TSTP Solution File: SWW473_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW473_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 11:07:24 EDT 2023
% Result : Theorem 27.73s 11.25s
% Output : CNFRefutation 27.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 332
% Syntax : Number of formulae : 350 ( 16 unt; 322 typ; 0 def)
% Number of atoms : 44 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 10 ~; 9 |; 1 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 91 ( 90 usr)
% Number of type conns : 333 ( 179 >; 154 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 231 ( 231 usr; 53 con; 0-3 aty)
% Number of variables : 42 (; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
%$ hBOOL > insert_pname > insert_nat > insert_fun_nat_bool > insert_fun_a_bool > insert_a > insert2003652156l_bool > insert1457093509l_bool > insert1325755072e_bool > insert1117693814l_bool > image_pname_pname > image_pname_nat > image_pname_a > image_nat_pname > image_nat_fun_a_bool > image_nat_a > image_fun_nat_bool_a > image_fun_a_bool_nat > image_fun_a_bool_a > image_a_pname > image_a_nat > image_a_a > image_990671762_pname > image_876012084bool_a > image_573985017bool_a > image_526090948bool_a > image_496248727ol_nat > image_47868345e_bool > image_349102846bool_a > image_26036933t_bool > image_2129980159t_bool > image_2089570637ol_nat > image_1921560913_pname > image_1874789623l_bool > image_1854862208_pname > image_1802975832ol_nat > image_1705983821_pname > image_1655916159e_bool > image_1642285373l_bool > image_1607900221l_bool > image_1604018183_pname > image_1551609309ol_nat > image_1420695166l_bool > image_1283814551_pname > image_1208015684l_bool > image_1154884483l_bool > image_112932426a_bool > image_1079571347ol_nat > hAPP_pname_bool > hAPP_pname_a > hAPP_p61793385e_bool > hAPP_p393069232l_bool > hAPP_p338031245l_bool > hAPP_p1534023578a_bool > hAPP_nat_nat > hAPP_nat_fun_a_bool > hAPP_nat_bool > hAPP_n215258509l_bool > hAPP_n1699378549t_bool > hAPP_n1025906991e_bool > hAPP_n1006566506l_bool > hAPP_fun_a_bool_nat > hAPP_fun_a_bool_bool > hAPP_f98387925ol_nat > hAPP_f937997336l_bool > hAPP_f921600141ol_nat > hAPP_f800510211t_bool > hAPP_f760187903l_bool > hAPP_f759274231e_bool > hAPP_f696928925ol_nat > hAPP_f621171935l_bool > hAPP_f595608956l_bool > hAPP_f559147733l_bool > hAPP_f556039215l_bool > hAPP_f55526627ol_nat > hAPP_f54304608l_bool > hAPP_f510955609l_bool > hAPP_f434788991l_bool > hAPP_f389811538l_bool > hAPP_f292226953l_bool > hAPP_f285962445l_bool > hAPP_f22106695ol_nat > hAPP_f2117159681l_bool > hAPP_f2050579477a_bool > hAPP_f2009550088ol_nat > hAPP_f198738859l_bool > hAPP_f1951378235l_bool > hAPP_f1935102916l_bool > hAPP_f1772781669l_bool > hAPP_f1759205631l_bool > hAPP_f1748468828l_bool > hAPP_f1690079119ol_nat > hAPP_f1664156314l_bool > hAPP_f1637334154l_bool > hAPP_f1631501043l_bool > hAPP_f1476298914l_bool > hAPP_f1434722111l_bool > hAPP_f1363661463l_bool > hAPP_f1295398978l_bool > hAPP_f1253658590ol_nat > hAPP_f1246832597l_bool > hAPP_f1050622307l_bool > hAPP_f103356543l_bool > hAPP_bool_bool > hAPP_b589554111l_bool > hAPP_a_fun_bool_bool > hAPP_a_fun_a_bool > hAPP_a_bool > hAPP_a93125764e_bool > hAPP_a85458249l_bool > cOMBS_nat_bool_bool > cOMBS_a_bool_bool > cOMBS_568398431l_bool > cOMBS_350070575l_bool > cOMBS_1187019125l_bool > cOMBS_1035972772l_bool > cOMBB_bool_bool_nat > cOMBB_bool_bool_a > cOMBB_675860798_pname > cOMBB_647938656_pname > cOMBB_444170502t_bool > cOMBB_338059395a_bool > cOMBB_307249310e_bool > cOMBB_238756964t_bool > cOMBB_2140588453a_bool > cOMBB_2095475776e_bool > cOMBB_1972296269bool_a > cOMBB_1897541054_pname > cOMBB_1015721476ol_nat > #nlpp > p > minus_minus_nat > collect_pname > collect_nat > collect_fun_nat_bool > collect_fun_a_bool > collect_a > collec792590109l_bool > collec707592106l_bool > collec1974731493e_bool > collec1874991203l_bool > collec1635217238l_bool > collec1613912337l_bool > collec1015864663l_bool > cOMBC_pname_a_bool > cOMBC_nat_nat_bool > cOMBC_a_a_bool > cOMBC_7971162l_bool > cOMBC_636888218l_bool > cOMBC_595898202l_bool > cOMBC_336095980l_bool > cOMBC_331553030l_bool > cOMBC_226598744l_bool > cOMBC_1988546018l_bool > cOMBC_1880041174l_bool > cOMBC_1732670874l_bool > cOMBC_1693257480l_bool > cOMBC_1355376034l_bool > cOMBC_1284144636l_bool > cOMBC_1269652216l_bool > cOMBC_1245412066l_bool > cOMBC_1149511130e_bool > cOMBC_1058051404l_bool > u > suc > pn > ord_less_eq_nat > ord_le967226251l_bool > ord_le675606854l_bool > ord_le65145710l_bool > ord_le313189616e_bool > ord_le1568362934t_bool > ord_le1454342156l_bool > ord_le1375671464l_bool > ord_le1375614389l_bool > ord_le1311769555a_bool > na > mgt_call > member_pname > member_nat > member_fun_nat_bool > member_fun_a_bool > member_a > member799430823e_bool > g > finite_finite_pname > finite_finite_nat > finite_finite_a > finite_card_pname > finite_card_nat > finite_card_a > finite786885583l_bool > finite719726885l_bool > finite595471783e_bool > finite347923420a_bool > finite346522414t_bool > finite269641166l_bool > finite2012431853t_bool > finite1701474069l_bool > finite1659325229l_bool > finite1491191519l_bool > finite1381704300l_bool > finite1352710292l_bool > finite1343359508l_bool > finite1340463720e_bool > finite1306199131a_bool > fimplies > fequal_pname > fequal_nat > fequal_fun_nat_bool > fequal_fun_a_bool > fequal_a > fequal533582459e_bool > fdisj > fconj > fNot > #skF_12 > #skF_16 > #skF_15 > #skF_13 > #skF_10 > #skF_14 > #skF_3 > #skF_2 > #skF_11 > #skF_6 > #skF_4 > #skF_8 > #skF_5 > #skF_1 > #skF_17 > #skF_9 > #skF_7
%Foreground sorts:
tff(fun_fu821463397t_bool,type,
fun_fu821463397t_bool: $tType ).
tff(fun_fu140186515l_bool,type,
fun_fu140186515l_bool: $tType ).
tff(fun_fu410713561e_bool,type,
fun_fu410713561e_bool: $tType ).
tff(fun_nat_fun_a_bool,type,
fun_nat_fun_a_bool: $tType ).
tff(fun_a_1255737515l_bool,type,
fun_a_1255737515l_bool: $tType ).
tff(fun_fu821736593l_bool,type,
fun_fu821736593l_bool: $tType ).
tff(fun_fu1730389579ol_nat,type,
fun_fu1730389579ol_nat: $tType ).
tff(fun_na1469252690l_bool,type,
fun_na1469252690l_bool: $tType ).
tff(fun_fu2020802748ol_nat,type,
fun_fu2020802748ol_nat: $tType ).
tff(fun_bool_bool,type,
fun_bool_bool: $tType ).
tff(fun_fu1499449723_pname,type,
fun_fu1499449723_pname: $tType ).
tff(fun_fu1137991347l_bool,type,
fun_fu1137991347l_bool: $tType ).
tff(fun_fu754241017l_bool,type,
fun_fu754241017l_bool: $tType ).
tff(fun_fu1175941238_pname,type,
fun_fu1175941238_pname: $tType ).
tff(fun_fu399576434l_bool,type,
fun_fu399576434l_bool: $tType ).
tff(fun_fu881587263_pname,type,
fun_fu881587263_pname: $tType ).
tff(fun_fu885608257l_bool,type,
fun_fu885608257l_bool: $tType ).
tff(fun_a_pname,type,
fun_a_pname: $tType ).
tff(fun_fu802393907l_bool,type,
fun_fu802393907l_bool: $tType ).
tff(fun_nat_bool,type,
fun_nat_bool: $tType ).
tff(fun_fu418465139l_bool,type,
fun_fu418465139l_bool: $tType ).
tff(fun_fu1731003005a_bool,type,
fun_fu1731003005a_bool: $tType ).
tff(fun_fu48515398ol_nat,type,
fun_fu48515398ol_nat: $tType ).
tff(fun_fun_a_bool_bool,type,
fun_fun_a_bool_bool: $tType ).
tff(fun_pn250273176l_bool,type,
fun_pn250273176l_bool: $tType ).
tff(fun_fu1217155507l_bool,type,
fun_fu1217155507l_bool: $tType ).
tff(pname,type,
pname: $tType ).
tff(fun_fu1430349052l_bool,type,
fun_fu1430349052l_bool: $tType ).
tff(fun_pn406123357t_bool,type,
fun_pn406123357t_bool: $tType ).
tff(fun_fun_a_bool_nat,type,
fun_fun_a_bool_nat: $tType ).
tff(fun_na2122364079l_bool,type,
fun_na2122364079l_bool: $tType ).
tff(fun_fu554186387l_bool,type,
fun_fu554186387l_bool: $tType ).
tff(fun_a_fun_a_bool,type,
fun_a_fun_a_bool: $tType ).
tff(fun_fun_a_bool_a,type,
fun_fun_a_bool_a: $tType ).
tff(fun_bo1549164019l_bool,type,
fun_bo1549164019l_bool: $tType ).
tff(fun_a_fun_bool_bool,type,
fun_a_fun_bool_bool: $tType ).
tff(fun_fu425979586l_bool,type,
fun_fu425979586l_bool: $tType ).
tff(fun_a_fun_pname_bool,type,
fun_a_fun_pname_bool: $tType ).
tff(fun_a_a,type,
fun_a_a: $tType ).
tff(fun_fu31783638l_bool,type,
fun_fu31783638l_bool: $tType ).
tff(fun_fun_nat_bool_a,type,
fun_fun_nat_bool_a: $tType ).
tff(fun_a_bool,type,
fun_a_bool: $tType ).
tff(fun_fun_pname_bool_a,type,
fun_fun_pname_bool_a: $tType ).
tff(fun_fu1664106117_pname,type,
fun_fu1664106117_pname: $tType ).
tff(nat,type,
nat: $tType ).
tff(fun_fu1668467777ol_nat,type,
fun_fu1668467777ol_nat: $tType ).
tff(fun_fu1471507361l_bool,type,
fun_fu1471507361l_bool: $tType ).
tff(fun_fu1436348701l_bool,type,
fun_fu1436348701l_bool: $tType ).
tff(fun_fu897950882bool_a,type,
fun_fu897950882bool_a: $tType ).
tff(fun_pname_nat,type,
fun_pname_nat: $tType ).
tff(fun_fu911136611l_bool,type,
fun_fu911136611l_bool: $tType ).
tff(x_a,type,
x_a: $tType ).
tff(fun_nat_fun_nat_bool,type,
fun_nat_fun_nat_bool: $tType ).
tff(fun_na1632405922l_bool,type,
fun_na1632405922l_bool: $tType ).
tff(fun_nat_a,type,
fun_nat_a: $tType ).
tff(bool,type,
bool: $tType ).
tff(fun_fun_a_bool_pname,type,
fun_fun_a_bool_pname: $tType ).
tff(fun_fu411113733ol_nat,type,
fun_fu411113733ol_nat: $tType ).
tff(fun_fu61768826l_bool,type,
fun_fu61768826l_bool: $tType ).
tff(fun_fu2087345469l_bool,type,
fun_fu2087345469l_bool: $tType ).
tff(fun_fu255076663l_bool,type,
fun_fu255076663l_bool: $tType ).
tff(fun_na936072029e_bool,type,
fun_na936072029e_bool: $tType ).
tff(fun_fu616551101l_bool,type,
fun_fu616551101l_bool: $tType ).
tff(fun_pname_pname,type,
fun_pname_pname: $tType ).
tff(fun_fu1086940979l_bool,type,
fun_fu1086940979l_bool: $tType ).
tff(fun_fu386216885l_bool,type,
fun_fu386216885l_bool: $tType ).
tff(fun_nat_nat,type,
fun_nat_nat: $tType ).
tff(fun_nat_pname,type,
fun_nat_pname: $tType ).
tff(fun_pname_a,type,
fun_pname_a: $tType ).
tff(fun_pname_bool,type,
fun_pname_bool: $tType ).
tff(fun_pname_fun_a_bool,type,
fun_pname_fun_a_bool: $tType ).
tff(fun_na1436237685l_bool,type,
fun_na1436237685l_bool: $tType ).
tff(fun_fu2065874474l_bool,type,
fun_fu2065874474l_bool: $tType ).
tff(fun_fu1438281908l_bool,type,
fun_fu1438281908l_bool: $tType ).
tff(fun_fu931343505l_bool,type,
fun_fu931343505l_bool: $tType ).
tff(fun_pn800050071e_bool,type,
fun_pn800050071e_bool: $tType ).
tff(fun_pn422929397l_bool,type,
fun_pn422929397l_bool: $tType ).
tff(fun_fu1701008009ol_nat,type,
fun_fu1701008009ol_nat: $tType ).
tff(fun_fun_nat_bool_nat,type,
fun_fun_nat_bool_nat: $tType ).
tff(fun_fu1373417771bool_a,type,
fun_fu1373417771bool_a: $tType ).
tff(fun_fu1016514960l_bool,type,
fun_fu1016514960l_bool: $tType ).
tff(fun_fu814369080l_bool,type,
fun_fu814369080l_bool: $tType ).
tff(fun_pn1165013435l_bool,type,
fun_pn1165013435l_bool: $tType ).
tff(fun_fu1911931399l_bool,type,
fun_fu1911931399l_bool: $tType ).
tff(fun_pn1038293468l_bool,type,
fun_pn1038293468l_bool: $tType ).
tff(fun_fu665170229_pname,type,
fun_fu665170229_pname: $tType ).
tff(fun_fu2061654492bool_a,type,
fun_fu2061654492bool_a: $tType ).
tff(fun_a_nat,type,
fun_a_nat: $tType ).
tff(fun_fu1297083715ol_nat,type,
fun_fu1297083715ol_nat: $tType ).
tff(fun_fu1971389424l_bool,type,
fun_fu1971389424l_bool: $tType ).
%Background operators:
%Foreground operators:
tff(hAPP_a_fun_a_bool,type,
hAPP_a_fun_a_bool: ( fun_a_fun_a_bool * x_a ) > fun_a_bool ).
tff(image_349102846bool_a,type,
image_349102846bool_a: ( fun_fu2061654492bool_a * fun_fu399576434l_bool ) > fun_a_bool ).
tff(hAPP_f1759205631l_bool,type,
hAPP_f1759205631l_bool: ( fun_fu1086940979l_bool * fun_fu399576434l_bool ) > fun_fu1438281908l_bool ).
tff(ord_le1311769555a_bool,type,
ord_le1311769555a_bool: fun_fu1471507361l_bool ).
tff(finite1340463720e_bool,type,
finite1340463720e_bool: fun_fu1730389579ol_nat ).
tff(ord_le967226251l_bool,type,
ord_le967226251l_bool: fun_fu821736593l_bool ).
tff(finite_finite_pname,type,
finite_finite_pname: fun_fu1430349052l_bool ).
tff('#skF_12',type,
'#skF_12': ( fun_pname_bool * fun_pname_bool ) > pname ).
tff(fequal533582459e_bool,type,
fequal533582459e_bool: fun_fu802393907l_bool ).
tff(hAPP_f2117159681l_bool,type,
hAPP_f2117159681l_bool: ( fun_fu911136611l_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).
tff('#skF_16',type,
'#skF_16': ( fun_nat_bool * nat ) > nat ).
tff(cOMBC_1732670874l_bool,type,
cOMBC_1732670874l_bool: fun_fu1471507361l_bool > fun_fu1471507361l_bool ).
tff('#skF_15',type,
'#skF_15': ( fun_pname_a * fun_a_bool * fun_pname_bool ) > pname ).
tff('#skF_13',type,
'#skF_13': ( nat * fun_nat_bool * nat ) > nat ).
tff(image_1154884483l_bool,type,
image_1154884483l_bool: ( fun_pn1165013435l_bool * fun_pname_bool ) > fun_fu814369080l_bool ).
tff(hAPP_f1935102916l_bool,type,
hAPP_f1935102916l_bool: ( fun_fu399576434l_bool * fun_fu1430349052l_bool ) > bool ).
tff(fequal_nat,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(cOMBB_2095475776e_bool,type,
cOMBB_2095475776e_bool: ( fun_bo1549164019l_bool * fun_fu1430349052l_bool ) > fun_fu31783638l_bool ).
tff(hAPP_f98387925ol_nat,type,
hAPP_f98387925ol_nat: ( fun_fu1701008009ol_nat * fun_fu399576434l_bool ) > nat ).
tff(hAPP_f292226953l_bool,type,
hAPP_f292226953l_bool: ( fun_fu255076663l_bool * fun_fu885608257l_bool ) > bool ).
tff(p,type,
p: fun_a_bool > fun_fun_a_bool_bool ).
tff(finite346522414t_bool,type,
finite346522414t_bool: fun_fu411113733ol_nat ).
tff(finite_card_pname,type,
finite_card_pname: fun_fu1668467777ol_nat ).
tff(na,type,
na: nat ).
tff(insert_fun_a_bool,type,
insert_fun_a_bool: ( fun_a_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).
tff(hAPP_f556039215l_bool,type,
hAPP_f556039215l_bool: ( fun_fu931343505l_bool * fun_pname_bool ) > fun_fu399576434l_bool ).
tff(cOMBC_331553030l_bool,type,
cOMBC_331553030l_bool: fun_fu418465139l_bool > fun_fu418465139l_bool ).
tff(hAPP_f1772781669l_bool,type,
hAPP_f1772781669l_bool: ( fun_fu140186515l_bool * fun_fu425979586l_bool ) > fun_fu814369080l_bool ).
tff('#skF_10',type,
'#skF_10': ( fun_nat_bool * fun_nat_bool ) > nat ).
tff(finite2012431853t_bool,type,
finite2012431853t_bool: fun_fu814369080l_bool ).
tff(hAPP_f55526627ol_nat,type,
hAPP_f55526627ol_nat: ( fun_fu1730389579ol_nat * fun_fu1430349052l_bool ) > nat ).
tff(finite1352710292l_bool,type,
finite1352710292l_bool: fun_fu1297083715ol_nat ).
tff(ord_le1375671464l_bool,type,
ord_le1375671464l_bool: fun_fu1086940979l_bool ).
tff(image_1802975832ol_nat,type,
image_1802975832ol_nat: ( fun_fu2020802748ol_nat * fun_fu885608257l_bool ) > fun_nat_bool ).
tff(hAPP_pname_a,type,
hAPP_pname_a: ( fun_pname_a * pname ) > x_a ).
tff(image_a_a,type,
image_a_a: ( fun_a_a * fun_a_bool ) > fun_a_bool ).
tff(cOMBB_bool_bool_a,type,
cOMBB_bool_bool_a: ( fun_bool_bool * fun_a_bool ) > fun_a_bool ).
tff(insert1457093509l_bool,type,
insert1457093509l_bool: ( fun_fun_a_bool_bool * fun_fu885608257l_bool ) > fun_fu885608257l_bool ).
tff(finite347923420a_bool,type,
finite347923420a_bool: fun_fu885608257l_bool ).
tff(member_nat,type,
member_nat: fun_na1436237685l_bool ).
tff(finite_card_nat,type,
finite_card_nat: fun_fun_nat_bool_nat ).
tff(insert1117693814l_bool,type,
insert1117693814l_bool: ( fun_fu1430349052l_bool * fun_fu399576434l_bool ) > fun_fu399576434l_bool ).
tff(cOMBB_307249310e_bool,type,
cOMBB_307249310e_bool: ( fun_bool_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).
tff(image_pname_nat,type,
image_pname_nat: ( fun_pname_nat * fun_pname_bool ) > fun_nat_bool ).
tff(cOMBC_1284144636l_bool,type,
cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).
tff(cOMBC_1880041174l_bool,type,
cOMBC_1880041174l_bool: fun_fu386216885l_bool > fun_fu911136611l_bool ).
tff(cOMBB_bool_bool_nat,type,
cOMBB_bool_bool_nat: ( fun_bool_bool * fun_nat_bool ) > fun_nat_bool ).
tff(cOMBC_a_a_bool,type,
cOMBC_a_a_bool: fun_a_fun_a_bool > fun_a_fun_a_bool ).
tff(insert_nat,type,
insert_nat: ( nat * fun_nat_bool ) > fun_nat_bool ).
tff(hAPP_f198738859l_bool,type,
hAPP_f198738859l_bool: ( fun_fu554186387l_bool * fun_a_bool ) > fun_bool_bool ).
tff(cOMBB_1897541054_pname,type,
cOMBB_1897541054_pname: ( fun_a_fun_a_bool * fun_pname_a ) > fun_pname_fun_a_bool ).
tff(cOMBC_1988546018l_bool,type,
cOMBC_1988546018l_bool: fun_fu931343505l_bool > fun_fu2087345469l_bool ).
tff(fNot,type,
fNot: fun_bool_bool ).
tff(hAPP_f800510211t_bool,type,
hAPP_f800510211t_bool: ( fun_fu821463397t_bool * fun_nat_bool ) > fun_nat_bool ).
tff(image_fun_a_bool_a,type,
image_fun_a_bool_a: ( fun_fun_a_bool_a * fun_fun_a_bool_bool ) > fun_a_bool ).
tff(image_1642285373l_bool,type,
image_1642285373l_bool: ( fun_pn422929397l_bool * fun_pname_bool ) > fun_fu399576434l_bool ).
tff(collect_fun_a_bool,type,
collect_fun_a_bool: fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
tff(hAPP_n1006566506l_bool,type,
hAPP_n1006566506l_bool: ( fun_na1469252690l_bool * nat ) > fun_bool_bool ).
tff(hAPP_bool_bool,type,
hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).
tff(collec1015864663l_bool,type,
collec1015864663l_bool: fun_fu814369080l_bool > fun_fu814369080l_bool ).
tff(image_pname_pname,type,
image_pname_pname: ( fun_pname_pname * fun_pname_bool ) > fun_pname_bool ).
tff('#skF_14',type,
'#skF_14': ( nat * nat ) > nat ).
tff(fequal_pname,type,
fequal_pname: fun_pn800050071e_bool ).
tff(hAPP_p61793385e_bool,type,
hAPP_p61793385e_bool: ( fun_pn800050071e_bool * pname ) > fun_pname_bool ).
tff(finite1701474069l_bool,type,
finite1701474069l_bool: fun_fu61768826l_bool ).
tff(mgt_call,type,
mgt_call: fun_pname_a ).
tff(cOMBC_1693257480l_bool,type,
cOMBC_1693257480l_bool: fun_fu1217155507l_bool > fun_fu1217155507l_bool ).
tff(ord_le1454342156l_bool,type,
ord_le1454342156l_bool: fun_fu140186515l_bool ).
tff(cOMBC_1269652216l_bool,type,
cOMBC_1269652216l_bool: fun_fu1137991347l_bool > fun_fu1137991347l_bool ).
tff(image_nat_pname,type,
image_nat_pname: ( fun_nat_pname * fun_nat_bool ) > fun_pname_bool ).
tff(ord_le1568362934t_bool,type,
ord_le1568362934t_bool: fun_fu1217155507l_bool ).
tff('#skF_3',type,
'#skF_3': ( nat * nat * fun_na936072029e_bool ) > nat ).
tff(collec707592106l_bool,type,
collec707592106l_bool: fun_fu885608257l_bool > fun_fu885608257l_bool ).
tff(hAPP_f1951378235l_bool,type,
hAPP_f1951378235l_bool: ( fun_fu1436348701l_bool * fun_nat_bool ) > fun_fu814369080l_bool ).
tff(hAPP_f1637334154l_bool,type,
hAPP_f1637334154l_bool: ( fun_fu814369080l_bool * fun_fu425979586l_bool ) > bool ).
tff(fequal_a,type,
fequal_a: fun_a_fun_a_bool ).
tff(image_1854862208_pname,type,
image_1854862208_pname: ( fun_fun_a_bool_pname * fun_fun_a_bool_bool ) > fun_pname_bool ).
tff(finite1381704300l_bool,type,
finite1381704300l_bool: fun_fu255076663l_bool ).
tff(hAPP_f921600141ol_nat,type,
hAPP_f921600141ol_nat: ( fun_fu1668467777ol_nat * fun_pname_bool ) > nat ).
tff(image_nat_a,type,
image_nat_a: ( fun_nat_a * fun_nat_bool ) > fun_a_bool ).
tff(cOMBB_238756964t_bool,type,
cOMBB_238756964t_bool: ( fun_bool_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).
tff(image_2089570637ol_nat,type,
image_2089570637ol_nat: ( fun_fu411113733ol_nat * fun_fu814369080l_bool ) > fun_nat_bool ).
tff(cOMBC_595898202l_bool,type,
cOMBC_595898202l_bool: fun_fu140186515l_bool > fun_fu140186515l_bool ).
tff(hAPP_f1050622307l_bool,type,
hAPP_f1050622307l_bool: ( fun_fu821736593l_bool * fun_fu885608257l_bool ) > fun_fu255076663l_bool ).
tff(hAPP_p1534023578a_bool,type,
hAPP_p1534023578a_bool: ( fun_pname_fun_a_bool * pname ) > fun_a_bool ).
tff(hAPP_f510955609l_bool,type,
hAPP_f510955609l_bool: ( fun_fu1911931399l_bool * fun_fu1430349052l_bool ) > fun_fu399576434l_bool ).
tff(hAPP_n1699378549t_bool,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(minus_minus_nat,type,
minus_minus_nat: nat > fun_nat_nat ).
tff(cOMBC_636888218l_bool,type,
cOMBC_636888218l_bool: fun_fu821736593l_bool > fun_fu821736593l_bool ).
tff(hAPP_a_bool,type,
hAPP_a_bool: ( fun_a_bool * x_a ) > bool ).
tff(fimplies,type,
fimplies: fun_bo1549164019l_bool ).
tff(ord_le313189616e_bool,type,
ord_le313189616e_bool: fun_fu802393907l_bool ).
tff(hAPP_f1434722111l_bool,type,
hAPP_f1434722111l_bool: ( fun_fu418465139l_bool * fun_fun_a_bool_bool ) > fun_fu885608257l_bool ).
tff(hAPP_f559147733l_bool,type,
hAPP_f559147733l_bool: ( fun_fu2087345469l_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).
tff(member_fun_a_bool,type,
member_fun_a_bool: fun_fu386216885l_bool ).
tff(image_pname_a,type,
image_pname_a: ( fun_pname_a * fun_pname_bool ) > fun_a_bool ).
tff(finite_finite_a,type,
finite_finite_a: fun_fun_a_bool_bool ).
tff(cOMBS_1035972772l_bool,type,
cOMBS_1035972772l_bool: ( fun_fu554186387l_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).
tff(cOMBS_350070575l_bool,type,
cOMBS_350070575l_bool: ( fun_fu31783638l_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).
tff(hAPP_f54304608l_bool,type,
hAPP_f54304608l_bool: ( fun_fu425979586l_bool * fun_nat_bool ) > bool ).
tff(image_fun_a_bool_nat,type,
image_fun_a_bool_nat: ( fun_fun_a_bool_nat * fun_fun_a_bool_bool ) > fun_nat_bool ).
tff(image_nat_fun_a_bool,type,
image_nat_fun_a_bool: ( fun_nat_fun_a_bool * fun_nat_bool ) > fun_fun_a_bool_bool ).
tff(insert2003652156l_bool,type,
insert2003652156l_bool: ( fun_fu425979586l_bool * fun_fu814369080l_bool ) > fun_fu814369080l_bool ).
tff(cOMBB_1972296269bool_a,type,
cOMBB_1972296269bool_a: ( fun_bo1549164019l_bool * fun_a_bool ) > fun_a_fun_bool_bool ).
tff(fdisj,type,
fdisj: fun_bo1549164019l_bool ).
tff('#skF_2',type,
'#skF_2': ( nat * nat * fun_nat_fun_nat_bool ) > nat ).
tff(cOMBC_nat_nat_bool,type,
cOMBC_nat_nat_bool: fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).
tff(hAPP_f2009550088ol_nat,type,
hAPP_f2009550088ol_nat: ( fun_fu2020802748ol_nat * fun_fun_a_bool_bool ) > nat ).
tff(hAPP_f2050579477a_bool,type,
hAPP_f2050579477a_bool: ( fun_fu1731003005a_bool * fun_a_bool ) > fun_a_bool ).
tff('#skF_11',type,
'#skF_11': ( fun_a_bool * fun_a_bool ) > x_a ).
tff(cOMBC_226598744l_bool,type,
cOMBC_226598744l_bool: fun_na1436237685l_bool > fun_fu821463397t_bool ).
tff('#skF_6',type,
'#skF_6': ( fun_pname_a * fun_pname_bool ) > pname ).
tff(hAPP_n215258509l_bool,type,
hAPP_n215258509l_bool: ( fun_na1436237685l_bool * nat ) > fun_fu425979586l_bool ).
tff(image_1604018183_pname,type,
image_1604018183_pname: ( fun_fu881587263_pname * fun_fu814369080l_bool ) > fun_pname_bool ).
tff(insert1325755072e_bool,type,
insert1325755072e_bool: ( fun_pname_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).
tff(hAPP_a93125764e_bool,type,
hAPP_a93125764e_bool: ( fun_a_fun_pname_bool * x_a ) > fun_pname_bool ).
tff(fconj,type,
fconj: fun_bo1549164019l_bool ).
tff(member799430823e_bool,type,
member799430823e_bool: fun_fu931343505l_bool ).
tff('#skF_4',type,
'#skF_4': ( nat * nat * fun_nat_nat ) > nat ).
tff(cOMBB_338059395a_bool,type,
cOMBB_338059395a_bool: ( fun_bo1549164019l_bool * fun_fun_a_bool_bool ) > fun_fu554186387l_bool ).
tff(cOMBS_a_bool_bool,type,
cOMBS_a_bool_bool: ( fun_a_fun_bool_bool * fun_a_bool ) > fun_a_bool ).
tff(hAPP_nat_fun_a_bool,type,
hAPP_nat_fun_a_bool: ( fun_nat_fun_a_bool * nat ) > fun_a_bool ).
tff(hAPP_a_fun_bool_bool,type,
hAPP_a_fun_bool_bool: ( fun_a_fun_bool_bool * x_a ) > fun_bool_bool ).
tff(hAPP_n1025906991e_bool,type,
hAPP_n1025906991e_bool: ( fun_na936072029e_bool * nat ) > fun_pname_bool ).
tff(image_2129980159t_bool,type,
image_2129980159t_bool: ( fun_pn406123357t_bool * fun_pname_bool ) > fun_fu425979586l_bool ).
tff(finite595471783e_bool,type,
finite595471783e_bool: fun_fu399576434l_bool ).
tff(ord_le65145710l_bool,type,
ord_le65145710l_bool: fun_fu1137991347l_bool ).
tff('#skF_8',type,
'#skF_8': ( fun_a_bool * fun_pname_a * fun_pname_bool ) > fun_pname_bool ).
tff(finite719726885l_bool,type,
finite719726885l_bool: fun_fu1971389424l_bool ).
tff(hAPP_f1295398978l_bool,type,
hAPP_f1295398978l_bool: ( fun_fu1971389424l_bool * fun_fu61768826l_bool ) > bool ).
tff(image_47868345e_bool,type,
image_47868345e_bool: ( fun_pn800050071e_bool * fun_pname_bool ) > fun_fu1430349052l_bool ).
tff(hAPP_f759274231e_bool,type,
hAPP_f759274231e_bool: ( fun_fu410713561e_bool * fun_pname_bool ) > fun_pname_bool ).
tff(hAPP_f1246832597l_bool,type,
hAPP_f1246832597l_bool: ( fun_fu616551101l_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).
tff(insert_fun_nat_bool,type,
insert_fun_nat_bool: ( fun_nat_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).
tff(hAPP_nat_bool,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(hAPP_f1690079119ol_nat,type,
hAPP_f1690079119ol_nat: ( fun_fu1297083715ol_nat * fun_fu814369080l_bool ) > nat ).
tff(cOMBB_647938656_pname,type,
cOMBB_647938656_pname: ( fun_bool_bool * fun_pname_bool ) > fun_pname_bool ).
tff(finite1659325229l_bool,type,
finite1659325229l_bool: fun_fu48515398ol_nat ).
tff(image_a_pname,type,
image_a_pname: ( fun_a_pname * fun_a_bool ) > fun_pname_bool ).
tff(image_1079571347ol_nat,type,
image_1079571347ol_nat: ( fun_fu1730389579ol_nat * fun_fu399576434l_bool ) > fun_nat_bool ).
tff('#skF_5',type,
'#skF_5': ( nat * nat * fun_nat_fun_a_bool ) > nat ).
tff(collect_fun_nat_bool,type,
collect_fun_nat_bool: fun_fu425979586l_bool > fun_fu425979586l_bool ).
tff(hAPP_a85458249l_bool,type,
hAPP_a85458249l_bool: ( fun_a_1255737515l_bool * x_a ) > fun_fun_a_bool_bool ).
tff(hAPP_fun_a_bool_bool,type,
hAPP_fun_a_bool_bool: ( fun_fun_a_bool_bool * fun_a_bool ) > bool ).
tff(collec1635217238l_bool,type,
collec1635217238l_bool: fun_fu255076663l_bool > fun_fu255076663l_bool ).
tff(hAPP_pname_bool,type,
hAPP_pname_bool: ( fun_pname_bool * pname ) > bool ).
tff(finite786885583l_bool,type,
finite786885583l_bool: fun_fu1438281908l_bool ).
tff(finite1343359508l_bool,type,
finite1343359508l_bool: fun_fu754241017l_bool ).
tff(collec792590109l_bool,type,
collec792590109l_bool: fun_fu1438281908l_bool > fun_fu1438281908l_bool ).
tff(cOMBS_1187019125l_bool,type,
cOMBS_1187019125l_bool: ( fun_fu1016514960l_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).
tff(image_990671762_pname,type,
image_990671762_pname: ( fun_fu1175941238_pname * fun_fu885608257l_bool ) > fun_pname_bool ).
tff(image_fun_nat_bool_a,type,
image_fun_nat_bool_a: ( fun_fun_nat_bool_a * fun_fu425979586l_bool ) > fun_a_bool ).
tff(hAPP_f760187903l_bool,type,
hAPP_f760187903l_bool: ( fun_fu1137991347l_bool * fun_fu814369080l_bool ) > fun_fu61768826l_bool ).
tff(cOMBC_1058051404l_bool,type,
cOMBC_1058051404l_bool: fun_pn422929397l_bool > fun_fu410713561e_bool ).
tff(finite1491191519l_bool,type,
finite1491191519l_bool: fun_fu2065874474l_bool ).
tff(finite269641166l_bool,type,
finite269641166l_bool: fun_fu1701008009ol_nat ).
tff(insert_a,type,
insert_a: ( x_a * fun_a_bool ) > fun_a_bool ).
tff(hAPP_f389811538l_bool,type,
hAPP_f389811538l_bool: ( fun_fu1438281908l_bool * fun_fu399576434l_bool ) > bool ).
tff(image_1874789623l_bool,type,
image_1874789623l_bool: ( fun_na2122364079l_bool * fun_nat_bool ) > fun_fu399576434l_bool ).
tff(image_496248727ol_nat,type,
image_496248727ol_nat: ( fun_fun_nat_bool_nat * fun_fu425979586l_bool ) > fun_nat_bool ).
tff(cOMBS_nat_bool_bool,type,
cOMBS_nat_bool_bool: ( fun_na1469252690l_bool * fun_nat_bool ) > fun_nat_bool ).
tff(hAPP_f1631501043l_bool,type,
hAPP_f1631501043l_bool: ( fun_fu1471507361l_bool * fun_a_bool ) > fun_fun_a_bool_bool ).
tff(hAPP_f621171935l_bool,type,
hAPP_f621171935l_bool: ( fun_fu885608257l_bool * fun_fun_a_bool_bool ) > bool ).
tff(hAPP_f285962445l_bool,type,
hAPP_f285962445l_bool: ( fun_fu386216885l_bool * fun_a_bool ) > fun_fu885608257l_bool ).
tff(cOMBC_1245412066l_bool,type,
cOMBC_1245412066l_bool: fun_fu1436348701l_bool > fun_fu616551101l_bool ).
tff(collec1613912337l_bool,type,
collec1613912337l_bool: fun_fu399576434l_bool > fun_fu399576434l_bool ).
tff('#skF_1',type,
'#skF_1': ( fun_pname_a * fun_pname_bool * fun_a_bool ) > fun_pname_bool ).
tff(g,type,
g: fun_a_bool ).
tff(member_a,type,
member_a: fun_a_1255737515l_bool ).
tff(hAPP_nat_nat,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(image_1420695166l_bool,type,
image_1420695166l_bool: ( fun_pn1038293468l_bool * fun_pname_bool ) > fun_fu885608257l_bool ).
tff(hAPP_f1748468828l_bool,type,
hAPP_f1748468828l_bool: ( fun_fu1016514960l_bool * fun_nat_bool ) > fun_bool_bool ).
tff(finite_finite_nat,type,
finite_finite_nat: fun_fu425979586l_bool ).
tff(cOMBB_675860798_pname,type,
cOMBB_675860798_pname: ( fun_bo1549164019l_bool * fun_pname_bool ) > fun_pn250273176l_bool ).
tff(hAPP_f22106695ol_nat,type,
hAPP_f22106695ol_nat: ( fun_fun_nat_bool_nat * fun_nat_bool ) > nat ).
tff(finite_card_a,type,
finite_card_a: fun_fun_a_bool_nat ).
tff(hAPP_f1476298914l_bool,type,
hAPP_f1476298914l_bool: ( fun_fu31783638l_bool * fun_pname_bool ) > fun_bool_bool ).
tff(image_1208015684l_bool,type,
image_1208015684l_bool: ( fun_na1632405922l_bool * fun_nat_bool ) > fun_fu885608257l_bool ).
tff(hAPP_p338031245l_bool,type,
hAPP_p338031245l_bool: ( fun_pn422929397l_bool * pname ) > fun_fu1430349052l_bool ).
tff(image_876012084bool_a,type,
image_876012084bool_a: ( fun_fun_pname_bool_a * fun_fu1430349052l_bool ) > fun_a_bool ).
tff(hAPP_f1253658590ol_nat,type,
hAPP_f1253658590ol_nat: ( fun_fu48515398ol_nat * fun_fu885608257l_bool ) > nat ).
tff(collec1874991203l_bool,type,
collec1874991203l_bool: fun_fu61768826l_bool > fun_fu61768826l_bool ).
tff(collec1974731493e_bool,type,
collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
tff(hAPP_f937997336l_bool,type,
hAPP_f937997336l_bool: ( fun_fu61768826l_bool * fun_fu814369080l_bool ) > bool ).
tff(cOMBC_7971162l_bool,type,
cOMBC_7971162l_bool: fun_fu1911931399l_bool > fun_fu1911931399l_bool ).
tff('#skF_17',type,
'#skF_17': fun_nat_bool > nat ).
tff(image_573985017bool_a,type,
image_573985017bool_a: ( fun_fu1373417771bool_a * fun_fu885608257l_bool ) > fun_a_bool ).
tff(ord_le675606854l_bool,type,
ord_le675606854l_bool: fun_fu1911931399l_bool ).
tff(cOMBC_1149511130e_bool,type,
cOMBC_1149511130e_bool: fun_pn800050071e_bool > fun_pn800050071e_bool ).
tff(collect_pname,type,
collect_pname: fun_pname_bool > fun_pname_bool ).
tff(hBOOL,type,
hBOOL: bool > $o ).
tff(image_1283814551_pname,type,
image_1283814551_pname: ( fun_fu1499449723_pname * fun_fu1430349052l_bool ) > fun_pname_bool ).
tff(collect_a,type,
collect_a: fun_a_bool > fun_a_bool ).
tff(image_a_nat,type,
image_a_nat: ( fun_a_nat * fun_a_bool ) > fun_nat_bool ).
tff(member_fun_nat_bool,type,
member_fun_nat_bool: fun_fu1436348701l_bool ).
tff(hAPP_b589554111l_bool,type,
hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).
tff(cOMBC_pname_a_bool,type,
cOMBC_pname_a_bool: fun_pname_fun_a_bool > fun_a_fun_pname_bool ).
tff(fequal_fun_a_bool,type,
fequal_fun_a_bool: fun_fu1471507361l_bool ).
tff(image_112932426a_bool,type,
image_112932426a_bool: ( fun_pname_fun_a_bool * fun_pname_bool ) > fun_fun_a_bool_bool ).
tff(hAPP_f1664156314l_bool,type,
hAPP_f1664156314l_bool: ( fun_fu1430349052l_bool * fun_pname_bool ) > bool ).
tff(image_1655916159e_bool,type,
image_1655916159e_bool: ( fun_na936072029e_bool * fun_nat_bool ) > fun_fu1430349052l_bool ).
tff(hAPP_f434788991l_bool,type,
hAPP_f434788991l_bool: ( fun_fu802393907l_bool * fun_pname_bool ) > fun_fu1430349052l_bool ).
tff(hAPP_fun_a_bool_nat,type,
hAPP_fun_a_bool_nat: ( fun_fun_a_bool_nat * fun_a_bool ) > nat ).
tff(suc,type,
suc: fun_nat_nat ).
tff(fequal_fun_nat_bool,type,
fequal_fun_nat_bool: fun_fu1217155507l_bool ).
tff(image_1921560913_pname,type,
image_1921560913_pname: ( fun_fu665170229_pname * fun_fu425979586l_bool ) > fun_pname_bool ).
tff('#skF_9',type,
'#skF_9': ( x_a * fun_pname_a * fun_pname_bool ) > pname ).
tff(u,type,
u: fun_pname_bool ).
tff(cOMBB_2140588453a_bool,type,
cOMBB_2140588453a_bool: ( fun_bool_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).
tff(cOMBS_568398431l_bool,type,
cOMBS_568398431l_bool: ( fun_pn250273176l_bool * fun_pname_bool ) > fun_pname_bool ).
tff(cOMBC_1355376034l_bool,type,
cOMBC_1355376034l_bool: fun_a_1255737515l_bool > fun_fu1731003005a_bool ).
tff(insert_pname,type,
insert_pname: ( pname * fun_pname_bool ) > fun_pname_bool ).
tff(hAPP_f595608956l_bool,type,
hAPP_f595608956l_bool: ( fun_fu2065874474l_bool * fun_fu1438281908l_bool ) > bool ).
tff(cOMBB_1015721476ol_nat,type,
cOMBB_1015721476ol_nat: ( fun_bo1549164019l_bool * fun_nat_bool ) > fun_na1469252690l_bool ).
tff(member_pname,type,
member_pname: fun_pn422929397l_bool ).
tff(image_1705983821_pname,type,
image_1705983821_pname: ( fun_fu1664106117_pname * fun_fu399576434l_bool ) > fun_pname_bool ).
tff(pn,type,
pn: pname ).
tff(hAPP_f696928925ol_nat,type,
hAPP_f696928925ol_nat: ( fun_fu411113733ol_nat * fun_fu425979586l_bool ) > nat ).
tff(finite1306199131a_bool,type,
finite1306199131a_bool: fun_fu2020802748ol_nat ).
tff(image_1607900221l_bool,type,
image_1607900221l_bool: ( fun_na1436237685l_bool * fun_nat_bool ) > fun_fu814369080l_bool ).
tff(image_26036933t_bool,type,
image_26036933t_bool: ( fun_nat_fun_nat_bool * fun_nat_bool ) > fun_fu425979586l_bool ).
tff(image_526090948bool_a,type,
image_526090948bool_a: ( fun_fu897950882bool_a * fun_fu814369080l_bool ) > fun_a_bool ).
tff(ord_less_eq_nat,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(collect_nat,type,
collect_nat: fun_nat_bool > fun_nat_bool ).
tff(image_1551609309ol_nat,type,
image_1551609309ol_nat: ( fun_fu1668467777ol_nat * fun_fu1430349052l_bool ) > fun_nat_bool ).
tff('#skF_7',type,
'#skF_7': ( x_a * fun_pname_a * fun_pname_bool ) > pname ).
tff(ord_le1375614389l_bool,type,
ord_le1375614389l_bool: fun_fu418465139l_bool ).
tff(cOMBC_336095980l_bool,type,
cOMBC_336095980l_bool: fun_fu1086940979l_bool > fun_fu1086940979l_bool ).
tff(hAPP_p393069232l_bool,type,
hAPP_p393069232l_bool: ( fun_pn250273176l_bool * pname ) > fun_bool_bool ).
tff(hAPP_f1363661463l_bool,type,
hAPP_f1363661463l_bool: ( fun_fu754241017l_bool * fun_fu255076663l_bool ) > bool ).
tff(hAPP_f103356543l_bool,type,
hAPP_f103356543l_bool: ( fun_fu1217155507l_bool * fun_nat_bool ) > fun_fu425979586l_bool ).
tff(cOMBB_444170502t_bool,type,
cOMBB_444170502t_bool: ( fun_bo1549164019l_bool * fun_fu425979586l_bool ) > fun_fu1016514960l_bool ).
tff(f_1679,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f_1122,axiom,
! [A_1: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> ( insert_pname(A_1,A) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_insert__absorb) ).
tff(f_1392,axiom,
! [F: fun_pname_a,A_1: pname,B: fun_pname_bool] : ( image_pname_a(F,insert_pname(A_1,B)) = insert_a(hAPP_pname_a(F,A_1),image_pname_a(F,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_image__insert) ).
tff(f_1072,axiom,
! [Y_1: x_a,A: fun_a_bool,X_2: x_a] :
( hBOOL(hAPP_a_bool(insert_a(Y_1,A),X_2))
<=> ( ( Y_1 = X_2 )
| hBOOL(hAPP_a_bool(A,X_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_insert__code) ).
tff(f_1278,axiom,
! [X_2: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
<=> hBOOL(hAPP_a_bool(A,X_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_mem__def) ).
tff(f_1126,axiom,
! [A_1: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))
=> ( insert_a(A_1,A) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_insert__absorb) ).
tff(f_1054,axiom,
! [A_1: x_a,B_1: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A)))
<=> ( ( A_1 = B_1 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_insert__iff) ).
tff(f_1676,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f_1345,axiom,
! [X_2: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_2,A)),B))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_insert__subset) ).
tff(f_1683,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
tff(c_919,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnfTransformation,[status(thm)],[f_1679]) ).
tff(c_1352,plain,
! [A_1_957: pname,A_958: fun_pname_bool] :
( ( insert_pname(A_1_957,A_958) = A_958 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1_957),A_958)) ),
inference(cnfTransformation,[status(thm)],[f_1122]) ).
tff(c_1365,plain,
insert_pname(pn,u) = u,
inference(resolution,[status(thm)],[c_919,c_1352]) ).
tff(c_3882,plain,
! [F_1323: fun_pname_a,A_1_1324: pname,B_1325: fun_pname_bool] : ( insert_a(hAPP_pname_a(F_1323,A_1_1324),image_pname_a(F_1323,B_1325)) = image_pname_a(F_1323,insert_pname(A_1_1324,B_1325)) ),
inference(cnfTransformation,[status(thm)],[f_1392]) ).
tff(c_544,plain,
! [Y_1_455: x_a,A_456: fun_a_bool] : hBOOL(hAPP_a_bool(insert_a(Y_1_455,A_456),Y_1_455)),
inference(cnfTransformation,[status(thm)],[f_1072]) ).
tff(c_3940,plain,
! [F_1326: fun_pname_a,A_1_1327: pname,B_1328: fun_pname_bool] : hBOOL(hAPP_a_bool(image_pname_a(F_1326,insert_pname(A_1_1327,B_1328)),hAPP_pname_a(F_1326,A_1_1327))),
inference(superposition,[status(thm),theory(equality)],[c_3882,c_544]) ).
tff(c_3964,plain,
! [F_1329: fun_pname_a] : hBOOL(hAPP_a_bool(image_pname_a(F_1329,u),hAPP_pname_a(F_1329,pn))),
inference(superposition,[status(thm),theory(equality)],[c_1365,c_3940]) ).
tff(c_651,plain,
! [X_2_547: x_a,A_548: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2_547),A_548))
| ~ hBOOL(hAPP_a_bool(A_548,X_2_547)) ),
inference(cnfTransformation,[status(thm)],[f_1278]) ).
tff(c_2382,plain,
! [A_1_1114: x_a,A_1115: fun_a_bool] :
( ( insert_a(A_1_1114,A_1115) = A_1115 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1_1114),A_1115)) ),
inference(cnfTransformation,[status(thm)],[f_1126]) ).
tff(c_2389,plain,
! [X_2_547: x_a,A_548: fun_a_bool] :
( ( insert_a(X_2_547,A_548) = A_548 )
| ~ hBOOL(hAPP_a_bool(A_548,X_2_547)) ),
inference(resolution,[status(thm)],[c_651,c_2382]) ).
tff(c_3994,plain,
! [F_1336: fun_pname_a] : ( insert_a(hAPP_pname_a(F_1336,pn),image_pname_a(F_1336,u)) = image_pname_a(F_1336,u) ),
inference(resolution,[status(thm)],[c_3964,c_2389]) ).
tff(c_526,plain,
! [B_1_447: x_a,A_448: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1_447),insert_a(B_1_447,A_448))),
inference(cnfTransformation,[status(thm)],[f_1054]) ).
tff(c_4045,plain,
! [F_1336: fun_pname_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F_1336,pn)),image_pname_a(F_1336,u))),
inference(superposition,[status(thm),theory(equality)],[c_3994,c_526]) ).
tff(c_913,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnfTransformation,[status(thm)],[f_1676]) ).
tff(c_33311,plain,
! [X_2_2351: x_a,A_2352: fun_a_bool,B_2353: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_2_2351,A_2352)),B_2353))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2352),B_2353))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2_2351),B_2353)) ),
inference(cnfTransformation,[status(thm)],[f_1345]) ).
tff(c_923,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(cnfTransformation,[status(thm)],[f_1683]) ).
tff(c_33354,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))) ),
inference(resolution,[status(thm)],[c_33311,c_923]) ).
tff(c_33433,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4045,c_913,c_33354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWW473_1 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.37 % Computer : n031.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 19:51:30 EDT 2023
% 0.16/0.37 % CPUTime :
% 27.73/11.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.73/11.26
% 27.73/11.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.73/11.29
% 27.73/11.29 Inference rules
% 27.73/11.29 ----------------------
% 27.73/11.29 #Ref : 3
% 27.73/11.29 #Sup : 8519
% 27.73/11.29 #Fact : 2
% 27.73/11.29 #Define : 0
% 27.73/11.29 #Split : 5
% 27.73/11.29 #Chain : 0
% 27.73/11.29 #Close : 0
% 27.73/11.29
% 27.73/11.29 Ordering : KBO
% 27.73/11.29
% 27.73/11.29 Simplification rules
% 27.73/11.29 ----------------------
% 27.73/11.29 #Subsume : 885
% 27.73/11.29 #Demod : 4208
% 27.73/11.29 #Tautology : 4005
% 27.73/11.29 #SimpNegUnit : 108
% 27.73/11.29 #BackRed : 63
% 27.73/11.29
% 27.73/11.29 #Partial instantiations: 0
% 27.73/11.29 #Strategies tried : 1
% 27.73/11.29
% 27.73/11.29 Timing (in seconds)
% 27.73/11.29 ----------------------
% 27.73/11.29 Preprocessing : 1.60
% 27.73/11.29 Parsing : 0.97
% 27.73/11.29 CNF conversion : 0.10
% 27.73/11.29 Main loop : 8.44
% 27.73/11.29 Inferencing : 1.97
% 27.73/11.29 Reduction : 4.25
% 27.73/11.30 Demodulation : 3.65
% 27.73/11.30 BG Simplification : 0.18
% 27.73/11.30 Subsumption : 1.62
% 27.73/11.30 Abstraction : 0.13
% 27.73/11.30 MUC search : 0.00
% 27.73/11.30 Cooper : 0.00
% 27.73/11.30 Total : 10.09
% 27.73/11.30 Index Insertion : 0.00
% 27.73/11.30 Index Deletion : 0.00
% 27.73/11.30 Index Matching : 0.00
% 27.73/11.30 BG Taut test : 0.00
%------------------------------------------------------------------------------