449um_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) )
= ( member947389014um_a_b @ ( produc176426981um_a_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(11,axiom,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
( ( ord_le615126793um_a_b @ A @ B )
=> ( ord_le1739761029tant_a @ ( domain1362581744um_a_b @ A ) @ ( domain1362581744um_a_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Domain__mono) ).
thf(375,plain,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
( ( ord_le615126793um_a_b @ A @ B )
=> ( ord_le1739761029tant_a @ ( domain1362581744um_a_b @ A ) @ ( domain1362581744um_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(123,axiom,
! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( ( insert271595217at_nat @ A @ bot_bo2130386637at_nat )
= ( insert271595217at_nat @ B @ C ) )
= ( ( B = A )
& ( ord_le841296385at_nat @ C @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_singleton__insert__inj__eq) ).
thf(733,plain,
! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( ( insert271595217at_nat @ A @ bot_bo2130386637at_nat )
= ( insert271595217at_nat @ B @ C ) )
= ( ( B = A )
& ( ord_le841296385at_nat @ C @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(263,axiom,
! [A: set_Pr409224873um_a_b,B: set_Sum_sum_a_b] :
( ( labele577278695um_a_b @ ( labele1729654377um_a_b @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_labeled__graph_Osel_I2_J) ).
thf(1154,plain,
! [A: set_Pr409224873um_a_b,B: set_Sum_sum_a_b] :
( ( labele577278695um_a_b @ ( labele1729654377um_a_b @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(160,axiom,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b,C: set_Pr1647387645at_nat,D: set_Pr1647387645at_nat,E: set_Pr409224873um_a_b] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ( ord_le1909159005at_nat @ C @ D )
=> ( ( edge_p1382426714tant_a @ B @ D @ E )
=> ( edge_p1382426714tant_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_edge__preserving__subset) ).
thf(843,plain,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b,C: set_Pr1647387645at_nat,D: set_Pr1647387645at_nat,E: set_Pr409224873um_a_b] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ( ord_le1909159005at_nat @ C @ D )
=> ( ( edge_p1382426714tant_a @ B @ D @ E )
=> ( edge_p1382426714tant_a @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(342,axiom,
! [A: labele431970251um_a_b,B: set_Pr55236280um_a_b] :
( ( graph_1763806717um_a_b @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ A @ B )
= ( ( B = bot_bo1217542988um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_graph__homomorphism__empty) ).
thf(1388,plain,
! [A: labele431970251um_a_b,B: set_Pr55236280um_a_b] :
( ( graph_1763806717um_a_b @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ A @ B )
= ( ( B = bot_bo1217542988um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(126,axiom,
! [A: produc1124793815um_a_b,B: set_Pr386468381um_a_b,C: product_prod_nat_nat] :
( ( member1294585472um_a_b @ A @ ( image_320480233um_a_b @ B @ ( insert271595217at_nat @ C @ bot_bo2130386637at_nat ) ) )
= ( member834135910um_a_b @ ( produc335036333um_a_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Image__singleton__iff) ).
thf(743,plain,
! [A: produc1124793815um_a_b,B: set_Pr386468381um_a_b,C: product_prod_nat_nat] :
( ( member1294585472um_a_b @ A @ ( image_320480233um_a_b @ B @ ( insert271595217at_nat @ C @ bot_bo2130386637at_nat ) ) )
= ( member834135910um_a_b @ ( produc335036333um_a_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(24,axiom,
! [A: standard_Constant_a,B: standard_Constant_a,C: set_St761939237tant_a] :
( ( ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a )
= ( insert1909710879tant_a @ B @ C ) )
= ( ( B = A )
& ( ord_le1739761029tant_a @ C @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_singleton__insert__inj__eq) ).
thf(413,plain,
! [A: standard_Constant_a,B: standard_Constant_a,C: set_St761939237tant_a] :
( ( ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a )
= ( insert1909710879tant_a @ B @ C ) )
= ( ( B = A )
& ( ord_le1739761029tant_a @ C @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(72,axiom,
( ord_le615126793um_a_b
= ( ^ [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
! [C: produc1963079155um_a_b] :
( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_subset__iff) ).
thf(562,plain,
( ord_le615126793um_a_b
= ( ^ [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
! [C: produc1963079155um_a_b] :
( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(180,axiom,
! [A: labele431970251um_a_b] :
( ( ord_le615126793um_a_b @ ( labele1939049654um_a_b @ A ) @ ( labele1939049654um_a_b @ ( restri1162247455um_a_b @ A ) ) )
=> ( A
= ( restri1162247455um_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_restrict__subsD) ).
thf(904,plain,
! [A: labele431970251um_a_b] :
( ( ord_le615126793um_a_b @ ( labele1939049654um_a_b @ A ) @ ( labele1939049654um_a_b @ ( restri1162247455um_a_b @ A ) ) )
=> ( A
= ( restri1162247455um_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(204,axiom,
! [A: sum_sum_a_b > $o,B: sum_sum_a_b > $o] :
( ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ A ) @ ( collect_Sum_sum_a_b @ B ) )
= ( ! [C: sum_sum_a_b] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_Collect__mono__iff) ).
thf(975,plain,
! [A: sum_sum_a_b > $o,B: sum_sum_a_b > $o] :
( ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ A ) @ ( collect_Sum_sum_a_b @ B ) )
= ( ! [C: sum_sum_a_b] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(215,axiom,
! [A: labele935650037_a_nat,B: labele935650037_a_nat] :
( ( ( ( labele195203296_a_nat @ A )
= ( labele195203296_a_nat @ B ) )
& ( ( labele1810595089_a_nat @ A )
= ( labele1810595089_a_nat @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_labeled__graph_Oexpand) ).
thf(1007,plain,
! [A: labele935650037_a_nat,B: labele935650037_a_nat] :
( ( ( ( labele195203296_a_nat @ A )
= ( labele195203296_a_nat @ B ) )
& ( ( labele1810595089_a_nat @ A )
= ( labele1810595089_a_nat @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(112,axiom,
! [A: set_Pr409224873um_a_b] :
( ( collec1254333256um_a_b
@ ^ [B: produc1963079155um_a_b] : ( member1998628618um_a_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Collect__mem__eq) ).
thf(694,plain,
! [A: set_Pr409224873um_a_b] :
( ( collec1254333256um_a_b
@ ^ [B: produc1963079155um_a_b] : ( member1998628618um_a_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(191,axiom,
! [A: labele935650037_a_nat > $o,B: labele935650037_a_nat] :
( ! [C: set_Pr1647387645at_nat,D: set_nat] : ( A @ ( labele16114835_a_nat @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_labeled__graph_Oinduct) ).
thf(936,plain,
! [A: labele935650037_a_nat > $o,B: labele935650037_a_nat] :
( ! [C: set_Pr1647387645at_nat,D: set_nat] : ( A @ ( labele16114835_a_nat @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(76,axiom,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
=> ~ ! [C: sum_sum_a_b] :
~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_Domain_Ocases) ).
thf(572,plain,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
=> ~ ! [C: sum_sum_a_b] :
~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(302,axiom,
! [A: nat,B: set_nat,C: nat] :
( ( ~ ( member_nat @ A @ B )
=> ( A = C ) )
=> ( member_nat @ A @ ( insert_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_insertCI) ).
thf(1271,plain,
! [A: nat,B: set_nat,C: nat] :
( ( ~ ( member_nat @ A @ B )
=> ( A = C ) )
=> ( member_nat @ A @ ( insert_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(49,axiom,
! [A: set_Pr409224873um_a_b] :
( ( ( domain1362581744um_a_b @ A )
= bot_bo1160111033tant_a )
= ( A = bot_bo1262634813um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Domain__empty__iff) ).
thf(498,plain,
! [A: set_Pr409224873um_a_b] :
( ( ( domain1362581744um_a_b @ A )
= bot_bo1160111033tant_a )
= ( A = bot_bo1262634813um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(291,axiom,
member_Sum_sum_a_b @ v @ ( labele577278695um_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_v) ).
thf(1239,plain,
member_Sum_sum_a_b @ v @ ( labele577278695um_a_b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(41,axiom,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( insert_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ B ) )
= ( insert_Sum_sum_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_insert__absorb2) ).
thf(466,plain,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( insert_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ B ) )
= ( insert_Sum_sum_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(241,axiom,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b,C: set_nat,D: set_nat] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ A @ C ) @ ( image_256773707um_a_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Image__mono) ).
thf(1090,plain,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b,C: set_nat,D: set_nat] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ A @ C ) @ ( image_256773707um_a_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(287,axiom,
! [A: labele431970251um_a_b,B: set_Pr653770722um_a_b] :
( ( graph_502887975um_a_b @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ A @ B )
= ( ( B = bot_bo1892785270um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_graph__homomorphism__empty) ).
thf(1224,plain,
! [A: labele431970251um_a_b,B: set_Pr653770722um_a_b] :
( ( graph_502887975um_a_b @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ A @ B )
= ( ( B = bot_bo1892785270um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(331,axiom,
! [A: produc1124793815um_a_b] :
~ ( member1294585472um_a_b @ A @ bot_bo575978147um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_emptyE) ).
thf(1356,plain,
! [A: produc1124793815um_a_b] :
~ ( member1294585472um_a_b @ A @ bot_bo575978147um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(87,axiom,
! [A: set_Pr1916610317um_a_b,B: set_Pr1916610317um_a_b] :
( ! [C: sum_sum_a_b,D: sum_sum_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ C @ D ) @ A )
=> ( member947389014um_a_b @ ( produc176426981um_a_b @ C @ D ) @ B ) )
=> ( ord_le1059794605um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_subrelI) ).
thf(604,plain,
! [A: set_Pr1916610317um_a_b,B: set_Pr1916610317um_a_b] :
( ! [C: sum_sum_a_b,D: sum_sum_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ C @ D ) @ A )
=> ( member947389014um_a_b @ ( produc176426981um_a_b @ C @ D ) @ B ) )
=> ( ord_le1059794605um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(277,axiom,
( g
= ( restri1162247455um_a_b @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_g) ).
thf(1194,plain,
( g
= ( restri1162247455um_a_b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(250,axiom,
mainta522127984um_a_b @ ( standa997693288tant_a @ standard_S_Idt_a ) @ g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349__092_060open_062maintained_A_Isymmetry__rule_AS__Idt_J_AG_092_060close_062) ).
thf(1117,plain,
mainta522127984um_a_b @ ( standa997693288tant_a @ standard_S_Idt_a ) @ g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(124,axiom,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
( ! [C: standard_Constant_a,D: produc1548871597um_a_b] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ C @ D ) @ A )
=> ( member1998628618um_a_b @ ( produc1697725733um_a_b @ C @ D ) @ B ) )
=> ( ord_le615126793um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_subrelI) ).
thf(736,plain,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
( ! [C: standard_Constant_a,D: produc1548871597um_a_b] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ C @ D ) @ A )
=> ( member1998628618um_a_b @ ( produc1697725733um_a_b @ C @ D ) @ B ) )
=> ( ord_le615126793um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(74,axiom,
! [A: produc1963079155um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_singletonI) ).
thf(567,plain,
! [A: produc1963079155um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(90,axiom,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b,C: set_Sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_1918588449um_a_b @ B @ C ) )
=> ~ ! [D: sum_sum_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ D @ A ) @ B )
=> ~ ( member_Sum_sum_a_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_ImageE) ).
thf(616,plain,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b,C: set_Sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_1918588449um_a_b @ B @ C ) )
=> ~ ! [D: sum_sum_a_b] :
( ( member947389014um_a_b @ ( produc176426981um_a_b @ D @ A ) @ B )
=> ~ ( member_Sum_sum_a_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(338,axiom,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b,C: set_Pr1174980151um_a_b] :
( ( ord_le823954903um_a_b @ ( insert983991207um_a_b @ A @ B ) @ C )
= ( ( member1294585472um_a_b @ A @ C )
& ( ord_le823954903um_a_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_insert__subset) ).
thf(1376,plain,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b,C: set_Pr1174980151um_a_b] :
( ( ord_le823954903um_a_b @ ( insert983991207um_a_b @ A @ B ) @ C )
= ( ( member1294585472um_a_b @ A @ C )
& ( ord_le823954903um_a_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(12,axiom,
! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,C: set_Pr1916610317um_a_b] :
( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ C ) )
=> ( ( A != B )
=> ( member947389014um_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insertE) ).
thf(377,plain,
! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,C: set_Pr1916610317um_a_b] :
( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ C ) )
=> ( ( A != B )
=> ( member947389014um_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(209,axiom,
! [A: set_Pr375490359_b_nat,B: set_Pr409224873um_a_b,C: set_Pr1647387645at_nat,D: sum_sum_a_b,E: nat,F: sum_sum_a_b,G: nat,H: standard_Constant_a] :
( ( edge_p749155930tant_a @ A @ B @ C )
=> ( ( member1249152_b_nat @ ( produc522153487_b_nat @ D @ E ) @ A )
=> ( ( member1249152_b_nat @ ( produc522153487_b_nat @ F @ G ) @ A )
=> ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ H @ ( produc176426981um_a_b @ D @ F ) ) @ B )
=> ( member1696759390at_nat @ ( produc407553657at_nat @ H @ ( product_Pair_nat_nat @ E @ G ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_edge__preserving__atomic) ).
thf(990,plain,
! [A: set_Pr375490359_b_nat,B: set_Pr409224873um_a_b,C: set_Pr1647387645at_nat,D: sum_sum_a_b,E: nat,F: sum_sum_a_b,G: nat,H: standard_Constant_a] :
( ( edge_p749155930tant_a @ A @ B @ C )
=> ( ( member1249152_b_nat @ ( produc522153487_b_nat @ D @ E ) @ A )
=> ( ( member1249152_b_nat @ ( produc522153487_b_nat @ F @ G ) @ A )
=> ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ H @ ( produc176426981um_a_b @ D @ F ) ) @ B )
=> ( member1696759390at_nat @ ( produc407553657at_nat @ H @ ( product_Pair_nat_nat @ E @ G ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(53,axiom,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
=> ~ ! [C: produc1548871597um_a_b] :
~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_DomainE) ).
thf(509,plain,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
=> ~ ! [C: produc1548871597um_a_b] :
~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(31,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: standard_Constant_a] :
( ( ( insert1909710879tant_a @ A @ B )
= ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) )
= ( ( A = C )
& ( ord_le1739761029tant_a @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_singleton__insert__inj__eq_H) ).
thf(434,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: standard_Constant_a] :
( ( ( insert1909710879tant_a @ A @ B )
= ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) )
= ( ( A = C )
& ( ord_le1739761029tant_a @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(149,axiom,
! [A: set_St761939237tant_a] :
( ( image_127502653at_nat @ bot_bo810816657at_nat @ A )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Image__empty1) ).
thf(811,plain,
! [A: set_St761939237tant_a] :
( ( image_127502653at_nat @ bot_bo810816657at_nat @ A )
= bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(57,axiom,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ C ) )
= ( ( A = B )
| ( member_Sum_sum_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_insert__iff) ).
thf(520,plain,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ C ) )
= ( ( A = B )
| ( member_Sum_sum_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(177,axiom,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ! [C: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) )
=> ( ord_le192794300um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_subsetI) ).
thf(895,plain,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ! [C: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) )
=> ( ord_le192794300um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(134,axiom,
! [A: set_Pr409224873um_a_b] : ( ord_le615126793um_a_b @ bot_bo1262634813um_a_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_empty__subsetI) ).
thf(769,plain,
! [A: set_Pr409224873um_a_b] : ( ord_le615126793um_a_b @ bot_bo1262634813um_a_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(271,axiom,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_set_nat )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_Collect__empty__eq) ).
thf(1177,plain,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_set_nat )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(232,axiom,
! [A: set_Pr1647387645at_nat,B: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_labeled__graph_Osel_I2_J) ).
thf(1061,plain,
! [A: set_Pr1647387645at_nat,B: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(144,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_bot__nat__def) ).
thf(799,plain,
bot_bot_nat = zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(266,axiom,
! [A: labele431970251um_a_b] :
( ( restri1162247455um_a_b @ ( restri1162247455um_a_b @ A ) )
= ( restri1162247455um_a_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_restrict__idemp) ).
thf(1162,plain,
! [A: labele431970251um_a_b] :
( ( restri1162247455um_a_b @ ( restri1162247455um_a_b @ A ) )
= ( restri1162247455um_a_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(121,axiom,
! [A: produc1548871597um_a_b,B: set_Pr409224873um_a_b,C: set_St761939237tant_a] :
( ( member947389014um_a_b @ A @ ( image_2023280617um_a_b @ B @ C ) )
=> ~ ! [D: standard_Constant_a] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ D @ A ) @ B )
=> ~ ( member1632892294tant_a @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_ImageE) ).
thf(726,plain,
! [A: produc1548871597um_a_b,B: set_Pr409224873um_a_b,C: set_St761939237tant_a] :
( ( member947389014um_a_b @ A @ ( image_2023280617um_a_b @ B @ C ) )
=> ~ ! [D: standard_Constant_a] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ D @ A ) @ B )
=> ~ ( member1632892294tant_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(93,axiom,
! [A: set_Pr409224873um_a_b] :
( ( ord_le615126793um_a_b @ A @ bot_bo1262634813um_a_b )
= ( A = bot_bo1262634813um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_subset__empty) ).
thf(626,plain,
! [A: set_Pr409224873um_a_b] :
( ( ord_le615126793um_a_b @ A @ bot_bo1262634813um_a_b )
= ( A = bot_bo1262634813um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(184,axiom,
( standa1410829644tant_a
= ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_nonempty__rule__def) ).
thf(915,plain,
( standa1410829644tant_a
= ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(193,axiom,
! [A: set_Pr1902304780_b_nat] :
( ( image_128716052_b_nat @ A @ bot_bo575978147um_a_b )
= bot_bot_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Image__empty2) ).
thf(943,plain,
! [A: set_Pr1902304780_b_nat] :
( ( image_128716052_b_nat @ A @ bot_bo575978147um_a_b )
= bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(220,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_bot__nat__0_Oextremum__unique) ).
thf(1022,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(154,axiom,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b] :
( ( ( insert_Sum_sum_a_b @ A @ B )
= ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) )
= ( ( A = C )
& ( ord_le192794300um_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_singleton__insert__inj__eq_H) ).
thf(827,plain,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b] :
( ( ( insert_Sum_sum_a_b @ A @ B )
= ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) )
= ( ( A = C )
& ( ord_le192794300um_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(234,axiom,
! [A: set_Pr1174980151um_a_b,B: produc1124793815um_a_b] :
( ( A = bot_bo575978147um_a_b )
=> ~ ( member1294585472um_a_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_equals0D) ).
thf(1066,plain,
! [A: set_Pr1174980151um_a_b,B: produc1124793815um_a_b] :
( ( A = bot_bo575978147um_a_b )
=> ~ ( member1294585472um_a_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(138,axiom,
! [A: set_Pr1174980151um_a_b] :
( ( collec492052930um_a_b
@ ^ [B: produc1124793815um_a_b] : ( member1294585472um_a_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Collect__mem__eq) ).
thf(780,plain,
! [A: set_Pr1174980151um_a_b] :
( ( collec492052930um_a_b
@ ^ [B: produc1124793815um_a_b] : ( member1294585472um_a_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(38,axiom,
! [A: set_Sum_sum_a_b] :
( ( ? [B: sum_sum_a_b] : ( member_Sum_sum_a_b @ B @ A ) )
= ( A != bot_bo1491243248um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_ex__in__conv) ).
thf(455,plain,
! [A: set_Sum_sum_a_b] :
( ( ? [B: sum_sum_a_b] : ( member_Sum_sum_a_b @ B @ A ) )
= ( A != bot_bo1491243248um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(88,axiom,
! [A: set_Pr409224873um_a_b,B: produc1963079155um_a_b] :
( ( A = bot_bo1262634813um_a_b )
=> ~ ( member1998628618um_a_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_equals0D) ).
thf(608,plain,
! [A: set_Pr409224873um_a_b,B: produc1963079155um_a_b] :
( ( A = bot_bo1262634813um_a_b )
=> ~ ( member1998628618um_a_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(245,axiom,
! [A: labele431970251um_a_b,B: set_Pr1174980151um_a_b] :
( ( graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ A @ B )
= ( ( B = bot_bo575978147um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_graph__homomorphism__empty) ).
thf(1102,plain,
! [A: labele431970251um_a_b,B: set_Pr1174980151um_a_b] :
( ( graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ A @ B )
= ( ( B = bot_bo575978147um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(30,axiom,
! [A: set_Pr409224873um_a_b] :
( ( ? [B: produc1963079155um_a_b] : ( member1998628618um_a_b @ B @ A ) )
= ( A != bot_bo1262634813um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_ex__in__conv) ).
thf(431,plain,
! [A: set_Pr409224873um_a_b] :
( ( ? [B: produc1963079155um_a_b] : ( member1998628618um_a_b @ B @ A ) )
= ( A != bot_bo1262634813um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(98,axiom,
! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ C ) )
= ( ( A = B )
| ( member701585322at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_insert__iff) ).
thf(653,plain,
! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ C ) )
= ( ( A = B )
| ( member701585322at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(183,axiom,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
= ( ? [C: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Domain__iff) ).
thf(912,plain,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
= ( ? [C: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(109,axiom,
! [A: produc1963079155um_a_b > $o] :
( ( ( collec1254333256um_a_b @ A )
= bot_bo1262634813um_a_b )
= ( ! [B: produc1963079155um_a_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Collect__empty__eq) ).
thf(685,plain,
! [A: produc1963079155um_a_b > $o] :
( ( ( collec1254333256um_a_b @ A )
= bot_bo1262634813um_a_b )
= ( ! [B: produc1963079155um_a_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(269,axiom,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
=> ( ( ord_le192794300um_a_b @ B @ C )
=> ( ord_le192794300um_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_subset__trans) ).
thf(1171,plain,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
=> ( ( ord_le192794300um_a_b @ B @ C )
=> ( ord_le192794300um_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(227,axiom,
! [A: labele431970251um_a_b] :
( A
= ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ A ) @ ( labele577278695um_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_labeled__graph_Oexhaust__sel) ).
thf(1044,plain,
! [A: labele431970251um_a_b] :
( A
= ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ A ) @ ( labele577278695um_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(294,axiom,
! [A: produc1032616263at_nat] :
~ ( member1696759390at_nat @ A @ bot_bo810816657at_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_empty__iff) ).
thf(1245,plain,
! [A: produc1032616263at_nat] :
~ ( member1696759390at_nat @ A @ bot_bo810816657at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(237,axiom,
! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,C: set_Pr1174980151um_a_b] :
( ( ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b )
= ( insert983991207um_a_b @ B @ C ) )
= ( ( B = A )
& ( ord_le823954903um_a_b @ C @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_singleton__insert__inj__eq) ).
thf(1076,plain,
! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,C: set_Pr1174980151um_a_b] :
( ( ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b )
= ( insert983991207um_a_b @ B @ C ) )
= ( ( B = A )
& ( ord_le823954903um_a_b @ C @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(224,axiom,
! [A: set_Pr1986765409at_nat] :
( ( image_nat_nat @ A @ bot_bot_set_nat )
= bot_bot_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Image__empty2) ).
thf(1034,plain,
! [A: set_Pr1986765409at_nat] :
( ( image_nat_nat @ A @ bot_bot_set_nat )
= bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(28,axiom,
! [A: standard_Constant_a,B: produc1548871597um_a_b,C: set_Pr409224873um_a_b] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ C )
=> ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_Domain_ODomainI) ).
thf(426,plain,
! [A: standard_Constant_a,B: produc1548871597um_a_b,C: set_Pr409224873um_a_b] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ C )
=> ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(82,axiom,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
=> ~ ! [C: produc1548871597um_a_b] :
~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_Domain_Ocases) ).
thf(589,plain,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
=> ~ ! [C: produc1548871597um_a_b] :
~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(101,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: produc1548871597um_a_b,D: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ B )
=> ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ C ) @ D )
=> ( member947389014um_a_b @ C @ ( image_2023280617um_a_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rev__ImageI) ).
thf(663,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: produc1548871597um_a_b,D: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ B )
=> ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ C ) @ D )
=> ( member947389014um_a_b @ C @ ( image_2023280617um_a_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(188,axiom,
! [A: labele935650037_a_nat] :
( A
= ( labele16114835_a_nat @ ( labele195203296_a_nat @ A ) @ ( labele1810595089_a_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_labeled__graph_Oexhaust__sel) ).
thf(927,plain,
! [A: labele935650037_a_nat] :
( A
= ( labele16114835_a_nat @ ( labele195203296_a_nat @ A ) @ ( labele1810595089_a_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(303,axiom,
! [A: sum_sum_a_b,B: sum_sum_a_b] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ A @ B ) ) @ ( labele1939049654um_a_b @ g ) )
= ( ( member_Sum_sum_a_b @ A @ ( labele577278695um_a_b @ g ) )
& ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_v__gr) ).
thf(1277,plain,
! [A: sum_sum_a_b,B: sum_sum_a_b] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ A @ B ) ) @ ( labele1939049654um_a_b @ g ) )
= ( ( member_Sum_sum_a_b @ A @ ( labele577278695um_a_b @ g ) )
& ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(256,axiom,
! [A: set_Pr1155046920um_a_b] :
( ( image_166667464um_a_b @ A @ bot_bot_set_nat )
= bot_bo225809273um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Image__empty2) ).
thf(1134,plain,
! [A: set_Pr1155046920um_a_b] :
( ( image_166667464um_a_b @ A @ bot_bot_set_nat )
= bot_bo225809273um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(128,axiom,
! [A: set_St761939237tant_a] :
( ( image_2023280617um_a_b @ bot_bo1262634813um_a_b @ A )
= bot_bo225809273um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Image__empty1) ).
thf(749,plain,
! [A: set_St761939237tant_a] :
( ( image_2023280617um_a_b @ bot_bo1262634813um_a_b @ A )
= bot_bo225809273um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(229,axiom,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat,C: standard_Constant_a > $o] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
=> ( ! [D: standard_Constant_a,E: product_prod_nat_nat] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Domain_Oinducts) ).
thf(1049,plain,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat,C: standard_Constant_a > $o] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
=> ( ! [D: standard_Constant_a,E: product_prod_nat_nat] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(202,axiom,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
= ( ? [C: product_prod_nat_nat] : ( member1696759390at_nat @ ( produc407553657at_nat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Domain__iff) ).
thf(968,plain,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
= ( ? [C: product_prod_nat_nat] : ( member1696759390at_nat @ ( produc407553657at_nat @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(39,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: standard_Constant_a] :
( ( ~ ( member1632892294tant_a @ A @ B )
=> ( A = C ) )
=> ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_insertCI) ).
thf(458,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: standard_Constant_a] :
( ( ~ ( member1632892294tant_a @ A @ B )
=> ( A = C ) )
=> ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(153,axiom,
! [A: labele935650037_a_nat] :
~ ! [B: set_Pr1647387645at_nat,C: set_nat] :
( A
!= ( labele16114835_a_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_labeled__graph_Oexhaust) ).
thf(823,plain,
! [A: labele935650037_a_nat] :
~ ! [B: set_Pr1647387645at_nat,C: set_nat] :
( A
!= ( labele16114835_a_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(59,axiom,
! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,C: set_Pr409224873um_a_b] :
( ( ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b )
= ( insert323157027um_a_b @ B @ C ) )
= ( ( B = A )
& ( ord_le615126793um_a_b @ C @ ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_singleton__insert__inj__eq) ).
thf(525,plain,
! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,C: set_Pr409224873um_a_b] :
( ( ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b )
= ( insert323157027um_a_b @ B @ C ) )
= ( ( B = A )
& ( ord_le615126793um_a_b @ C @ ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(221,axiom,
! [A: nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ ( insert_nat @ A @ B ) @ C )
= ( ( member_nat @ A @ C )
& ( ord_less_eq_set_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_insert__subset) ).
thf(1025,plain,
! [A: nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ ( insert_nat @ A @ B ) @ C )
= ( ( member_nat @ A @ C )
& ( ord_less_eq_set_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(203,axiom,
! [A: set_Pr1647387645at_nat,B: set_Pr1647387645at_nat] :
( ! [C: standard_Constant_a,D: product_prod_nat_nat] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ C @ D ) @ A )
=> ( member1696759390at_nat @ ( produc407553657at_nat @ C @ D ) @ B ) )
=> ( ord_le1909159005at_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_subrelI) ).
thf(971,plain,
! [A: set_Pr1647387645at_nat,B: set_Pr1647387645at_nat] :
( ! [C: standard_Constant_a,D: product_prod_nat_nat] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ C @ D ) @ A )
=> ( member1696759390at_nat @ ( produc407553657at_nat @ C @ D ) @ B ) )
=> ( ord_le1909159005at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(289,axiom,
! [A: labele431970251um_a_b,B: set_Pr1916610317um_a_b] :
( ( graph_611893540um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ A @ B )
= ( ( B = bot_bo225809273um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_graph__homomorphism__empty) ).
thf(1230,plain,
! [A: labele431970251um_a_b,B: set_Pr1916610317um_a_b] :
( ( graph_611893540um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ A @ B )
= ( ( B = bot_bo225809273um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(210,axiom,
( ord_le192794300um_a_b
= ( ^ [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
! [C: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_subset__eq) ).
thf(993,plain,
( ord_le192794300um_a_b
= ( ^ [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
! [C: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(117,axiom,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
( ! [C: produc1124793815um_a_b] :
( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) )
=> ( ord_le823954903um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_subsetI) ).
thf(712,plain,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
( ! [C: produc1124793815um_a_b] :
( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) )
=> ( ord_le823954903um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(70,axiom,
! [A: set_Pr1916610317um_a_b] : ( ord_le1059794605um_a_b @ bot_bo225809273um_a_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_empty__subsetI) ).
thf(557,plain,
! [A: set_Pr1916610317um_a_b] : ( ord_le1059794605um_a_b @ bot_bo225809273um_a_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(79,axiom,
! [A: sum_sum_a_b] :
~ ( member_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_emptyE) ).
thf(580,plain,
! [A: sum_sum_a_b] :
~ ( member_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(164,axiom,
edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062) ).
thf(855,plain,
edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(105,axiom,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_subsetD) ).
thf(673,plain,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(34,axiom,
! [A: labele431970251um_a_b > $o,B: labele431970251um_a_b] :
( ! [C: set_Pr409224873um_a_b,D: set_Sum_sum_a_b] : ( A @ ( labele1729654377um_a_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_labeled__graph_Oinduct) ).
thf(441,plain,
! [A: labele431970251um_a_b > $o,B: labele431970251um_a_b] :
( ! [C: set_Pr409224873um_a_b,D: set_Sum_sum_a_b] : ( A @ ( labele1729654377um_a_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(159,axiom,
! [A: set_nat] :
( ( ? [B: nat] : ( member_nat @ B @ A ) )
= ( A != bot_bot_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_ex__in__conv) ).
thf(840,plain,
! [A: set_nat] :
( ( ? [B: nat] : ( member_nat @ B @ A ) )
= ( A != bot_bot_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(286,axiom,
! [A: set_nat] :
( ! [B: nat] :
~ ( member_nat @ B @ A )
=> ( A = bot_bot_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_equals0I) ).
thf(1220,plain,
! [A: set_nat] :
( ! [B: nat] :
~ ( member_nat @ B @ A )
=> ( A = bot_bot_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(275,axiom,
! [A: standard_Constant_a,B: product_prod_nat_nat,C: set_Pr1647387645at_nat,D: set_St761939237tant_a] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ C )
=> ( ( member1632892294tant_a @ A @ D )
=> ( member701585322at_nat @ B @ ( image_127502653at_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_ImageI) ).
thf(1188,plain,
! [A: standard_Constant_a,B: product_prod_nat_nat,C: set_Pr1647387645at_nat,D: set_St761939237tant_a] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ C )
=> ( ( member1632892294tant_a @ A @ D )
=> ( member701585322at_nat @ B @ ( image_127502653at_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(274,axiom,
( standa63370785tant_a
= ( ^ [A: standard_Constant_a] : ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_reflexivity__rule__def) ).
thf(1186,plain,
( standa63370785tant_a
= ( ^ [A: standard_Constant_a] : ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(196,axiom,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( A = B )
=> ( ord_le192794300um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_equalityD1) ).
thf(951,plain,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( A = B )
=> ( ord_le192794300um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(148,axiom,
! [A: nat,B: set_Pr1986765409at_nat,C: set_nat] :
( ( member_nat @ A @ ( image_nat_nat @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Image__iff) ).
thf(808,plain,
! [A: nat,B: set_Pr1986765409at_nat,C: set_nat] :
( ( member_nat @ A @ ( image_nat_nat @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(66,axiom,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
= ( ? [C: sum_sum_a_b,D: sum_sum_a_b] :
( ( A = C )
& ( member947389014um_a_b @ ( produc176426981um_a_b @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Domain_Osimps) ).
thf(544,plain,
! [A: sum_sum_a_b,B: set_Pr1916610317um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ B ) )
= ( ? [C: sum_sum_a_b,D: sum_sum_a_b] :
( ( A = C )
& ( member947389014um_a_b @ ( produc176426981um_a_b @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(181,axiom,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_insertI1) ).
thf(907,plain,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(298,axiom,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( A = B )
=> ( ord_le192794300um_a_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_equalityD2) ).
thf(1257,plain,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( A = B )
=> ( ord_le192794300um_a_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(258,axiom,
mainta522127984um_a_b @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350__092_060open_062maintained_A_Itransitive__rule_AS__Idt_J_AG_092_060close_062) ).
thf(1141,plain,
mainta522127984um_a_b @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(99,axiom,
! [A: set_Sum_sum_a_b] :
( ! [B: sum_sum_a_b] :
~ ( member_Sum_sum_a_b @ B @ A )
=> ( A = bot_bo1491243248um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_equals0I) ).
thf(656,plain,
! [A: set_Sum_sum_a_b] :
( ! [B: sum_sum_a_b] :
~ ( member_Sum_sum_a_b @ B @ A )
=> ( A = bot_bo1491243248um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(89,axiom,
! [A: sum_sum_a_b,B: sum_sum_a_b > $o] :
( ( member_Sum_sum_a_b @ A @ ( collect_Sum_sum_a_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_mem__Collect__eq) ).
thf(613,plain,
! [A: sum_sum_a_b,B: sum_sum_a_b > $o] :
( ( member_Sum_sum_a_b @ A @ ( collect_Sum_sum_a_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(306,axiom,
! [A: labele935650037_a_nat,B: set_Pr1986765409at_nat] :
( ( graph_2130075512at_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ A @ B )
= ( ( B = bot_bo2130386637at_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_graph__homomorphism__empty) ).
thf(1284,plain,
! [A: labele935650037_a_nat,B: set_Pr1986765409at_nat] :
( ( graph_2130075512at_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ A @ B )
= ( ( B = bot_bo2130386637at_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(330,axiom,
! [A: produc1124793815um_a_b > $o] :
( ( bot_bo575978147um_a_b
= ( collec492052930um_a_b @ A ) )
= ( ! [B: produc1124793815um_a_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_empty__Collect__eq) ).
thf(1353,plain,
! [A: produc1124793815um_a_b > $o] :
( ( bot_bo575978147um_a_b
= ( collec492052930um_a_b @ A ) )
= ( ! [B: produc1124793815um_a_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(35,axiom,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
= ( ? [C: standard_Constant_a,D: produc1548871597um_a_b] :
( ( A = C )
& ( member1998628618um_a_b @ ( produc1697725733um_a_b @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Domain_Osimps) ).
thf(446,plain,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
= ( ? [C: standard_Constant_a,D: produc1548871597um_a_b] :
( ( A = C )
& ( member1998628618um_a_b @ ( produc1697725733um_a_b @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(84,axiom,
! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,C: set_Pr409224873um_a_b] :
( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ C ) )
=> ( ( A != B )
=> ( member1998628618um_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_insertE) ).
thf(595,plain,
! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,C: set_Pr409224873um_a_b] :
( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ C ) )
=> ( ( A != B )
=> ( member1998628618um_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(171,axiom,
! [A: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ bot_bo1491243248um_a_b )
= ( A = bot_bo1491243248um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_subset__empty) ).
thf(876,plain,
! [A: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ bot_bo1491243248um_a_b )
= ( A = bot_bo1491243248um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(166,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ A @ B ) @ C ) )
= ( insert_nat @ A @ ( domain_nat_nat @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Domain__insert) ).
thf(859,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ A @ B ) @ C ) )
= ( insert_nat @ A @ ( domain_nat_nat @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(292,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1647387645at_nat,C: set_Pr1647387645at_nat,D: nat,E: nat,F: nat,G: nat,H: standard_Constant_a] :
( ( edge_p170421892tant_a @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ A )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ G ) @ A )
=> ( ( member1696759390at_nat @ ( produc407553657at_nat @ H @ ( product_Pair_nat_nat @ D @ F ) ) @ B )
=> ( member1696759390at_nat @ ( produc407553657at_nat @ H @ ( product_Pair_nat_nat @ E @ G ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_edge__preserving__atomic) ).
thf(1240,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1647387645at_nat,C: set_Pr1647387645at_nat,D: nat,E: nat,F: nat,G: nat,H: standard_Constant_a] :
( ( edge_p170421892tant_a @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ A )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ G ) @ A )
=> ( ( member1696759390at_nat @ ( produc407553657at_nat @ H @ ( product_Pair_nat_nat @ D @ F ) ) @ B )
=> ( member1696759390at_nat @ ( produc407553657at_nat @ H @ ( product_Pair_nat_nat @ E @ G ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(205,axiom,
! [A: set_Pr1647387645at_nat] :
( ( ord_le1909159005at_nat @ A @ bot_bo810816657at_nat )
= ( A = bot_bo810816657at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_subset__empty) ).
thf(978,plain,
! [A: set_Pr1647387645at_nat] :
( ( ord_le1909159005at_nat @ A @ bot_bo810816657at_nat )
= ( A = bot_bo810816657at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(15,axiom,
! [A: produc1548871597um_a_b,B: set_Pr1916610317um_a_b] :
( ( insert1435405693um_a_b @ A @ ( insert1435405693um_a_b @ A @ B ) )
= ( insert1435405693um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_insert__absorb2) ).
thf(386,plain,
! [A: produc1548871597um_a_b,B: set_Pr1916610317um_a_b] :
( ( insert1435405693um_a_b @ A @ ( insert1435405693um_a_b @ A @ B ) )
= ( insert1435405693um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(272,axiom,
! [A: set_nat] :
( ( image_256773707um_a_b @ bot_bo575978147um_a_b @ A )
= bot_bo1491243248um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Image__empty1) ).
thf(1180,plain,
! [A: set_nat] :
( ( image_256773707um_a_b @ bot_bo575978147um_a_b @ A )
= bot_bo1491243248um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(64,axiom,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_in__mono) ).
thf(539,plain,
! [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
( ( ord_le823954903um_a_b @ A @ B )
=> ( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(110,axiom,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b,C: sum_sum_a_b,D: set_Pr653770722um_a_b] :
( ( member1294585472um_a_b @ A @ B )
=> ( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ C ) @ D )
=> ( member_Sum_sum_a_b @ C @ ( image_869585130um_a_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_rev__ImageI) ).
thf(688,plain,
! [A: produc1124793815um_a_b,B: set_Pr1174980151um_a_b,C: sum_sum_a_b,D: set_Pr653770722um_a_b] :
( ( member1294585472um_a_b @ A @ B )
=> ( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ C ) @ D )
=> ( member_Sum_sum_a_b @ C @ ( image_869585130um_a_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(216,axiom,
! [A: set_nat] :
( ( labele16114835_a_nat @ bot_bo810816657at_nat @ A )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_graph__empty__e) ).
thf(1010,plain,
! [A: set_nat] :
( ( labele16114835_a_nat @ bot_bo810816657at_nat @ A )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(309,axiom,
! [A: set_Pr1647387645at_nat,B: set_nat,C: set_Pr1647387645at_nat,D: set_nat] :
( ( ( labele16114835_a_nat @ A @ B )
= ( labele16114835_a_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_labeled__graph_Oinject) ).
thf(1289,plain,
! [A: set_Pr1647387645at_nat,B: set_nat,C: set_Pr1647387645at_nat,D: set_nat] :
( ( ( labele16114835_a_nat @ A @ B )
= ( labele16114835_a_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(135,axiom,
! [A: produc1124793815um_a_b,B: produc1124793815um_a_b > $o] :
( ( member1294585472um_a_b @ A @ ( collec492052930um_a_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_mem__Collect__eq) ).
thf(771,plain,
! [A: produc1124793815um_a_b,B: produc1124793815um_a_b > $o] :
( ( member1294585472um_a_b @ A @ ( collec492052930um_a_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(247,axiom,
! [A: nat,B: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
= ( ? [C: nat,D: sum_sum_a_b] :
( ( A = C )
& ( member1294585472um_a_b @ ( produc1808556047um_a_b @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Domain_Osimps) ).
thf(1108,plain,
! [A: nat,B: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
= ( ? [C: nat,D: sum_sum_a_b] :
( ( A = C )
& ( member1294585472um_a_b @ ( produc1808556047um_a_b @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(264,axiom,
! [A: produc1124793815um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_singletonI) ).
thf(1157,plain,
! [A: produc1124793815um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(319,axiom,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_set_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_emptyE) ).
thf(1321,plain,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(114,axiom,
! [A: set_Pr1916610317um_a_b] :
( ( ( domain2069673178um_a_b @ A )
= bot_bo1491243248um_a_b )
= ( A = bot_bo225809273um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Domain__empty__iff) ).
thf(699,plain,
! [A: set_Pr1916610317um_a_b] :
( ( ( domain2069673178um_a_b @ A )
= bot_bo1491243248um_a_b )
= ( A = bot_bo225809273um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(341,axiom,
! [A: nat,B: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
=> ~ ! [C: sum_sum_a_b] :
~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_DomainE) ).
thf(1385,plain,
! [A: nat,B: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
=> ~ ! [C: sum_sum_a_b] :
~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(56,axiom,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
( ( ord_le615126793um_a_b @ A @ B )
=> ( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_in__mono) ).
thf(517,plain,
! [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
( ( ord_le615126793um_a_b @ A @ B )
=> ( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(194,axiom,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
=> ~ ! [C: product_prod_nat_nat] :
~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Domain_Ocases) ).
thf(946,plain,
! [A: standard_Constant_a,B: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ B ) )
=> ~ ! [C: product_prod_nat_nat] :
~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(95,axiom,
( ( domain1362581744um_a_b @ bot_bo1262634813um_a_b )
= bot_bo1160111033tant_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Domain__empty) ).
thf(632,plain,
( ( domain1362581744um_a_b @ bot_bo1262634813um_a_b )
= bot_bo1160111033tant_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(20,axiom,
! [A: produc1548871597um_a_b,B: set_Pr409224873um_a_b,C: set_St761939237tant_a] :
( ( member947389014um_a_b @ A @ ( image_2023280617um_a_b @ B @ C ) )
= ( ? [D: standard_Constant_a] :
( ( member1632892294tant_a @ D @ C )
& ( member1998628618um_a_b @ ( produc1697725733um_a_b @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Image__iff) ).
thf(401,plain,
! [A: produc1548871597um_a_b,B: set_Pr409224873um_a_b,C: set_St761939237tant_a] :
( ( member947389014um_a_b @ A @ ( image_2023280617um_a_b @ B @ C ) )
= ( ? [D: standard_Constant_a] :
( ( member1632892294tant_a @ D @ C )
& ( member1998628618um_a_b @ ( produc1697725733um_a_b @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(211,axiom,
! [A: set_Pr1647387645at_nat,B: set_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_labeled__graph_Osel_I1_J) ).
thf(995,plain,
! [A: set_Pr1647387645at_nat,B: set_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(26,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ ( insert271595217at_nat @ A @ B ) @ C )
= ( ( member701585322at_nat @ A @ C )
& ( ord_le841296385at_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_insert__subset) ).
thf(418,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ ( insert271595217at_nat @ A @ B ) @ C )
= ( ( member701585322at_nat @ A @ C )
& ( ord_le841296385at_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(140,axiom,
! [A: set_Pr409224873um_a_b,B: set_Sum_sum_a_b,C: set_Pr409224873um_a_b,D: set_Sum_sum_a_b] :
( ( ( labele1729654377um_a_b @ A @ B )
= ( labele1729654377um_a_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_labeled__graph_Oinject) ).
thf(786,plain,
! [A: set_Pr409224873um_a_b,B: set_Sum_sum_a_b,C: set_Pr409224873um_a_b,D: set_Sum_sum_a_b] :
( ( ( labele1729654377um_a_b @ A @ B )
= ( labele1729654377um_a_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(132,axiom,
! [A: sum_sum_a_b,B: set_Pr653770722um_a_b,C: set_Pr1174980151um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_869585130um_a_b @ B @ C ) )
=> ~ ! [D: produc1124793815um_a_b] :
( ( member748122307um_a_b @ ( produc831476262um_a_b @ D @ A ) @ B )
=> ~ ( member1294585472um_a_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_ImageE) ).
thf(763,plain,
! [A: sum_sum_a_b,B: set_Pr653770722um_a_b,C: set_Pr1174980151um_a_b] :
( ( member_Sum_sum_a_b @ A @ ( image_869585130um_a_b @ B @ C ) )
=> ~ ! [D: produc1124793815um_a_b] :
( ( member748122307um_a_b @ ( produc831476262um_a_b @ D @ A ) @ B )
=> ~ ( member1294585472um_a_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(14,axiom,
! [A: produc1548871597um_a_b] :
~ ( member947389014um_a_b @ A @ bot_bo225809273um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_empty__iff) ).
thf(383,plain,
! [A: produc1548871597um_a_b] :
~ ( member947389014um_a_b @ A @ bot_bo225809273um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(178,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: product_prod_nat_nat,D: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ B )
=> ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ C ) @ D )
=> ( member701585322at_nat @ C @ ( image_127502653at_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rev__ImageI) ).
thf(899,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: product_prod_nat_nat,D: set_Pr1647387645at_nat] :
( ( member1632892294tant_a @ A @ B )
=> ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ C ) @ D )
=> ( member701585322at_nat @ C @ ( image_127502653at_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(68,axiom,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_insertI1) ).
thf(549,plain,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(63,axiom,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b] :
( ( insert323157027um_a_b @ A @ ( insert323157027um_a_b @ A @ B ) )
= ( insert323157027um_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_insert__absorb2) ).
thf(536,plain,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b] :
( ( insert323157027um_a_b @ A @ ( insert323157027um_a_b @ A @ B ) )
= ( insert323157027um_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(118,axiom,
! [A: labele431970251um_a_b] :
~ ! [B: set_Pr409224873um_a_b,C: set_Sum_sum_a_b] :
( A
!= ( labele1729654377um_a_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_labeled__graph_Oexhaust) ).
thf(716,plain,
! [A: labele431970251um_a_b] :
~ ! [B: set_Pr409224873um_a_b,C: set_Sum_sum_a_b] :
( A
!= ( labele1729654377um_a_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(3,axiom,
! [A: produc1548871597um_a_b,B: set_Pr1916610317um_a_b,C: produc1548871597um_a_b] :
( ( ~ ( member947389014um_a_b @ A @ B )
=> ( A = C ) )
=> ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_insertCI) ).
thf(346,plain,
! [A: produc1548871597um_a_b,B: set_Pr1916610317um_a_b,C: produc1548871597um_a_b] :
( ( ~ ( member947389014um_a_b @ A @ B )
=> ( A = C ) )
=> ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(316,axiom,
! [A: standard_Constant_a,B: product_prod_nat_nat,C: set_Pr1647387645at_nat] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ C )
=> ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Domain_ODomainI) ).
thf(1309,plain,
! [A: standard_Constant_a,B: product_prod_nat_nat,C: set_Pr1647387645at_nat] :
( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ C )
=> ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(328,axiom,
! [A: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ bot_bo1491243248um_a_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_empty__subsetI) ).
thf(1348,plain,
! [A: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ bot_bo1491243248um_a_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(91,axiom,
! [A: set_Pr1916610317um_a_b] :
( ( ord_le1059794605um_a_b @ A @ bot_bo225809273um_a_b )
= ( A = bot_bo225809273um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_subset__empty) ).
thf(620,plain,
! [A: set_Pr1916610317um_a_b] :
( ( ord_le1059794605um_a_b @ A @ bot_bo225809273um_a_b )
= ( A = bot_bo225809273um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(129,axiom,
! [A: set_Pr1916610317um_a_b] :
( ( image_1918588449um_a_b @ A @ bot_bo1491243248um_a_b )
= bot_bo1491243248um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Image__empty2) ).
thf(752,plain,
! [A: set_Pr1916610317um_a_b] :
( ( image_1918588449um_a_b @ A @ bot_bo1491243248um_a_b )
= bot_bo1491243248um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(304,axiom,
graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ g @ f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66__092_060open_062graph__homomorphism_A_ILG_A_123_125_A_1230_125_J_AG_Af_092_060close_062) ).
thf(1280,plain,
graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ g @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(314,axiom,
! [A: standard_Constant_a,B: product_prod_nat_nat,C: set_Pr1647387645at_nat] :
( ( domain1060562500at_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ B ) @ C ) )
= ( insert1909710879tant_a @ A @ ( domain1060562500at_nat @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Domain__insert) ).
thf(1303,plain,
! [A: standard_Constant_a,B: product_prod_nat_nat,C: set_Pr1647387645at_nat] :
( ( domain1060562500at_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ B ) @ C ) )
= ( insert1909710879tant_a @ A @ ( domain1060562500at_nat @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(261,axiom,
! [A: produc1124793815um_a_b > $o] :
( ( ( collec492052930um_a_b @ A )
= bot_bo575978147um_a_b )
= ( ! [B: produc1124793815um_a_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Collect__empty__eq) ).
thf(1148,plain,
! [A: produc1124793815um_a_b > $o] :
( ( ( collec492052930um_a_b @ A )
= bot_bo575978147um_a_b )
= ( ! [B: produc1124793815um_a_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(295,axiom,
! [A: labele935650037_a_nat,B: set_Pr375490359_b_nat] :
( ( graph_165730638_b_nat @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ A @ B )
= ( ( B = bot_bo1923972003_b_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_graph__homomorphism__empty) ).
thf(1248,plain,
! [A: labele935650037_a_nat,B: set_Pr375490359_b_nat] :
( ( graph_165730638_b_nat @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ A @ B )
= ( ( B = bot_bo1923972003_b_nat )
& ( A
= ( restri572569417_a_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(156,axiom,
unival2092813468um_a_b @ bot_bo575978147um_a_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_univalent__empty) ).
thf(833,plain,
unival2092813468um_a_b @ bot_bo575978147um_a_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(23,axiom,
! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ C ) )
=> ( ( A != B )
=> ( member701585322at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_insertE) ).
thf(410,plain,
! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ C ) )
=> ( ( A != B )
=> ( member701585322at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(73,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
( ( ( insert271595217at_nat @ A @ B )
= ( insert271595217at_nat @ C @ bot_bo2130386637at_nat ) )
= ( ( A = C )
& ( ord_le841296385at_nat @ B @ ( insert271595217at_nat @ C @ bot_bo2130386637at_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_singleton__insert__inj__eq_H) ).
thf(564,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
( ( ( insert271595217at_nat @ A @ B )
= ( insert271595217at_nat @ C @ bot_bo2130386637at_nat ) )
= ( ( A = C )
& ( ord_le841296385at_nat @ B @ ( insert271595217at_nat @ C @ bot_bo2130386637at_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(145,axiom,
! [A: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_subset__refl) ).
thf(801,plain,
! [A: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(318,axiom,
! [A: nat,B: set_Pr1174980151um_a_b,C: nat > $o] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
=> ( ! [D: nat,E: sum_sum_a_b] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_Domain_Oinducts) ).
thf(1314,plain,
! [A: nat,B: set_Pr1174980151um_a_b,C: nat > $o] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
=> ( ! [D: nat,E: sum_sum_a_b] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(133,axiom,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_insertI1) ).
thf(767,plain,
! [A: sum_sum_a_b,B: set_Sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(230,axiom,
! [A: nat,B: set_nat,C: nat] :
( ( ( insert_nat @ A @ B )
= ( insert_nat @ C @ bot_bot_set_nat ) )
= ( ( A = C )
& ( ord_less_eq_set_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_singleton__insert__inj__eq_H) ).
thf(1056,plain,
! [A: nat,B: set_nat,C: nat] :
( ( ( insert_nat @ A @ B )
= ( insert_nat @ C @ bot_bot_set_nat ) )
= ( ( A = C )
& ( ord_less_eq_set_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(308,axiom,
unival860567212at_nat @ bot_bo810816657at_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_univalent__empty) ).
thf(1288,plain,
unival860567212at_nat @ bot_bo810816657at_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(199,axiom,
! [A: nat,B: sum_sum_a_b,C: set_Pr1174980151um_a_b] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ C )
=> ( member_nat @ A @ ( domain1368163076um_a_b @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Domain_ODomainI) ).
thf(960,plain,
! [A: nat,B: sum_sum_a_b,C: set_Pr1174980151um_a_b] :
( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ C )
=> ( member_nat @ A @ ( domain1368163076um_a_b @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(197,axiom,
! [A: set_Pr1174980151um_a_b] : ( ord_le823954903um_a_b @ bot_bo575978147um_a_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_empty__subsetI) ).
thf(955,plain,
! [A: set_Pr1174980151um_a_b] : ( ord_le823954903um_a_b @ bot_bo575978147um_a_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(143,axiom,
! [A: nat,B: sum_sum_a_b,C: set_Pr1174980151um_a_b] :
( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ C ) )
= ( insert_nat @ A @ ( domain1368163076um_a_b @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Domain__insert) ).
thf(796,plain,
! [A: nat,B: sum_sum_a_b,C: set_Pr1174980151um_a_b] :
( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ C ) )
= ( insert_nat @ A @ ( domain1368163076um_a_b @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(32,axiom,
( ord_le823954903um_a_b
= ( ^ [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
! [C: produc1124793815um_a_b] :
( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_subset__eq) ).
thf(437,plain,
( ord_le823954903um_a_b
= ( ^ [A: set_Pr1174980151um_a_b,B: set_Pr1174980151um_a_b] :
! [C: produc1124793815um_a_b] :
( ( member1294585472um_a_b @ C @ A )
=> ( member1294585472um_a_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(325,axiom,
! [A: nat,B: set_Pr1986765409at_nat,C: nat > $o] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
=> ( ! [D: nat,E: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Domain_Oinducts) ).
thf(1335,plain,
! [A: nat,B: set_Pr1986765409at_nat,C: nat > $o] :
( ( member_nat @ A @ ( domain_nat_nat @ B ) )
=> ( ! [D: nat,E: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(119,axiom,
! [A: sum_sum_a_b] :
~ ( member_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_empty__iff) ).
thf(720,plain,
! [A: sum_sum_a_b] :
~ ( member_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(267,axiom,
! [A: sum_sum_a_b,B: set_Pr1174980151um_a_b,C: set_nat] :
( ( member_Sum_sum_a_b @ A @ ( image_256773707um_a_b @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( member1294585472um_a_b @ ( produc1808556047um_a_b @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Image__iff) ).
thf(1165,plain,
! [A: sum_sum_a_b,B: set_Pr1174980151um_a_b,C: set_nat] :
( ( member_Sum_sum_a_b @ A @ ( image_256773707um_a_b @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( member1294585472um_a_b @ ( produc1808556047um_a_b @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(125,axiom,
! [A: set_Pr409224873um_a_b] :
( ( ! [B: produc1963079155um_a_b] :
~ ( member1998628618um_a_b @ B @ A ) )
= ( A = bot_bo1262634813um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_all__not__in__conv) ).
thf(740,plain,
! [A: set_Pr409224873um_a_b] :
( ( ! [B: produc1963079155um_a_b] :
~ ( member1998628618um_a_b @ B @ A ) )
= ( A = bot_bo1262634813um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(208,axiom,
! [A: sum_sum_a_b,B: set_Pr1174980151um_a_b,C: nat] :
( ( member_Sum_sum_a_b @ A @ ( image_256773707um_a_b @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
= ( member1294585472um_a_b @ ( produc1808556047um_a_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Image__singleton__iff) ).
thf(987,plain,
! [A: sum_sum_a_b,B: set_Pr1174980151um_a_b,C: nat] :
( ( member_Sum_sum_a_b @ A @ ( image_256773707um_a_b @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
= ( member1294585472um_a_b @ ( produc1808556047um_a_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(40,axiom,
! [A: set_Pr1647387645at_nat,B: set_Pr1647387645at_nat] :
( ( ord_le1909159005at_nat @ A @ B )
=> ( ord_le1739761029tant_a @ ( domain1060562500at_nat @ A ) @ ( domain1060562500at_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Domain__mono) ).
thf(464,plain,
! [A: set_Pr1647387645at_nat,B: set_Pr1647387645at_nat] :
( ( ord_le1909159005at_nat @ A @ B )
=> ( ord_le1739761029tant_a @ ( domain1060562500at_nat @ A ) @ ( domain1060562500at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(299,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat,D: set_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ C )
=> ( ( member_nat @ A @ D )
=> ( member_nat @ B @ ( image_nat_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_ImageI) ).
thf(1261,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat,D: set_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ C )
=> ( ( member_nat @ A @ D )
=> ( member_nat @ B @ ( image_nat_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(60,axiom,
( ord_le615126793um_a_b
= ( ^ [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
! [C: produc1963079155um_a_b] :
( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_subset__eq) ).
thf(528,plain,
( ord_le615126793um_a_b
= ( ^ [A: set_Pr409224873um_a_b,B: set_Pr409224873um_a_b] :
! [C: produc1963079155um_a_b] :
( ( member1998628618um_a_b @ C @ A )
=> ( member1998628618um_a_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(120,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: set_St761939237tant_a] :
( ( ord_le1739761029tant_a @ ( insert1909710879tant_a @ A @ B ) @ C )
= ( ( member1632892294tant_a @ A @ C )
& ( ord_le1739761029tant_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_insert__subset) ).
thf(723,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: set_St761939237tant_a] :
( ( ord_le1739761029tant_a @ ( insert1909710879tant_a @ A @ B ) @ C )
= ( ( member1632892294tant_a @ A @ C )
& ( ord_le1739761029tant_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(214,axiom,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
=> ( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_subsetD) ).
thf(1004,plain,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b,C: sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
=> ( ( member_Sum_sum_a_b @ C @ A )
=> ( member_Sum_sum_a_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(111,axiom,
! [A: sum_sum_a_b > $o] :
( ( bot_bo1491243248um_a_b
= ( collect_Sum_sum_a_b @ A ) )
= ( ! [B: sum_sum_a_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_empty__Collect__eq) ).
thf(691,plain,
! [A: sum_sum_a_b > $o] :
( ( bot_bo1491243248um_a_b
= ( collect_Sum_sum_a_b @ A ) )
= ( ! [B: sum_sum_a_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(170,axiom,
! [A: set_Pr1647387645at_nat,B: produc1032616263at_nat] :
( ( A = bot_bo810816657at_nat )
=> ~ ( member1696759390at_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_equals0D) ).
thf(871,plain,
! [A: set_Pr1647387645at_nat,B: produc1032616263at_nat] :
( ( A = bot_bo810816657at_nat )
=> ~ ( member1696759390at_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(50,axiom,
! [A: produc1124793815um_a_b,B: sum_sum_a_b,C: set_Pr653770722um_a_b,D: set_Pr1174980151um_a_b] :
( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ C )
=> ( ( member1294585472um_a_b @ A @ D )
=> ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_ImageI) ).
thf(501,plain,
! [A: produc1124793815um_a_b,B: sum_sum_a_b,C: set_Pr653770722um_a_b,D: set_Pr1174980151um_a_b] :
( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ C )
=> ( ( member1294585472um_a_b @ A @ D )
=> ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(9,axiom,
! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,C: set_Pr1916610317um_a_b] :
( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ C ) )
= ( ( A = B )
| ( member947389014um_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_insert__iff) ).
thf(369,plain,
! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,C: set_Pr1916610317um_a_b] :
( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ C ) )
= ( ( A = B )
| ( member947389014um_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(242,axiom,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
=> ( ( ord_le192794300um_a_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_subset__antisym) ).
thf(1093,plain,
! [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
=> ( ( ord_le192794300um_a_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(18,axiom,
! [A: standard_Constant_a,B: standard_Constant_a,C: set_St761939237tant_a] :
( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ C ) )
= ( ( A = B )
| ( member1632892294tant_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_insert__iff) ).
thf(395,plain,
! [A: standard_Constant_a,B: standard_Constant_a,C: set_St761939237tant_a] :
( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ C ) )
= ( ( A = B )
| ( member1632892294tant_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(301,axiom,
! [A: nat,B: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
=> ~ ! [C: sum_sum_a_b] :
~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Domain_Ocases) ).
thf(1268,plain,
! [A: nat,B: set_Pr1174980151um_a_b] :
( ( member_nat @ A @ ( domain1368163076um_a_b @ B ) )
=> ~ ! [C: sum_sum_a_b] :
~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(77,axiom,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ C ) )
=> ( ( A != B )
=> ( member_Sum_sum_a_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_insertE) ).
thf(575,plain,
! [A: sum_sum_a_b,B: sum_sum_a_b,C: set_Sum_sum_a_b] :
( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ C ) )
=> ( ( A != B )
=> ( member_Sum_sum_a_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(323,axiom,
! [A: set_Pr1916610317um_a_b,B: set_Pr1916610317um_a_b] :
( ( ord_le1059794605um_a_b @ A @ B )
=> ( ord_le192794300um_a_b @ ( domain2069673178um_a_b @ A ) @ ( domain2069673178um_a_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_Domain__mono) ).
thf(1331,plain,
! [A: set_Pr1916610317um_a_b,B: set_Pr1916610317um_a_b] :
( ( ord_le1059794605um_a_b @ A @ B )
=> ( ord_le192794300um_a_b @ ( domain2069673178um_a_b @ A ) @ ( domain2069673178um_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(45,axiom,
! [A: sum_sum_a_b,B: set_Pr1994339542um_a_b,C: standard_Constant_a] :
( ( member_Sum_sum_a_b @ A @ ( image_2129435242um_a_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1641046175um_a_b @ ( produc584843310um_a_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Image__singleton__iff) ).
thf(486,plain,
! [A: sum_sum_a_b,B: set_Pr1994339542um_a_b,C: standard_Constant_a] :
( ( member_Sum_sum_a_b @ A @ ( image_2129435242um_a_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1641046175um_a_b @ ( produc584843310um_a_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(146,axiom,
! [A: labele431970251um_a_b,B: set_Pr304595758um_a_b] :
( ( graph_166346565um_a_b @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ A @ B )
= ( ( B = bot_bo627753370um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_graph__homomorphism__empty) ).
thf(803,plain,
! [A: labele431970251um_a_b,B: set_Pr304595758um_a_b] :
( ( graph_166346565um_a_b @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ A @ B )
= ( ( B = bot_bo627753370um_a_b )
& ( A
= ( restri1162247455um_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(187,axiom,
! [A: nat,B: set_Pr1986765409at_nat,C: set_nat] :
( ( member_nat @ A @ ( image_nat_nat @ B @ C ) )
=> ~ ! [D: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ A ) @ B )
=> ~ ( member_nat @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_ImageE) ).
thf(923,plain,
! [A: nat,B: set_Pr1986765409at_nat,C: set_nat] :
( ( member_nat @ A @ ( image_nat_nat @ B @ C ) )
=> ~ ! [D: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ A ) @ B )
=> ~ ( member_nat @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(225,axiom,
! [A: set_nat,B: nat] :
( ( A = bot_bot_set_nat )
=> ~ ( member_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_equals0D) ).
thf(1037,plain,
! [A: set_nat,B: nat] :
( ( A = bot_bot_set_nat )
=> ~ ( member_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(240,axiom,
( ( (=) @ set_Sum_sum_a_b )
= ( ^ [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
& ( ord_le192794300um_a_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_set__eq__subset) ).
thf(1088,plain,
( ( (=) @ set_Sum_sum_a_b )
= ( ^ [A: set_Sum_sum_a_b,B: set_Sum_sum_a_b] :
( ( ord_le192794300um_a_b @ A @ B )
& ( ord_le192794300um_a_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(83,axiom,
! [A: set_Pr1916610317um_a_b,B: set_Pr409224873um_a_b,C: set_Pr409224873um_a_b,D: sum_sum_a_b,E: sum_sum_a_b,F: sum_sum_a_b,G: sum_sum_a_b,H: standard_Constant_a] :
( ( edge_p1871801392tant_a @ A @ B @ C )
=> ( ( member947389014um_a_b @ ( produc176426981um_a_b @ D @ E ) @ A )
=> ( ( member947389014um_a_b @ ( produc176426981um_a_b @ F @ G ) @ A )
=> ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ H @ ( produc176426981um_a_b @ D @ F ) ) @ B )
=> ( member1998628618um_a_b @ ( produc1697725733um_a_b @ H @ ( produc176426981um_a_b @ E @ G ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_edge__preserving__atomic) ).
thf(592,plain,
! [A: set_Pr1916610317um_a_b,B: set_Pr409224873um_a_b,C: set_Pr409224873um_a_b,D: sum_sum_a_b,E: sum_sum_a_b,F: sum_sum_a_b,G: sum_sum_a_b,H: standard_Constant_a] :
( ( edge_p1871801392tant_a @ A @ B @ C )
=> ( ( member947389014um_a_b @ ( produc176426981um_a_b @ D @ E ) @ A )
=> ( ( member947389014um_a_b @ ( produc176426981um_a_b @ F @ G ) @ A )
=> ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ H @ ( produc176426981um_a_b @ D @ F ) ) @ B )
=> ( member1998628618um_a_b @ ( produc1697725733um_a_b @ H @ ( produc176426981um_a_b @ E @ G ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(48,axiom,
! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_singletonI) ).
thf(496,plain,
! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(7,axiom,
! [A: produc1548871597um_a_b] : ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_singletonI) ).
thf(364,plain,
! [A: produc1548871597um_a_b] : ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(116,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_eq__imp__le) ).
thf(708,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(173,axiom,
! [A: set_Pr1174980151um_a_b] :
( ( image_256773707um_a_b @ A @ bot_bot_set_nat )
= bot_bo1491243248um_a_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Image__empty2) ).
thf(882,plain,
! [A: set_Pr1174980151um_a_b] :
( ( image_256773707um_a_b @ A @ bot_bot_set_nat )
= bot_bo1491243248um_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(42,axiom,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b,C: standard_Constant_a > $o] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
=> ( ! [D: standard_Constant_a,E: produc1548871597um_a_b] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_Domain_Oinducts) ).
thf(469,plain,
! [A: standard_Constant_a,B: set_Pr409224873um_a_b,C: standard_Constant_a > $o] :
( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ B ) )
=> ( ! [D: standard_Constant_a,E: produc1548871597um_a_b] :
( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(335,axiom,
! [A: product_prod_nat_nat,B: set_Pr1647387645at_nat,C: set_St761939237tant_a] :
( ( member701585322at_nat @ A @ ( image_127502653at_nat @ B @ C ) )
= ( ? [D: standard_Constant_a] :
( ( member1632892294tant_a @ D @ C )
& ( member1696759390at_nat @ ( produc407553657at_nat @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Image__iff) ).
thf(1367,plain,
! [A: product_prod_nat_nat,B: set_Pr1647387645at_nat,C: set_St761939237tant_a] :
( ( member701585322at_nat @ A @ ( image_127502653at_nat @ B @ C ) )
= ( ? [D: standard_Constant_a] :
( ( member1632892294tant_a @ D @ C )
& ( member1696759390at_nat @ ( produc407553657at_nat @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(130,axiom,
unival118648434um_a_b @ bot_bo225809273um_a_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_univalent__empty) ).
thf(755,plain,
unival118648434um_a_b @ bot_bo225809273um_a_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(106,axiom,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b,C: set_Pr409224873um_a_b] :
( ( ord_le615126793um_a_b @ ( insert323157027um_a_b @ A @ B ) @ C )
= ( ( member1998628618um_a_b @ A @ C )
& ( ord_le615126793um_a_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_insert__subset) ).
thf(676,plain,
! [A: produc1963079155um_a_b,B: set_Pr409224873um_a_b,C: set_Pr409224873um_a_b] :
( ( ord_le615126793um_a_b @ ( insert323157027um_a_b @ A @ B ) @ C )
= ( ( member1998628618um_a_b @ A @ C )
& ( ord_le615126793um_a_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1471,plain,
$false,
inference(e,[status(thm)],[892,629,1168,1105,846,962,941,777,352,909,1031,666,1295,523,730,1142,1205,449,1137,533,1233,1342,930,670,814,1327,404,1196,1001,885,1359,1254,1243,1127,389,1287,1298,372,504,1264,1059,949,542,917,702,357,1191,559,1379,421,1013,416,1362,817,902,756,789,1373,623,834,1151,1020,806,1183,480,981,634,866,660,998,1345,428,849,507,1119,774,1074,452,920,380,793,1306,1199,366,1311,1047,512,439,957,746,1042,862,1174,820,392,407,1370,1217,598,1365,879,852,889,1159,1079,682,1281,583,830,493,1210,551,1128,1350,578,697,1017,1328,1064,1096,869,1111,1227,783,1118,669,476,637,489,1214,1207,679,547,1028,1082,1292,933,837,1099,515,1382,1131,984,569,1324,1114,1333,343,1202,360,398,1071,530,586,965,1251,1146,856,1301,601,375,733,1154,843,1388,743,413,562,904,975,1007,694,936,572,1271,498,1239,466,1090,1224,1356,604,1194,1117,736,567,616,1376,377,990,509,434,811,520,895,769,1177,1061,799,1162,726,626,915,943,1022,827,1066,780,455,608,1102,431,653,912,685,1171,1044,1245,1076,1034,426,589,663,927,1277,1134,749,1049,968,458,823,525,1025,971,1230,993,712,557,580,855,673,441,840,1220,1188,1186,951,808,544,907,1257,1141,656,613,1284,1353,446,595,876,859,1240,978,386,1180,539,688,1010,1289,771,1108,1157,1321,699,1385,517,946,632,401,995,418,786,763,383,899,549,536,716,346,1309,1348,620,752,1280,1303,1148,1248,833,410,564,801,1314,767,1056,1288,960,955,796,437,1335,720,1165,740,987,464,1261,528,723,1004,691,871,501,369,1093,395,1268,575,1331,486,803,923,1037,1088,592,496,364,708,882,469,1367,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP179^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % 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
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Tue Sep 29 20:06:33 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 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
% 0.40/0.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/0.62 % [INFO] Parsing done (216ms).
% 1.29/0.62 % [INFO] Running in sequential loop mode.
% 2.01/0.82 % [INFO] eprover registered as external prover.
% 2.01/0.82 % [INFO] Scanning for conjecture ...
% 2.29/0.91 % [INFO] Found a conjecture (or negated_conjecture) and 352 axioms. Running axiom selection ...
% 2.29/1.01 % [INFO] Axiom selection finished. Selected 340 axioms (removed 12 axioms).
% 3.06/1.14 % [INFO] Problem is higher-order (TPTP THF).
% 3.06/1.15 % [INFO] Type checking passed.
% 3.06/1.15 % [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 ...
% 10.09/2.84 % External prover 'e' found a proof!
% 10.09/2.84 % [INFO] Killing All external provers ...
% 10.09/2.84 % Time passed: 2645ms (effective reasoning time: 2210ms)
% 10.09/2.84 % 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)>
% 10.09/2.84 % Axioms used in derivation (340): fact_39_restrict__idemp, fact_62_Image__empty2, fact_232_subsetI, fact_295_equals0I, fact_285_equals0D, fact_180_insert__subset, fact_349__092_060open_062maintained_A_Isymmetry__rule_AS__Idt_J_AG_092_060close_062, fact_311_subset__eq, fact_258_insert__absorb2, fact_74_rev__ImageI, fact_169_univalent__empty, fact_197_empty__subsetI, fact_149_labeled__graph_Oexhaust__sel, fact_313_equalityD2, fact_14_Domain__insert, fact_115_Domain_Ocases, fact_238_insertCI, fact_275_restrict__subsD, fact_6_graph__single, fact_137_labeled__graph_Osel_I1_J, fact_167_univalent__empty, fact_5_d, fact_43__092_060open_062_IS__Idt_M_Av_M_Av_J_A_092_060in_062_Aedges_AG_092_060close_062, fact_289_equals0D, fact_252_insert__absorb2, fact_162_singleton__insert__inj__eq, fact_120_Domain__iff, fact_194_empty__subsetI, fact_170_mem__Collect__eq, fact_191_singletonI, fact_309_subset__eq, fact_31_Domain__empty, fact_291_equals0I, fact_57_Image__empty2, fact_267_graph__homomorphism__empty, fact_85_Image__iff, fact_125_DomainE, fact_348_gr_I2_J, fact_182_insert__subset, fact_4_f, fact_142_Domain__empty__iff, fact_67_labeled__graph_Oexhaust, fact_107_Domain_ODomainI, fact_171_mem__Collect__eq, fact_246_insert__iff, fact_60_Image__empty2, fact_189_singletonI, fact_227_empty__Collect__eq, fact_54_Image__empty2, fact_308_equalityE, fact_213_all__not__in__conv, fact_224_Collect__empty__eq, fact_228_empty__Collect__eq, fact_90_ImageE, fact_325_insertE, fact_249_insert__iff, fact_32_Domain__empty, fact_222_Collect__empty__eq, fact_218_all__not__in__conv, fact_16_Image__singleton__iff, fact_175_Collect__mem__eq, fact_56_Image__empty2, fact_34_Image__empty1, fact_168_univalent__empty, fact_135_labeled__graph_Osel_I2_J, fact_157_singleton__insert__inj__eq_H, fact_30_Domain__empty, fact_161_singleton__insert__inj__eq, fact_253_insert__absorb2, fact_38_restrict__idemp, fact_345_le__0__eq, fact_109_Domain_Osimps, fact_66__092_060open_062graph__homomorphism_A_ILG_A_123_125_A_1230_125_J_AG_Af_092_060close_062, fact_243_insert__iff, fact_230_empty__Collect__eq, fact_50_ImageI, fact_128_Domain__mono, fact_96_Image__mono, fact_205_reflexivity__rule__def, fact_283_emptyE, fact_155_singleton__insert__inj__eq_H, fact_1_v, fact_288_equals0D, fact_199_subset__empty, fact_320_set__eq__subset, fact_256_insert__absorb2, fact_280_emptyE, fact_72_rev__ImageI, fact_265_graph__homomorphism__empty, fact_45_ImageI, fact_81_Image__iff, fact_317_subset__refl, fact_259_graph__homomorphism__empty, fact_274_subrelI, fact_281_emptyE, fact_98_Domain_Oinducts, fact_156_singleton__insert__inj__eq_H, fact_22_Image__singleton__iff, fact_272_subrelI, fact_193_empty__subsetI, fact_321_Collect__mono__iff, fact_187_singletonI, fact_203_subset__empty, fact_173_Collect__mem__eq, fact_334_le0, fact_254_insert__absorb2, fact_326_insertE, fact_184_singletonI, fact_33_Domain__empty, fact_154_singleton__insert__inj__eq_H, fact_172_mem__Collect__eq, fact_17_Image__singleton__iff, fact_88_ImageE, fact_303_in__mono, fact_198_subset__empty, fact_350__092_060open_062maintained_A_Itransitive__rule_AS__Idt_J_AG_092_060close_062, fact_123_DomainE, fact_247_insert__iff, fact_202_subset__empty, fact_59_Image__empty2, fact_255_insert__absorb2, fact_68_labeled__graph_Oexhaust, fact_69_labeled__graph_Oinduct, fact_144_edge__preserving__atomic, fact_304_in__mono, fact_305_subsetD, fact_178_insert__subset, fact_322_insertE, fact_290_equals0I, fact_335_bot__nat__0_Oextremum, fact_229_empty__Collect__eq, fact_122_Domain__iff, fact_11_Domain__insert, fact_58_Image__empty2, fact_47_ImageI, fact_212_empty__iff, fact_64_vertices__restrict, fact_147_edge__preserving__atomic, fact_239_insertCI, fact_251_insert__absorb2, fact_12_Domain__insert, fact_121_Domain__iff, fact_21_Image__singleton__iff, fact_310_subset__eq, fact_331_insertI1, fact_103_Domain_ODomainI, fact_270_subrelI, fact_73_rev__ImageI, fact_323_insertE, fact_200_subset__empty, fact_146_edge__preserving__atomic, fact_328_insertE, fact_35_Image__empty1, fact_89_ImageE, fact_338_le__antisym, fact_276_restrict__subsD, fact_316_subset__iff, fact_271_subrelI, fact_164_singleton__insert__inj__eq, fact_297_ex__in__conv, fact_82_Image__iff, fact_145_edge__preserving__atomic, fact_188_singletonI, fact_119_Domain__iff, fact_277_zero__reorient, fact_302_in__mono, fact_217_all__not__in__conv, fact_28_labeled__graph_Ocollapse, fact_37_Image__empty1, fact_240_insertCI, fact_216_all__not__in__conv, fact_110_Domain_Osimps, fact_65_vertices__restrict, fact_327_insertE, fact_87_ImageE, fact_268_graph__homomorphism__empty, fact_23_Image__singleton__iff, fact_150_singleton__insert__inj__eq_H, fact_263_graph__homomorphism__empty, fact_18_Image__singleton__iff, fact_260_graph__homomorphism__empty, fact_100_Domain_Oinducts, fact_248_insert__iff, fact_63_Image__empty2, fact_49_ImageI, fact_7_graph__single, fact_134_labeled__graph_Oexpand, fact_160_singleton__insert__inj__eq, fact_206_nonempty__rule__def, fact_299_ex__in__conv, fact_116_Domain_Ocases, fact_117_Domain_Ocases, fact_226_empty__Collect__eq, fact_333_insertI1, fact_324_insertE, fact_347_gr_I1_J, fact_262_graph__homomorphism__empty, fact_138_labeled__graph_Osel_I1_J, fact_190_singletonI, fact_132_Domain__mono, fact_13_Domain__insert, fact_207_empty__iff, fact_139_Domain__empty__iff, fact_40_labeled__graph_Oinject, fact_159_singleton__insert__inj__eq, fact_282_emptyE, fact_166_univalent__empty, fact_29_Domain__empty, fact_185_singletonI, fact_221_Collect__empty__eq, fact_336_Nat_Oex__has__greatest__nat, fact_315_subset__iff, fact_181_insert__subset, fact_329_insertE, fact_101_Domain_Oinducts, fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062, fact_113_Domain_Ocases, fact_92_ImageE, fact_332_insertI1, fact_71_rev__ImageI, fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_244_insert__iff, fact_153_singleton__insert__inj__eq_H, fact_211_empty__iff, fact_83_Image__iff, fact_312_equalityD1, fact_231_subsetI, fact_286_equals0D, fact_241_insertCI, fact_344_bot__nat__0_Oextremum__unique, fact_210_empty__iff, fact_314_subset__iff, fact_99_Domain_Oinducts, fact_307_subsetD, fact_279_emptyE, fact_337_nat__le__linear, fact_76_rev__ImageI, fact_151_singleton__insert__inj__eq_H, fact_41_labeled__graph_Oinject, fact_340_le__trans, fact_10_Domain__insert, fact_339_eq__imp__le, fact_55_Image__empty2, fact_269_edge__preserving__subset, fact_77_rev__ImageI, fact_141_Domain__empty__iff, fact_196_empty__subsetI, fact_341_le__refl, fact_148_labeled__graph_Oexhaust__sel, fact_351__092_060open_062maintained_A_Icongruence__rule_AS__Idt_Al_J_AG_092_060close_062, fact_133_labeled__graph_Oexpand, fact_42_v__gr, fact_118_Domain__iff, fact_223_Collect__empty__eq, fact_102_Domain_Oinducts, fact_319_subset__trans, fact_298_ex__in__conv, fact_306_subsetD, fact_237_insertCI, fact_220_Collect__empty__eq, fact_126_DomainE, fact_186_singletonI, fact_143_Domain__empty__iff, fact_84_Image__iff, fact_112_Domain_Osimps, fact_330_insertI1, fact_130_Domain__mono, fact_127_DomainE, fact_245_insert__iff, fact_136_labeled__graph_Osel_I2_J, fact_165_singleton__insert__inj__eq, fact_15_Image__singleton__iff, fact_3_r, fact_176_insert__subset, fact_215_all__not__in__conv, fact_266_graph__homomorphism__empty, fact_97_Image__mono, fact_201_subset__empty, fact_294_equals0I, fact_86_ImageE, fact_209_empty__iff, fact_26_graph__empty__e, fact_214_all__not__in__conv, fact_225_empty__Collect__eq, fact_177_insert__subset, fact_20_Image__singleton__iff, fact_183_insert__subset, fact_250_insert__iff, fact_174_Collect__mem__eq, fact_106_Domain_ODomainI, fact_242_insertCI, fact_158_singleton__insert__inj__eq, fact_234_subset__antisym, fact_131_Domain__mono, fact_264_graph__homomorphism__empty, fact_233_subsetI, fact_108_Domain_Osimps, fact_318_Collect__mono, fact_9_u, fact_346_less__eq__nat_Osimps_I1_J, fact_152_singleton__insert__inj__eq_H, fact_27_labeled__graph_Ocollapse, fact_204_le__zero__eq, fact_261_graph__homomorphism__empty, fact_163_singleton__insert__inj__eq, fact_25_graph__empty__e, fact_36_Image__empty1, fact_70_labeled__graph_Oinduct, fact_257_insert__absorb2, fact_236_insertCI, fact_284_equals0D, fact_61_Image__empty2, fact_44_ImageI, fact_343_bot__nat__0_Oextremum__uniqueI, fact_293_equals0I, fact_278_emptyE, fact_208_empty__iff, fact_192_empty__subsetI, fact_140_Domain__empty__iff, fact_104_Domain_ODomainI, fact_273_subrelI, fact_105_Domain_ODomainI, fact_342_bot__nat__def, fact_19_Image__singleton__iff, fact_300_ex__in__conv, fact_179_insert__subset, fact_301_ex__in__conv, fact_195_empty__subsetI, fact_0_g, fact_124_DomainE, fact_111_Domain_Osimps, fact_46_ImageI, fact_235_insertCI, fact_287_equals0D, fact_24_Image__singleton__iff, fact_129_Domain__mono, fact_292_equals0I, fact_114_Domain_Ocases, fact_296_ex__in__conv, fact_219_Collect__empty__eq
% 10.09/2.84 % No. of inferences in proof: 684
% 10.09/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2645 ms resp. 2210 ms w/o parsing
% 10.92/2.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.92/2.98 % [INFO] Killing All external provers ...
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