TSTP Solution File: SWW473_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW473_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n018.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 : Sat Sep 2 14:10:26 EDT 2023
% Result : Theorem 0.28s 0.65s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1042
% Syntax : Number of formulae : 2522 ( 630 unt; 322 typ; 0 def)
% Number of atoms : 4830 ( 705 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 4090 (1460 ~;1506 |; 185 &)
% ( 475 <=>; 464 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 91 ( 90 usr)
% Number of type conns : 322 ( 179 >; 143 *; 0 +; 0 <<)
% Number of predicates : 402 ( 400 usr; 400 prp; 0-2 aty)
% Number of functors : 231 ( 231 usr; 53 con; 0-3 aty)
% Number of variables : 3947 (;3901 !; 46 ?;3947 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
x_a: $tType ).
tff(type_def_6,type,
pname: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
fun_a_a: $tType ).
tff(type_def_10,type,
fun_a_pname: $tType ).
tff(type_def_11,type,
fun_a_bool: $tType ).
tff(type_def_12,type,
fun_a_nat: $tType ).
tff(type_def_13,type,
fun_a_fun_a_bool: $tType ).
tff(type_def_14,type,
fun_a_fun_pname_bool: $tType ).
tff(type_def_15,type,
fun_a_fun_bool_bool: $tType ).
tff(type_def_16,type,
fun_a_1255737515l_bool: $tType ).
tff(type_def_17,type,
fun_pname_a: $tType ).
tff(type_def_18,type,
fun_pname_pname: $tType ).
tff(type_def_19,type,
fun_pname_bool: $tType ).
tff(type_def_20,type,
fun_pname_nat: $tType ).
tff(type_def_21,type,
fun_pname_fun_a_bool: $tType ).
tff(type_def_22,type,
fun_pn800050071e_bool: $tType ).
tff(type_def_23,type,
fun_pn250273176l_bool: $tType ).
tff(type_def_24,type,
fun_pn406123357t_bool: $tType ).
tff(type_def_25,type,
fun_pn1038293468l_bool: $tType ).
tff(type_def_26,type,
fun_pn422929397l_bool: $tType ).
tff(type_def_27,type,
fun_pn1165013435l_bool: $tType ).
tff(type_def_28,type,
fun_bool_bool: $tType ).
tff(type_def_29,type,
fun_bo1549164019l_bool: $tType ).
tff(type_def_30,type,
fun_nat_a: $tType ).
tff(type_def_31,type,
fun_nat_pname: $tType ).
tff(type_def_32,type,
fun_nat_bool: $tType ).
tff(type_def_33,type,
fun_nat_nat: $tType ).
tff(type_def_34,type,
fun_nat_fun_a_bool: $tType ).
tff(type_def_35,type,
fun_na936072029e_bool: $tType ).
tff(type_def_36,type,
fun_na1469252690l_bool: $tType ).
tff(type_def_37,type,
fun_nat_fun_nat_bool: $tType ).
tff(type_def_38,type,
fun_na1632405922l_bool: $tType ).
tff(type_def_39,type,
fun_na2122364079l_bool: $tType ).
tff(type_def_40,type,
fun_na1436237685l_bool: $tType ).
tff(type_def_41,type,
fun_fun_a_bool_a: $tType ).
tff(type_def_42,type,
fun_fun_a_bool_pname: $tType ).
tff(type_def_43,type,
fun_fun_a_bool_bool: $tType ).
tff(type_def_44,type,
fun_fun_a_bool_nat: $tType ).
tff(type_def_45,type,
fun_fu1731003005a_bool: $tType ).
tff(type_def_46,type,
fun_fu554186387l_bool: $tType ).
tff(type_def_47,type,
fun_fu1471507361l_bool: $tType ).
tff(type_def_48,type,
fun_fu386216885l_bool: $tType ).
tff(type_def_49,type,
fun_fun_pname_bool_a: $tType ).
tff(type_def_50,type,
fun_fu1499449723_pname: $tType ).
tff(type_def_51,type,
fun_fu1430349052l_bool: $tType ).
tff(type_def_52,type,
fun_fu1668467777ol_nat: $tType ).
tff(type_def_53,type,
fun_fu410713561e_bool: $tType ).
tff(type_def_54,type,
fun_fu31783638l_bool: $tType ).
tff(type_def_55,type,
fun_fu802393907l_bool: $tType ).
tff(type_def_56,type,
fun_fu931343505l_bool: $tType ).
tff(type_def_57,type,
fun_fun_nat_bool_a: $tType ).
tff(type_def_58,type,
fun_fu665170229_pname: $tType ).
tff(type_def_59,type,
fun_fu425979586l_bool: $tType ).
tff(type_def_60,type,
fun_fun_nat_bool_nat: $tType ).
tff(type_def_61,type,
fun_fu1016514960l_bool: $tType ).
tff(type_def_62,type,
fun_fu821463397t_bool: $tType ).
tff(type_def_63,type,
fun_fu1217155507l_bool: $tType ).
tff(type_def_64,type,
fun_fu1436348701l_bool: $tType ).
tff(type_def_65,type,
fun_fu1373417771bool_a: $tType ).
tff(type_def_66,type,
fun_fu1175941238_pname: $tType ).
tff(type_def_67,type,
fun_fu885608257l_bool: $tType ).
tff(type_def_68,type,
fun_fu2020802748ol_nat: $tType ).
tff(type_def_69,type,
fun_fu911136611l_bool: $tType ).
tff(type_def_70,type,
fun_fu418465139l_bool: $tType ).
tff(type_def_71,type,
fun_fu2061654492bool_a: $tType ).
tff(type_def_72,type,
fun_fu1664106117_pname: $tType ).
tff(type_def_73,type,
fun_fu399576434l_bool: $tType ).
tff(type_def_74,type,
fun_fu1730389579ol_nat: $tType ).
tff(type_def_75,type,
fun_fu2087345469l_bool: $tType ).
tff(type_def_76,type,
fun_fu1911931399l_bool: $tType ).
tff(type_def_77,type,
fun_fu897950882bool_a: $tType ).
tff(type_def_78,type,
fun_fu881587263_pname: $tType ).
tff(type_def_79,type,
fun_fu814369080l_bool: $tType ).
tff(type_def_80,type,
fun_fu411113733ol_nat: $tType ).
tff(type_def_81,type,
fun_fu616551101l_bool: $tType ).
tff(type_def_82,type,
fun_fu140186515l_bool: $tType ).
tff(type_def_83,type,
fun_fu255076663l_bool: $tType ).
tff(type_def_84,type,
fun_fu48515398ol_nat: $tType ).
tff(type_def_85,type,
fun_fu821736593l_bool: $tType ).
tff(type_def_86,type,
fun_fu1438281908l_bool: $tType ).
tff(type_def_87,type,
fun_fu1701008009ol_nat: $tType ).
tff(type_def_88,type,
fun_fu1086940979l_bool: $tType ).
tff(type_def_89,type,
fun_fu61768826l_bool: $tType ).
tff(type_def_90,type,
fun_fu1297083715ol_nat: $tType ).
tff(type_def_91,type,
fun_fu1137991347l_bool: $tType ).
tff(type_def_92,type,
fun_fu754241017l_bool: $tType ).
tff(type_def_93,type,
fun_fu2065874474l_bool: $tType ).
tff(type_def_94,type,
fun_fu1971389424l_bool: $tType ).
tff(func_def_0,type,
cOMBB_1897541054_pname: ( fun_a_fun_a_bool * fun_pname_a ) > fun_pname_fun_a_bool ).
tff(func_def_1,type,
cOMBB_bool_bool_a: ( fun_bool_bool * fun_a_bool ) > fun_a_bool ).
tff(func_def_2,type,
cOMBB_647938656_pname: ( fun_bool_bool * fun_pname_bool ) > fun_pname_bool ).
tff(func_def_3,type,
cOMBB_bool_bool_nat: ( fun_bool_bool * fun_nat_bool ) > fun_nat_bool ).
tff(func_def_4,type,
cOMBB_2140588453a_bool: ( fun_bool_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).
tff(func_def_5,type,
cOMBB_307249310e_bool: ( fun_bool_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_6,type,
cOMBB_238756964t_bool: ( fun_bool_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).
tff(func_def_7,type,
cOMBB_1972296269bool_a: ( fun_bo1549164019l_bool * fun_a_bool ) > fun_a_fun_bool_bool ).
tff(func_def_8,type,
cOMBB_675860798_pname: ( fun_bo1549164019l_bool * fun_pname_bool ) > fun_pn250273176l_bool ).
tff(func_def_9,type,
cOMBB_1015721476ol_nat: ( fun_bo1549164019l_bool * fun_nat_bool ) > fun_na1469252690l_bool ).
tff(func_def_10,type,
cOMBB_338059395a_bool: ( fun_bo1549164019l_bool * fun_fun_a_bool_bool ) > fun_fu554186387l_bool ).
tff(func_def_11,type,
cOMBB_2095475776e_bool: ( fun_bo1549164019l_bool * fun_fu1430349052l_bool ) > fun_fu31783638l_bool ).
tff(func_def_12,type,
cOMBB_444170502t_bool: ( fun_bo1549164019l_bool * fun_fu425979586l_bool ) > fun_fu1016514960l_bool ).
tff(func_def_13,type,
cOMBC_a_a_bool: fun_a_fun_a_bool > fun_a_fun_a_bool ).
tff(func_def_14,type,
cOMBC_1355376034l_bool: fun_a_1255737515l_bool > fun_fu1731003005a_bool ).
tff(func_def_15,type,
cOMBC_pname_a_bool: fun_pname_fun_a_bool > fun_a_fun_pname_bool ).
tff(func_def_16,type,
cOMBC_1149511130e_bool: fun_pn800050071e_bool > fun_pn800050071e_bool ).
tff(func_def_17,type,
cOMBC_1058051404l_bool: fun_pn422929397l_bool > fun_fu410713561e_bool ).
tff(func_def_18,type,
cOMBC_nat_nat_bool: fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).
tff(func_def_19,type,
cOMBC_226598744l_bool: fun_na1436237685l_bool > fun_fu821463397t_bool ).
tff(func_def_20,type,
cOMBC_1732670874l_bool: fun_fu1471507361l_bool > fun_fu1471507361l_bool ).
tff(func_def_21,type,
cOMBC_1880041174l_bool: fun_fu386216885l_bool > fun_fu911136611l_bool ).
tff(func_def_22,type,
cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).
tff(func_def_23,type,
cOMBC_1988546018l_bool: fun_fu931343505l_bool > fun_fu2087345469l_bool ).
tff(func_def_24,type,
cOMBC_1693257480l_bool: fun_fu1217155507l_bool > fun_fu1217155507l_bool ).
tff(func_def_25,type,
cOMBC_1245412066l_bool: fun_fu1436348701l_bool > fun_fu616551101l_bool ).
tff(func_def_26,type,
cOMBC_331553030l_bool: fun_fu418465139l_bool > fun_fu418465139l_bool ).
tff(func_def_27,type,
cOMBC_7971162l_bool: fun_fu1911931399l_bool > fun_fu1911931399l_bool ).
tff(func_def_28,type,
cOMBC_595898202l_bool: fun_fu140186515l_bool > fun_fu140186515l_bool ).
tff(func_def_29,type,
cOMBC_636888218l_bool: fun_fu821736593l_bool > fun_fu821736593l_bool ).
tff(func_def_30,type,
cOMBC_336095980l_bool: fun_fu1086940979l_bool > fun_fu1086940979l_bool ).
tff(func_def_31,type,
cOMBC_1269652216l_bool: fun_fu1137991347l_bool > fun_fu1137991347l_bool ).
tff(func_def_32,type,
cOMBS_a_bool_bool: ( fun_a_fun_bool_bool * fun_a_bool ) > fun_a_bool ).
tff(func_def_33,type,
cOMBS_568398431l_bool: ( fun_pn250273176l_bool * fun_pname_bool ) > fun_pname_bool ).
tff(func_def_34,type,
cOMBS_nat_bool_bool: ( fun_na1469252690l_bool * fun_nat_bool ) > fun_nat_bool ).
tff(func_def_35,type,
cOMBS_1035972772l_bool: ( fun_fu554186387l_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).
tff(func_def_36,type,
cOMBS_350070575l_bool: ( fun_fu31783638l_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_37,type,
cOMBS_1187019125l_bool: ( fun_fu1016514960l_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).
tff(func_def_38,type,
finite_card_a: fun_fun_a_bool_nat ).
tff(func_def_39,type,
finite_card_pname: fun_fu1668467777ol_nat ).
tff(func_def_40,type,
finite_card_nat: fun_fun_nat_bool_nat ).
tff(func_def_41,type,
finite1306199131a_bool: fun_fu2020802748ol_nat ).
tff(func_def_42,type,
finite1340463720e_bool: fun_fu1730389579ol_nat ).
tff(func_def_43,type,
finite346522414t_bool: fun_fu411113733ol_nat ).
tff(func_def_44,type,
finite1659325229l_bool: fun_fu48515398ol_nat ).
tff(func_def_45,type,
finite269641166l_bool: fun_fu1701008009ol_nat ).
tff(func_def_46,type,
finite1352710292l_bool: fun_fu1297083715ol_nat ).
tff(func_def_47,type,
finite_finite_a: fun_fun_a_bool_bool ).
tff(func_def_48,type,
finite_finite_pname: fun_fu1430349052l_bool ).
tff(func_def_49,type,
finite_finite_nat: fun_fu425979586l_bool ).
tff(func_def_50,type,
finite347923420a_bool: fun_fu885608257l_bool ).
tff(func_def_51,type,
finite595471783e_bool: fun_fu399576434l_bool ).
tff(func_def_52,type,
finite2012431853t_bool: fun_fu814369080l_bool ).
tff(func_def_53,type,
finite1381704300l_bool: fun_fu255076663l_bool ).
tff(func_def_54,type,
finite786885583l_bool: fun_fu1438281908l_bool ).
tff(func_def_55,type,
finite1701474069l_bool: fun_fu61768826l_bool ).
tff(func_def_56,type,
finite1343359508l_bool: fun_fu754241017l_bool ).
tff(func_def_57,type,
finite1491191519l_bool: fun_fu2065874474l_bool ).
tff(func_def_58,type,
finite719726885l_bool: fun_fu1971389424l_bool ).
tff(func_def_59,type,
minus_minus_nat: nat > fun_nat_nat ).
tff(func_def_60,type,
suc: fun_nat_nat ).
tff(func_def_61,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_62,type,
ord_le1311769555a_bool: fun_fu1471507361l_bool ).
tff(func_def_63,type,
ord_le313189616e_bool: fun_fu802393907l_bool ).
tff(func_def_64,type,
ord_le1568362934t_bool: fun_fu1217155507l_bool ).
tff(func_def_65,type,
ord_le1375614389l_bool: fun_fu418465139l_bool ).
tff(func_def_66,type,
ord_le675606854l_bool: fun_fu1911931399l_bool ).
tff(func_def_67,type,
ord_le1454342156l_bool: fun_fu140186515l_bool ).
tff(func_def_68,type,
ord_le967226251l_bool: fun_fu821736593l_bool ).
tff(func_def_69,type,
ord_le1375671464l_bool: fun_fu1086940979l_bool ).
tff(func_def_70,type,
ord_le65145710l_bool: fun_fu1137991347l_bool ).
tff(func_def_71,type,
collect_a: fun_a_bool > fun_a_bool ).
tff(func_def_72,type,
collect_pname: fun_pname_bool > fun_pname_bool ).
tff(func_def_73,type,
collect_nat: fun_nat_bool > fun_nat_bool ).
tff(func_def_74,type,
collect_fun_a_bool: fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
tff(func_def_75,type,
collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
tff(func_def_76,type,
collect_fun_nat_bool: fun_fu425979586l_bool > fun_fu425979586l_bool ).
tff(func_def_77,type,
collec707592106l_bool: fun_fu885608257l_bool > fun_fu885608257l_bool ).
tff(func_def_78,type,
collec1613912337l_bool: fun_fu399576434l_bool > fun_fu399576434l_bool ).
tff(func_def_79,type,
collec1015864663l_bool: fun_fu814369080l_bool > fun_fu814369080l_bool ).
tff(func_def_80,type,
collec1635217238l_bool: fun_fu255076663l_bool > fun_fu255076663l_bool ).
tff(func_def_81,type,
collec792590109l_bool: fun_fu1438281908l_bool > fun_fu1438281908l_bool ).
tff(func_def_82,type,
collec1874991203l_bool: fun_fu61768826l_bool > fun_fu61768826l_bool ).
tff(func_def_83,type,
image_a_a: ( fun_a_a * fun_a_bool ) > fun_a_bool ).
tff(func_def_84,type,
image_a_pname: ( fun_a_pname * fun_a_bool ) > fun_pname_bool ).
tff(func_def_85,type,
image_a_nat: ( fun_a_nat * fun_a_bool ) > fun_nat_bool ).
tff(func_def_86,type,
image_pname_a: ( fun_pname_a * fun_pname_bool ) > fun_a_bool ).
tff(func_def_87,type,
image_pname_pname: ( fun_pname_pname * fun_pname_bool ) > fun_pname_bool ).
tff(func_def_88,type,
image_pname_nat: ( fun_pname_nat * fun_pname_bool ) > fun_nat_bool ).
tff(func_def_89,type,
image_112932426a_bool: ( fun_pname_fun_a_bool * fun_pname_bool ) > fun_fun_a_bool_bool ).
tff(func_def_90,type,
image_47868345e_bool: ( fun_pn800050071e_bool * fun_pname_bool ) > fun_fu1430349052l_bool ).
tff(func_def_91,type,
image_2129980159t_bool: ( fun_pn406123357t_bool * fun_pname_bool ) > fun_fu425979586l_bool ).
tff(func_def_92,type,
image_1420695166l_bool: ( fun_pn1038293468l_bool * fun_pname_bool ) > fun_fu885608257l_bool ).
tff(func_def_93,type,
image_1642285373l_bool: ( fun_pn422929397l_bool * fun_pname_bool ) > fun_fu399576434l_bool ).
tff(func_def_94,type,
image_1154884483l_bool: ( fun_pn1165013435l_bool * fun_pname_bool ) > fun_fu814369080l_bool ).
tff(func_def_95,type,
image_nat_a: ( fun_nat_a * fun_nat_bool ) > fun_a_bool ).
tff(func_def_96,type,
image_nat_pname: ( fun_nat_pname * fun_nat_bool ) > fun_pname_bool ).
tff(func_def_97,type,
image_nat_fun_a_bool: ( fun_nat_fun_a_bool * fun_nat_bool ) > fun_fun_a_bool_bool ).
tff(func_def_98,type,
image_1655916159e_bool: ( fun_na936072029e_bool * fun_nat_bool ) > fun_fu1430349052l_bool ).
tff(func_def_99,type,
image_26036933t_bool: ( fun_nat_fun_nat_bool * fun_nat_bool ) > fun_fu425979586l_bool ).
tff(func_def_100,type,
image_1208015684l_bool: ( fun_na1632405922l_bool * fun_nat_bool ) > fun_fu885608257l_bool ).
tff(func_def_101,type,
image_1874789623l_bool: ( fun_na2122364079l_bool * fun_nat_bool ) > fun_fu399576434l_bool ).
tff(func_def_102,type,
image_1607900221l_bool: ( fun_na1436237685l_bool * fun_nat_bool ) > fun_fu814369080l_bool ).
tff(func_def_103,type,
image_fun_a_bool_a: ( fun_fun_a_bool_a * fun_fun_a_bool_bool ) > fun_a_bool ).
tff(func_def_104,type,
image_1854862208_pname: ( fun_fun_a_bool_pname * fun_fun_a_bool_bool ) > fun_pname_bool ).
tff(func_def_105,type,
image_fun_a_bool_nat: ( fun_fun_a_bool_nat * fun_fun_a_bool_bool ) > fun_nat_bool ).
tff(func_def_106,type,
image_876012084bool_a: ( fun_fun_pname_bool_a * fun_fu1430349052l_bool ) > fun_a_bool ).
tff(func_def_107,type,
image_1283814551_pname: ( fun_fu1499449723_pname * fun_fu1430349052l_bool ) > fun_pname_bool ).
tff(func_def_108,type,
image_1551609309ol_nat: ( fun_fu1668467777ol_nat * fun_fu1430349052l_bool ) > fun_nat_bool ).
tff(func_def_109,type,
image_fun_nat_bool_a: ( fun_fun_nat_bool_a * fun_fu425979586l_bool ) > fun_a_bool ).
tff(func_def_110,type,
image_1921560913_pname: ( fun_fu665170229_pname * fun_fu425979586l_bool ) > fun_pname_bool ).
tff(func_def_111,type,
image_496248727ol_nat: ( fun_fun_nat_bool_nat * fun_fu425979586l_bool ) > fun_nat_bool ).
tff(func_def_112,type,
image_573985017bool_a: ( fun_fu1373417771bool_a * fun_fu885608257l_bool ) > fun_a_bool ).
tff(func_def_113,type,
image_990671762_pname: ( fun_fu1175941238_pname * fun_fu885608257l_bool ) > fun_pname_bool ).
tff(func_def_114,type,
image_1802975832ol_nat: ( fun_fu2020802748ol_nat * fun_fu885608257l_bool ) > fun_nat_bool ).
tff(func_def_115,type,
image_349102846bool_a: ( fun_fu2061654492bool_a * fun_fu399576434l_bool ) > fun_a_bool ).
tff(func_def_116,type,
image_1705983821_pname: ( fun_fu1664106117_pname * fun_fu399576434l_bool ) > fun_pname_bool ).
tff(func_def_117,type,
image_1079571347ol_nat: ( fun_fu1730389579ol_nat * fun_fu399576434l_bool ) > fun_nat_bool ).
tff(func_def_118,type,
image_526090948bool_a: ( fun_fu897950882bool_a * fun_fu814369080l_bool ) > fun_a_bool ).
tff(func_def_119,type,
image_1604018183_pname: ( fun_fu881587263_pname * fun_fu814369080l_bool ) > fun_pname_bool ).
tff(func_def_120,type,
image_2089570637ol_nat: ( fun_fu411113733ol_nat * fun_fu814369080l_bool ) > fun_nat_bool ).
tff(func_def_121,type,
insert_a: ( x_a * fun_a_bool ) > fun_a_bool ).
tff(func_def_122,type,
insert_pname: ( pname * fun_pname_bool ) > fun_pname_bool ).
tff(func_def_123,type,
insert_nat: ( nat * fun_nat_bool ) > fun_nat_bool ).
tff(func_def_124,type,
insert_fun_a_bool: ( fun_a_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).
tff(func_def_125,type,
insert1325755072e_bool: ( fun_pname_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_126,type,
insert_fun_nat_bool: ( fun_nat_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).
tff(func_def_127,type,
insert1457093509l_bool: ( fun_fun_a_bool_bool * fun_fu885608257l_bool ) > fun_fu885608257l_bool ).
tff(func_def_128,type,
insert1117693814l_bool: ( fun_fu1430349052l_bool * fun_fu399576434l_bool ) > fun_fu399576434l_bool ).
tff(func_def_129,type,
insert2003652156l_bool: ( fun_fu425979586l_bool * fun_fu814369080l_bool ) > fun_fu814369080l_bool ).
tff(func_def_130,type,
fNot: fun_bool_bool ).
tff(func_def_131,type,
fconj: fun_bo1549164019l_bool ).
tff(func_def_132,type,
fdisj: fun_bo1549164019l_bool ).
tff(func_def_133,type,
fequal_a: fun_a_fun_a_bool ).
tff(func_def_134,type,
fequal_pname: fun_pn800050071e_bool ).
tff(func_def_135,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(func_def_136,type,
fequal_fun_a_bool: fun_fu1471507361l_bool ).
tff(func_def_137,type,
fequal533582459e_bool: fun_fu802393907l_bool ).
tff(func_def_138,type,
fequal_fun_nat_bool: fun_fu1217155507l_bool ).
tff(func_def_139,type,
fimplies: fun_bo1549164019l_bool ).
tff(func_def_140,type,
hAPP_a_bool: ( fun_a_bool * x_a ) > bool ).
tff(func_def_141,type,
hAPP_a_fun_a_bool: ( fun_a_fun_a_bool * x_a ) > fun_a_bool ).
tff(func_def_142,type,
hAPP_a93125764e_bool: ( fun_a_fun_pname_bool * x_a ) > fun_pname_bool ).
tff(func_def_143,type,
hAPP_a_fun_bool_bool: ( fun_a_fun_bool_bool * x_a ) > fun_bool_bool ).
tff(func_def_144,type,
hAPP_a85458249l_bool: ( fun_a_1255737515l_bool * x_a ) > fun_fun_a_bool_bool ).
tff(func_def_145,type,
hAPP_pname_a: ( fun_pname_a * pname ) > x_a ).
tff(func_def_146,type,
hAPP_pname_bool: ( fun_pname_bool * pname ) > bool ).
tff(func_def_147,type,
hAPP_p1534023578a_bool: ( fun_pname_fun_a_bool * pname ) > fun_a_bool ).
tff(func_def_148,type,
hAPP_p61793385e_bool: ( fun_pn800050071e_bool * pname ) > fun_pname_bool ).
tff(func_def_149,type,
hAPP_p393069232l_bool: ( fun_pn250273176l_bool * pname ) > fun_bool_bool ).
tff(func_def_150,type,
hAPP_p338031245l_bool: ( fun_pn422929397l_bool * pname ) > fun_fu1430349052l_bool ).
tff(func_def_151,type,
hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).
tff(func_def_152,type,
hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).
tff(func_def_153,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(func_def_154,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(func_def_155,type,
hAPP_nat_fun_a_bool: ( fun_nat_fun_a_bool * nat ) > fun_a_bool ).
tff(func_def_156,type,
hAPP_n1025906991e_bool: ( fun_na936072029e_bool * nat ) > fun_pname_bool ).
tff(func_def_157,type,
hAPP_n1006566506l_bool: ( fun_na1469252690l_bool * nat ) > fun_bool_bool ).
tff(func_def_158,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_159,type,
hAPP_n215258509l_bool: ( fun_na1436237685l_bool * nat ) > fun_fu425979586l_bool ).
tff(func_def_160,type,
hAPP_fun_a_bool_bool: ( fun_fun_a_bool_bool * fun_a_bool ) > bool ).
tff(func_def_161,type,
hAPP_fun_a_bool_nat: ( fun_fun_a_bool_nat * fun_a_bool ) > nat ).
tff(func_def_162,type,
hAPP_f2050579477a_bool: ( fun_fu1731003005a_bool * fun_a_bool ) > fun_a_bool ).
tff(func_def_163,type,
hAPP_f198738859l_bool: ( fun_fu554186387l_bool * fun_a_bool ) > fun_bool_bool ).
tff(func_def_164,type,
hAPP_f1631501043l_bool: ( fun_fu1471507361l_bool * fun_a_bool ) > fun_fun_a_bool_bool ).
tff(func_def_165,type,
hAPP_f285962445l_bool: ( fun_fu386216885l_bool * fun_a_bool ) > fun_fu885608257l_bool ).
tff(func_def_166,type,
hAPP_f1664156314l_bool: ( fun_fu1430349052l_bool * fun_pname_bool ) > bool ).
tff(func_def_167,type,
hAPP_f921600141ol_nat: ( fun_fu1668467777ol_nat * fun_pname_bool ) > nat ).
tff(func_def_168,type,
hAPP_f759274231e_bool: ( fun_fu410713561e_bool * fun_pname_bool ) > fun_pname_bool ).
tff(func_def_169,type,
hAPP_f1476298914l_bool: ( fun_fu31783638l_bool * fun_pname_bool ) > fun_bool_bool ).
tff(func_def_170,type,
hAPP_f434788991l_bool: ( fun_fu802393907l_bool * fun_pname_bool ) > fun_fu1430349052l_bool ).
tff(func_def_171,type,
hAPP_f556039215l_bool: ( fun_fu931343505l_bool * fun_pname_bool ) > fun_fu399576434l_bool ).
tff(func_def_172,type,
hAPP_f54304608l_bool: ( fun_fu425979586l_bool * fun_nat_bool ) > bool ).
tff(func_def_173,type,
hAPP_f22106695ol_nat: ( fun_fun_nat_bool_nat * fun_nat_bool ) > nat ).
tff(func_def_174,type,
hAPP_f1748468828l_bool: ( fun_fu1016514960l_bool * fun_nat_bool ) > fun_bool_bool ).
tff(func_def_175,type,
hAPP_f800510211t_bool: ( fun_fu821463397t_bool * fun_nat_bool ) > fun_nat_bool ).
tff(func_def_176,type,
hAPP_f103356543l_bool: ( fun_fu1217155507l_bool * fun_nat_bool ) > fun_fu425979586l_bool ).
tff(func_def_177,type,
hAPP_f1951378235l_bool: ( fun_fu1436348701l_bool * fun_nat_bool ) > fun_fu814369080l_bool ).
tff(func_def_178,type,
hAPP_f621171935l_bool: ( fun_fu885608257l_bool * fun_fun_a_bool_bool ) > bool ).
tff(func_def_179,type,
hAPP_f2009550088ol_nat: ( fun_fu2020802748ol_nat * fun_fun_a_bool_bool ) > nat ).
tff(func_def_180,type,
hAPP_f2117159681l_bool: ( fun_fu911136611l_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).
tff(func_def_181,type,
hAPP_f1434722111l_bool: ( fun_fu418465139l_bool * fun_fun_a_bool_bool ) > fun_fu885608257l_bool ).
tff(func_def_182,type,
hAPP_f1935102916l_bool: ( fun_fu399576434l_bool * fun_fu1430349052l_bool ) > bool ).
tff(func_def_183,type,
hAPP_f55526627ol_nat: ( fun_fu1730389579ol_nat * fun_fu1430349052l_bool ) > nat ).
tff(func_def_184,type,
hAPP_f559147733l_bool: ( fun_fu2087345469l_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_185,type,
hAPP_f510955609l_bool: ( fun_fu1911931399l_bool * fun_fu1430349052l_bool ) > fun_fu399576434l_bool ).
tff(func_def_186,type,
hAPP_f1637334154l_bool: ( fun_fu814369080l_bool * fun_fu425979586l_bool ) > bool ).
tff(func_def_187,type,
hAPP_f696928925ol_nat: ( fun_fu411113733ol_nat * fun_fu425979586l_bool ) > nat ).
tff(func_def_188,type,
hAPP_f1246832597l_bool: ( fun_fu616551101l_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).
tff(func_def_189,type,
hAPP_f1772781669l_bool: ( fun_fu140186515l_bool * fun_fu425979586l_bool ) > fun_fu814369080l_bool ).
tff(func_def_190,type,
hAPP_f292226953l_bool: ( fun_fu255076663l_bool * fun_fu885608257l_bool ) > bool ).
tff(func_def_191,type,
hAPP_f1253658590ol_nat: ( fun_fu48515398ol_nat * fun_fu885608257l_bool ) > nat ).
tff(func_def_192,type,
hAPP_f1050622307l_bool: ( fun_fu821736593l_bool * fun_fu885608257l_bool ) > fun_fu255076663l_bool ).
tff(func_def_193,type,
hAPP_f389811538l_bool: ( fun_fu1438281908l_bool * fun_fu399576434l_bool ) > bool ).
tff(func_def_194,type,
hAPP_f98387925ol_nat: ( fun_fu1701008009ol_nat * fun_fu399576434l_bool ) > nat ).
tff(func_def_195,type,
hAPP_f1759205631l_bool: ( fun_fu1086940979l_bool * fun_fu399576434l_bool ) > fun_fu1438281908l_bool ).
tff(func_def_196,type,
hAPP_f937997336l_bool: ( fun_fu61768826l_bool * fun_fu814369080l_bool ) > bool ).
tff(func_def_197,type,
hAPP_f1690079119ol_nat: ( fun_fu1297083715ol_nat * fun_fu814369080l_bool ) > nat ).
tff(func_def_198,type,
hAPP_f760187903l_bool: ( fun_fu1137991347l_bool * fun_fu814369080l_bool ) > fun_fu61768826l_bool ).
tff(func_def_199,type,
hAPP_f1363661463l_bool: ( fun_fu754241017l_bool * fun_fu255076663l_bool ) > bool ).
tff(func_def_200,type,
hAPP_f595608956l_bool: ( fun_fu2065874474l_bool * fun_fu1438281908l_bool ) > bool ).
tff(func_def_201,type,
hAPP_f1295398978l_bool: ( fun_fu1971389424l_bool * fun_fu61768826l_bool ) > bool ).
tff(func_def_202,type,
member_a: fun_a_1255737515l_bool ).
tff(func_def_203,type,
member_pname: fun_pn422929397l_bool ).
tff(func_def_204,type,
member_nat: fun_na1436237685l_bool ).
tff(func_def_205,type,
member_fun_a_bool: fun_fu386216885l_bool ).
tff(func_def_206,type,
member799430823e_bool: fun_fu931343505l_bool ).
tff(func_def_207,type,
member_fun_nat_bool: fun_fu1436348701l_bool ).
tff(func_def_208,type,
g: fun_a_bool ).
tff(func_def_209,type,
p: fun_a_bool > fun_fun_a_bool_bool ).
tff(func_def_210,type,
u: fun_pname_bool ).
tff(func_def_211,type,
mgt_call: fun_pname_a ).
tff(func_def_212,type,
na: nat ).
tff(func_def_213,type,
pn: pname ).
tff(func_def_214,type,
sK0: ( fun_nat_bool * nat ) > nat ).
tff(func_def_215,type,
sK1: fun_nat_bool > nat ).
tff(func_def_216,type,
sK2: ( fun_pname_a * fun_pname_bool ) > pname ).
tff(func_def_217,type,
sK3: nat > nat ).
tff(func_def_218,type,
sK4: ( fun_nat_bool * fun_nat_bool ) > nat ).
tff(func_def_219,type,
sK5: ( fun_a_bool * fun_a_bool ) > x_a ).
tff(func_def_220,type,
sK6: ( fun_pname_bool * fun_pname_bool ) > pname ).
tff(func_def_221,type,
sK7: ( fun_pname_a * fun_pname_bool * fun_a_bool ) > fun_pname_bool ).
tff(func_def_222,type,
sK8: fun_nat_bool > nat ).
tff(func_def_223,type,
sK9: ( x_a * fun_pname_a * fun_pname_bool ) > pname ).
tff(func_def_224,type,
sK10: fun_nat_nat > nat ).
tff(func_def_225,type,
sK11: fun_nat_fun_nat_bool > nat ).
tff(func_def_226,type,
sK12: fun_nat_fun_a_bool > nat ).
tff(func_def_227,type,
sK13: fun_na936072029e_bool > nat ).
tff(func_def_228,type,
sK14: ( fun_pname_a * fun_a_bool * fun_pname_bool ) > pname ).
tff(func_def_229,type,
sK15: ( x_a * fun_pname_a * fun_pname_bool ) > pname ).
tff(func_def_230,type,
sK16: ( fun_a_bool * fun_pname_a * fun_pname_bool ) > fun_pname_bool ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(f4533,plain,
$false,
inference(avatar_sat_refutation,[],[f1641,f1646,f1650,f1654,f1658,f1662,f1666,f1670,f1675,f1679,f1683,f1687,f1691,f1695,f1699,f1704,f1709,f1714,f1718,f1722,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1846,f1850,f1854,f1858,f1877,f1888,f1892,f1896,f1900,f1904,f1908,f1912,f1916,f1920,f1924,f1928,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1960,f1964,f1968,f1972,f1976,f1980,f1984,f1988,f1992,f1996,f2000,f2004,f2008,f2012,f2016,f2020,f2024,f2028,f2032,f2036,f2040,f2044,f2048,f2052,f2056,f2060,f2064,f2068,f2072,f2076,f2080,f2084,f2088,f2092,f2096,f2100,f2104,f2108,f2112,f2117,f2121,f2125,f2129,f2133,f2137,f2141,f2145,f2149,f2153,f2157,f2161,f2165,f2169,f2179,f2183,f2207,f2220,f2224,f2229,f2233,f2237,f2241,f2245,f2249,f2253,f2257,f2261,f2265,f2269,f2273,f2277,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2317,f2321,f2325,f2351,f2491,f2496,f2500,f2504,f2508,f2512,f2516,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2556,f2560,f2564,f2568,f2573,f2577,f2581,f2585,f2589,f2593,f2597,f2601,f2605,f2609,f2614,f2618,f2622,f2626,f2630,f2634,f2638,f2642,f2646,f2650,f2658,f2662,f2666,f2670,f2674,f2678,f2682,f2686,f2690,f2694,f2731,f2748,f2752,f2756,f2763,f2767,f2771,f2775,f2779,f2783,f2787,f2791,f2795,f2800,f2853,f2858,f2862,f2866,f2870,f2874,f2878,f2882,f2886,f2890,f2894,f2898,f2902,f2906,f2910,f2914,f2918,f2922,f2926,f2930,f2934,f2938,f2942,f2946,f2950,f2954,f2958,f2962,f2966,f2970,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3041,f3137,f3141,f3153,f3157,f3161,f3165,f3169,f3173,f3177,f3181,f3185,f3189,f3245,f3256,f3260,f3264,f3268,f3272,f3276,f3280,f3284,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3316,f3320,f3324,f3328,f3332,f3336,f3340,f3344,f3348,f3352,f3356,f3360,f3364,f3368,f3372,f3376,f3380,f3384,f3388,f3392,f3396,f3400,f3404,f3408,f3412,f3416,f3435,f3439,f3443,f3447,f3451,f3455,f3459,f3463,f3467,f3471,f3481,f3485,f3489,f3493,f3497,f3501,f3505,f3509,f3585,f3697,f3777,f3781,f3785,f3789,f3793,f3797,f3802,f3806,f3810,f3871,f3875,f3879,f3883,f3887,f3891,f3895,f3899,f3903,f3907,f3911,f3915,f4057,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4108,f4112,f4116,f4120,f4124,f4128,f4253,f4257,f4261,f4265,f4269,f4273,f4277,f4281,f4285,f4289,f4293,f4297,f4301,f4305,f4309,f4349,f4417,f4421,f4425,f4429,f4434,f4438,f4442,f4446,f4489,f4493,f4497,f4501,f4505,f4509,f4532]) ).
tff(f4532,plain,
( ~ spl17_9
| ~ spl17_321
| spl17_390 ),
inference(avatar_split_clause,[],[f4481,f4431,f3461,f1672]) ).
tff(f1672,plain,
( spl17_9
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
tff(f3461,plain,
( spl17_321
<=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_321])]) ).
tff(f4431,plain,
( spl17_390
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_390])]) ).
tff(f4481,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ~ spl17_321
| spl17_390 ),
inference(resolution,[],[f4433,f3462]) ).
tff(f3462,plain,
( ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
| ~ spl17_321 ),
inference(avatar_component_clause,[],[f3461]) ).
tff(f4433,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
| spl17_390 ),
inference(avatar_component_clause,[],[f4431]) ).
tff(f4509,plain,
spl17_399,
inference(avatar_split_clause,[],[f1480,f4507]) ).
tff(f4507,plain,
( spl17_399
<=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
( ( insert_pname(X1,X0) = insert_pname(X1,X2) )
| ( X0 != X2 )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_399])]) ).
tff(f1480,plain,
! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
( ( insert_pname(X1,X0) = insert_pname(X1,X2) )
| ( X0 != X2 )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f1069]) ).
tff(f1069,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( ( ( ( insert_pname(X1,X0) = insert_pname(X1,X2) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( insert_pname(X1,X0) != insert_pname(X1,X2) ) ) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(nnf_transformation,[],[f937]) ).
tff(f937,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( ( ( insert_pname(X1,X0) = insert_pname(X1,X2) )
<=> ( X0 = X2 ) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(flattening,[],[f936]) ).
tff(f936,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( ( ( insert_pname(X1,X0) = insert_pname(X1,X2) )
<=> ( X0 = X2 ) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f671]) ).
tff(f671,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
=> ( ( insert_pname(X1,X0) = insert_pname(X1,X2) )
<=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f218]) ).
tff(f218,axiom,
! [X7: fun_pname_bool,X8: pname,X2: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X7))
=> ( ( insert_pname(X8,X2) = insert_pname(X8,X7) )
<=> ( X2 = X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_217_insert__ident) ).
tff(f4505,plain,
spl17_398,
inference(avatar_split_clause,[],[f1479,f4503]) ).
tff(f4503,plain,
( spl17_398
<=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
( ( X0 = X2 )
| ( insert_pname(X1,X0) != insert_pname(X1,X2) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_398])]) ).
tff(f1479,plain,
! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
( ( X0 = X2 )
| ( insert_pname(X1,X0) != insert_pname(X1,X2) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f1069]) ).
tff(f4501,plain,
spl17_397,
inference(avatar_split_clause,[],[f1476,f4499]) ).
tff(f4499,plain,
( spl17_397
<=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
( ( insert_a(X1,X0) = insert_a(X1,X2) )
| ( X0 != X2 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_397])]) ).
tff(f1476,plain,
! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
( ( insert_a(X1,X0) = insert_a(X1,X2) )
| ( X0 != X2 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f1067]) ).
tff(f1067,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( ( ( ( insert_a(X1,X0) = insert_a(X1,X2) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( insert_a(X1,X0) != insert_a(X1,X2) ) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(nnf_transformation,[],[f934]) ).
tff(f934,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( ( ( insert_a(X1,X0) = insert_a(X1,X2) )
<=> ( X0 = X2 ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(flattening,[],[f933]) ).
tff(f933,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( ( ( insert_a(X1,X0) = insert_a(X1,X2) )
<=> ( X0 = X2 ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f669]) ).
tff(f669,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
=> ( ( insert_a(X1,X0) = insert_a(X1,X2) )
<=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f219]) ).
tff(f219,axiom,
! [X7: fun_a_bool,X8: x_a,X2: fun_a_bool] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7))
=> ( ( insert_a(X8,X2) = insert_a(X8,X7) )
<=> ( X2 = X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_218_insert__ident) ).
tff(f4497,plain,
spl17_396,
inference(avatar_split_clause,[],[f1475,f4495]) ).
tff(f4495,plain,
( spl17_396
<=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
( ( X0 = X2 )
| ( insert_a(X1,X0) != insert_a(X1,X2) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_396])]) ).
tff(f1475,plain,
! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
( ( X0 = X2 )
| ( insert_a(X1,X0) != insert_a(X1,X2) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f1067]) ).
tff(f4493,plain,
spl17_395,
inference(avatar_split_clause,[],[f1472,f4491]) ).
tff(f4491,plain,
( spl17_395
<=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
( ( insert_nat(X1,X0) = insert_nat(X1,X2) )
| ( X0 != X2 )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_395])]) ).
tff(f1472,plain,
! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
( ( insert_nat(X1,X0) = insert_nat(X1,X2) )
| ( X0 != X2 )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f1065]) ).
tff(f1065,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( ( ( ( insert_nat(X1,X0) = insert_nat(X1,X2) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( insert_nat(X1,X0) != insert_nat(X1,X2) ) ) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(nnf_transformation,[],[f931]) ).
tff(f931,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( ( ( insert_nat(X1,X0) = insert_nat(X1,X2) )
<=> ( X0 = X2 ) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(flattening,[],[f930]) ).
tff(f930,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( ( ( insert_nat(X1,X0) = insert_nat(X1,X2) )
<=> ( X0 = X2 ) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f667]) ).
tff(f667,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
=> ( ( insert_nat(X1,X0) = insert_nat(X1,X2) )
<=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f217]) ).
tff(f217,axiom,
! [X7: fun_nat_bool,X8: nat,X2: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X7))
=> ( ( insert_nat(X8,X2) = insert_nat(X8,X7) )
<=> ( X2 = X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_216_insert__ident) ).
tff(f4489,plain,
spl17_394,
inference(avatar_split_clause,[],[f1471,f4487]) ).
tff(f4487,plain,
( spl17_394
<=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
( ( X0 = X2 )
| ( insert_nat(X1,X0) != insert_nat(X1,X2) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_394])]) ).
tff(f1471,plain,
! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
( ( X0 = X2 )
| ( insert_nat(X1,X0) != insert_nat(X1,X2) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f1065]) ).
tff(f4446,plain,
spl17_393,
inference(avatar_split_clause,[],[f1465,f4444]) ).
tff(f4444,plain,
( spl17_393
<=> ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK7(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_393])]) ).
tff(f1465,plain,
! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK7(X0,X1,X2)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(cnf_transformation,[],[f1062]) ).
tff(f1062,plain,
! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
( ( ( image_pname_a(X0,sK7(X0,X1,X2)) = X2 )
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK7(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK7(X0,X1,X2)),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f925,f1061]) ).
tff(f1061,plain,
! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
( ? [X3: fun_pname_bool] :
( ( image_pname_a(X0,X3) = X2 )
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
=> ( ( image_pname_a(X0,sK7(X0,X1,X2)) = X2 )
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK7(X0,X1,X2)))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK7(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f925,plain,
! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
( ? [X3: fun_pname_bool] :
( ( image_pname_a(X0,X3) = X2 )
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(flattening,[],[f924]) ).
tff(f924,plain,
! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
( ? [X3: fun_pname_bool] :
( ( image_pname_a(X0,X3) = X2 )
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(ennf_transformation,[],[f664]) ).
tff(f664,plain,
! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
=> ? [X3: fun_pname_bool] :
( ( image_pname_a(X0,X3) = X2 )
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
inference(rectify,[],[f171]) ).
tff(f171,axiom,
! [X6: fun_pname_a,X2: fun_pname_bool,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_pname_a(X6,X2)))
=> ? [X24: fun_pname_bool] :
( ( image_pname_a(X6,X24) = X7 )
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_170_finite__subset__image) ).
tff(f4442,plain,
spl17_392,
inference(avatar_split_clause,[],[f1323,f4440]) ).
tff(f4440,plain,
( spl17_392
<=> ! [X0: pname,X1: fun_pname_bool] :
( ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_392])]) ).
tff(f1323,plain,
! [X0: pname,X1: fun_pname_bool] :
( ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f874]) ).
tff(f874,plain,
! [X0: pname,X1: fun_pname_bool] :
( ( ( ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) )
& ( ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) )
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f564]) ).
tff(f564,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) ) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)) ) ) ) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X8: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
=> ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X8,X2)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2)) ) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
=> ( hAPP_f921600141ol_nat(finite_card_pname,X2) = hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X8,X2)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_102_card__insert__if) ).
tff(f4438,plain,
spl17_391,
inference(avatar_split_clause,[],[f1300,f4436]) ).
tff(f4436,plain,
( spl17_391
<=> ! [X0: x_a,X1: fun_a_bool] :
( ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_391])]) ).
tff(f1300,plain,
! [X0: x_a,X1: fun_a_bool] :
( ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f848]) ).
tff(f848,plain,
! [X0: x_a,X1: fun_a_bool] :
( ( ( ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) )
& ( ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f542]) ).
tff(f542,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
=> ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) ) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
=> ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)) ) ) ) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X8: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
=> ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X8,X2)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2)) ) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
=> ( hAPP_fun_a_bool_nat(finite_card_a,X2) = hAPP_fun_a_bool_nat(finite_card_a,insert_a(X8,X2)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_103_card__insert__if) ).
tff(f4434,plain,
( ~ spl17_390
| ~ spl17_18
| spl17_1
| ~ spl17_383 ),
inference(avatar_split_clause,[],[f4392,f4303,f1638,f1711,f4431]) ).
tff(f1711,plain,
( spl17_18
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
tff(f1638,plain,
( spl17_1
<=> 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))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
tff(f4303,plain,
( spl17_383
<=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_383])]) ).
tff(f4392,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)))
| spl17_1
| ~ spl17_383 ),
inference(resolution,[],[f4304,f1640]) ).
tff(f1640,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)))
| spl17_1 ),
inference(avatar_component_clause,[],[f1638]) ).
tff(f4304,plain,
( ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ spl17_383 ),
inference(avatar_component_clause,[],[f4303]) ).
tff(f4429,plain,
spl17_389,
inference(avatar_split_clause,[],[f1286,f4427]) ).
tff(f4427,plain,
( spl17_389
<=> ! [X0: nat,X1: fun_nat_bool] :
( ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_389])]) ).
tff(f1286,plain,
! [X0: nat,X1: fun_nat_bool] :
( ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f831]) ).
tff(f831,plain,
! [X0: nat,X1: fun_nat_bool] :
( ( ( ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) )
& ( ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f529]) ).
tff(f529,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
=> ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) ) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
=> ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)) ) ) ) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X8: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
=> ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X8,X2)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2)) ) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
=> ( hAPP_f22106695ol_nat(finite_card_nat,X2) = hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X8,X2)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_101_card__insert__if) ).
tff(f4425,plain,
spl17_388,
inference(avatar_split_clause,[],[f1257,f4423]) ).
tff(f4423,plain,
( spl17_388
<=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) )
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_388])]) ).
tff(f1257,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) )
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f791]) ).
tff(f791,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( ( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) )
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1)) )
& ( ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1)) ) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f501]) ).
tff(f501,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
=> ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) ) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
=> ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)) ) ) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X8: fun_nat_bool,X2: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X8),X2))
=> ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X8,X2)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2)) ) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X8),X2))
=> ( hAPP_f696928925ol_nat(finite346522414t_bool,X2) = hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X8,X2)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_98_card__insert__if) ).
tff(f4421,plain,
spl17_387,
inference(avatar_split_clause,[],[f1255,f4419]) ).
tff(f4419,plain,
( spl17_387
<=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) )
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_387])]) ).
tff(f1255,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) )
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f790]) ).
tff(f790,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( ( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) )
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1)) )
& ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1)) ) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f500]) ).
tff(f500,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
=> ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) ) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
=> ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)) ) ) ) ),
inference(rectify,[],[f101]) ).
tff(f101,axiom,
! [X8: fun_a_bool,X2: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X8),X2))
=> ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X8,X2)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)) ) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X8),X2))
=> ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X2) = hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X8,X2)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_100_card__insert__if) ).
tff(f4417,plain,
spl17_386,
inference(avatar_split_clause,[],[f1253,f4415]) ).
tff(f4415,plain,
( spl17_386
<=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) )
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_386])]) ).
tff(f1253,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) )
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f789]) ).
tff(f789,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) )
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1)) )
& ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1)) ) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f499]) ).
tff(f499,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
=> ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) ) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
=> ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)) ) ) ) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X8: fun_pname_bool,X2: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X8),X2))
=> ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X8,X2)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)) ) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X8),X2))
=> ( hAPP_f55526627ol_nat(finite1340463720e_bool,X2) = hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X8,X2)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_99_card__insert__if) ).
tff(f4349,plain,
( spl17_385
| ~ spl17_58
| ~ spl17_281 ),
inference(avatar_split_clause,[],[f3472,f3286,f1894,f4347]) ).
tff(f4347,plain,
( spl17_385
<=> ! [X0: x_a] : ( hAPP_a_fun_a_bool(fequal_a,X0) = insert_a(X0,hAPP_a_fun_a_bool(fequal_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_385])]) ).
tff(f1894,plain,
( spl17_58
<=> ! [X0: x_a] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_58])]) ).
tff(f3286,plain,
( spl17_281
<=> ! [X2: x_a,X3: fun_a_bool] :
( ( insert_a(X2,X3) = X3 )
| ~ hBOOL(hAPP_a_bool(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_281])]) ).
tff(f3472,plain,
( ! [X0: x_a] : ( hAPP_a_fun_a_bool(fequal_a,X0) = insert_a(X0,hAPP_a_fun_a_bool(fequal_a,X0)) )
| ~ spl17_58
| ~ spl17_281 ),
inference(resolution,[],[f3287,f1895]) ).
tff(f1895,plain,
( ! [X0: x_a] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X0))
| ~ spl17_58 ),
inference(avatar_component_clause,[],[f1894]) ).
tff(f3287,plain,
( ! [X2: x_a,X3: fun_a_bool] :
( ~ hBOOL(hAPP_a_bool(X3,X2))
| ( insert_a(X2,X3) = X3 ) )
| ~ spl17_281 ),
inference(avatar_component_clause,[],[f3286]) ).
tff(f4309,plain,
spl17_384,
inference(avatar_split_clause,[],[f1567,f4307]) ).
tff(f4307,plain,
( spl17_384
<=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_384])]) ).
tff(f1567,plain,
! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ),
inference(cnf_transformation,[],[f1110]) ).
tff(f1110,plain,
! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
& ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2)) ) ),
inference(flattening,[],[f1109]) ).
tff(f1109,plain,
! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
& ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2)) ) ),
inference(nnf_transformation,[],[f728]) ).
tff(f728,plain,
! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
inference(rectify,[],[f274]) ).
tff(f274,axiom,
! [X8: pname,X2: fun_pname_bool,X7: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X8,X2)),X7))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_273_insert__subset) ).
tff(f4305,plain,
spl17_383,
inference(avatar_split_clause,[],[f1561,f4303]) ).
tff(f1561,plain,
! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
inference(cnf_transformation,[],[f1106]) ).
tff(f1106,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
inference(flattening,[],[f1105]) ).
tff(f1105,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
inference(nnf_transformation,[],[f726]) ).
tff(f726,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
inference(rectify,[],[f275]) ).
tff(f275,axiom,
! [X8: x_a,X2: fun_a_bool,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X8,X2)),X7))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_274_insert__subset) ).
tff(f4301,plain,
spl17_382,
inference(avatar_split_clause,[],[f1549,f4299]) ).
tff(f4299,plain,
( spl17_382
<=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_382])]) ).
tff(f1549,plain,
! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ),
inference(cnf_transformation,[],[f1094]) ).
tff(f1094,plain,
! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
& ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2)) ) ),
inference(flattening,[],[f1093]) ).
tff(f1093,plain,
! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
& ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2)) ) ),
inference(nnf_transformation,[],[f722]) ).
tff(f722,plain,
! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
inference(rectify,[],[f273]) ).
tff(f273,axiom,
! [X8: nat,X2: fun_nat_bool,X7: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X8,X2)),X7))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_272_insert__subset) ).
tff(f4297,plain,
( spl17_381
| ~ spl17_69
| ~ spl17_272 ),
inference(avatar_split_clause,[],[f3419,f3243,f1938,f4295]) ).
tff(f4295,plain,
( spl17_381
<=> ! [X3: nat] : ( hAPP_n1699378549t_bool(fequal_nat,X3) = insert_nat(X3,hAPP_n1699378549t_bool(fequal_nat,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_381])]) ).
tff(f1938,plain,
( spl17_69
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_69])]) ).
tff(f3243,plain,
( spl17_272
<=> ! [X2: nat,X3: fun_nat_bool] :
( ( insert_nat(X2,X3) = X3 )
| ~ hBOOL(hAPP_nat_bool(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_272])]) ).
tff(f3419,plain,
( ! [X3: nat] : ( hAPP_n1699378549t_bool(fequal_nat,X3) = insert_nat(X3,hAPP_n1699378549t_bool(fequal_nat,X3)) )
| ~ spl17_69
| ~ spl17_272 ),
inference(resolution,[],[f3244,f1939]) ).
tff(f1939,plain,
( ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X0))
| ~ spl17_69 ),
inference(avatar_component_clause,[],[f1938]) ).
tff(f3244,plain,
( ! [X2: nat,X3: fun_nat_bool] :
( ~ hBOOL(hAPP_nat_bool(X3,X2))
| ( insert_nat(X2,X3) = X3 ) )
| ~ spl17_272 ),
inference(avatar_component_clause,[],[f3243]) ).
tff(f4293,plain,
spl17_380,
inference(avatar_split_clause,[],[f1481,f4291]) ).
tff(f4291,plain,
( spl17_380
<=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_380])]) ).
tff(f1481,plain,
! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X0)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f1070]) ).
tff(f1070,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X0))) ) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(nnf_transformation,[],[f938]) ).
tff(f938,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X0)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f672]) ).
tff(f672,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X1,X0)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) ) ),
inference(rectify,[],[f277]) ).
tff(f277,axiom,
! [X7: fun_pname_bool,X8: pname,X2: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X8,X7)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_276_subset__insert) ).
tff(f4289,plain,
spl17_379,
inference(avatar_split_clause,[],[f1477,f4287]) ).
tff(f4287,plain,
( spl17_379
<=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_379])]) ).
tff(f1477,plain,
! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f1068]) ).
tff(f1068,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0))) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(nnf_transformation,[],[f935]) ).
tff(f935,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f670]) ).
tff(f670,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) ) ),
inference(rectify,[],[f278]) ).
tff(f278,axiom,
! [X7: fun_a_bool,X8: x_a,X2: fun_a_bool] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X8,X7)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_277_subset__insert) ).
tff(f4285,plain,
spl17_378,
inference(avatar_split_clause,[],[f1473,f4283]) ).
tff(f4283,plain,
( spl17_378
<=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_378])]) ).
tff(f1473,plain,
! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X0)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f1066]) ).
tff(f1066,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X0))) ) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(nnf_transformation,[],[f932]) ).
tff(f932,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X0)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f668]) ).
tff(f668,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X1,X0)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) ) ),
inference(rectify,[],[f276]) ).
tff(f276,axiom,
! [X7: fun_nat_bool,X8: nat,X2: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X8,X7)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_275_subset__insert) ).
tff(f4281,plain,
spl17_377,
inference(avatar_split_clause,[],[f1467,f4279]) ).
tff(f4279,plain,
( spl17_377
<=> ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
( ( image_pname_a(X0,sK7(X0,X1,X2)) = X2 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_377])]) ).
tff(f1467,plain,
! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
( ( image_pname_a(X0,sK7(X0,X1,X2)) = X2 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(cnf_transformation,[],[f1062]) ).
tff(f4277,plain,
spl17_376,
inference(avatar_split_clause,[],[f1326,f4275]) ).
tff(f4275,plain,
( spl17_376
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_376])]) ).
tff(f1326,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f880]) ).
tff(f880,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(flattening,[],[f879]) ).
tff(f879,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f567]) ).
tff(f567,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1))) ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X2: fun_pname_bool,X7: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X7))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_83_card__mono) ).
tff(f4273,plain,
spl17_375,
inference(avatar_split_clause,[],[f1303,f4271]) ).
tff(f4271,plain,
( spl17_375
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_375])]) ).
tff(f1303,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f854]) ).
tff(f854,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(flattening,[],[f853]) ).
tff(f853,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f545]) ).
tff(f545,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1))) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X2: fun_a_bool,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X7))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_84_card__mono) ).
tff(f4269,plain,
spl17_374,
inference(avatar_split_clause,[],[f1289,f4267]) ).
tff(f4267,plain,
( spl17_374
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_374])]) ).
tff(f1289,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f837]) ).
tff(f837,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f836]) ).
tff(f836,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f532]) ).
tff(f532,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1))) ) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X2: fun_nat_bool,X7: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X7))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_85_card__mono) ).
tff(f4265,plain,
spl17_373,
inference(avatar_split_clause,[],[f1266,f4263]) ).
tff(f4263,plain,
( spl17_373
<=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_373])]) ).
tff(f1266,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f809]) ).
tff(f809,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(flattening,[],[f808]) ).
tff(f808,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f510]) ).
tff(f510,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X2: fun_fu425979586l_bool,X7: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),X7))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X7))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_80_card__mono) ).
tff(f4261,plain,
spl17_372,
inference(avatar_split_clause,[],[f1265,f4259]) ).
tff(f4259,plain,
( spl17_372
<=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_372])]) ).
tff(f1265,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f807]) ).
tff(f807,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(flattening,[],[f806]) ).
tff(f806,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f509]) ).
tff(f509,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X2: fun_fun_a_bool_bool,X7: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),X7))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X7))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_82_card__mono) ).
tff(f4257,plain,
spl17_371,
inference(avatar_split_clause,[],[f1264,f4255]) ).
tff(f4255,plain,
( spl17_371
<=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_371])]) ).
tff(f1264,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f805]) ).
tff(f805,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(flattening,[],[f804]) ).
tff(f804,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f508]) ).
tff(f508,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X2: fun_fu1430349052l_bool,X7: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),X7))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X7))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_81_card__mono) ).
tff(f4253,plain,
( spl17_370
| ~ spl17_10
| ~ spl17_272 ),
inference(avatar_split_clause,[],[f3417,f3243,f1677,f4251]) ).
tff(f4251,plain,
( spl17_370
<=> ! [X0: nat] : ( hAPP_n1699378549t_bool(ord_less_eq_nat,X0) = insert_nat(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_370])]) ).
tff(f1677,plain,
( spl17_10
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
tff(f3417,plain,
( ! [X0: nat] : ( hAPP_n1699378549t_bool(ord_less_eq_nat,X0) = insert_nat(X0,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)) )
| ~ spl17_10
| ~ spl17_272 ),
inference(resolution,[],[f3244,f1678]) ).
tff(f1678,plain,
( ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0))
| ~ spl17_10 ),
inference(avatar_component_clause,[],[f1677]) ).
tff(f4128,plain,
spl17_369,
inference(avatar_split_clause,[],[f1558,f4126]) ).
tff(f4126,plain,
( spl17_369
<=> ! [X0: fun_a_bool,X3: fun_pname_bool,X2: fun_pname_bool,X1: fun_pname_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ( image_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_369])]) ).
tff(f1558,plain,
! [X2: fun_pname_bool,X3: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ( image_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(cnf_transformation,[],[f1104]) ).
tff(f1104,plain,
! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ! [X3: fun_pname_bool] :
( ( image_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) )
& ( ( ( image_pname_a(X1,sK16(X0,X1,X2)) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK16(X0,X1,X2)),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f1102,f1103]) ).
tff(f1103,plain,
! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
( ? [X4: fun_pname_bool] :
( ( image_pname_a(X1,X4) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X2)) )
=> ( ( image_pname_a(X1,sK16(X0,X1,X2)) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK16(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1102,plain,
! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ! [X3: fun_pname_bool] :
( ( image_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) )
& ( ? [X4: fun_pname_bool] :
( ( image_pname_a(X1,X4) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
inference(rectify,[],[f1101]) ).
tff(f1101,plain,
! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ! [X3: fun_pname_bool] :
( ( image_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) )
& ( ? [X3: fun_pname_bool] :
( ( image_pname_a(X1,X3) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
inference(nnf_transformation,[],[f725]) ).
tff(f725,plain,
! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
<=> ? [X3: fun_pname_bool] :
( ( image_pname_a(X1,X3) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) ),
inference(rectify,[],[f287]) ).
tff(f287,axiom,
! [X7: fun_a_bool,X6: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_pname_a(X6,X2)))
<=> ? [X35: fun_pname_bool] :
( ( image_pname_a(X6,X35) = X7 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X35),X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_286_subset__image__iff) ).
tff(f4124,plain,
spl17_368,
inference(avatar_split_clause,[],[f1552,f4122]) ).
tff(f4122,plain,
( spl17_368
<=> ! [X0: x_a,X3: pname,X2: fun_pname_bool,X1: fun_pname_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ( hAPP_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_368])]) ).
tff(f1552,plain,
! [X2: fun_pname_bool,X3: pname,X0: x_a,X1: fun_pname_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ( hAPP_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ),
inference(cnf_transformation,[],[f1098]) ).
tff(f1098,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ! [X3: pname] :
( ( hAPP_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) )
& ( ( ( hAPP_pname_a(X1,sK15(X0,X1,X2)) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK15(X0,X1,X2)),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f1096,f1097]) ).
tff(f1097,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( ? [X4: pname] :
( ( hAPP_pname_a(X1,X4) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X2)) )
=> ( ( hAPP_pname_a(X1,sK15(X0,X1,X2)) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK15(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1096,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ! [X3: pname] :
( ( hAPP_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) )
& ( ? [X4: pname] :
( ( hAPP_pname_a(X1,X4) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
inference(rectify,[],[f1095]) ).
tff(f1095,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
| ! [X3: pname] :
( ( hAPP_pname_a(X1,X3) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) )
& ( ? [X3: pname] :
( ( hAPP_pname_a(X1,X3) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
inference(nnf_transformation,[],[f723]) ).
tff(f723,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
<=> ? [X3: pname] :
( ( hAPP_pname_a(X1,X3) = X0 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) ),
inference(rectify,[],[f261]) ).
tff(f261,axiom,
! [X32: x_a,X6: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),image_pname_a(X6,X2)))
<=> ? [X27: pname] :
( ( hAPP_pname_a(X6,X27) = X32 )
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_260_image__iff) ).
tff(f4120,plain,
spl17_367,
inference(avatar_split_clause,[],[f1534,f4118]) ).
tff(f4118,plain,
( spl17_367
<=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK14(X0,X1,X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_367])]) ).
tff(f1534,plain,
! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK14(X0,X1,X2))),X1)) ),
inference(cnf_transformation,[],[f1084]) ).
tff(f1084,plain,
! [X0: fun_pname_a,X1: fun_a_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK14(X0,X1,X2))),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK14(X0,X1,X2)),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f1009,f1083]) ).
tff(f1083,plain,
! [X0: fun_pname_a,X1: fun_a_bool,X2: fun_pname_bool] :
( ? [X3: pname] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK14(X0,X1,X2))),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK14(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1009,plain,
! [X0: fun_pname_a,X1: fun_a_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| ? [X3: pname] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) ),
inference(ennf_transformation,[],[f717]) ).
tff(f717,plain,
! [X0: fun_pname_a,X1: fun_a_bool,X2: fun_pname_bool] :
( ! [X3: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) ),
inference(rectify,[],[f295]) ).
tff(f295,axiom,
! [X6: fun_pname_a,X7: fun_a_bool,X2: fun_pname_bool] :
( ! [X27: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X6,X27)),X7)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X6,X2)),X7)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_294_image__subsetI) ).
tff(f4116,plain,
spl17_366,
inference(avatar_split_clause,[],[f1466,f4114]) ).
tff(f4114,plain,
( spl17_366
<=> ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK7(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_366])]) ).
tff(f1466,plain,
! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK7(X0,X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(cnf_transformation,[],[f1062]) ).
tff(f4112,plain,
spl17_365,
inference(avatar_split_clause,[],[f1464,f4110]) ).
tff(f4110,plain,
( spl17_365
<=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),hAPP_nat_nat(suc,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_365])]) ).
tff(f1464,plain,
! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),hAPP_nat_nat(suc,X2)) ),
inference(cnf_transformation,[],[f663]) ).
tff(f663,plain,
! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),X1)),hAPP_nat_nat(suc,X2)) ),
inference(rectify,[],[f161]) ).
tff(f161,axiom,
! [X12: nat,X11: nat,X19: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X12)),X11)),hAPP_nat_nat(suc,X19)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X12),X11)),X19) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_160_Suc__diff__diff) ).
tff(f4108,plain,
spl17_364,
inference(avatar_split_clause,[],[f1415,f4106]) ).
tff(f4106,plain,
( spl17_364
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_364])]) ).
tff(f1415,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ),
inference(cnf_transformation,[],[f1057]) ).
tff(f1057,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f1056]) ).
tff(f1056,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f617]) ).
tff(f617,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
inference(rectify,[],[f135]) ).
tff(f135,axiom,
! [X10: fun_a_bool,X9: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X10),X9))))
<=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X9)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X10))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_134_finite__Collect__disjI) ).
tff(f4099,plain,
spl17_363,
inference(avatar_split_clause,[],[f1346,f4097]) ).
tff(f4097,plain,
( spl17_363
<=> ! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,X1) = X0 )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_363])]) ).
tff(f1346,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,X1) = X0 )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(cnf_transformation,[],[f912]) ).
tff(f912,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,X1) = X0 )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(flattening,[],[f911]) ).
tff(f911,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,X1) = X0 )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(ennf_transformation,[],[f586]) ).
tff(f586,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> ( hAPP_nat_nat(suc,X1) = X0 ) ) ),
inference(rectify,[],[f155]) ).
tff(f155,axiom,
! [X12: nat,X11: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_nat_nat(suc,X11)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
=> ( hAPP_nat_nat(suc,X11) = X12 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_154_le__SucE) ).
tff(f4095,plain,
spl17_362,
inference(avatar_split_clause,[],[f1333,f4093]) ).
tff(f4093,plain,
( spl17_362
<=> ! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X0)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_362])]) ).
tff(f1333,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X0)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f891]) ).
tff(f891,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X0)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f574]) ).
tff(f574,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X0)) ) ),
inference(rectify,[],[f117]) ).
tff(f117,axiom,
! [X11: nat,X12: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X12))
=> ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X12)),X11) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X12),X11)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_116_Suc__diff__le) ).
tff(f4091,plain,
spl17_361,
inference(avatar_split_clause,[],[f1322,f4089]) ).
tff(f4089,plain,
( spl17_361
<=> ! [X0: pname,X1: fun_pname_bool] :
( ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_361])]) ).
tff(f1322,plain,
! [X0: pname,X1: fun_pname_bool] :
( ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f874]) ).
tff(f4087,plain,
spl17_360,
inference(avatar_split_clause,[],[f1299,f4085]) ).
tff(f4085,plain,
( spl17_360
<=> ! [X0: x_a,X1: fun_a_bool] :
( ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_360])]) ).
tff(f1299,plain,
! [X0: x_a,X1: fun_a_bool] :
( ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f848]) ).
tff(f4083,plain,
spl17_359,
inference(avatar_split_clause,[],[f1285,f4081]) ).
tff(f4081,plain,
( spl17_359
<=> ! [X0: nat,X1: fun_nat_bool] :
( ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_359])]) ).
tff(f1285,plain,
! [X0: nat,X1: fun_nat_bool] :
( ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)) )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f831]) ).
tff(f4079,plain,
spl17_358,
inference(avatar_split_clause,[],[f1256,f4077]) ).
tff(f4077,plain,
( spl17_358
<=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_358])]) ).
tff(f1256,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)) )
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f791]) ).
tff(f4075,plain,
spl17_357,
inference(avatar_split_clause,[],[f1254,f4073]) ).
tff(f4073,plain,
( spl17_357
<=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_357])]) ).
tff(f1254,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)) )
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f790]) ).
tff(f4071,plain,
spl17_356,
inference(avatar_split_clause,[],[f1252,f4069]) ).
tff(f4069,plain,
( spl17_356
<=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_356])]) ).
tff(f1252,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)) )
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f789]) ).
tff(f4057,plain,
( spl17_355
| ~ spl17_231
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3645,f3583,f2888,f4055]) ).
tff(f4055,plain,
( spl17_355
<=> ! [X18: pname,X17: pname] : hBOOL(hAPP_pname_bool(insert_pname(X18,insert_pname(X17,u)),pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_355])]) ).
tff(f2888,plain,
( spl17_231
<=> ! [X2: pname,X3: pname,X4: fun_pname_bool] : hBOOL(hAPP_pname_bool(insert_pname(X3,insert_pname(X2,X4)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_231])]) ).
tff(f3583,plain,
( spl17_332
<=> ! [X1: pname] : ( insert_pname(X1,u) = insert_pname(pn,insert_pname(X1,u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_332])]) ).
tff(f3645,plain,
( ! [X18: pname,X17: pname] : hBOOL(hAPP_pname_bool(insert_pname(X18,insert_pname(X17,u)),pn))
| ~ spl17_231
| ~ spl17_332 ),
inference(superposition,[],[f2889,f3584]) ).
tff(f3584,plain,
( ! [X1: pname] : ( insert_pname(X1,u) = insert_pname(pn,insert_pname(X1,u)) )
| ~ spl17_332 ),
inference(avatar_component_clause,[],[f3583]) ).
tff(f2889,plain,
( ! [X2: pname,X3: pname,X4: fun_pname_bool] : hBOOL(hAPP_pname_bool(insert_pname(X3,insert_pname(X2,X4)),X2))
| ~ spl17_231 ),
inference(avatar_component_clause,[],[f2888]) ).
tff(f3915,plain,
spl17_354,
inference(avatar_split_clause,[],[f1517,f3913]) ).
tff(f3913,plain,
( spl17_354
<=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_354])]) ).
tff(f1517,plain,
! [X2: fun_pname_bool,X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f990]) ).
tff(f990,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(flattening,[],[f989]) ).
tff(f989,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f705]) ).
tff(f705,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) ) ),
inference(rectify,[],[f248]) ).
tff(f248,axiom,
! [X31: fun_pname_bool,X2: fun_pname_bool,X7: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),X31))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X31)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_247_subset__trans) ).
tff(f3911,plain,
( spl17_353
| ~ spl17_24
| ~ spl17_332 ),
inference(avatar_split_clause,[],[f3635,f3583,f1736,f3909]) ).
tff(f3909,plain,
( spl17_353
<=> ! [X3: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),insert_pname(X3,u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_353])]) ).
tff(f1736,plain,
( spl17_24
<=> ! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).
tff(f3635,plain,
( ! [X3: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),insert_pname(X3,u)))
| ~ spl17_24
| ~ spl17_332 ),
inference(superposition,[],[f1737,f3584]) ).
tff(f1737,plain,
( ! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X0,X1)))
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f1736]) ).
tff(f3907,plain,
spl17_352,
inference(avatar_split_clause,[],[f1510,f3905]) ).
tff(f3905,plain,
( spl17_352
<=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_352])]) ).
tff(f1510,plain,
! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f979]) ).
tff(f979,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(flattening,[],[f978]) ).
tff(f978,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f698]) ).
tff(f698,plain,
! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) ),
inference(rectify,[],[f243]) ).
tff(f243,axiom,
! [X7: fun_pname_bool,X8: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_242_set__rev__mp) ).
tff(f3903,plain,
spl17_351,
inference(avatar_split_clause,[],[f1506,f3901]) ).
tff(f3901,plain,
( spl17_351
<=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_351])]) ).
tff(f1506,plain,
! [X2: fun_a_bool,X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f974]) ).
tff(f974,plain,
! [X0: fun_a_bool,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(flattening,[],[f973]) ).
tff(f973,plain,
! [X0: fun_a_bool,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f694]) ).
tff(f694,plain,
! [X0: fun_a_bool,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ) ),
inference(rectify,[],[f249]) ).
tff(f249,axiom,
! [X31: fun_a_bool,X2: fun_a_bool,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),X31))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X31)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_248_subset__trans) ).
tff(f3899,plain,
spl17_350,
inference(avatar_split_clause,[],[f1500,f3897]) ).
tff(f3897,plain,
( spl17_350
<=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_350])]) ).
tff(f1500,plain,
! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f964]) ).
tff(f964,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(flattening,[],[f963]) ).
tff(f963,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f688]) ).
tff(f688,plain,
! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ),
inference(rectify,[],[f242]) ).
tff(f242,axiom,
! [X7: fun_a_bool,X8: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_241_set__rev__mp) ).
tff(f3895,plain,
spl17_349,
inference(avatar_split_clause,[],[f1498,f3893]) ).
tff(f3893,plain,
( spl17_349
<=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_349])]) ).
tff(f1498,plain,
! [X2: fun_nat_bool,X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f961]) ).
tff(f961,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(flattening,[],[f960]) ).
tff(f960,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f686]) ).
tff(f686,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) ) ),
inference(rectify,[],[f247]) ).
tff(f247,axiom,
! [X31: fun_nat_bool,X2: fun_nat_bool,X7: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),X31))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X31)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_246_subset__trans) ).
tff(f3891,plain,
spl17_348,
inference(avatar_split_clause,[],[f1492,f3889]) ).
tff(f3889,plain,
( spl17_348
<=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_348])]) ).
tff(f1492,plain,
! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f951]) ).
tff(f951,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(flattening,[],[f950]) ).
tff(f950,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f680]) ).
tff(f680,plain,
! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ),
inference(rectify,[],[f241]) ).
tff(f241,axiom,
! [X7: fun_nat_bool,X8: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_240_set__rev__mp) ).
tff(f3887,plain,
spl17_347,
inference(avatar_split_clause,[],[f1485,f3885]) ).
tff(f3885,plain,
( spl17_347
<=> ! [X2: nat,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_347])]) ).
tff(f1485,plain,
! [X2: nat,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f942]) ).
tff(f942,plain,
! [X0: nat,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(flattening,[],[f941]) ).
tff(f941,plain,
! [X0: nat,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f675]) ).
tff(f675,plain,
! [X0: nat,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ) ),
inference(rectify,[],[f125]) ).
tff(f125,axiom,
! [X19: nat,X20: nat,X21: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),X21))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),X19)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_124_le__trans) ).
tff(f3883,plain,
spl17_346,
inference(avatar_split_clause,[],[f1484,f3881]) ).
tff(f3881,plain,
( spl17_346
<=> ! [X2: nat,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_346])]) ).
tff(f1484,plain,
! [X2: nat,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f940]) ).
tff(f940,plain,
! [X0: nat,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f674]) ).
tff(f674,plain,
! [X0: nat,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X0)),hAPP_nat_nat(minus_minus_nat(X2),X0))) ),
inference(rectify,[],[f167]) ).
tff(f167,axiom,
! [X23: nat,X12: nat,X11: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X12),X23)),hAPP_nat_nat(minus_minus_nat(X11),X23))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_166_diff__le__mono) ).
tff(f3879,plain,
spl17_345,
inference(avatar_split_clause,[],[f1483,f3877]) ).
tff(f3877,plain,
( spl17_345
<=> ! [X2: nat,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_345])]) ).
tff(f1483,plain,
! [X2: nat,X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(cnf_transformation,[],[f939]) ).
tff(f939,plain,
! [X0: nat,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(ennf_transformation,[],[f673]) ).
tff(f673,plain,
! [X0: nat,X1: nat,X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X2)),hAPP_nat_nat(minus_minus_nat(X0),X1))) ),
inference(rectify,[],[f168]) ).
tff(f168,axiom,
! [X23: nat,X12: nat,X11: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X23),X11)),hAPP_nat_nat(minus_minus_nat(X23),X12))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_167_diff__le__mono2) ).
tff(f3875,plain,
spl17_344,
inference(avatar_split_clause,[],[f1469,f3873]) ).
tff(f3873,plain,
( spl17_344
<=> ! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK8(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_344])]) ).
tff(f1469,plain,
! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK8(X1))))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f1064]) ).
tff(f1064,plain,
! [X0: nat,X1: fun_nat_bool,X2: nat] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ( ~ hBOOL(hAPP_nat_bool(X1,sK8(X1)))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK8(X1)))) )
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f929,f1063]) ).
tff(f1063,plain,
! [X1: fun_nat_bool] :
( ? [X3: nat] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
=> ( ~ hBOOL(hAPP_nat_bool(X1,sK8(X1)))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK8(X1)))) ) ),
introduced(choice_axiom,[]) ).
tff(f929,plain,
! [X0: nat,X1: fun_nat_bool,X2: nat] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ? [X3: nat] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(flattening,[],[f928]) ).
tff(f928,plain,
! [X0: nat,X1: fun_nat_bool,X2: nat] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ? [X3: nat] :
( ~ hBOOL(hAPP_nat_bool(X1,X3))
& hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(ennf_transformation,[],[f666]) ).
tff(f666,plain,
! [X0: nat,X1: fun_nat_bool,X2: nat] :
( hBOOL(hAPP_nat_bool(X1,X2))
=> ( ! [X3: nat] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3)))
=> hBOOL(hAPP_nat_bool(X1,X3)) )
=> hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0))) ) ),
inference(rectify,[],[f293]) ).
tff(f293,axiom,
! [X36: nat,X10: fun_nat_bool,X13: nat] :
( hBOOL(hAPP_nat_bool(X10,X13))
=> ( ! [X26: nat] :
( hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(suc,X26)))
=> hBOOL(hAPP_nat_bool(X10,X26)) )
=> hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(minus_minus_nat(X13),X36))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_292_zero__induct__lemma) ).
tff(f3871,plain,
spl17_343,
inference(avatar_split_clause,[],[f1214,f3869]) ).
tff(f3869,plain,
( spl17_343
<=> ! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(X0,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_343])]) ).
tff(f1214,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(X0,X1)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f1020]) ).
tff(f1020,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,sK2(X0,X1)))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(X0,X1)),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f752,f1019]) ).
tff(f1019,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( ? [X2: pname] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,sK2(X0,X1)))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK2(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f752,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( ? [X2: pname] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(flattening,[],[f751]) ).
tff(f751,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( ? [X2: pname] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f462]) ).
tff(f462,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
=> ? [X2: pname] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) ) ),
inference(rectify,[],[f176]) ).
tff(f176,axiom,
! [X6: fun_pname_a,X2: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X6,X2)))
=> ? [X27: pname] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X6)),hAPP_pname_a(X6,X27))))))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_175_pigeonhole__infinite) ).
tff(f3810,plain,
spl17_342,
inference(avatar_split_clause,[],[f1556,f3808]) ).
tff(f3808,plain,
( spl17_342
<=> ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK16(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_342])]) ).
tff(f1556,plain,
! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK16(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ),
inference(cnf_transformation,[],[f1104]) ).
tff(f3806,plain,
spl17_341,
inference(avatar_split_clause,[],[f1550,f3804]) ).
tff(f3804,plain,
( spl17_341
<=> ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK15(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_341])]) ).
tff(f1550,plain,
! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK15(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
inference(cnf_transformation,[],[f1098]) ).
tff(f3802,plain,
( spl17_340
| ~ spl17_18
| ~ spl17_326 ),
inference(avatar_split_clause,[],[f3763,f3487,f1711,f3799]) ).
tff(f3799,plain,
( spl17_340
<=> ( g = image_pname_a(mgt_call,sK16(g,mgt_call,u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_340])]) ).
tff(f3487,plain,
( spl17_326
<=> ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( ( image_pname_a(X1,sK16(X0,X1,X2)) = X0 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_326])]) ).
tff(f3763,plain,
( ( g = image_pname_a(mgt_call,sK16(g,mgt_call,u)) )
| ~ spl17_18
| ~ spl17_326 ),
inference(resolution,[],[f3488,f1713]) ).
tff(f1713,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f1711]) ).
tff(f3488,plain,
( ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ( image_pname_a(X1,sK16(X0,X1,X2)) = X0 ) )
| ~ spl17_326 ),
inference(avatar_component_clause,[],[f3487]) ).
tff(f3797,plain,
spl17_339,
inference(avatar_split_clause,[],[f1533,f3795]) ).
tff(f3795,plain,
( spl17_339
<=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK14(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_339])]) ).
tff(f1533,plain,
! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK14(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f1084]) ).
tff(f3793,plain,
spl17_338,
inference(avatar_split_clause,[],[f1522,f3791]) ).
tff(f3791,plain,
( spl17_338
<=> ! [X2: fun_pname_bool,X0: pname,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_338])]) ).
tff(f1522,plain,
! [X2: fun_pname_bool,X0: pname,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2))) ),
inference(cnf_transformation,[],[f997]) ).
tff(f997,plain,
! [X0: pname,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2))) ),
inference(flattening,[],[f996]) ).
tff(f996,plain,
! [X0: pname,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2))) ),
inference(ennf_transformation,[],[f709]) ).
tff(f709,plain,
! [X0: pname,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X1,X2)))
=> ( ( X0 != X1 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
inference(rectify,[],[f188]) ).
tff(f188,axiom,
! [X5: pname,X28: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),insert_pname(X28,X2)))
=> ( ( X5 != X28 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_187_insertE) ).
tff(f3789,plain,
spl17_337,
inference(avatar_split_clause,[],[f1521,f3787]) ).
tff(f3787,plain,
( spl17_337
<=> ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_337])]) ).
tff(f1521,plain,
! [X2: fun_a_bool,X0: x_a,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2))) ),
inference(cnf_transformation,[],[f995]) ).
tff(f995,plain,
! [X0: x_a,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2))) ),
inference(flattening,[],[f994]) ).
tff(f994,plain,
! [X0: x_a,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2))) ),
inference(ennf_transformation,[],[f708]) ).
tff(f708,plain,
! [X0: x_a,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X1,X2)))
=> ( ( X0 != X1 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
inference(rectify,[],[f189]) ).
tff(f189,axiom,
! [X5: x_a,X28: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),insert_a(X28,X2)))
=> ( ( X5 != X28 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_188_insertE) ).
tff(f3785,plain,
spl17_336,
inference(avatar_split_clause,[],[f1520,f3783]) ).
tff(f3783,plain,
( spl17_336
<=> ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK9(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_336])]) ).
tff(f1520,plain,
! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK9(X0,X1,X2)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
inference(cnf_transformation,[],[f1074]) ).
tff(f1074,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK9(X0,X1,X2)),X2))
& ( hAPP_pname_a(X1,sK9(X0,X1,X2)) = X0 ) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f993,f1073]) ).
tff(f1073,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( ? [X3: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& ( hAPP_pname_a(X1,X3) = X0 ) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK9(X0,X1,X2)),X2))
& ( hAPP_pname_a(X1,sK9(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f993,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( ? [X3: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
& ( hAPP_pname_a(X1,X3) = X0 ) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
inference(ennf_transformation,[],[f707]) ).
tff(f707,plain,
! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
=> ~ ! [X3: pname] :
( ( hAPP_pname_a(X1,X3) = X0 )
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) ),
inference(rectify,[],[f289]) ).
tff(f289,axiom,
! [X28: x_a,X6: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X28),image_pname_a(X6,X2)))
=> ~ ! [X27: pname] :
( ( hAPP_pname_a(X6,X27) = X28 )
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_288_imageE) ).
tff(f3781,plain,
spl17_335,
inference(avatar_split_clause,[],[f1518,f3779]) ).
tff(f3779,plain,
( spl17_335
<=> ! [X2: fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_335])]) ).
tff(f1518,plain,
! [X2: fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X1,X2))) ),
inference(cnf_transformation,[],[f992]) ).
tff(f992,plain,
! [X0: nat,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X1,X2))) ),
inference(flattening,[],[f991]) ).
tff(f991,plain,
! [X0: nat,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X1,X2))) ),
inference(ennf_transformation,[],[f706]) ).
tff(f706,plain,
! [X0: nat,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X1,X2)))
=> ( ( X0 != X1 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
inference(rectify,[],[f187]) ).
tff(f187,axiom,
! [X5: nat,X28: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),insert_nat(X28,X2)))
=> ( ( X5 != X28 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_186_insertE) ).
tff(f3777,plain,
spl17_334,
inference(avatar_split_clause,[],[f1147,f3775]) ).
tff(f3775,plain,
( spl17_334
<=> ! [X4: nat,X0: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK1(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_334])]) ).
tff(f1147,plain,
! [X0: fun_nat_bool,X4: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK1(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(cnf_transformation,[],[f1018]) ).
tff(f1018,plain,
! [X0: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0)) ) )
& ( ! [X4: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK1(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f1015,f1017,f1016]) ).
tff(f1016,plain,
! [X0: fun_nat_bool,X1: nat] :
( ? [X2: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,X1)),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1017,plain,
! [X0: fun_nat_bool] :
( ? [X3: nat] :
! [X4: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
=> ! [X4: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK1(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1015,plain,
! [X0: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1: nat] :
? [X2: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
& ( ? [X3: nat] :
! [X4: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f1014]) ).
tff(f1014,plain,
! [X0: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ! [X1: nat] :
? [X2: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
& ( ? [X1: nat] :
! [X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(nnf_transformation,[],[f740]) ).
tff(f740,plain,
! [X0: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
<=> ? [X1: nat] :
! [X2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
inference(ennf_transformation,[],[f400]) ).
tff(f400,plain,
! [X0: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
<=> ? [X1: nat] :
! [X2: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ),
inference(rectify,[],[f300]) ).
tff(f300,axiom,
! [X40: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X40))
<=> ? [X38: nat] :
! [X27: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X40))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X38)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_299_finite__nat__set__iff__bounded__le) ).
tff(f3697,plain,
( ~ spl17_2
| spl17_333
| ~ spl17_18
| ~ spl17_317 ),
inference(avatar_split_clause,[],[f3692,f3445,f1711,f3694,f1643]) ).
tff(f1643,plain,
( spl17_2
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
tff(f3694,plain,
( spl17_333
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_333])]) ).
tff(f3445,plain,
( spl17_317
<=> ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_317])]) ).
tff(f3692,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
| ~ spl17_18
| ~ spl17_317 ),
inference(resolution,[],[f3446,f1713]) ).
tff(f3446,plain,
( ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) )
| ~ spl17_317 ),
inference(avatar_component_clause,[],[f3445]) ).
tff(f3585,plain,
( spl17_332
| ~ spl17_145
| ~ spl17_157 ),
inference(avatar_split_clause,[],[f2479,f2348,f2279,f3583]) ).
tff(f2279,plain,
( spl17_145
<=> ! [X2: fun_pname_bool,X0: pname,X1: pname] : ( insert_pname(X0,insert_pname(X1,X2)) = insert_pname(X1,insert_pname(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_145])]) ).
tff(f2348,plain,
( spl17_157
<=> ( u = insert_pname(pn,u) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_157])]) ).
tff(f2479,plain,
( ! [X1: pname] : ( insert_pname(X1,u) = insert_pname(pn,insert_pname(X1,u)) )
| ~ spl17_145
| ~ spl17_157 ),
inference(superposition,[],[f2280,f2350]) ).
tff(f2350,plain,
( ( u = insert_pname(pn,u) )
| ~ spl17_157 ),
inference(avatar_component_clause,[],[f2348]) ).
tff(f2280,plain,
( ! [X2: fun_pname_bool,X0: pname,X1: pname] : ( insert_pname(X0,insert_pname(X1,X2)) = insert_pname(X1,insert_pname(X0,X2)) )
| ~ spl17_145 ),
inference(avatar_component_clause,[],[f2279]) ).
tff(f3509,plain,
spl17_331,
inference(avatar_split_clause,[],[f1631,f3507]) ).
tff(f3507,plain,
( spl17_331
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_331])]) ).
tff(f1631,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))) ),
inference(forward_demodulation,[],[f1630,f1118]) ).
tff(f1118,plain,
! [X0: fun_pname_bool] : ( collect_pname(X0) = X0 ),
inference(cnf_transformation,[],[f371]) ).
tff(f371,plain,
! [X0: fun_pname_bool] : ( collect_pname(X0) = X0 ),
inference(rectify,[],[f256]) ).
tff(f256,axiom,
! [X10: fun_pname_bool] : ( collect_pname(X10) = X10 ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_255_Collect__def) ).
tff(f1630,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
inference(forward_demodulation,[],[f1629,f1118]) ).
tff(f1629,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
inference(forward_demodulation,[],[f1418,f1118]) ).
tff(f1418,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
inference(cnf_transformation,[],[f1059]) ).
tff(f1059,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
& ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f1058]) ).
tff(f1058,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
& ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f618]) ).
tff(f618,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ) ),
inference(rectify,[],[f130]) ).
tff(f130,axiom,
! [X10: fun_pname_bool,X9: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X10),X9))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X9)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X10))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_129_finite__Collect__disjI) ).
tff(f3505,plain,
spl17_330,
inference(avatar_split_clause,[],[f1624,f3503]) ).
tff(f3503,plain,
( spl17_330
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_330])]) ).
tff(f1624,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))) ),
inference(forward_demodulation,[],[f1623,f1122]) ).
tff(f1122,plain,
! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 ),
inference(cnf_transformation,[],[f375]) ).
tff(f375,plain,
! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 ),
inference(rectify,[],[f260]) ).
tff(f260,axiom,
! [X10: fun_nat_bool] : ( collect_nat(X10) = X10 ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_259_Collect__def) ).
tff(f1623,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(forward_demodulation,[],[f1622,f1122]) ).
tff(f1622,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(forward_demodulation,[],[f1412,f1122]) ).
tff(f1412,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(cnf_transformation,[],[f1055]) ).
tff(f1055,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
& ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f1054]) ).
tff(f1054,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
& ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f616]) ).
tff(f616,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ) ),
inference(rectify,[],[f134]) ).
tff(f134,axiom,
! [X10: fun_nat_bool,X9: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X10),X9))))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X9)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X10))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_133_finite__Collect__disjI) ).
tff(f3501,plain,
spl17_329,
inference(avatar_split_clause,[],[f1617,f3499]) ).
tff(f3499,plain,
( spl17_329
<=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_329])]) ).
tff(f1617,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))) ),
inference(forward_demodulation,[],[f1616,f1121]) ).
tff(f1121,plain,
! [X0: fun_fu425979586l_bool] : ( collect_fun_nat_bool(X0) = X0 ),
inference(cnf_transformation,[],[f374]) ).
tff(f374,plain,
! [X0: fun_fu425979586l_bool] : ( collect_fun_nat_bool(X0) = X0 ),
inference(rectify,[],[f257]) ).
tff(f257,axiom,
! [X10: fun_fu425979586l_bool] : ( collect_fun_nat_bool(X10) = X10 ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_256_Collect__def) ).
tff(f1616,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(forward_demodulation,[],[f1615,f1121]) ).
tff(f1615,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(forward_demodulation,[],[f1409,f1121]) ).
tff(f1409,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(cnf_transformation,[],[f1053]) ).
tff(f1053,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
& ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f1052]) ).
tff(f1052,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
& ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f615]) ).
tff(f615,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ) ),
inference(rectify,[],[f131]) ).
tff(f131,axiom,
! [X10: fun_fu425979586l_bool,X9: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X10),X9))))
<=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X9)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X10))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_130_finite__Collect__disjI) ).
tff(f3497,plain,
spl17_328,
inference(avatar_split_clause,[],[f1610,f3495]) ).
tff(f3495,plain,
( spl17_328
<=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_328])]) ).
tff(f1610,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))) ),
inference(forward_demodulation,[],[f1609,f1120]) ).
tff(f1120,plain,
! [X0: fun_fun_a_bool_bool] : ( collect_fun_a_bool(X0) = X0 ),
inference(cnf_transformation,[],[f373]) ).
tff(f373,plain,
! [X0: fun_fun_a_bool_bool] : ( collect_fun_a_bool(X0) = X0 ),
inference(rectify,[],[f259]) ).
tff(f259,axiom,
! [X10: fun_fun_a_bool_bool] : ( collect_fun_a_bool(X10) = X10 ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_258_Collect__def) ).
tff(f1609,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
inference(forward_demodulation,[],[f1608,f1120]) ).
tff(f1608,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
inference(forward_demodulation,[],[f1406,f1120]) ).
tff(f1406,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
inference(cnf_transformation,[],[f1051]) ).
tff(f1051,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
& ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f1050]) ).
tff(f1050,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
& ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f614]) ).
tff(f614,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ) ),
inference(rectify,[],[f133]) ).
tff(f133,axiom,
! [X10: fun_fun_a_bool_bool,X9: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X10),X9))))
<=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X9)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X10))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_132_finite__Collect__disjI) ).
tff(f3493,plain,
spl17_327,
inference(avatar_split_clause,[],[f1603,f3491]) ).
tff(f3491,plain,
( spl17_327
<=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_327])]) ).
tff(f1603,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))) ),
inference(forward_demodulation,[],[f1602,f1119]) ).
tff(f1119,plain,
! [X0: fun_fu1430349052l_bool] : ( collec1974731493e_bool(X0) = X0 ),
inference(cnf_transformation,[],[f372]) ).
tff(f372,plain,
! [X0: fun_fu1430349052l_bool] : ( collec1974731493e_bool(X0) = X0 ),
inference(rectify,[],[f258]) ).
tff(f258,axiom,
! [X10: fun_fu1430349052l_bool] : ( collec1974731493e_bool(X10) = X10 ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_257_Collect__def) ).
tff(f1602,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
inference(forward_demodulation,[],[f1601,f1119]) ).
tff(f1601,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
inference(forward_demodulation,[],[f1403,f1119]) ).
tff(f1403,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
inference(cnf_transformation,[],[f1049]) ).
tff(f1049,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
& ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
inference(flattening,[],[f1048]) ).
tff(f1048,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
& ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
inference(nnf_transformation,[],[f613]) ).
tff(f613,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ) ),
inference(rectify,[],[f132]) ).
tff(f132,axiom,
! [X10: fun_fu1430349052l_bool,X9: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X10),X9))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X9)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X10))) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_131_finite__Collect__disjI) ).
tff(f3489,plain,
spl17_326,
inference(avatar_split_clause,[],[f1557,f3487]) ).
tff(f1557,plain,
! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( ( image_pname_a(X1,sK16(X0,X1,X2)) = X0 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ),
inference(cnf_transformation,[],[f1104]) ).
tff(f3485,plain,
spl17_325,
inference(avatar_split_clause,[],[f1551,f3483]) ).
tff(f3483,plain,
( spl17_325
<=> ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( ( hAPP_pname_a(X1,sK15(X0,X1,X2)) = X0 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_325])]) ).
tff(f1551,plain,
! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( ( hAPP_pname_a(X1,sK15(X0,X1,X2)) = X0 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
inference(cnf_transformation,[],[f1098]) ).
tff(f3481,plain,
spl17_324,
inference(avatar_split_clause,[],[f1519,f3479]) ).
tff(f3479,plain,
( spl17_324
<=> ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( ( hAPP_pname_a(X1,sK9(X0,X1,X2)) = X0 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_324])]) ).
tff(f1519,plain,
! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( ( hAPP_pname_a(X1,sK9(X0,X1,X2)) = X0 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
inference(cnf_transformation,[],[f1074]) ).
tff(f3471,plain,
spl17_323,
inference(avatar_split_clause,[],[f1513,f3469]) ).
tff(f3469,plain,
( spl17_323
<=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_323])]) ).
tff(f1513,plain,
! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f982]) ).
tff(f982,plain,
! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f701]) ).
tff(f701,plain,
! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),insert_pname(X0,X2))) ),
inference(rectify,[],[f283]) ).
tff(f283,axiom,
! [X5: pname,X31: fun_pname_bool,X34: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X31),X34))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X5,X31)),insert_pname(X5,X34))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_282_insert__mono) ).
tff(f3467,plain,
spl17_322,
inference(avatar_split_clause,[],[f1512,f3465]) ).
tff(f3465,plain,
( spl17_322
<=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_322])]) ).
tff(f1512,plain,
! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f981]) ).
tff(f981,plain,
! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f700]) ).
tff(f700,plain,
! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))) ),
inference(rectify,[],[f288]) ).
tff(f288,axiom,
! [X6: fun_pname_a,X2: fun_pname_bool,X7: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X6,X2)),image_pname_a(X6,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_287_image__mono) ).
tff(f3463,plain,
spl17_321,
inference(avatar_split_clause,[],[f1508,f3461]) ).
tff(f1508,plain,
! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f976]) ).
tff(f976,plain,
! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f696]) ).
tff(f696,plain,
! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2))) ),
inference(rectify,[],[f262]) ).
tff(f262,axiom,
! [X6: fun_pname_a,X8: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X6,X8)),image_pname_a(X6,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_261_imageI) ).
tff(f3459,plain,
spl17_320,
inference(avatar_split_clause,[],[f1502,f3457]) ).
tff(f3457,plain,
( spl17_320
<=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_320])]) ).
tff(f1502,plain,
! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f966]) ).
tff(f966,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f690]) ).
tff(f690,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),insert_a(X0,X2))) ),
inference(rectify,[],[f284]) ).
tff(f284,axiom,
! [X5: x_a,X31: fun_a_bool,X34: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X31),X34))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X5,X31)),insert_a(X5,X34))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_283_insert__mono) ).
tff(f3455,plain,
spl17_319,
inference(avatar_split_clause,[],[f1494,f3453]) ).
tff(f3453,plain,
( spl17_319
<=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_319])]) ).
tff(f1494,plain,
! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f953]) ).
tff(f953,plain,
! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f682]) ).
tff(f682,plain,
! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),insert_nat(X0,X2))) ),
inference(rectify,[],[f282]) ).
tff(f282,axiom,
! [X5: nat,X31: fun_nat_bool,X34: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X31),X34))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X5,X31)),insert_nat(X5,X34))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_281_insert__mono) ).
tff(f3451,plain,
spl17_318,
inference(avatar_split_clause,[],[f1470,f3449]) ).
tff(f3449,plain,
( spl17_318
<=> ! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(X1,sK8(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_318])]) ).
tff(f1470,plain,
! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X2),X0)))
| ~ hBOOL(hAPP_nat_bool(X1,sK8(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f1064]) ).
tff(f3447,plain,
spl17_317,
inference(avatar_split_clause,[],[f1468,f3445]) ).
tff(f1468,plain,
! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(cnf_transformation,[],[f927]) ).
tff(f927,plain,
! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(flattening,[],[f926]) ).
tff(f926,plain,
! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(ennf_transformation,[],[f665]) ).
tff(f665,plain,
! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f170]) ).
tff(f170,axiom,
! [X7: fun_a_bool,X6: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_pname_a(X6,X2)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_169_finite__surj) ).
tff(f3443,plain,
spl17_316,
inference(avatar_split_clause,[],[f1420,f3441]) ).
tff(f3441,plain,
( spl17_316
<=> ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_316])]) ).
tff(f1420,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1060]) ).
tff(f1060,plain,
! [X0: nat,X1: nat] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ) ),
inference(nnf_transformation,[],[f619]) ).
tff(f619,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f157]) ).
tff(f157,axiom,
! [X14: nat,X22: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),hAPP_nat_nat(suc,X22)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X22)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_156_Suc__le__mono) ).
tff(f3439,plain,
spl17_315,
inference(avatar_split_clause,[],[f1419,f3437]) ).
tff(f3437,plain,
( spl17_315
<=> ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_315])]) ).
tff(f1419,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ),
inference(cnf_transformation,[],[f1060]) ).
tff(f3435,plain,
spl17_314,
inference(avatar_split_clause,[],[f1321,f3433]) ).
tff(f3433,plain,
( spl17_314
<=> ! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_314])]) ).
tff(f1321,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f873]) ).
tff(f873,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f563]) ).
tff(f563,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X6: fun_pname_a,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_61_card__image__le) ).
tff(f3416,plain,
spl17_313,
inference(avatar_split_clause,[],[f1320,f3414]) ).
tff(f3414,plain,
( spl17_313
<=> ! [X0: fun_pname_pname,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_313])]) ).
tff(f1320,plain,
! [X0: fun_pname_pname,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f872]) ).
tff(f872,plain,
! [X0: fun_pname_pname,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f562]) ).
tff(f562,plain,
! [X0: fun_pname_pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X6: fun_pname_pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_69_card__image__le) ).
tff(f3412,plain,
spl17_312,
inference(avatar_split_clause,[],[f1319,f3410]) ).
tff(f3410,plain,
( spl17_312
<=> ! [X0: fun_pname_nat,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_312])]) ).
tff(f1319,plain,
! [X0: fun_pname_nat,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f871]) ).
tff(f871,plain,
! [X0: fun_pname_nat,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f561]) ).
tff(f561,plain,
! [X0: fun_pname_nat,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X6: fun_pname_nat,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_54_card__image__le) ).
tff(f3408,plain,
spl17_311,
inference(avatar_split_clause,[],[f1318,f3406]) ).
tff(f3406,plain,
( spl17_311
<=> ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_311])]) ).
tff(f1318,plain,
! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f870]) ).
tff(f870,plain,
! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f560]) ).
tff(f560,plain,
! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X6: fun_pname_fun_a_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_72_card__image__le) ).
tff(f3404,plain,
spl17_310,
inference(avatar_split_clause,[],[f1317,f3402]) ).
tff(f3402,plain,
( spl17_310
<=> ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_310])]) ).
tff(f1317,plain,
! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f869]) ).
tff(f869,plain,
! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f559]) ).
tff(f559,plain,
! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X6: fun_pn800050071e_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_71_card__image__le) ).
tff(f3400,plain,
spl17_309,
inference(avatar_split_clause,[],[f1316,f3398]) ).
tff(f3398,plain,
( spl17_309
<=> ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_309])]) ).
tff(f1316,plain,
! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f868]) ).
tff(f868,plain,
! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f558]) ).
tff(f558,plain,
! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X6: fun_pn406123357t_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_70_card__image__le) ).
tff(f3396,plain,
spl17_308,
inference(avatar_split_clause,[],[f1315,f3394]) ).
tff(f3394,plain,
( spl17_308
<=> ! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_308])]) ).
tff(f1315,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f867]) ).
tff(f867,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f557]) ).
tff(f557,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X0,X1)))) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X8: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X8,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_95_card__insert__le) ).
tff(f3392,plain,
spl17_307,
inference(avatar_split_clause,[],[f1298,f3390]) ).
tff(f3390,plain,
( spl17_307
<=> ! [X0: fun_a_a,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_307])]) ).
tff(f1298,plain,
! [X0: fun_a_a,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f847]) ).
tff(f847,plain,
! [X0: fun_a_a,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f541]) ).
tff(f541,plain,
! [X0: fun_a_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X6: fun_a_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X6,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_68_card__image__le) ).
tff(f3388,plain,
spl17_306,
inference(avatar_split_clause,[],[f1297,f3386]) ).
tff(f3386,plain,
( spl17_306
<=> ! [X0: fun_a_pname,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_306])]) ).
tff(f1297,plain,
! [X0: fun_a_pname,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f846]) ).
tff(f846,plain,
! [X0: fun_a_pname,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f540]) ).
tff(f540,plain,
! [X0: fun_a_pname,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X6: fun_a_pname,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X6,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_59_card__image__le) ).
tff(f3384,plain,
spl17_305,
inference(avatar_split_clause,[],[f1296,f3382]) ).
tff(f3382,plain,
( spl17_305
<=> ! [X0: fun_a_nat,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_305])]) ).
tff(f1296,plain,
! [X0: fun_a_nat,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f845]) ).
tff(f845,plain,
! [X0: fun_a_nat,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f539]) ).
tff(f539,plain,
! [X0: fun_a_nat,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X6: fun_a_nat,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X6,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_55_card__image__le) ).
tff(f3380,plain,
spl17_304,
inference(avatar_split_clause,[],[f1295,f3378]) ).
tff(f3378,plain,
( spl17_304
<=> ! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_304])]) ).
tff(f1295,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f844]) ).
tff(f844,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f538]) ).
tff(f538,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X0,X1)))) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X8: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X8,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_97_card__insert__le) ).
tff(f3376,plain,
( spl17_303
| ~ spl17_10
| ~ spl17_260 ),
inference(avatar_split_clause,[],[f3197,f3135,f1677,f3374]) ).
tff(f3374,plain,
( spl17_303
<=> ! [X0: nat] : ( hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_303])]) ).
tff(f3135,plain,
( spl17_260
<=> ! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_260])]) ).
tff(f3197,plain,
( ! [X0: nat] : ( hAPP_nat_nat(minus_minus_nat(X0),hAPP_nat_nat(minus_minus_nat(X0),X0)) = X0 )
| ~ spl17_10
| ~ spl17_260 ),
inference(resolution,[],[f3136,f1678]) ).
tff(f3136,plain,
( ! [X0: nat,X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 ) )
| ~ spl17_260 ),
inference(avatar_component_clause,[],[f3135]) ).
tff(f3372,plain,
spl17_302,
inference(avatar_split_clause,[],[f1284,f3370]) ).
tff(f3370,plain,
( spl17_302
<=> ! [X0: fun_nat_a,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_302])]) ).
tff(f1284,plain,
! [X0: fun_nat_a,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f830]) ).
tff(f830,plain,
! [X0: fun_nat_a,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f528]) ).
tff(f528,plain,
! [X0: fun_nat_a,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X6: fun_nat_a,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X6,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_73_card__image__le) ).
tff(f3368,plain,
spl17_301,
inference(avatar_split_clause,[],[f1283,f3366]) ).
tff(f3366,plain,
( spl17_301
<=> ! [X0: fun_nat_pname,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_301])]) ).
tff(f1283,plain,
! [X0: fun_nat_pname,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f829]) ).
tff(f829,plain,
! [X0: fun_nat_pname,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f527]) ).
tff(f527,plain,
! [X0: fun_nat_pname,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X6: fun_nat_pname,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X6,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_60_card__image__le) ).
tff(f3364,plain,
spl17_300,
inference(avatar_split_clause,[],[f1282,f3362]) ).
tff(f3362,plain,
( spl17_300
<=> ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_300])]) ).
tff(f1282,plain,
! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f828]) ).
tff(f828,plain,
! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f526]) ).
tff(f526,plain,
! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X6: fun_nat_fun_a_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X6,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_76_card__image__le) ).
tff(f3360,plain,
spl17_299,
inference(avatar_split_clause,[],[f1281,f3358]) ).
tff(f3358,plain,
( spl17_299
<=> ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_299])]) ).
tff(f1281,plain,
! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f827]) ).
tff(f827,plain,
! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f525]) ).
tff(f525,plain,
! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X6: fun_na936072029e_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X6,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_75_card__image__le) ).
tff(f3356,plain,
spl17_298,
inference(avatar_split_clause,[],[f1280,f3354]) ).
tff(f3354,plain,
( spl17_298
<=> ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_298])]) ).
tff(f1280,plain,
! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f826]) ).
tff(f826,plain,
! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f524]) ).
tff(f524,plain,
! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X6: fun_nat_fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X6,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_74_card__image__le) ).
tff(f3352,plain,
spl17_297,
inference(avatar_split_clause,[],[f1279,f3350]) ).
tff(f3350,plain,
( spl17_297
<=> ! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_297])]) ).
tff(f1279,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f825]) ).
tff(f825,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f523]) ).
tff(f523,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X0,X1)))) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X8: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X8,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_96_card__insert__le) ).
tff(f3348,plain,
spl17_296,
inference(avatar_split_clause,[],[f1251,f3346]) ).
tff(f3346,plain,
( spl17_296
<=> ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_296])]) ).
tff(f1251,plain,
! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f788]) ).
tff(f788,plain,
! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f498]) ).
tff(f498,plain,
! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X6: fun_fun_pname_bool_a,X2: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X6,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_66_card__image__le) ).
tff(f3344,plain,
spl17_295,
inference(avatar_split_clause,[],[f1250,f3342]) ).
tff(f3342,plain,
( spl17_295
<=> ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_295])]) ).
tff(f1250,plain,
! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f787]) ).
tff(f787,plain,
! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f497]) ).
tff(f497,plain,
! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X6: fun_fun_a_bool_a,X2: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X6,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_65_card__image__le) ).
tff(f3340,plain,
spl17_294,
inference(avatar_split_clause,[],[f1249,f3338]) ).
tff(f3338,plain,
( spl17_294
<=> ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_294])]) ).
tff(f1249,plain,
! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f786]) ).
tff(f786,plain,
! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f496]) ).
tff(f496,plain,
! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X6: fun_fun_nat_bool_a,X2: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X6,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_67_card__image__le) ).
tff(f3336,plain,
spl17_293,
inference(avatar_split_clause,[],[f1248,f3334]) ).
tff(f3334,plain,
( spl17_293
<=> ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_293])]) ).
tff(f1248,plain,
! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f785]) ).
tff(f785,plain,
! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f495]) ).
tff(f495,plain,
! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X6: fun_fun_a_bool_pname,X2: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X6,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_79_card__image__le) ).
tff(f3332,plain,
( spl17_292
| ~ spl17_120
| ~ spl17_134 ),
inference(avatar_split_clause,[],[f2333,f2235,f2143,f3330]) ).
tff(f3330,plain,
( spl17_292
<=> ! [X0: pname,X1: fun_pname_bool] :
( ( insert_pname(X0,X1) = X1 )
| ~ hBOOL(hAPP_pname_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_292])]) ).
tff(f2143,plain,
( spl17_120
<=> ! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_120])]) ).
tff(f2235,plain,
( spl17_134
<=> ! [X0: pname,X1: fun_pname_bool] :
( ( insert_pname(X0,X1) = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_134])]) ).
tff(f2333,plain,
( ! [X0: pname,X1: fun_pname_bool] :
( ( insert_pname(X0,X1) = X1 )
| ~ hBOOL(hAPP_pname_bool(X1,X0)) )
| ~ spl17_120
| ~ spl17_134 ),
inference(resolution,[],[f2236,f2144]) ).
tff(f2144,plain,
( ! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) )
| ~ spl17_120 ),
inference(avatar_component_clause,[],[f2143]) ).
tff(f2236,plain,
( ! [X0: pname,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ( insert_pname(X0,X1) = X1 ) )
| ~ spl17_134 ),
inference(avatar_component_clause,[],[f2235]) ).
tff(f3328,plain,
spl17_291,
inference(avatar_split_clause,[],[f1247,f3326]) ).
tff(f3326,plain,
( spl17_291
<=> ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_291])]) ).
tff(f1247,plain,
! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f784]) ).
tff(f784,plain,
! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f494]) ).
tff(f494,plain,
! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X6: fun_fu1499449723_pname,X2: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X6,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_78_card__image__le) ).
tff(f3324,plain,
spl17_290,
inference(avatar_split_clause,[],[f1246,f3322]) ).
tff(f3322,plain,
( spl17_290
<=> ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_290])]) ).
tff(f1246,plain,
! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f783]) ).
tff(f783,plain,
! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f493]) ).
tff(f493,plain,
! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X6: fun_fu665170229_pname,X2: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X6,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_77_card__image__le) ).
tff(f3320,plain,
spl17_289,
inference(avatar_split_clause,[],[f1245,f3318]) ).
tff(f3318,plain,
( spl17_289
<=> ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_289])]) ).
tff(f1245,plain,
! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f782]) ).
tff(f782,plain,
! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f492]) ).
tff(f492,plain,
! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X6: fun_fun_nat_bool_nat,X2: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X6,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_56_card__image__le) ).
tff(f3316,plain,
spl17_288,
inference(avatar_split_clause,[],[f1244,f3314]) ).
tff(f3314,plain,
( spl17_288
<=> ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_288])]) ).
tff(f1244,plain,
! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f781]) ).
tff(f781,plain,
! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f491]) ).
tff(f491,plain,
! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X6: fun_fun_a_bool_nat,X2: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X6,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_58_card__image__le) ).
tff(f3312,plain,
spl17_287,
inference(avatar_split_clause,[],[f1243,f3310]) ).
tff(f3310,plain,
( spl17_287
<=> ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_287])]) ).
tff(f1243,plain,
! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f780]) ).
tff(f780,plain,
! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f490]) ).
tff(f490,plain,
! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X6: fun_fu1668467777ol_nat,X2: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X6,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_57_card__image__le) ).
tff(f3308,plain,
spl17_286,
inference(avatar_split_clause,[],[f1242,f3306]) ).
tff(f3306,plain,
( spl17_286
<=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_286])]) ).
tff(f1242,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f779]) ).
tff(f779,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f489]) ).
tff(f489,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X0,X1)))) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X8: fun_pname_bool,X2: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X8,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_93_card__insert__le) ).
tff(f3304,plain,
spl17_285,
inference(avatar_split_clause,[],[f1241,f3302]) ).
tff(f3302,plain,
( spl17_285
<=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_285])]) ).
tff(f1241,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f778]) ).
tff(f778,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f488]) ).
tff(f488,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X0,X1)))) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X8: fun_a_bool,X2: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X8,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_94_card__insert__le) ).
tff(f3300,plain,
spl17_284,
inference(avatar_split_clause,[],[f1240,f3298]) ).
tff(f3298,plain,
( spl17_284
<=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_284])]) ).
tff(f1240,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f777]) ).
tff(f777,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f487]) ).
tff(f487,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X0,X1)))) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X8: fun_nat_bool,X2: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X8,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_92_card__insert__le) ).
tff(f3296,plain,
spl17_283,
inference(avatar_split_clause,[],[f1227,f3294]) ).
tff(f3294,plain,
( spl17_283
<=> ! [X0: fun_fu897950882bool_a,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_283])]) ).
tff(f1227,plain,
! [X0: fun_fu897950882bool_a,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(cnf_transformation,[],[f764]) ).
tff(f764,plain,
! [X0: fun_fu897950882bool_a,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(ennf_transformation,[],[f474]) ).
tff(f474,plain,
! [X0: fun_fu897950882bool_a,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X0,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1))) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X6: fun_fu897950882bool_a,X2: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X6,X2))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_62_card__image__le) ).
tff(f3292,plain,
spl17_282,
inference(avatar_split_clause,[],[f1226,f3290]) ).
tff(f3290,plain,
( spl17_282
<=> ! [X0: fun_fu2061654492bool_a,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_282])]) ).
tff(f1226,plain,
! [X0: fun_fu2061654492bool_a,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(cnf_transformation,[],[f763]) ).
tff(f763,plain,
! [X0: fun_fu2061654492bool_a,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(ennf_transformation,[],[f473]) ).
tff(f473,plain,
! [X0: fun_fu2061654492bool_a,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X0,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1))) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X6: fun_fu2061654492bool_a,X2: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X6,X2))),hAPP_f98387925ol_nat(finite269641166l_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_63_card__image__le) ).
tff(f3288,plain,
( spl17_281
| ~ spl17_117
| ~ spl17_131 ),
inference(avatar_split_clause,[],[f2329,f2222,f2131,f3286]) ).
tff(f2131,plain,
( spl17_117
<=> ! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_117])]) ).
tff(f2222,plain,
( spl17_131
<=> ! [X0: x_a,X1: fun_a_bool] :
( ( insert_a(X0,X1) = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_131])]) ).
tff(f2329,plain,
( ! [X2: x_a,X3: fun_a_bool] :
( ( insert_a(X2,X3) = X3 )
| ~ hBOOL(hAPP_a_bool(X3,X2)) )
| ~ spl17_117
| ~ spl17_131 ),
inference(resolution,[],[f2223,f2132]) ).
tff(f2132,plain,
( ! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) )
| ~ spl17_117 ),
inference(avatar_component_clause,[],[f2131]) ).
tff(f2223,plain,
( ! [X0: x_a,X1: fun_a_bool] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ( insert_a(X0,X1) = X1 ) )
| ~ spl17_131 ),
inference(avatar_component_clause,[],[f2222]) ).
tff(f3284,plain,
spl17_280,
inference(avatar_split_clause,[],[f1225,f3282]) ).
tff(f3282,plain,
( spl17_280
<=> ! [X0: fun_fu1373417771bool_a,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_280])]) ).
tff(f1225,plain,
! [X0: fun_fu1373417771bool_a,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(cnf_transformation,[],[f762]) ).
tff(f762,plain,
! [X0: fun_fu1373417771bool_a,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(ennf_transformation,[],[f472]) ).
tff(f472,plain,
! [X0: fun_fu1373417771bool_a,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X0,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1))) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X6: fun_fu1373417771bool_a,X2: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X6,X2))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_64_card__image__le) ).
tff(f3280,plain,
spl17_279,
inference(avatar_split_clause,[],[f1178,f3278]) ).
tff(f3278,plain,
( spl17_279
<=> ! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_279])]) ).
tff(f1178,plain,
! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)) ),
inference(cnf_transformation,[],[f429]) ).
tff(f429,plain,
! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)) ),
inference(rectify,[],[f201]) ).
tff(f201,axiom,
! [X5: x_a,X10: fun_a_bool] : ( insert_a(X5,collect_a(X10)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5))),X10)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_200_insert__Collect) ).
tff(f3276,plain,
spl17_278,
inference(avatar_split_clause,[],[f1171,f3274]) ).
tff(f3274,plain,
( spl17_278
<=> ! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_278])]) ).
tff(f1171,plain,
! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ),
inference(cnf_transformation,[],[f422]) ).
tff(f422,plain,
! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ),
inference(rectify,[],[f195]) ).
tff(f195,axiom,
! [X5: x_a,X7: fun_a_bool] : ( insert_a(X5,X7) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_194_insert__compr) ).
tff(f3272,plain,
spl17_277,
inference(avatar_split_clause,[],[f1169,f3270]) ).
tff(f3270,plain,
( spl17_277
<=> ! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_277])]) ).
tff(f1169,plain,
! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) ),
inference(cnf_transformation,[],[f420]) ).
tff(f420,plain,
! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) ),
inference(rectify,[],[f194]) ).
tff(f194,axiom,
! [X5: pname,X7: fun_pname_bool] : ( insert_pname(X5,X7) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X5)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_193_insert__compr) ).
tff(f3268,plain,
spl17_276,
inference(avatar_split_clause,[],[f1167,f3266]) ).
tff(f3266,plain,
( spl17_276
<=> ! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_276])]) ).
tff(f1167,plain,
! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) ),
inference(cnf_transformation,[],[f418]) ).
tff(f418,plain,
! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) ),
inference(rectify,[],[f264]) ).
tff(f264,axiom,
! [X27: nat,X33: fun_nat_bool] : ( insert_nat(X27,X33) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X27)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X33))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_263_insert__compr__raw) ).
tff(f3264,plain,
spl17_275,
inference(avatar_split_clause,[],[f1165,f3262]) ).
tff(f3262,plain,
( spl17_275
<=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X0,X1) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_275])]) ).
tff(f1165,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X0,X1) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))) ),
inference(cnf_transformation,[],[f416]) ).
tff(f416,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X0,X1) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))) ),
inference(rectify,[],[f269]) ).
tff(f269,axiom,
! [X27: fun_a_bool,X33: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X27,X33) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X27)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X33))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_268_insert__compr__raw) ).
tff(f3260,plain,
spl17_274,
inference(avatar_split_clause,[],[f1163,f3258]) ).
tff(f3258,plain,
( spl17_274
<=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X0,X1) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_274])]) ).
tff(f1163,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X0,X1) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))) ),
inference(cnf_transformation,[],[f414]) ).
tff(f414,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X0,X1) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))) ),
inference(rectify,[],[f197]) ).
tff(f197,axiom,
! [X5: fun_pname_bool,X7: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X5,X7) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X5)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_196_insert__compr) ).
tff(f3256,plain,
spl17_273,
inference(avatar_split_clause,[],[f1161,f3254]) ).
tff(f3254,plain,
( spl17_273
<=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X0,X1) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_273])]) ).
tff(f1161,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X0,X1) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))) ),
inference(cnf_transformation,[],[f412]) ).
tff(f412,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X0,X1) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))) ),
inference(rectify,[],[f196]) ).
tff(f196,axiom,
! [X5: fun_nat_bool,X7: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X5,X7) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X5)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_195_insert__compr) ).
tff(f3245,plain,
( spl17_272
| ~ spl17_114
| ~ spl17_130 ),
inference(avatar_split_clause,[],[f2327,f2218,f2119,f3243]) ).
tff(f2119,plain,
( spl17_114
<=> ! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_114])]) ).
tff(f2218,plain,
( spl17_130
<=> ! [X0: nat,X1: fun_nat_bool] :
( ( insert_nat(X0,X1) = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_130])]) ).
tff(f2327,plain,
( ! [X2: nat,X3: fun_nat_bool] :
( ( insert_nat(X2,X3) = X3 )
| ~ hBOOL(hAPP_nat_bool(X3,X2)) )
| ~ spl17_114
| ~ spl17_130 ),
inference(resolution,[],[f2219,f2120]) ).
tff(f2120,plain,
( ! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) )
| ~ spl17_114 ),
inference(avatar_component_clause,[],[f2119]) ).
tff(f2219,plain,
( ! [X0: nat,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ( insert_nat(X0,X1) = X1 ) )
| ~ spl17_130 ),
inference(avatar_component_clause,[],[f2218]) ).
tff(f3189,plain,
spl17_271,
inference(avatar_split_clause,[],[f1636,f3187]) ).
tff(f3187,plain,
( spl17_271
<=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
( ( image_pname_a(X0,insert_pname(X1,X2)) = image_pname_a(X0,X2) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_271])]) ).
tff(f1636,plain,
! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
( ( image_pname_a(X0,insert_pname(X1,X2)) = image_pname_a(X0,X2) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(forward_demodulation,[],[f1509,f1458]) ).
tff(f1458,plain,
! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] : ( image_pname_a(X0,insert_pname(X1,X2)) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)) ),
inference(cnf_transformation,[],[f657]) ).
tff(f657,plain,
! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] : ( image_pname_a(X0,insert_pname(X1,X2)) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)) ),
inference(rectify,[],[f285]) ).
tff(f285,axiom,
! [X6: fun_pname_a,X5: pname,X7: fun_pname_bool] : ( image_pname_a(X6,insert_pname(X5,X7)) = insert_a(hAPP_pname_a(X6,X5),image_pname_a(X6,X7)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_284_image__insert) ).
tff(f1509,plain,
! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
( ( image_pname_a(X0,X2) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f977]) ).
tff(f977,plain,
! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] :
( ( image_pname_a(X0,X2) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f697]) ).
tff(f697,plain,
! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> ( image_pname_a(X0,X2) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)) ) ),
inference(rectify,[],[f286]) ).
tff(f286,axiom,
! [X6: fun_pname_a,X8: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
=> ( image_pname_a(X6,X2) = insert_a(hAPP_pname_a(X6,X8),image_pname_a(X6,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_285_insert__image) ).
tff(f3185,plain,
spl17_270,
inference(avatar_split_clause,[],[f1579,f3183]) ).
tff(f3183,plain,
( spl17_270
<=> ! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_270])]) ).
tff(f1579,plain,
! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)) ),
inference(forward_demodulation,[],[f1177,f1118]) ).
tff(f1177,plain,
! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,collect_pname(X1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)) ),
inference(cnf_transformation,[],[f428]) ).
tff(f428,plain,
! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,collect_pname(X1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0))),X1)) ),
inference(rectify,[],[f200]) ).
tff(f200,axiom,
! [X5: pname,X10: fun_pname_bool] : ( insert_pname(X5,collect_pname(X10)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X5))),X10)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_199_insert__Collect) ).
tff(f3181,plain,
spl17_269,
inference(avatar_split_clause,[],[f1578,f3179]) ).
tff(f3179,plain,
( spl17_269
<=> ! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_269])]) ).
tff(f1578,plain,
! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)) ),
inference(forward_demodulation,[],[f1176,f1122]) ).
tff(f1176,plain,
! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,collect_nat(X1)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)) ),
inference(cnf_transformation,[],[f427]) ).
tff(f427,plain,
! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,collect_nat(X1)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)) ),
inference(rectify,[],[f199]) ).
tff(f199,axiom,
! [X5: nat,X10: fun_nat_bool] : ( insert_nat(X5,collect_nat(X10)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X5))),X10)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_198_insert__Collect) ).
tff(f3177,plain,
spl17_268,
inference(avatar_split_clause,[],[f1577,f3175]) ).
tff(f3175,plain,
( spl17_268
<=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X0,X1) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_268])]) ).
tff(f1577,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X0,X1) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)) ),
inference(forward_demodulation,[],[f1175,f1120]) ).
tff(f1175,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X0,collect_fun_a_bool(X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)) ),
inference(cnf_transformation,[],[f426]) ).
tff(f426,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X0,collect_fun_a_bool(X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X0))),X1)) ),
inference(rectify,[],[f204]) ).
tff(f204,axiom,
! [X5: fun_a_bool,X10: fun_fun_a_bool_bool] : ( insert_fun_a_bool(X5,collect_fun_a_bool(X10)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X5))),X10)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_203_insert__Collect) ).
tff(f3173,plain,
spl17_267,
inference(avatar_split_clause,[],[f1576,f3171]) ).
tff(f3171,plain,
( spl17_267
<=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X0,X1) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_267])]) ).
tff(f1576,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X0,X1) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)) ),
inference(forward_demodulation,[],[f1174,f1119]) ).
tff(f1174,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X0,collec1974731493e_bool(X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)) ),
inference(cnf_transformation,[],[f425]) ).
tff(f425,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X0,collec1974731493e_bool(X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X0))),X1)) ),
inference(rectify,[],[f203]) ).
tff(f203,axiom,
! [X5: fun_pname_bool,X10: fun_fu1430349052l_bool] : ( insert1325755072e_bool(X5,collec1974731493e_bool(X10)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X5))),X10)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_202_insert__Collect) ).
tff(f3169,plain,
spl17_266,
inference(avatar_split_clause,[],[f1575,f3167]) ).
tff(f3167,plain,
( spl17_266
<=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X0,X1) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_266])]) ).
tff(f1575,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X0,X1) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)) ),
inference(forward_demodulation,[],[f1173,f1121]) ).
tff(f1173,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X0,collect_fun_nat_bool(X1)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)) ),
inference(cnf_transformation,[],[f424]) ).
tff(f424,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X0,collect_fun_nat_bool(X1)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X0))),X1)) ),
inference(rectify,[],[f202]) ).
tff(f202,axiom,
! [X5: fun_nat_bool,X10: fun_fu425979586l_bool] : ( insert_fun_nat_bool(X5,collect_fun_nat_bool(X10)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X5))),X10)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_201_insert__Collect) ).
tff(f3165,plain,
spl17_265,
inference(avatar_split_clause,[],[f1463,f3163]) ).
tff(f3163,plain,
( spl17_265
<=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_265])]) ).
tff(f1463,plain,
! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1) ),
inference(cnf_transformation,[],[f662]) ).
tff(f662,plain,
! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X0),X2)),X1) ),
inference(rectify,[],[f129]) ).
tff(f129,axiom,
! [X20: nat,X21: nat,X19: nat] : ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X20),X21)),X19) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X20),X19)),X21) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_128_diff__commute) ).
tff(f3161,plain,
spl17_264,
inference(avatar_split_clause,[],[f1344,f3159]) ).
tff(f3159,plain,
( spl17_264
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_264])]) ).
tff(f1344,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1)) ),
inference(cnf_transformation,[],[f909]) ).
tff(f909,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1)) ),
inference(flattening,[],[f908]) ).
tff(f908,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1)) ),
inference(ennf_transformation,[],[f584]) ).
tff(f584,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f179]) ).
tff(f179,axiom,
! [X2: fun_pname_bool,X7: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),X2))
=> ( X2 = X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_178_equalityI) ).
tff(f3157,plain,
spl17_263,
inference(avatar_split_clause,[],[f1341,f3155]) ).
tff(f3155,plain,
( spl17_263
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_263])]) ).
tff(f1341,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(cnf_transformation,[],[f904]) ).
tff(f904,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(flattening,[],[f903]) ).
tff(f903,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(ennf_transformation,[],[f581]) ).
tff(f581,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f180]) ).
tff(f180,axiom,
! [X2: fun_a_bool,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),X2))
=> ( X2 = X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_179_equalityI) ).
tff(f3153,plain,
spl17_262,
inference(avatar_split_clause,[],[f1337,f3151]) ).
tff(f3151,plain,
( spl17_262
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_262])]) ).
tff(f1337,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(cnf_transformation,[],[f898]) ).
tff(f898,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(flattening,[],[f897]) ).
tff(f897,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(ennf_transformation,[],[f578]) ).
tff(f578,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f178]) ).
tff(f178,axiom,
! [X2: fun_nat_bool,X7: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),X2))
=> ( X2 = X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_177_equalityI) ).
tff(f3141,plain,
spl17_261,
inference(avatar_split_clause,[],[f1334,f3139]) ).
tff(f3139,plain,
( spl17_261
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_261])]) ).
tff(f1334,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f893]) ).
tff(f893,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(flattening,[],[f892]) ).
tff(f892,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f575]) ).
tff(f575,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f124]) ).
tff(f124,axiom,
! [X12: nat,X11: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X12))
=> ( X11 = X12 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_123_le__antisym) ).
tff(f3137,plain,
spl17_260,
inference(avatar_split_clause,[],[f1332,f3135]) ).
tff(f1332,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f890]) ).
tff(f890,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f573]) ).
tff(f573,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> ( hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X0)) = X0 ) ),
inference(rectify,[],[f166]) ).
tff(f166,axiom,
! [X20: nat,X11: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),X11))
=> ( hAPP_nat_nat(minus_minus_nat(X11),hAPP_nat_nat(minus_minus_nat(X11),X20)) = X20 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_165_diff__diff__cancel) ).
tff(f3041,plain,
( spl17_259
| ~ spl17_157
| ~ spl17_231 ),
inference(avatar_split_clause,[],[f3008,f2888,f2348,f3039]) ).
tff(f3039,plain,
( spl17_259
<=> ! [X11: pname] : hBOOL(hAPP_pname_bool(insert_pname(X11,u),pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_259])]) ).
tff(f3008,plain,
( ! [X11: pname] : hBOOL(hAPP_pname_bool(insert_pname(X11,u),pn))
| ~ spl17_157
| ~ spl17_231 ),
inference(superposition,[],[f2889,f2350]) ).
tff(f2998,plain,
spl17_258,
inference(avatar_split_clause,[],[f1566,f2996]) ).
tff(f2996,plain,
( spl17_258
<=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_258])]) ).
tff(f1566,plain,
! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1110]) ).
tff(f2994,plain,
spl17_257,
inference(avatar_split_clause,[],[f1565,f2992]) ).
tff(f2992,plain,
( spl17_257
<=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_257])]) ).
tff(f1565,plain,
! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1110]) ).
tff(f2990,plain,
spl17_256,
inference(avatar_split_clause,[],[f1560,f2988]) ).
tff(f2988,plain,
( spl17_256
<=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_256])]) ).
tff(f1560,plain,
! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1106]) ).
tff(f2986,plain,
spl17_255,
inference(avatar_split_clause,[],[f1559,f2984]) ).
tff(f2984,plain,
( spl17_255
<=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_255])]) ).
tff(f1559,plain,
! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1106]) ).
tff(f2982,plain,
spl17_254,
inference(avatar_split_clause,[],[f1548,f2980]) ).
tff(f2980,plain,
( spl17_254
<=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_254])]) ).
tff(f1548,plain,
! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1094]) ).
tff(f2978,plain,
( spl17_253
| ~ spl17_128
| ~ spl17_144 ),
inference(avatar_split_clause,[],[f2706,f2275,f2181,f2976]) ).
tff(f2976,plain,
( spl17_253
<=> ! [X2: nat,X3: nat,X4: fun_nat_bool] : hBOOL(hAPP_nat_bool(insert_nat(X3,insert_nat(X2,X4)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_253])]) ).
tff(f2181,plain,
( spl17_128
<=> ! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_128])]) ).
tff(f2275,plain,
( spl17_144
<=> ! [X2: fun_nat_bool,X0: nat,X1: nat] : ( insert_nat(X0,insert_nat(X1,X2)) = insert_nat(X1,insert_nat(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_144])]) ).
tff(f2706,plain,
( ! [X2: nat,X3: nat,X4: fun_nat_bool] : hBOOL(hAPP_nat_bool(insert_nat(X3,insert_nat(X2,X4)),X2))
| ~ spl17_128
| ~ spl17_144 ),
inference(superposition,[],[f2182,f2276]) ).
tff(f2276,plain,
( ! [X2: fun_nat_bool,X0: nat,X1: nat] : ( insert_nat(X0,insert_nat(X1,X2)) = insert_nat(X1,insert_nat(X0,X2)) )
| ~ spl17_144 ),
inference(avatar_component_clause,[],[f2275]) ).
tff(f2182,plain,
( ! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X0))
| ~ spl17_128 ),
inference(avatar_component_clause,[],[f2181]) ).
tff(f2974,plain,
spl17_252,
inference(avatar_split_clause,[],[f1547,f2972]) ).
tff(f2972,plain,
( spl17_252
<=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_252])]) ).
tff(f1547,plain,
! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1094]) ).
tff(f2970,plain,
spl17_251,
inference(avatar_split_clause,[],[f1511,f2968]) ).
tff(f2968,plain,
( spl17_251
<=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_251])]) ).
tff(f1511,plain,
! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(cnf_transformation,[],[f980]) ).
tff(f980,plain,
! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(ennf_transformation,[],[f699]) ).
tff(f699,plain,
! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X0,X2))) ),
inference(rectify,[],[f280]) ).
tff(f280,axiom,
! [X28: pname,X2: fun_pname_bool,X7: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),insert_pname(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_279_subset__insertI2) ).
tff(f2966,plain,
spl17_250,
inference(avatar_split_clause,[],[f1507,f2964]) ).
tff(f2964,plain,
( spl17_250
<=> ! [X2: fun_pname_bool,X0: pname,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_250])]) ).
tff(f1507,plain,
! [X2: fun_pname_bool,X0: pname,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(cnf_transformation,[],[f975]) ).
tff(f975,plain,
! [X0: pname,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(ennf_transformation,[],[f695]) ).
tff(f695,plain,
! [X0: pname,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2))) ),
inference(rectify,[],[f221]) ).
tff(f221,axiom,
! [X28: pname,X5: pname,X7: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),X7))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),insert_pname(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_220_insertI2) ).
tff(f2962,plain,
spl17_249,
inference(avatar_split_clause,[],[f1501,f2960]) ).
tff(f2960,plain,
( spl17_249
<=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_249])]) ).
tff(f1501,plain,
! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(cnf_transformation,[],[f965]) ).
tff(f965,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(ennf_transformation,[],[f689]) ).
tff(f689,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X0,X2))) ),
inference(rectify,[],[f281]) ).
tff(f281,axiom,
! [X28: x_a,X2: fun_a_bool,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_280_subset__insertI2) ).
tff(f2958,plain,
spl17_248,
inference(avatar_split_clause,[],[f1499,f2956]) ).
tff(f2956,plain,
( spl17_248
<=> ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_248])]) ).
tff(f1499,plain,
! [X2: fun_a_bool,X0: x_a,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(cnf_transformation,[],[f962]) ).
tff(f962,plain,
! [X0: x_a,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(ennf_transformation,[],[f687]) ).
tff(f687,plain,
! [X0: x_a,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2))) ),
inference(rectify,[],[f222]) ).
tff(f222,axiom,
! [X28: x_a,X5: x_a,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),X7))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),insert_a(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_221_insertI2) ).
tff(f2954,plain,
spl17_247,
inference(avatar_split_clause,[],[f1493,f2952]) ).
tff(f2952,plain,
( spl17_247
<=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_247])]) ).
tff(f1493,plain,
! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(cnf_transformation,[],[f952]) ).
tff(f952,plain,
! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(ennf_transformation,[],[f681]) ).
tff(f681,plain,
! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X0,X2))) ),
inference(rectify,[],[f279]) ).
tff(f279,axiom,
! [X28: nat,X2: fun_nat_bool,X7: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),insert_nat(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_278_subset__insertI2) ).
tff(f2950,plain,
spl17_246,
inference(avatar_split_clause,[],[f1491,f2948]) ).
tff(f2948,plain,
( spl17_246
<=> ! [X2: fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_246])]) ).
tff(f1491,plain,
! [X2: fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(cnf_transformation,[],[f949]) ).
tff(f949,plain,
! [X0: nat,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(ennf_transformation,[],[f679]) ).
tff(f679,plain,
! [X0: nat,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2))) ),
inference(rectify,[],[f220]) ).
tff(f220,axiom,
! [X28: nat,X5: nat,X7: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X7))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),insert_nat(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_219_insertI2) ).
tff(f2946,plain,
spl17_245,
inference(avatar_split_clause,[],[f1414,f2944]) ).
tff(f2944,plain,
( spl17_245
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_245])]) ).
tff(f1414,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1057]) ).
tff(f2942,plain,
spl17_244,
inference(avatar_split_clause,[],[f1413,f2940]) ).
tff(f2940,plain,
( spl17_244
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_244])]) ).
tff(f1413,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1057]) ).
tff(f2938,plain,
spl17_243,
inference(avatar_split_clause,[],[f1377,f2936]) ).
tff(f2936,plain,
( spl17_243
<=> ! [X0: nat,X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_243])]) ).
tff(f1377,plain,
! [X0: nat,X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ),
inference(cnf_transformation,[],[f1035]) ).
tff(f1035,plain,
! [X0: nat,X1: nat] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f601]) ).
tff(f601,plain,
! [X0: nat,X1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ),
inference(rectify,[],[f159]) ).
tff(f159,axiom,
! [X22: nat,X14: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X22)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_158_not__less__eq__eq) ).
tff(f2934,plain,
( spl17_242
| ~ spl17_127
| ~ spl17_146 ),
inference(avatar_split_clause,[],[f2696,f2283,f2177,f2932]) ).
tff(f2932,plain,
( spl17_242
<=> ! [X2: x_a,X3: x_a,X4: fun_a_bool] : hBOOL(hAPP_a_bool(insert_a(X3,insert_a(X2,X4)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_242])]) ).
tff(f2177,plain,
( spl17_127
<=> ! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_a_bool(insert_a(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_127])]) ).
tff(f2283,plain,
( spl17_146
<=> ! [X2: fun_a_bool,X0: x_a,X1: x_a] : ( insert_a(X0,insert_a(X1,X2)) = insert_a(X1,insert_a(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_146])]) ).
tff(f2696,plain,
( ! [X2: x_a,X3: x_a,X4: fun_a_bool] : hBOOL(hAPP_a_bool(insert_a(X3,insert_a(X2,X4)),X2))
| ~ spl17_127
| ~ spl17_146 ),
inference(superposition,[],[f2178,f2284]) ).
tff(f2284,plain,
( ! [X2: fun_a_bool,X0: x_a,X1: x_a] : ( insert_a(X0,insert_a(X1,X2)) = insert_a(X1,insert_a(X0,X2)) )
| ~ spl17_146 ),
inference(avatar_component_clause,[],[f2283]) ).
tff(f2178,plain,
( ! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_a_bool(insert_a(X0,X1),X0))
| ~ spl17_127 ),
inference(avatar_component_clause,[],[f2177]) ).
tff(f2930,plain,
spl17_241,
inference(avatar_split_clause,[],[f1376,f2928]) ).
tff(f2928,plain,
( spl17_241
<=> ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_241])]) ).
tff(f1376,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1035]) ).
tff(f2926,plain,
spl17_240,
inference(avatar_split_clause,[],[f1366,f2924]) ).
tff(f2924,plain,
( spl17_240
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_240])]) ).
tff(f1366,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1028]) ).
tff(f1028,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(X0,X1)),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f923,f1027]) ).
tff(f1027,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ? [X2: pname] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(X0,X1)),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f923,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| ? [X2: pname] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) ),
inference(ennf_transformation,[],[f597]) ).
tff(f597,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ! [X2: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) ),
inference(rectify,[],[f292]) ).
tff(f292,axiom,
! [X7: fun_pname_bool,X2: fun_pname_bool] :
( ! [X27: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X7)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_291_subsetI) ).
tff(f2922,plain,
spl17_239,
inference(avatar_split_clause,[],[f1365,f2920]) ).
tff(f2920,plain,
( spl17_239
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_239])]) ).
tff(f1365,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1028]) ).
tff(f2918,plain,
spl17_238,
inference(avatar_split_clause,[],[f1364,f2916]) ).
tff(f2916,plain,
( spl17_238
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK5(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_238])]) ).
tff(f1364,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK5(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1026]) ).
tff(f1026,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK5(X0,X1)),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK5(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f922,f1025]) ).
tff(f1025,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ? [X2: x_a] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK5(X0,X1)),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK5(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f922,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ? [X2: x_a] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) ),
inference(ennf_transformation,[],[f596]) ).
tff(f596,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ! [X2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ),
inference(rectify,[],[f291]) ).
tff(f291,axiom,
! [X7: fun_a_bool,X2: fun_a_bool] :
( ! [X27: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X2))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X7)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_290_subsetI) ).
tff(f2914,plain,
spl17_237,
inference(avatar_split_clause,[],[f1363,f2912]) ).
tff(f2912,plain,
( spl17_237
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK5(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_237])]) ).
tff(f1363,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK5(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1026]) ).
tff(f2910,plain,
spl17_236,
inference(avatar_split_clause,[],[f1362,f2908]) ).
tff(f2908,plain,
( spl17_236
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK4(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_236])]) ).
tff(f1362,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK4(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1024]) ).
tff(f1024,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK4(X0,X1)),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK4(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f921,f1023]) ).
tff(f1023,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ? [X2: nat] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK4(X0,X1)),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK4(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f921,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| ? [X2: nat] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
inference(ennf_transformation,[],[f595]) ).
tff(f595,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ! [X2: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) ),
inference(rectify,[],[f290]) ).
tff(f290,axiom,
! [X7: fun_nat_bool,X2: fun_nat_bool] :
( ! [X27: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X7)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_289_subsetI) ).
tff(f2906,plain,
spl17_235,
inference(avatar_split_clause,[],[f1361,f2904]) ).
tff(f2904,plain,
( spl17_235
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK4(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_235])]) ).
tff(f1361,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK4(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1024]) ).
tff(f2902,plain,
spl17_234,
inference(avatar_split_clause,[],[f1358,f2900]) ).
tff(f2900,plain,
( spl17_234
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_234])]) ).
tff(f1358,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ),
inference(cnf_transformation,[],[f919]) ).
tff(f919,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
inference(ennf_transformation,[],[f593]) ).
tff(f593,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) )
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0)))) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X9: fun_a_bool,X10: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X9)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X10))) )
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X10),X9)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_113_finite__Collect__conjI) ).
tff(f2898,plain,
spl17_233,
inference(avatar_split_clause,[],[f1357,f2896]) ).
tff(f2896,plain,
( spl17_233
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_233])]) ).
tff(f1357,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(cnf_transformation,[],[f919]) ).
tff(f2894,plain,
spl17_232,
inference(avatar_split_clause,[],[f1348,f2892]) ).
tff(f2892,plain,
( spl17_232
<=> ! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,sK3(X1)) = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_232])]) ).
tff(f1348,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,sK3(X1)) = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(cnf_transformation,[],[f1022]) ).
tff(f1022,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,sK3(X1)) = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f914,f1021]) ).
tff(f1021,plain,
! [X1: nat] :
( ? [X2: nat] : ( hAPP_nat_nat(suc,X2) = X1 )
=> ( hAPP_nat_nat(suc,sK3(X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f914,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] : ( hAPP_nat_nat(suc,X2) = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(ennf_transformation,[],[f588]) ).
tff(f588,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
=> ? [X2: nat] : ( hAPP_nat_nat(suc,X2) = X1 ) ),
inference(rectify,[],[f294]) ).
tff(f294,axiom,
! [X11: nat,X37: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X11)),X37))
=> ? [X38: nat] : ( hAPP_nat_nat(suc,X38) = X37 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_293_Suc__le__D) ).
tff(f2890,plain,
( spl17_231
| ~ spl17_123
| ~ spl17_145 ),
inference(avatar_split_clause,[],[f2652,f2279,f2155,f2888]) ).
tff(f2155,plain,
( spl17_123
<=> ! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_123])]) ).
tff(f2652,plain,
( ! [X2: pname,X3: pname,X4: fun_pname_bool] : hBOOL(hAPP_pname_bool(insert_pname(X3,insert_pname(X2,X4)),X2))
| ~ spl17_123
| ~ spl17_145 ),
inference(superposition,[],[f2156,f2280]) ).
tff(f2156,plain,
( ! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X0))
| ~ spl17_123 ),
inference(avatar_component_clause,[],[f2155]) ).
tff(f2886,plain,
spl17_230,
inference(avatar_split_clause,[],[f1347,f2884]) ).
tff(f2884,plain,
( spl17_230
<=> ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_230])]) ).
tff(f1347,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(cnf_transformation,[],[f913]) ).
tff(f913,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
inference(ennf_transformation,[],[f587]) ).
tff(f587,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f154]) ).
tff(f154,axiom,
! [X12: nat,X11: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X12)),X11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_153_Suc__leD) ).
tff(f2882,plain,
spl17_229,
inference(avatar_split_clause,[],[f1331,f2880]) ).
tff(f2880,plain,
( spl17_229
<=> ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_229])]) ).
tff(f1331,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f889]) ).
tff(f889,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f572]) ).
tff(f572,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
inference(rectify,[],[f156]) ).
tff(f156,axiom,
! [X12: nat,X11: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_nat_nat(suc,X11))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_155_le__SucI) ).
tff(f2878,plain,
spl17_228,
inference(avatar_split_clause,[],[f1325,f2876]) ).
tff(f2876,plain,
( spl17_228
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_228])]) ).
tff(f1325,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f878]) ).
tff(f878,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(flattening,[],[f877]) ).
tff(f877,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f566]) ).
tff(f566,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
inference(rectify,[],[f153]) ).
tff(f153,axiom,
! [X2: fun_pname_bool,X7: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_152_rev__finite__subset) ).
tff(f2874,plain,
spl17_227,
inference(avatar_split_clause,[],[f1302,f2872]) ).
tff(f2872,plain,
( spl17_227
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_227])]) ).
tff(f1302,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f852]) ).
tff(f852,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(flattening,[],[f851]) ).
tff(f851,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f544]) ).
tff(f544,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
inference(rectify,[],[f150]) ).
tff(f150,axiom,
! [X2: fun_a_bool,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_149_rev__finite__subset) ).
tff(f2870,plain,
spl17_226,
inference(avatar_split_clause,[],[f1288,f2868]) ).
tff(f2868,plain,
( spl17_226
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_226])]) ).
tff(f1288,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f835]) ).
tff(f835,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(flattening,[],[f834]) ).
tff(f834,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f531]) ).
tff(f531,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
inference(rectify,[],[f152]) ).
tff(f152,axiom,
! [X2: fun_nat_bool,X7: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_151_rev__finite__subset) ).
tff(f2866,plain,
spl17_225,
inference(avatar_split_clause,[],[f1263,f2864]) ).
tff(f2864,plain,
( spl17_225
<=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_225])]) ).
tff(f1263,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f803]) ).
tff(f803,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(flattening,[],[f802]) ).
tff(f802,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f507]) ).
tff(f507,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
inference(rectify,[],[f151]) ).
tff(f151,axiom,
! [X2: fun_fun_a_bool_bool,X7: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),X7))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_150_rev__finite__subset) ).
tff(f2862,plain,
spl17_224,
inference(avatar_split_clause,[],[f1262,f2860]) ).
tff(f2860,plain,
( spl17_224
<=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_224])]) ).
tff(f1262,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f801]) ).
tff(f801,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(flattening,[],[f800]) ).
tff(f800,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f506]) ).
tff(f506,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
inference(rectify,[],[f148]) ).
tff(f148,axiom,
! [X2: fun_fu425979586l_bool,X7: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),X7))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_147_rev__finite__subset) ).
tff(f2858,plain,
spl17_223,
inference(avatar_split_clause,[],[f1261,f2856]) ).
tff(f2856,plain,
( spl17_223
<=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_223])]) ).
tff(f1261,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f799]) ).
tff(f799,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(flattening,[],[f798]) ).
tff(f798,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f505]) ).
tff(f505,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
inference(rectify,[],[f149]) ).
tff(f149,axiom,
! [X2: fun_fu1430349052l_bool,X7: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),X7))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_148_rev__finite__subset) ).
tff(f2853,plain,
spl17_222,
inference(avatar_split_clause,[],[f1117,f2850]) ).
tff(f2850,plain,
( spl17_222
<=> ( hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_222])]) ).
tff(f1117,plain,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
inference(cnf_transformation,[],[f365]) ).
tff(f365,axiom,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',conj_3) ).
tff(f2800,plain,
( spl17_221
| ~ spl17_19
| ~ spl17_168 ),
inference(avatar_split_clause,[],[f2700,f2530,f1716,f2798]) ).
tff(f2798,plain,
( spl17_221
<=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_221])]) ).
tff(f1716,plain,
( spl17_19
<=> ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
tff(f2530,plain,
( spl17_168
<=> ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_168])]) ).
tff(f2700,plain,
( ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X0)))
| ~ spl17_19
| ~ spl17_168 ),
inference(resolution,[],[f2531,f1717]) ).
tff(f1717,plain,
( ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0))
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f1716]) ).
tff(f2531,plain,
( ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
| ~ spl17_168 ),
inference(avatar_component_clause,[],[f2530]) ).
tff(f2795,plain,
spl17_220,
inference(avatar_split_clause,[],[f1541,f2793]) ).
tff(f2793,plain,
( spl17_220
<=> ! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_220])]) ).
tff(f1541,plain,
! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2)) ),
inference(cnf_transformation,[],[f1090]) ).
tff(f1090,plain,
! [X0: nat,X1: fun_nat_bool,X2: nat] :
( ( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ( ~ hBOOL(hAPP_nat_bool(X1,X2))
& ( X0 != X2 ) ) )
& ( hBOOL(hAPP_nat_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2)) ) ),
inference(flattening,[],[f1089]) ).
tff(f1089,plain,
! [X0: nat,X1: fun_nat_bool,X2: nat] :
( ( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ( ~ hBOOL(hAPP_nat_bool(X1,X2))
& ( X0 != X2 ) ) )
& ( hBOOL(hAPP_nat_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2)) ) ),
inference(nnf_transformation,[],[f720]) ).
tff(f720,plain,
! [X0: nat,X1: fun_nat_bool,X2: nat] :
( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
<=> ( hBOOL(hAPP_nat_bool(X1,X2))
| ( X0 = X2 ) ) ),
inference(rectify,[],[f214]) ).
tff(f214,axiom,
! [X30: nat,X2: fun_nat_bool,X8: nat] :
( hBOOL(hAPP_nat_bool(insert_nat(X30,X2),X8))
<=> ( hBOOL(hAPP_nat_bool(X2,X8))
| ( X8 = X30 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_213_insert__code) ).
tff(f2791,plain,
spl17_219,
inference(avatar_split_clause,[],[f1538,f2789]) ).
tff(f2789,plain,
( spl17_219
<=> ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_a_bool(insert_a(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_219])]) ).
tff(f1538,plain,
! [X2: x_a,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_a_bool(insert_a(X0,X1),X2)) ),
inference(cnf_transformation,[],[f1088]) ).
tff(f1088,plain,
! [X0: x_a,X1: fun_a_bool,X2: x_a] :
( ( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| ( ~ hBOOL(hAPP_a_bool(X1,X2))
& ( X0 != X2 ) ) )
& ( hBOOL(hAPP_a_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_a_bool(insert_a(X0,X1),X2)) ) ),
inference(flattening,[],[f1087]) ).
tff(f1087,plain,
! [X0: x_a,X1: fun_a_bool,X2: x_a] :
( ( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| ( ~ hBOOL(hAPP_a_bool(X1,X2))
& ( X0 != X2 ) ) )
& ( hBOOL(hAPP_a_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_a_bool(insert_a(X0,X1),X2)) ) ),
inference(nnf_transformation,[],[f719]) ).
tff(f719,plain,
! [X0: x_a,X1: fun_a_bool,X2: x_a] :
( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
<=> ( hBOOL(hAPP_a_bool(X1,X2))
| ( X0 = X2 ) ) ),
inference(rectify,[],[f216]) ).
tff(f216,axiom,
! [X30: x_a,X2: fun_a_bool,X8: x_a] :
( hBOOL(hAPP_a_bool(insert_a(X30,X2),X8))
<=> ( hBOOL(hAPP_a_bool(X2,X8))
| ( X8 = X30 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_215_insert__code) ).
tff(f2787,plain,
spl17_218,
inference(avatar_split_clause,[],[f1535,f2785]) ).
tff(f2785,plain,
( spl17_218
<=> ! [X2: pname,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_218])]) ).
tff(f1535,plain,
! [X2: pname,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2)) ),
inference(cnf_transformation,[],[f1086]) ).
tff(f1086,plain,
! [X0: pname,X1: fun_pname_bool,X2: pname] :
( ( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ( ~ hBOOL(hAPP_pname_bool(X1,X2))
& ( X0 != X2 ) ) )
& ( hBOOL(hAPP_pname_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2)) ) ),
inference(flattening,[],[f1085]) ).
tff(f1085,plain,
! [X0: pname,X1: fun_pname_bool,X2: pname] :
( ( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ( ~ hBOOL(hAPP_pname_bool(X1,X2))
& ( X0 != X2 ) ) )
& ( hBOOL(hAPP_pname_bool(X1,X2))
| ( X0 = X2 )
| ~ hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2)) ) ),
inference(nnf_transformation,[],[f718]) ).
tff(f718,plain,
! [X0: pname,X1: fun_pname_bool,X2: pname] :
( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
<=> ( hBOOL(hAPP_pname_bool(X1,X2))
| ( X0 = X2 ) ) ),
inference(rectify,[],[f215]) ).
tff(f215,axiom,
! [X30: pname,X2: fun_pname_bool,X8: pname] :
( hBOOL(hAPP_pname_bool(insert_pname(X30,X2),X8))
<=> ( hBOOL(hAPP_pname_bool(X2,X8))
| ( X8 = X30 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_214_insert__code) ).
tff(f2783,plain,
spl17_217,
inference(avatar_split_clause,[],[f1462,f2781]) ).
tff(f2781,plain,
( spl17_217
<=> ! [X2: fun_pname_bool,X0: fun_fu31783638l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_217])]) ).
tff(f1462,plain,
! [X2: fun_pname_bool,X0: fun_fu31783638l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)) ),
inference(cnf_transformation,[],[f661]) ).
tff(f661,plain,
! [X0: fun_fu31783638l_bool,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] : ( hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)) ),
inference(rectify,[],[f345]) ).
tff(f345,axiom,
! [X41: fun_fu31783638l_bool,X42: fun_fu1430349052l_bool,X43: fun_pname_bool] : ( hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X41,X42),X43) = hAPP_bool_bool(hAPP_f1476298914l_bool(X41,X43),hAPP_f1664156314l_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).
tff(f2779,plain,
spl17_216,
inference(avatar_split_clause,[],[f1461,f2777]) ).
tff(f2777,plain,
( spl17_216
<=> ! [X2: fun_a_bool,X0: fun_fu554186387l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_216])]) ).
tff(f1461,plain,
! [X2: fun_a_bool,X0: fun_fu554186387l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)) ),
inference(cnf_transformation,[],[f660]) ).
tff(f660,plain,
! [X0: fun_fu554186387l_bool,X1: fun_fun_a_bool_bool,X2: fun_a_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)) ),
inference(rectify,[],[f338]) ).
tff(f338,axiom,
! [X41: fun_fu554186387l_bool,X42: fun_fun_a_bool_bool,X43: fun_a_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X41,X42),X43) = hAPP_bool_bool(hAPP_f198738859l_bool(X41,X43),hAPP_fun_a_bool_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).
tff(f2775,plain,
spl17_215,
inference(avatar_split_clause,[],[f1460,f2773]) ).
tff(f2773,plain,
( spl17_215
<=> ! [X2: fun_nat_bool,X0: fun_fu1016514960l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_215])]) ).
tff(f1460,plain,
! [X2: fun_nat_bool,X0: fun_fu1016514960l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)) ),
inference(cnf_transformation,[],[f659]) ).
tff(f659,plain,
! [X0: fun_fu1016514960l_bool,X1: fun_fu425979586l_bool,X2: fun_nat_bool] : ( hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)) ),
inference(rectify,[],[f342]) ).
tff(f342,axiom,
! [X41: fun_fu1016514960l_bool,X42: fun_fu425979586l_bool,X43: fun_nat_bool] : ( hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X41,X42),X43) = hAPP_bool_bool(hAPP_f1748468828l_bool(X41,X43),hAPP_f54304608l_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
tff(f2771,plain,
spl17_214,
inference(avatar_split_clause,[],[f1459,f2769]) ).
tff(f2769,plain,
( spl17_214
<=> ! [X2: nat,X0: fun_na1469252690l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_214])]) ).
tff(f1459,plain,
! [X2: nat,X0: fun_na1469252690l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f658]) ).
tff(f658,plain,
! [X0: fun_na1469252690l_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)) ),
inference(rectify,[],[f330]) ).
tff(f330,axiom,
! [X41: fun_na1469252690l_bool,X42: fun_nat_bool,X43: nat] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X41,X42),X43) = hAPP_bool_bool(hAPP_n1006566506l_bool(X41,X43),hAPP_nat_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
tff(f2767,plain,
spl17_213,
inference(avatar_split_clause,[],[f1458,f2765]) ).
tff(f2765,plain,
( spl17_213
<=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] : ( image_pname_a(X0,insert_pname(X1,X2)) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_213])]) ).
tff(f2763,plain,
spl17_212,
inference(avatar_split_clause,[],[f1457,f2761]) ).
tff(f2761,plain,
( spl17_212
<=> ! [X2: pname,X0: fun_pn250273176l_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_212])]) ).
tff(f1457,plain,
! [X2: pname,X0: fun_pn250273176l_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)) ),
inference(cnf_transformation,[],[f656]) ).
tff(f656,plain,
! [X0: fun_pn250273176l_bool,X1: fun_pname_bool,X2: pname] : ( hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)) ),
inference(rectify,[],[f332]) ).
tff(f332,axiom,
! [X41: fun_pn250273176l_bool,X42: fun_pname_bool,X43: pname] : ( hAPP_pname_bool(cOMBS_568398431l_bool(X41,X42),X43) = hAPP_bool_bool(hAPP_p393069232l_bool(X41,X43),hAPP_pname_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
tff(f2756,plain,
spl17_211,
inference(avatar_split_clause,[],[f1456,f2754]) ).
tff(f2754,plain,
( spl17_211
<=> ! [X2: x_a,X0: fun_a_fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_211])]) ).
tff(f1456,plain,
! [X2: x_a,X0: fun_a_fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f655]) ).
tff(f655,plain,
! [X0: fun_a_fun_bool_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)) ),
inference(rectify,[],[f322]) ).
tff(f322,axiom,
! [X41: fun_a_fun_bool_bool,X42: fun_a_bool,X43: x_a] : ( hAPP_a_bool(cOMBS_a_bool_bool(X41,X42),X43) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X41,X43),hAPP_a_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
tff(f2752,plain,
spl17_210,
inference(avatar_split_clause,[],[f1160,f2750]) ).
tff(f2750,plain,
( spl17_210
<=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_210])]) ).
tff(f1160,plain,
! [X0: nat,X1: nat] : ( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) ),
inference(cnf_transformation,[],[f411]) ).
tff(f411,plain,
! [X0: nat,X1: nat] : ( hAPP_nat_nat(minus_minus_nat(X0),X1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) ),
inference(rectify,[],[f162]) ).
tff(f162,axiom,
! [X12: nat,X11: nat] : ( hAPP_nat_nat(minus_minus_nat(X12),X11) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X12)),hAPP_nat_nat(suc,X11)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_161_diff__Suc__Suc) ).
tff(f2748,plain,
( spl17_209
| ~ spl17_23
| ~ spl17_133 ),
inference(avatar_split_clause,[],[f2331,f2231,f1732,f2746]) ).
tff(f2746,plain,
( spl17_209
<=> ! [X2: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(p(insert_a(X1,X2)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_209])]) ).
tff(f1732,plain,
( spl17_23
<=> ! [X0: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),insert_a(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
tff(f2231,plain,
( spl17_133
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_133])]) ).
tff(f2331,plain,
( ! [X2: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(p(insert_a(X1,X2)),X2))
| ~ spl17_23
| ~ spl17_133 ),
inference(resolution,[],[f2232,f1733]) ).
tff(f1733,plain,
( ! [X0: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),insert_a(X1,X0)))
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f1732]) ).
tff(f2232,plain,
( ! [X0: fun_a_bool,X1: fun_a_bool] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) )
| ~ spl17_133 ),
inference(avatar_component_clause,[],[f2231]) ).
tff(f2731,plain,
( spl17_208
| ~ spl17_18
| ~ spl17_133 ),
inference(avatar_split_clause,[],[f2332,f2231,f1711,f2728]) ).
tff(f2728,plain,
( spl17_208
<=> hBOOL(hAPP_fun_a_bool_bool(p(image_pname_a(mgt_call,u)),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_208])]) ).
tff(f2332,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(image_pname_a(mgt_call,u)),g))
| ~ spl17_18
| ~ spl17_133 ),
inference(resolution,[],[f2232,f1713]) ).
tff(f2694,plain,
spl17_207,
inference(avatar_split_clause,[],[f1635,f2692]) ).
tff(f2692,plain,
( spl17_207
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_207])]) ).
tff(f1635,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
inference(forward_demodulation,[],[f1634,f1118]) ).
tff(f1634,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1416,f1118]) ).
tff(f1416,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1059]) ).
tff(f2690,plain,
spl17_206,
inference(avatar_split_clause,[],[f1633,f2688]) ).
tff(f2688,plain,
( spl17_206
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_206])]) ).
tff(f1633,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(forward_demodulation,[],[f1632,f1118]) ).
tff(f1632,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1417,f1118]) ).
tff(f1417,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1059]) ).
tff(f2686,plain,
spl17_205,
inference(avatar_split_clause,[],[f1628,f2684]) ).
tff(f2684,plain,
( spl17_205
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_205])]) ).
tff(f1628,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(forward_demodulation,[],[f1627,f1122]) ).
tff(f1627,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1410,f1122]) ).
tff(f1410,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1055]) ).
tff(f2682,plain,
spl17_204,
inference(avatar_split_clause,[],[f1626,f2680]) ).
tff(f2680,plain,
( spl17_204
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_204])]) ).
tff(f1626,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(forward_demodulation,[],[f1625,f1122]) ).
tff(f1625,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1411,f1122]) ).
tff(f1411,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1055]) ).
tff(f2678,plain,
spl17_203,
inference(avatar_split_clause,[],[f1621,f2676]) ).
tff(f2676,plain,
( spl17_203
<=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_203])]) ).
tff(f1621,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
inference(forward_demodulation,[],[f1620,f1121]) ).
tff(f1620,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1407,f1121]) ).
tff(f1407,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1053]) ).
tff(f2674,plain,
spl17_202,
inference(avatar_split_clause,[],[f1619,f2672]) ).
tff(f2672,plain,
( spl17_202
<=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_202])]) ).
tff(f1619,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(forward_demodulation,[],[f1618,f1121]) ).
tff(f1618,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1408,f1121]) ).
tff(f1408,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1053]) ).
tff(f2670,plain,
spl17_201,
inference(avatar_split_clause,[],[f1614,f2668]) ).
tff(f2668,plain,
( spl17_201
<=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_201])]) ).
tff(f1614,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ),
inference(forward_demodulation,[],[f1613,f1120]) ).
tff(f1613,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1404,f1120]) ).
tff(f1404,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1051]) ).
tff(f2666,plain,
spl17_200,
inference(avatar_split_clause,[],[f1612,f2664]) ).
tff(f2664,plain,
( spl17_200
<=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_200])]) ).
tff(f1612,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(forward_demodulation,[],[f1611,f1120]) ).
tff(f1611,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1405,f1120]) ).
tff(f1405,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1051]) ).
tff(f2662,plain,
spl17_199,
inference(avatar_split_clause,[],[f1607,f2660]) ).
tff(f2660,plain,
( spl17_199
<=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_199])]) ).
tff(f1607,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ),
inference(forward_demodulation,[],[f1606,f1119]) ).
tff(f1606,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1401,f1119]) ).
tff(f1401,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1049]) ).
tff(f2658,plain,
spl17_198,
inference(avatar_split_clause,[],[f1605,f2656]) ).
tff(f2656,plain,
( spl17_198
<=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_198])]) ).
tff(f1605,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(forward_demodulation,[],[f1604,f1119]) ).
tff(f1604,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ),
inference(forward_demodulation,[],[f1402,f1119]) ).
tff(f1402,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ),
inference(cnf_transformation,[],[f1049]) ).
tff(f2650,plain,
spl17_197,
inference(avatar_split_clause,[],[f1600,f2648]) ).
tff(f2648,plain,
( spl17_197
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_197])]) ).
tff(f1600,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1599,f1118]) ).
tff(f1599,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(forward_demodulation,[],[f1359,f1118]) ).
tff(f1359,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(cnf_transformation,[],[f920]) ).
tff(f920,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ) ),
inference(ennf_transformation,[],[f594]) ).
tff(f594,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0)))) ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X9: fun_pname_bool,X10: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X9)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X10))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X10),X9)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_114_finite__Collect__conjI) ).
tff(f2646,plain,
spl17_196,
inference(avatar_split_clause,[],[f1598,f2644]) ).
tff(f2644,plain,
( spl17_196
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_196])]) ).
tff(f1598,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1597,f1118]) ).
tff(f1597,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
inference(forward_demodulation,[],[f1360,f1118]) ).
tff(f1360,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
inference(cnf_transformation,[],[f920]) ).
tff(f2642,plain,
spl17_195,
inference(avatar_split_clause,[],[f1596,f2640]) ).
tff(f2640,plain,
( spl17_195
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_195])]) ).
tff(f1596,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1595,f1122]) ).
tff(f1595,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(forward_demodulation,[],[f1355,f1122]) ).
tff(f1355,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(cnf_transformation,[],[f918]) ).
tff(f918,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ) ),
inference(ennf_transformation,[],[f592]) ).
tff(f592,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))) ),
inference(rectify,[],[f116]) ).
tff(f116,axiom,
! [X9: fun_nat_bool,X10: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X9)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X10))) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X10),X9)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_115_finite__Collect__conjI) ).
tff(f2638,plain,
spl17_194,
inference(avatar_split_clause,[],[f1594,f2636]) ).
tff(f2636,plain,
( spl17_194
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_194])]) ).
tff(f1594,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1593,f1122]) ).
tff(f1593,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(forward_demodulation,[],[f1356,f1122]) ).
tff(f1356,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
inference(cnf_transformation,[],[f918]) ).
tff(f2634,plain,
spl17_193,
inference(avatar_split_clause,[],[f1592,f2632]) ).
tff(f2632,plain,
( spl17_193
<=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_193])]) ).
tff(f1592,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1591,f1120]) ).
tff(f1591,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(forward_demodulation,[],[f1353,f1120]) ).
tff(f1353,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(cnf_transformation,[],[f917]) ).
tff(f917,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
& ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ) ),
inference(ennf_transformation,[],[f591]) ).
tff(f591,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) )
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0)))) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X9: fun_fun_a_bool_bool,X10: fun_fun_a_bool_bool] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X9)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X10))) )
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X10),X9)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_112_finite__Collect__conjI) ).
tff(f2630,plain,
spl17_192,
inference(avatar_split_clause,[],[f1590,f2628]) ).
tff(f2628,plain,
( spl17_192
<=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_192])]) ).
tff(f1590,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1589,f1120]) ).
tff(f1589,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
inference(forward_demodulation,[],[f1354,f1120]) ).
tff(f1354,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
inference(cnf_transformation,[],[f917]) ).
tff(f2626,plain,
spl17_191,
inference(avatar_split_clause,[],[f1588,f2624]) ).
tff(f2624,plain,
( spl17_191
<=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_191])]) ).
tff(f1588,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1587,f1121]) ).
tff(f1587,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(forward_demodulation,[],[f1351,f1121]) ).
tff(f1351,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(cnf_transformation,[],[f916]) ).
tff(f916,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
& ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ) ),
inference(ennf_transformation,[],[f590]) ).
tff(f590,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) )
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0)))) ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X9: fun_fu425979586l_bool,X10: fun_fu425979586l_bool] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X9)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X10))) )
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X10),X9)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_110_finite__Collect__conjI) ).
tff(f2622,plain,
spl17_190,
inference(avatar_split_clause,[],[f1586,f2620]) ).
tff(f2620,plain,
( spl17_190
<=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_190])]) ).
tff(f1586,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1585,f1121]) ).
tff(f1585,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(forward_demodulation,[],[f1352,f1121]) ).
tff(f1352,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
inference(cnf_transformation,[],[f916]) ).
tff(f2618,plain,
spl17_189,
inference(avatar_split_clause,[],[f1584,f2616]) ).
tff(f2616,plain,
( spl17_189
<=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_189])]) ).
tff(f1584,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1583,f1119]) ).
tff(f1583,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(forward_demodulation,[],[f1349,f1119]) ).
tff(f1349,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(cnf_transformation,[],[f915]) ).
tff(f915,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
| ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
& ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ) ),
inference(ennf_transformation,[],[f589]) ).
tff(f589,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0)))) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X9: fun_fu1430349052l_bool,X10: fun_fu1430349052l_bool] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X9)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X10))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X10),X9)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_111_finite__Collect__conjI) ).
tff(f2614,plain,
spl17_188,
inference(avatar_split_clause,[],[f1582,f2612]) ).
tff(f2612,plain,
( spl17_188
<=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_188])]) ).
tff(f1582,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))) ),
inference(forward_demodulation,[],[f1581,f1119]) ).
tff(f1581,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
inference(forward_demodulation,[],[f1350,f1119]) ).
tff(f1350,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
inference(cnf_transformation,[],[f915]) ).
tff(f2609,plain,
spl17_187,
inference(avatar_split_clause,[],[f1455,f2607]) ).
tff(f2607,plain,
( spl17_187
<=> ! [X2: fun_pname_bool,X0: fun_fu802393907l_bool,X1: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_187])]) ).
tff(f1455,plain,
! [X2: fun_pname_bool,X0: fun_fu802393907l_bool,X1: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f654]) ).
tff(f654,plain,
! [X0: fun_fu802393907l_bool,X1: fun_pname_bool,X2: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1) ),
inference(rectify,[],[f352]) ).
tff(f352,axiom,
! [X41: fun_fu802393907l_bool,X42: fun_pname_bool,X43: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X41),X42),X43) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
tff(f2605,plain,
spl17_186,
inference(avatar_split_clause,[],[f1454,f2603]) ).
tff(f2603,plain,
( spl17_186
<=> ! [X2: fun_pname_bool,X0: fun_fu931343505l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_186])]) ).
tff(f1454,plain,
! [X2: fun_pname_bool,X0: fun_fu931343505l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f653]) ).
tff(f653,plain,
! [X0: fun_fu931343505l_bool,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X0,X2),X1) ),
inference(rectify,[],[f355]) ).
tff(f355,axiom,
! [X41: fun_fu931343505l_bool,X42: fun_fu1430349052l_bool,X43: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X41),X42),X43) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_049) ).
tff(f2601,plain,
spl17_185,
inference(avatar_split_clause,[],[f1453,f2599]) ).
tff(f2599,plain,
( spl17_185
<=> ! [X2: fun_a_bool,X0: fun_fu1471507361l_bool,X1: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_185])]) ).
tff(f1453,plain,
! [X2: fun_a_bool,X0: fun_fu1471507361l_bool,X1: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f652]) ).
tff(f652,plain,
! [X0: fun_fu1471507361l_bool,X1: fun_a_bool,X2: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1) ),
inference(rectify,[],[f347]) ).
tff(f347,axiom,
! [X41: fun_fu1471507361l_bool,X42: fun_a_bool,X43: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X41),X42),X43) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
tff(f2597,plain,
spl17_184,
inference(avatar_split_clause,[],[f1452,f2595]) ).
tff(f2595,plain,
( spl17_184
<=> ! [X2: fun_a_bool,X0: fun_fu386216885l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_184])]) ).
tff(f1452,plain,
! [X2: fun_a_bool,X0: fun_fu386216885l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f651]) ).
tff(f651,plain,
! [X0: fun_fu386216885l_bool,X1: fun_fun_a_bool_bool,X2: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X0,X2),X1) ),
inference(rectify,[],[f353]) ).
tff(f353,axiom,
! [X41: fun_fu386216885l_bool,X42: fun_fun_a_bool_bool,X43: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X41),X42),X43) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
tff(f2593,plain,
spl17_183,
inference(avatar_split_clause,[],[f1451,f2591]) ).
tff(f2591,plain,
( spl17_183
<=> ! [X2: fun_nat_bool,X0: fun_fu1217155507l_bool,X1: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_183])]) ).
tff(f1451,plain,
! [X2: fun_nat_bool,X0: fun_fu1217155507l_bool,X1: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f650]) ).
tff(f650,plain,
! [X0: fun_fu1217155507l_bool,X1: fun_nat_bool,X2: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1) ),
inference(rectify,[],[f349]) ).
tff(f349,axiom,
! [X41: fun_fu1217155507l_bool,X42: fun_nat_bool,X43: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X41),X42),X43) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
tff(f2589,plain,
spl17_182,
inference(avatar_split_clause,[],[f1450,f2587]) ).
tff(f2587,plain,
( spl17_182
<=> ! [X2: fun_nat_bool,X0: fun_fu1436348701l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_182])]) ).
tff(f1450,plain,
! [X2: fun_nat_bool,X0: fun_fu1436348701l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f649]) ).
tff(f649,plain,
! [X0: fun_fu1436348701l_bool,X1: fun_fu425979586l_bool,X2: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X0,X2),X1) ),
inference(rectify,[],[f354]) ).
tff(f354,axiom,
! [X41: fun_fu1436348701l_bool,X42: fun_fu425979586l_bool,X43: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X41),X42),X43) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__048) ).
tff(f2585,plain,
spl17_181,
inference(avatar_split_clause,[],[f1449,f2583]) ).
tff(f2583,plain,
( spl17_181
<=> ! [X2: nat,X0: fun_nat_fun_nat_bool,X1: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_181])]) ).
tff(f1449,plain,
! [X2: nat,X0: fun_nat_fun_nat_bool,X1: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f648]) ).
tff(f648,plain,
! [X0: fun_nat_fun_nat_bool,X1: nat,X2: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1) ),
inference(rectify,[],[f328]) ).
tff(f328,axiom,
! [X41: fun_nat_fun_nat_bool,X42: nat,X43: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X41),X42),X43) = hAPP_nat_bool(hAPP_n1699378549t_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
tff(f2581,plain,
spl17_180,
inference(avatar_split_clause,[],[f1448,f2579]) ).
tff(f2579,plain,
( spl17_180
<=> ! [X2: nat,X0: fun_na1436237685l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_180])]) ).
tff(f1448,plain,
! [X2: nat,X0: fun_na1436237685l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f647]) ).
tff(f647,plain,
! [X0: fun_na1436237685l_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1) ),
inference(rectify,[],[f339]) ).
tff(f339,axiom,
! [X41: fun_na1436237685l_bool,X42: fun_nat_bool,X43: nat] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X41),X42),X43) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
tff(f2577,plain,
spl17_179,
inference(avatar_split_clause,[],[f1447,f2575]) ).
tff(f2575,plain,
( spl17_179
<=> ! [X2: fun_fun_a_bool_bool,X0: fun_fu418465139l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_179])]) ).
tff(f1447,plain,
! [X2: fun_fun_a_bool_bool,X0: fun_fu418465139l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f646]) ).
tff(f646,plain,
! [X0: fun_fu418465139l_bool,X1: fun_fun_a_bool_bool,X2: fun_fun_a_bool_bool] : ( hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1) ),
inference(rectify,[],[f356]) ).
tff(f356,axiom,
! [X41: fun_fu418465139l_bool,X42: fun_fun_a_bool_bool,X43: fun_fun_a_bool_bool] : ( hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X41),X42),X43) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
tff(f2573,plain,
spl17_178,
inference(avatar_split_clause,[],[f1446,f2571]) ).
tff(f2571,plain,
( spl17_178
<=> ! [X2: fun_fu425979586l_bool,X0: fun_fu140186515l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_178])]) ).
tff(f1446,plain,
! [X2: fun_fu425979586l_bool,X0: fun_fu140186515l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f645]) ).
tff(f645,plain,
! [X0: fun_fu140186515l_bool,X1: fun_fu425979586l_bool,X2: fun_fu425979586l_bool] : ( hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1) ),
inference(rectify,[],[f357]) ).
tff(f357,axiom,
! [X41: fun_fu140186515l_bool,X42: fun_fu425979586l_bool,X43: fun_fu425979586l_bool] : ( hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X41),X42),X43) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).
tff(f2568,plain,
spl17_177,
inference(avatar_split_clause,[],[f1445,f2566]) ).
tff(f2566,plain,
( spl17_177
<=> ! [X2: fun_fu1430349052l_bool,X0: fun_fu1911931399l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_177])]) ).
tff(f1445,plain,
! [X2: fun_fu1430349052l_bool,X0: fun_fu1911931399l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f644]) ).
tff(f644,plain,
! [X0: fun_fu1911931399l_bool,X1: fun_fu1430349052l_bool,X2: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1) ),
inference(rectify,[],[f358]) ).
tff(f358,axiom,
! [X41: fun_fu1911931399l_bool,X42: fun_fu1430349052l_bool,X43: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X41),X42),X43) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
tff(f2564,plain,
spl17_176,
inference(avatar_split_clause,[],[f1444,f2562]) ).
tff(f2562,plain,
( spl17_176
<=> ! [X2: x_a,X0: fun_a_fun_a_bool,X1: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_176])]) ).
tff(f1444,plain,
! [X2: x_a,X0: fun_a_fun_a_bool,X1: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f643]) ).
tff(f643,plain,
! [X0: fun_a_fun_a_bool,X1: x_a,X2: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ),
inference(rectify,[],[f318]) ).
tff(f318,axiom,
! [X41: fun_a_fun_a_bool,X42: x_a,X43: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X41),X42),X43) = hAPP_a_bool(hAPP_a_fun_a_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
tff(f2560,plain,
spl17_175,
inference(avatar_split_clause,[],[f1443,f2558]) ).
tff(f2558,plain,
( spl17_175
<=> ! [X2: pname,X0: fun_pn800050071e_bool,X1: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_175])]) ).
tff(f1443,plain,
! [X2: pname,X0: fun_pn800050071e_bool,X1: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f642]) ).
tff(f642,plain,
! [X0: fun_pn800050071e_bool,X1: pname,X2: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1) ),
inference(rectify,[],[f333]) ).
tff(f333,axiom,
! [X41: fun_pn800050071e_bool,X42: pname,X43: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X41),X42),X43) = hAPP_pname_bool(hAPP_p61793385e_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
tff(f2556,plain,
spl17_174,
inference(avatar_split_clause,[],[f1442,f2554]) ).
tff(f2554,plain,
( spl17_174
<=> ! [X2: pname,X0: fun_pn422929397l_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_174])]) ).
tff(f1442,plain,
! [X2: pname,X0: fun_pn422929397l_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f641]) ).
tff(f641,plain,
! [X0: fun_pn422929397l_bool,X1: fun_pname_bool,X2: pname] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1) ),
inference(rectify,[],[f346]) ).
tff(f346,axiom,
! [X41: fun_pn422929397l_bool,X42: fun_pname_bool,X43: pname] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X41),X42),X43) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
tff(f2552,plain,
spl17_173,
inference(avatar_split_clause,[],[f1441,f2550]) ).
tff(f2550,plain,
( spl17_173
<=> ! [X2: x_a,X0: fun_a_1255737515l_bool,X1: fun_a_bool] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_173])]) ).
tff(f1441,plain,
! [X2: x_a,X0: fun_a_1255737515l_bool,X1: fun_a_bool] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f640]) ).
tff(f640,plain,
! [X0: fun_a_1255737515l_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ),
inference(rectify,[],[f334]) ).
tff(f334,axiom,
! [X41: fun_a_1255737515l_bool,X42: fun_a_bool,X43: x_a] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X41),X42),X43) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
tff(f2548,plain,
spl17_172,
inference(avatar_split_clause,[],[f1440,f2546]) ).
tff(f2546,plain,
( spl17_172
<=> ! [X2: pname,X0: fun_pname_fun_a_bool,X1: x_a] : ( hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_172])]) ).
tff(f1440,plain,
! [X2: pname,X0: fun_pname_fun_a_bool,X1: x_a] : ( hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f639]) ).
tff(f639,plain,
! [X0: fun_pname_fun_a_bool,X1: x_a,X2: pname] : ( hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1) ),
inference(rectify,[],[f323]) ).
tff(f323,axiom,
! [X41: fun_pname_fun_a_bool,X42: x_a,X43: pname] : ( hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X41),X42),X43) = hAPP_a_bool(hAPP_p1534023578a_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
tff(f2544,plain,
spl17_171,
inference(avatar_split_clause,[],[f1439,f2542]) ).
tff(f2542,plain,
( spl17_171
<=> ! [X2: fun_fu885608257l_bool,X0: fun_fu821736593l_bool,X1: fun_fu885608257l_bool] : ( hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X0),X1),X2) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_171])]) ).
tff(f1439,plain,
! [X2: fun_fu885608257l_bool,X0: fun_fu821736593l_bool,X1: fun_fu885608257l_bool] : ( hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X0),X1),X2) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f638]) ).
tff(f638,plain,
! [X0: fun_fu821736593l_bool,X1: fun_fu885608257l_bool,X2: fun_fu885608257l_bool] : ( hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X0),X1),X2) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X0,X2),X1) ),
inference(rectify,[],[f359]) ).
tff(f359,axiom,
! [X41: fun_fu821736593l_bool,X42: fun_fu885608257l_bool,X43: fun_fu885608257l_bool] : ( hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X41),X42),X43) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).
tff(f2540,plain,
spl17_170,
inference(avatar_split_clause,[],[f1438,f2538]) ).
tff(f2538,plain,
( spl17_170
<=> ! [X2: fun_fu814369080l_bool,X0: fun_fu1137991347l_bool,X1: fun_fu814369080l_bool] : ( hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X0),X1),X2) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_170])]) ).
tff(f1438,plain,
! [X2: fun_fu814369080l_bool,X0: fun_fu1137991347l_bool,X1: fun_fu814369080l_bool] : ( hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X0),X1),X2) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f637]) ).
tff(f637,plain,
! [X0: fun_fu1137991347l_bool,X1: fun_fu814369080l_bool,X2: fun_fu814369080l_bool] : ( hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X0),X1),X2) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X0,X2),X1) ),
inference(rectify,[],[f360]) ).
tff(f360,axiom,
! [X41: fun_fu1137991347l_bool,X42: fun_fu814369080l_bool,X43: fun_fu814369080l_bool] : ( hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X41),X42),X43) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
tff(f2536,plain,
spl17_169,
inference(avatar_split_clause,[],[f1437,f2534]) ).
tff(f2534,plain,
( spl17_169
<=> ! [X2: fun_fu399576434l_bool,X0: fun_fu1086940979l_bool,X1: fun_fu399576434l_bool] : ( hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X0),X1),X2) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_169])]) ).
tff(f1437,plain,
! [X2: fun_fu399576434l_bool,X0: fun_fu1086940979l_bool,X1: fun_fu399576434l_bool] : ( hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X0),X1),X2) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X0,X2),X1) ),
inference(cnf_transformation,[],[f636]) ).
tff(f636,plain,
! [X0: fun_fu1086940979l_bool,X1: fun_fu399576434l_bool,X2: fun_fu399576434l_bool] : ( hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X0),X1),X2) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X0,X2),X1) ),
inference(rectify,[],[f361]) ).
tff(f361,axiom,
! [X41: fun_fu1086940979l_bool,X42: fun_fu399576434l_bool,X43: fun_fu399576434l_bool] : ( hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X41),X42),X43) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X41,X43),X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
tff(f2532,plain,
spl17_168,
inference(avatar_split_clause,[],[f1200,f2530]) ).
tff(f1200,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f451]) ).
tff(f451,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f127]) ).
tff(f127,axiom,
! [X12: nat,X11: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_126_nat__le__linear) ).
tff(f2528,plain,
spl17_167,
inference(avatar_split_clause,[],[f1149,f2526]) ).
tff(f2526,plain,
( spl17_167
<=> ! [X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_167])]) ).
tff(f1149,plain,
! [X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK0(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1018]) ).
tff(f2524,plain,
spl17_166,
inference(avatar_split_clause,[],[f1148,f2522]) ).
tff(f2522,plain,
( spl17_166
<=> ! [X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_166])]) ).
tff(f1148,plain,
! [X0: fun_nat_bool,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK0(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1018]) ).
tff(f2520,plain,
spl17_165,
inference(avatar_split_clause,[],[f1143,f2518]) ).
tff(f2518,plain,
( spl17_165
<=> ! [X0: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_165])]) ).
tff(f1143,plain,
! [X0: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ),
inference(cnf_transformation,[],[f736]) ).
tff(f736,plain,
! [X0: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ),
inference(ennf_transformation,[],[f396]) ).
tff(f396,plain,
! [X0: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0)))) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X2: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_8_finite__Collect__subsets) ).
tff(f2516,plain,
spl17_164,
inference(avatar_split_clause,[],[f1142,f2514]) ).
tff(f2514,plain,
( spl17_164
<=> ! [X0: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_164])]) ).
tff(f1142,plain,
! [X0: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ),
inference(cnf_transformation,[],[f735]) ).
tff(f735,plain,
! [X0: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ),
inference(ennf_transformation,[],[f395]) ).
tff(f395,plain,
! [X0: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0)))) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X2: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_7_finite__Collect__subsets) ).
tff(f2512,plain,
spl17_163,
inference(avatar_split_clause,[],[f1141,f2510]) ).
tff(f2510,plain,
( spl17_163
<=> ! [X0: fun_fu425979586l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_163])]) ).
tff(f1141,plain,
! [X0: fun_fu425979586l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
inference(cnf_transformation,[],[f734]) ).
tff(f734,plain,
! [X0: fun_fu425979586l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
inference(ennf_transformation,[],[f394]) ).
tff(f394,plain,
! [X0: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0)))) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X2: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_9_finite__Collect__subsets) ).
tff(f2508,plain,
spl17_162,
inference(avatar_split_clause,[],[f1140,f2506]) ).
tff(f2506,plain,
( spl17_162
<=> ! [X0: fun_fu399576434l_bool] :
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X0))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_162])]) ).
tff(f1140,plain,
! [X0: fun_fu399576434l_bool] :
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X0))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0)) ),
inference(cnf_transformation,[],[f733]) ).
tff(f733,plain,
! [X0: fun_fu399576434l_bool] :
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X0))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0)) ),
inference(ennf_transformation,[],[f393]) ).
tff(f393,plain,
! [X0: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X0))
=> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X0)))) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X2: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2))
=> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_5_finite__Collect__subsets) ).
tff(f2504,plain,
spl17_161,
inference(avatar_split_clause,[],[f1139,f2502]) ).
tff(f2502,plain,
( spl17_161
<=> ! [X0: fun_fu814369080l_bool] :
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X0))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_161])]) ).
tff(f1139,plain,
! [X0: fun_fu814369080l_bool] :
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X0))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0)) ),
inference(cnf_transformation,[],[f732]) ).
tff(f732,plain,
! [X0: fun_fu814369080l_bool] :
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X0))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0)) ),
inference(ennf_transformation,[],[f392]) ).
tff(f392,plain,
! [X0: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X0))
=> hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X0)))) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X2: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2))
=> hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_4_finite__Collect__subsets) ).
tff(f2500,plain,
spl17_160,
inference(avatar_split_clause,[],[f1138,f2498]) ).
tff(f2498,plain,
( spl17_160
<=> ! [X0: fun_fu885608257l_bool] :
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X0))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_160])]) ).
tff(f1138,plain,
! [X0: fun_fu885608257l_bool] :
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X0))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0)) ),
inference(cnf_transformation,[],[f731]) ).
tff(f731,plain,
! [X0: fun_fu885608257l_bool] :
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X0))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0)) ),
inference(ennf_transformation,[],[f391]) ).
tff(f391,plain,
! [X0: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X0))
=> hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X0)))) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X2: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2))
=> hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_6_finite__Collect__subsets) ).
tff(f2496,plain,
spl17_159,
inference(avatar_split_clause,[],[f1116,f2493]) ).
tff(f2493,plain,
( spl17_159
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_159])]) ).
tff(f1116,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
inference(cnf_transformation,[],[f364]) ).
tff(f364,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',conj_2) ).
tff(f2491,plain,
( spl17_158
| ~ spl17_12
| ~ spl17_133 ),
inference(avatar_split_clause,[],[f2330,f2231,f1685,f2489]) ).
tff(f2489,plain,
( spl17_158
<=> ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_158])]) ).
tff(f1685,plain,
( spl17_12
<=> ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
tff(f2330,plain,
( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0))
| ~ spl17_12
| ~ spl17_133 ),
inference(resolution,[],[f2232,f1686]) ).
tff(f1686,plain,
( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0))
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f1685]) ).
tff(f2351,plain,
( spl17_157
| ~ spl17_9
| ~ spl17_134 ),
inference(avatar_split_clause,[],[f2335,f2235,f1672,f2348]) ).
tff(f2335,plain,
( ( u = insert_pname(pn,u) )
| ~ spl17_9
| ~ spl17_134 ),
inference(resolution,[],[f2236,f1674]) ).
tff(f1674,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f1672]) ).
tff(f2325,plain,
spl17_156,
inference(avatar_split_clause,[],[f1574,f2323]) ).
tff(f2323,plain,
( spl17_156
<=> ! [X0: fun_pname_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_156])]) ).
tff(f1574,plain,
! [X0: fun_pname_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
inference(forward_demodulation,[],[f1146,f1119]) ).
tff(f1146,plain,
! [X0: fun_pname_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
inference(cnf_transformation,[],[f739]) ).
tff(f739,plain,
! [X0: fun_pname_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
inference(ennf_transformation,[],[f399]) ).
tff(f399,plain,
! [X0: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0)))) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_2_finite__Collect__subsets) ).
tff(f2321,plain,
spl17_155,
inference(avatar_split_clause,[],[f1573,f2319]) ).
tff(f2319,plain,
( spl17_155
<=> ! [X0: fun_a_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_155])]) ).
tff(f1573,plain,
! [X0: fun_a_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
inference(forward_demodulation,[],[f1145,f1120]) ).
tff(f1145,plain,
! [X0: fun_a_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
inference(cnf_transformation,[],[f738]) ).
tff(f738,plain,
! [X0: fun_a_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
inference(ennf_transformation,[],[f398]) ).
tff(f398,plain,
! [X0: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0)))) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_3_finite__Collect__subsets) ).
tff(f2317,plain,
spl17_154,
inference(avatar_split_clause,[],[f1572,f2315]) ).
tff(f2315,plain,
( spl17_154
<=> ! [X0: fun_nat_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_154])]) ).
tff(f1572,plain,
! [X0: fun_nat_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(forward_demodulation,[],[f1144,f1121]) ).
tff(f1144,plain,
! [X0: fun_nat_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(cnf_transformation,[],[f737]) ).
tff(f737,plain,
! [X0: fun_nat_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
inference(ennf_transformation,[],[f397]) ).
tff(f397,plain,
! [X0: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0)))) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_1_finite__Collect__subsets) ).
tff(f2313,plain,
spl17_153,
inference(avatar_split_clause,[],[f1528,f2311]) ).
tff(f2311,plain,
( spl17_153
<=> ! [X2: fun_pname_bool,X0: pname,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2)))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_153])]) ).
tff(f1528,plain,
! [X2: fun_pname_bool,X0: pname,X1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2)))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1000]) ).
tff(f1000,plain,
! [X0: pname,X1: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2)))
| ( ( X0 != X1 )
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
inference(ennf_transformation,[],[f712]) ).
tff(f712,plain,
! [X0: pname,X1: pname,X2: fun_pname_bool] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
=> ( X0 = X1 ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X0,X2))) ),
inference(rectify,[],[f185]) ).
tff(f185,axiom,
! [X28: pname,X5: pname,X7: fun_pname_bool] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),X7))
=> ( X5 = X28 ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),insert_pname(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_184_insertCI) ).
tff(f2309,plain,
spl17_152,
inference(avatar_split_clause,[],[f1526,f2307]) ).
tff(f2307,plain,
( spl17_152
<=> ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_152])]) ).
tff(f1526,plain,
! [X2: fun_a_bool,X0: x_a,X1: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f999]) ).
tff(f999,plain,
! [X0: x_a,X1: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
| ( ( X0 != X1 )
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
inference(ennf_transformation,[],[f711]) ).
tff(f711,plain,
! [X0: x_a,X1: x_a,X2: fun_a_bool] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
=> ( X0 = X1 ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2))) ),
inference(rectify,[],[f186]) ).
tff(f186,axiom,
! [X28: x_a,X5: x_a,X7: fun_a_bool] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),X7))
=> ( X5 = X28 ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),insert_a(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_185_insertCI) ).
tff(f2305,plain,
spl17_151,
inference(avatar_split_clause,[],[f1524,f2303]) ).
tff(f2303,plain,
( spl17_151
<=> ! [X2: fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2)))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_151])]) ).
tff(f1524,plain,
! [X2: fun_nat_bool,X0: nat,X1: nat] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2)))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f998]) ).
tff(f998,plain,
! [X0: nat,X1: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2)))
| ( ( X0 != X1 )
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f710]) ).
tff(f710,plain,
! [X0: nat,X1: nat,X2: fun_nat_bool] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
=> ( X0 = X1 ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X0,X2))) ),
inference(rectify,[],[f184]) ).
tff(f184,axiom,
! [X28: nat,X5: nat,X7: fun_nat_bool] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X7))
=> ( X5 = X28 ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),insert_nat(X28,X7))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_183_insertCI) ).
tff(f2301,plain,
spl17_150,
inference(avatar_split_clause,[],[f1436,f2299]) ).
tff(f2299,plain,
( spl17_150
<=> ! [X2: fun_pname_bool,X0: fun_bool_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_150])]) ).
tff(f1436,plain,
! [X2: fun_pname_bool,X0: fun_bool_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ),
inference(cnf_transformation,[],[f635]) ).
tff(f635,plain,
! [X0: fun_bool_bool,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] : ( hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ),
inference(rectify,[],[f343]) ).
tff(f343,axiom,
! [X41: fun_bool_bool,X42: fun_fu1430349052l_bool,X43: fun_pname_bool] : ( hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X41,X42),X43) = hAPP_bool_bool(X41,hAPP_f1664156314l_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
tff(f2297,plain,
spl17_149,
inference(avatar_split_clause,[],[f1435,f2295]) ).
tff(f2295,plain,
( spl17_149
<=> ! [X2: fun_a_bool,X0: fun_bool_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_149])]) ).
tff(f1435,plain,
! [X2: fun_a_bool,X0: fun_bool_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ),
inference(cnf_transformation,[],[f634]) ).
tff(f634,plain,
! [X0: fun_bool_bool,X1: fun_fun_a_bool_bool,X2: fun_a_bool] : ( hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ),
inference(rectify,[],[f336]) ).
tff(f336,axiom,
! [X41: fun_bool_bool,X42: fun_fun_a_bool_bool,X43: fun_a_bool] : ( hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X41,X42),X43) = hAPP_bool_bool(X41,hAPP_fun_a_bool_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).
tff(f2293,plain,
spl17_148,
inference(avatar_split_clause,[],[f1434,f2291]) ).
tff(f2291,plain,
( spl17_148
<=> ! [X2: fun_nat_bool,X0: fun_bool_bool,X1: fun_fu425979586l_bool] : ( hAPP_f54304608l_bool(cOMBB_238756964t_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_148])]) ).
tff(f1434,plain,
! [X2: fun_nat_bool,X0: fun_bool_bool,X1: fun_fu425979586l_bool] : ( hAPP_f54304608l_bool(cOMBB_238756964t_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)) ),
inference(cnf_transformation,[],[f633]) ).
tff(f633,plain,
! [X0: fun_bool_bool,X1: fun_fu425979586l_bool,X2: fun_nat_bool] : ( hAPP_f54304608l_bool(cOMBB_238756964t_bool(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_f54304608l_bool(X1,X2)) ),
inference(rectify,[],[f340]) ).
tff(f340,axiom,
! [X41: fun_bool_bool,X42: fun_fu425979586l_bool,X43: fun_nat_bool] : ( hAPP_f54304608l_bool(cOMBB_238756964t_bool(X41,X42),X43) = hAPP_bool_bool(X41,hAPP_f54304608l_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).
tff(f2289,plain,
spl17_147,
inference(avatar_split_clause,[],[f1433,f2287]) ).
tff(f2287,plain,
( spl17_147
<=> ! [X2: nat,X0: fun_bool_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_147])]) ).
tff(f1433,plain,
! [X2: nat,X0: fun_bool_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f632]) ).
tff(f632,plain,
! [X0: fun_bool_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)) ),
inference(rectify,[],[f329]) ).
tff(f329,axiom,
! [X41: fun_bool_bool,X42: fun_nat_bool,X43: nat] : ( hAPP_nat_bool(cOMBB_bool_bool_nat(X41,X42),X43) = hAPP_bool_bool(X41,hAPP_nat_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
tff(f2285,plain,
spl17_146,
inference(avatar_split_clause,[],[f1432,f2283]) ).
tff(f1432,plain,
! [X2: fun_a_bool,X0: x_a,X1: x_a] : ( insert_a(X0,insert_a(X1,X2)) = insert_a(X1,insert_a(X0,X2)) ),
inference(cnf_transformation,[],[f631]) ).
tff(f631,plain,
! [X0: x_a,X1: x_a,X2: fun_a_bool] : ( insert_a(X0,insert_a(X1,X2)) = insert_a(X1,insert_a(X0,X2)) ),
inference(rectify,[],[f210]) ).
tff(f210,axiom,
! [X8: x_a,X30: x_a,X2: fun_a_bool] : ( insert_a(X8,insert_a(X30,X2)) = insert_a(X30,insert_a(X8,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_209_insert__commute) ).
tff(f2281,plain,
spl17_145,
inference(avatar_split_clause,[],[f1431,f2279]) ).
tff(f1431,plain,
! [X2: fun_pname_bool,X0: pname,X1: pname] : ( insert_pname(X0,insert_pname(X1,X2)) = insert_pname(X1,insert_pname(X0,X2)) ),
inference(cnf_transformation,[],[f630]) ).
tff(f630,plain,
! [X0: pname,X1: pname,X2: fun_pname_bool] : ( insert_pname(X0,insert_pname(X1,X2)) = insert_pname(X1,insert_pname(X0,X2)) ),
inference(rectify,[],[f209]) ).
tff(f209,axiom,
! [X8: pname,X30: pname,X2: fun_pname_bool] : ( insert_pname(X8,insert_pname(X30,X2)) = insert_pname(X30,insert_pname(X8,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_208_insert__commute) ).
tff(f2277,plain,
spl17_144,
inference(avatar_split_clause,[],[f1430,f2275]) ).
tff(f1430,plain,
! [X2: fun_nat_bool,X0: nat,X1: nat] : ( insert_nat(X0,insert_nat(X1,X2)) = insert_nat(X1,insert_nat(X0,X2)) ),
inference(cnf_transformation,[],[f629]) ).
tff(f629,plain,
! [X0: nat,X1: nat,X2: fun_nat_bool] : ( insert_nat(X0,insert_nat(X1,X2)) = insert_nat(X1,insert_nat(X0,X2)) ),
inference(rectify,[],[f208]) ).
tff(f208,axiom,
! [X8: nat,X30: nat,X2: fun_nat_bool] : ( insert_nat(X8,insert_nat(X30,X2)) = insert_nat(X30,insert_nat(X8,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_207_insert__commute) ).
tff(f2273,plain,
spl17_143,
inference(avatar_split_clause,[],[f1429,f2271]) ).
tff(f2271,plain,
( spl17_143
<=> ! [X2: x_a,X0: fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_143])]) ).
tff(f1429,plain,
! [X2: x_a,X0: fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f628]) ).
tff(f628,plain,
! [X0: fun_bool_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)) ),
inference(rectify,[],[f321]) ).
tff(f321,axiom,
! [X41: fun_bool_bool,X42: fun_a_bool,X43: x_a] : ( hAPP_a_bool(cOMBB_bool_bool_a(X41,X42),X43) = hAPP_bool_bool(X41,hAPP_a_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
tff(f2269,plain,
spl17_142,
inference(avatar_split_clause,[],[f1428,f2267]) ).
tff(f2267,plain,
( spl17_142
<=> ! [X2: pname,X0: fun_bool_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_142])]) ).
tff(f1428,plain,
! [X2: pname,X0: fun_bool_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)) ),
inference(cnf_transformation,[],[f627]) ).
tff(f627,plain,
! [X0: fun_bool_bool,X1: fun_pname_bool,X2: pname] : ( hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)) ),
inference(rectify,[],[f331]) ).
tff(f331,axiom,
! [X41: fun_bool_bool,X42: fun_pname_bool,X43: pname] : ( hAPP_pname_bool(cOMBB_647938656_pname(X41,X42),X43) = hAPP_bool_bool(X41,hAPP_pname_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
tff(f2265,plain,
spl17_141,
inference(avatar_split_clause,[],[f1427,f2263]) ).
tff(f2263,plain,
( spl17_141
<=> ! [X2: pname,X0: fun_bo1549164019l_bool,X1: fun_pname_bool] : ( hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_141])]) ).
tff(f1427,plain,
! [X2: pname,X0: fun_bo1549164019l_bool,X1: fun_pname_bool] : ( hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)) ),
inference(cnf_transformation,[],[f626]) ).
tff(f626,plain,
! [X0: fun_bo1549164019l_bool,X1: fun_pname_bool,X2: pname] : ( hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)) ),
inference(rectify,[],[f344]) ).
tff(f344,axiom,
! [X41: fun_bo1549164019l_bool,X42: fun_pname_bool,X43: pname] : ( hAPP_p393069232l_bool(cOMBB_675860798_pname(X41,X42),X43) = hAPP_b589554111l_bool(X41,hAPP_pname_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_044) ).
tff(f2261,plain,
spl17_140,
inference(avatar_split_clause,[],[f1426,f2259]) ).
tff(f2259,plain,
( spl17_140
<=> ! [X2: fun_pname_bool,X0: fun_bo1549164019l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_140])]) ).
tff(f1426,plain,
! [X2: fun_pname_bool,X0: fun_bo1549164019l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ),
inference(cnf_transformation,[],[f625]) ).
tff(f625,plain,
! [X0: fun_bo1549164019l_bool,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] : ( hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ),
inference(rectify,[],[f351]) ).
tff(f351,axiom,
! [X41: fun_bo1549164019l_bool,X42: fun_fu1430349052l_bool,X43: fun_pname_bool] : ( hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X41,X42),X43) = hAPP_b589554111l_bool(X41,hAPP_f1664156314l_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_047) ).
tff(f2257,plain,
spl17_139,
inference(avatar_split_clause,[],[f1425,f2255]) ).
tff(f2255,plain,
( spl17_139
<=> ! [X2: fun_a_bool,X0: fun_bo1549164019l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_139])]) ).
tff(f1425,plain,
! [X2: fun_a_bool,X0: fun_bo1549164019l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ),
inference(cnf_transformation,[],[f624]) ).
tff(f624,plain,
! [X0: fun_bo1549164019l_bool,X1: fun_fun_a_bool_bool,X2: fun_a_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ),
inference(rectify,[],[f348]) ).
tff(f348,axiom,
! [X41: fun_bo1549164019l_bool,X42: fun_fun_a_bool_bool,X43: fun_a_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X41,X42),X43) = hAPP_b589554111l_bool(X41,hAPP_fun_a_bool_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_045) ).
tff(f2253,plain,
spl17_138,
inference(avatar_split_clause,[],[f1424,f2251]) ).
tff(f2251,plain,
( spl17_138
<=> ! [X2: fun_nat_bool,X0: fun_bo1549164019l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_138])]) ).
tff(f1424,plain,
! [X2: fun_nat_bool,X0: fun_bo1549164019l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)) ),
inference(cnf_transformation,[],[f623]) ).
tff(f623,plain,
! [X0: fun_bo1549164019l_bool,X1: fun_fu425979586l_bool,X2: fun_nat_bool] : ( hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)) ),
inference(rectify,[],[f350]) ).
tff(f350,axiom,
! [X41: fun_bo1549164019l_bool,X42: fun_fu425979586l_bool,X43: fun_nat_bool] : ( hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X41,X42),X43) = hAPP_b589554111l_bool(X41,hAPP_f54304608l_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_046) ).
tff(f2249,plain,
spl17_137,
inference(avatar_split_clause,[],[f1423,f2247]) ).
tff(f2247,plain,
( spl17_137
<=> ! [X2: nat,X0: fun_bo1549164019l_bool,X1: fun_nat_bool] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_137])]) ).
tff(f1423,plain,
! [X2: nat,X0: fun_bo1549164019l_bool,X1: fun_nat_bool] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f622]) ).
tff(f622,plain,
! [X0: fun_bo1549164019l_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)) ),
inference(rectify,[],[f341]) ).
tff(f341,axiom,
! [X41: fun_bo1549164019l_bool,X42: fun_nat_bool,X43: nat] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X41,X42),X43) = hAPP_b589554111l_bool(X41,hAPP_nat_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_043) ).
tff(f2245,plain,
spl17_136,
inference(avatar_split_clause,[],[f1422,f2243]) ).
tff(f2243,plain,
( spl17_136
<=> ! [X2: x_a,X0: fun_bo1549164019l_bool,X1: fun_a_bool] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_136])]) ).
tff(f1422,plain,
! [X2: x_a,X0: fun_bo1549164019l_bool,X1: fun_a_bool] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f621]) ).
tff(f621,plain,
! [X0: fun_bo1549164019l_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)) ),
inference(rectify,[],[f337]) ).
tff(f337,axiom,
! [X41: fun_bo1549164019l_bool,X42: fun_a_bool,X43: x_a] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X41,X42),X43) = hAPP_b589554111l_bool(X41,hAPP_a_bool(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
tff(f2241,plain,
spl17_135,
inference(avatar_split_clause,[],[f1421,f2239]) ).
tff(f2239,plain,
( spl17_135
<=> ! [X2: pname,X0: fun_a_fun_a_bool,X1: fun_pname_a] : ( hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_135])]) ).
tff(f1421,plain,
! [X2: pname,X0: fun_a_fun_a_bool,X1: fun_pname_a] : ( hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)) ),
inference(cnf_transformation,[],[f620]) ).
tff(f620,plain,
! [X0: fun_a_fun_a_bool,X1: fun_pname_a,X2: pname] : ( hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)) ),
inference(rectify,[],[f335]) ).
tff(f335,axiom,
! [X41: fun_a_fun_a_bool,X42: fun_pname_a,X43: pname] : ( hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X41,X42),X43) = hAPP_a_fun_a_bool(X41,hAPP_pname_a(X42,X43)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
tff(f2237,plain,
spl17_134,
inference(avatar_split_clause,[],[f1342,f2235]) ).
tff(f1342,plain,
! [X0: pname,X1: fun_pname_bool] :
( ( insert_pname(X0,X1) = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(cnf_transformation,[],[f905]) ).
tff(f905,plain,
! [X0: pname,X1: fun_pname_bool] :
( ( insert_pname(X0,X1) = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(ennf_transformation,[],[f582]) ).
tff(f582,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
=> ( insert_pname(X0,X1) = X1 ) ),
inference(rectify,[],[f224]) ).
tff(f224,axiom,
! [X5: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),X2))
=> ( insert_pname(X5,X2) = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_223_insert__absorb) ).
tff(f2233,plain,
spl17_133,
inference(avatar_split_clause,[],[f1339,f2231]) ).
tff(f1339,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(cnf_transformation,[],[f900]) ).
tff(f900,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
=> hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_0_assms_I1_J) ).
tff(f2229,plain,
( spl17_132
| ~ spl17_9
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f2211,f2139,f1672,f2226]) ).
tff(f2226,plain,
( spl17_132
<=> hBOOL(hAPP_pname_bool(u,pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_132])]) ).
tff(f2139,plain,
( spl17_119
<=> ! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_119])]) ).
tff(f2211,plain,
( hBOOL(hAPP_pname_bool(u,pn))
| ~ spl17_9
| ~ spl17_119 ),
inference(resolution,[],[f2140,f1674]) ).
tff(f2140,plain,
( ! [X0: pname,X1: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| hBOOL(hAPP_pname_bool(X1,X0)) )
| ~ spl17_119 ),
inference(avatar_component_clause,[],[f2139]) ).
tff(f2224,plain,
spl17_131,
inference(avatar_split_clause,[],[f1338,f2222]) ).
tff(f1338,plain,
! [X0: x_a,X1: fun_a_bool] :
( ( insert_a(X0,X1) = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
inference(cnf_transformation,[],[f899]) ).
tff(f899,plain,
! [X0: x_a,X1: fun_a_bool] :
( ( insert_a(X0,X1) = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
inference(ennf_transformation,[],[f579]) ).
tff(f579,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
=> ( insert_a(X0,X1) = X1 ) ),
inference(rectify,[],[f225]) ).
tff(f225,axiom,
! [X5: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),X2))
=> ( insert_a(X5,X2) = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_224_insert__absorb) ).
tff(f2220,plain,
spl17_130,
inference(avatar_split_clause,[],[f1335,f2218]) ).
tff(f1335,plain,
! [X0: nat,X1: fun_nat_bool] :
( ( insert_nat(X0,X1) = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(cnf_transformation,[],[f894]) ).
tff(f894,plain,
! [X0: nat,X1: fun_nat_bool] :
( ( insert_nat(X0,X1) = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(ennf_transformation,[],[f576]) ).
tff(f576,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
=> ( insert_nat(X0,X1) = X1 ) ),
inference(rectify,[],[f223]) ).
tff(f223,axiom,
! [X5: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X2))
=> ( insert_nat(X5,X2) = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_222_insert__absorb) ).
tff(f2207,plain,
( ~ spl17_129
| spl17_17
| ~ spl17_117 ),
inference(avatar_split_clause,[],[f2201,f2131,f1706,f2204]) ).
tff(f2204,plain,
( spl17_129
<=> hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_129])]) ).
tff(f1706,plain,
( spl17_17
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
tff(f2201,plain,
( ~ hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn)))
| spl17_17
| ~ spl17_117 ),
inference(resolution,[],[f2132,f1708]) ).
tff(f1708,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g))
| spl17_17 ),
inference(avatar_component_clause,[],[f1706]) ).
tff(f2183,plain,
( spl17_128
| ~ spl17_54 ),
inference(avatar_split_clause,[],[f1884,f1856,f2181]) ).
tff(f1856,plain,
( spl17_54
<=> ! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_54])]) ).
tff(f1884,plain,
( ! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X0))
| ~ spl17_54 ),
inference(equality_resolution,[],[f1857]) ).
tff(f1857,plain,
( ! [X2: nat,X0: nat,X1: fun_nat_bool] :
( ( X0 != X2 )
| hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2)) )
| ~ spl17_54 ),
inference(avatar_component_clause,[],[f1856]) ).
tff(f2179,plain,
( spl17_127
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f1883,f1852,f2177]) ).
tff(f1852,plain,
( spl17_53
<=> ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_53])]) ).
tff(f1883,plain,
( ! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_a_bool(insert_a(X0,X1),X0))
| ~ spl17_53 ),
inference(equality_resolution,[],[f1853]) ).
tff(f1853,plain,
( ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
( ( X0 != X2 )
| hBOOL(hAPP_a_bool(insert_a(X0,X1),X2)) )
| ~ spl17_53 ),
inference(avatar_component_clause,[],[f1852]) ).
tff(f2169,plain,
spl17_126,
inference(avatar_split_clause,[],[f1571,f2167]) ).
tff(f2167,plain,
( spl17_126
<=> ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_126])]) ).
tff(f1571,plain,
! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)) ),
inference(forward_demodulation,[],[f1135,f1122]) ).
tff(f1135,plain,
! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) ),
inference(cnf_transformation,[],[f388]) ).
tff(f388,plain,
! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) ),
inference(rectify,[],[f119]) ).
tff(f119,axiom,
! [X14: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X14))) = hAPP_nat_nat(suc,X14) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_118_card__Collect__le__nat) ).
tff(f2165,plain,
spl17_125,
inference(avatar_split_clause,[],[f1543,f2163]) ).
tff(f2163,plain,
( spl17_125
<=> ! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_125])]) ).
tff(f1543,plain,
! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(cnf_transformation,[],[f1090]) ).
tff(f2161,plain,
spl17_124,
inference(avatar_split_clause,[],[f1540,f2159]) ).
tff(f2159,plain,
( spl17_124
<=> ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_124])]) ).
tff(f1540,plain,
! [X2: x_a,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(cnf_transformation,[],[f1088]) ).
tff(f2157,plain,
( spl17_123
| ~ spl17_52 ),
inference(avatar_split_clause,[],[f1882,f1848,f2155]) ).
tff(f1848,plain,
( spl17_52
<=> ! [X2: pname,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_52])]) ).
tff(f1882,plain,
( ! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X0))
| ~ spl17_52 ),
inference(equality_resolution,[],[f1849]) ).
tff(f1849,plain,
( ! [X2: pname,X0: pname,X1: fun_pname_bool] :
( ( X0 != X2 )
| hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2)) )
| ~ spl17_52 ),
inference(avatar_component_clause,[],[f1848]) ).
tff(f2153,plain,
spl17_122,
inference(avatar_split_clause,[],[f1537,f2151]) ).
tff(f2151,plain,
( spl17_122
<=> ! [X2: pname,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_122])]) ).
tff(f1537,plain,
! [X2: pname,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(cnf_transformation,[],[f1086]) ).
tff(f2149,plain,
spl17_121,
inference(avatar_split_clause,[],[f1397,f2147]) ).
tff(f2147,plain,
( spl17_121
<=> ! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_121])]) ).
tff(f1397,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1045]) ).
tff(f1045,plain,
! [X0: nat,X1: nat] :
( ( ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ) ),
inference(nnf_transformation,[],[f611]) ).
tff(f611,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f121]) ).
tff(f121,axiom,
! [X17: nat,X18: nat] :
( ( hAPP_nat_nat(suc,X17) = hAPP_nat_nat(suc,X18) )
<=> ( X17 = X18 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_120_nat_Oinject) ).
tff(f2145,plain,
spl17_120,
inference(avatar_split_clause,[],[f1395,f2143]) ).
tff(f1395,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) ),
inference(cnf_transformation,[],[f1044]) ).
tff(f1044,plain,
! [X0: pname,X1: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) )
& ( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
inference(nnf_transformation,[],[f610]) ).
tff(f610,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
<=> hBOOL(hAPP_pname_bool(X1,X0)) ),
inference(rectify,[],[f255]) ).
tff(f255,axiom,
! [X8: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
<=> hBOOL(hAPP_pname_bool(X2,X8)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_254_mem__def) ).
tff(f2141,plain,
spl17_119,
inference(avatar_split_clause,[],[f1394,f2139]) ).
tff(f1394,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(cnf_transformation,[],[f1044]) ).
tff(f2137,plain,
spl17_118,
inference(avatar_split_clause,[],[f1392,f2135]) ).
tff(f2135,plain,
( spl17_118
<=> ! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_118])]) ).
tff(f1392,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1))) ),
inference(cnf_transformation,[],[f1043]) ).
tff(f1043,plain,
! [X0: pname,X1: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1))) ) ),
inference(nnf_transformation,[],[f609]) ).
tff(f609,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(rectify,[],[f137]) ).
tff(f137,axiom,
! [X5: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X5,X2)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_136_finite__insert) ).
tff(f2133,plain,
spl17_117,
inference(avatar_split_clause,[],[f1391,f2131]) ).
tff(f1391,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) ),
inference(cnf_transformation,[],[f1042]) ).
tff(f1042,plain,
! [X0: x_a,X1: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) )
& ( hBOOL(hAPP_a_bool(X1,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
inference(nnf_transformation,[],[f608]) ).
tff(f608,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
<=> hBOOL(hAPP_a_bool(X1,X0)) ),
inference(rectify,[],[f254]) ).
tff(f254,axiom,
! [X8: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
<=> hBOOL(hAPP_a_bool(X2,X8)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_253_mem__def) ).
tff(f2129,plain,
spl17_116,
inference(avatar_split_clause,[],[f1390,f2127]) ).
tff(f2127,plain,
( spl17_116
<=> ! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(X1,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_116])]) ).
tff(f1390,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(X1,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
inference(cnf_transformation,[],[f1042]) ).
tff(f2125,plain,
spl17_115,
inference(avatar_split_clause,[],[f1388,f2123]) ).
tff(f2123,plain,
( spl17_115
<=> ! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_115])]) ).
tff(f1388,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1))) ),
inference(cnf_transformation,[],[f1041]) ).
tff(f1041,plain,
! [X0: x_a,X1: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1))) ) ),
inference(nnf_transformation,[],[f607]) ).
tff(f607,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(rectify,[],[f138]) ).
tff(f138,axiom,
! [X5: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X5,X2)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_137_finite__insert) ).
tff(f2121,plain,
spl17_114,
inference(avatar_split_clause,[],[f1387,f2119]) ).
tff(f1387,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) ),
inference(cnf_transformation,[],[f1040]) ).
tff(f1040,plain,
! [X0: nat,X1: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X0)) )
& ( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f606]) ).
tff(f606,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
<=> hBOOL(hAPP_nat_bool(X1,X0)) ),
inference(rectify,[],[f253]) ).
tff(f253,axiom,
! [X8: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
<=> hBOOL(hAPP_nat_bool(X2,X8)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_252_mem__def) ).
tff(f2117,plain,
spl17_113,
inference(avatar_split_clause,[],[f1386,f2115]) ).
tff(f2115,plain,
( spl17_113
<=> ! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_113])]) ).
tff(f1386,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(X1,X0))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1040]) ).
tff(f2112,plain,
spl17_112,
inference(avatar_split_clause,[],[f1384,f2110]) ).
tff(f2110,plain,
( spl17_112
<=> ! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_112])]) ).
tff(f1384,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1))) ),
inference(cnf_transformation,[],[f1039]) ).
tff(f1039,plain,
! [X0: nat,X1: fun_nat_bool] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1))) ) ),
inference(nnf_transformation,[],[f605]) ).
tff(f605,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rectify,[],[f136]) ).
tff(f136,axiom,
! [X5: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X5,X2)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_135_finite__insert) ).
tff(f2108,plain,
spl17_111,
inference(avatar_split_clause,[],[f1382,f2106]) ).
tff(f2106,plain,
( spl17_111
<=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_111])]) ).
tff(f1382,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1))) ),
inference(cnf_transformation,[],[f1038]) ).
tff(f1038,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1))) ) ),
inference(nnf_transformation,[],[f604]) ).
tff(f604,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(rectify,[],[f140]) ).
tff(f140,axiom,
! [X5: fun_pname_bool,X2: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X5,X2)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_139_finite__insert) ).
tff(f2104,plain,
spl17_110,
inference(avatar_split_clause,[],[f1380,f2102]) ).
tff(f2102,plain,
( spl17_110
<=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_110])]) ).
tff(f1380,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1))) ),
inference(cnf_transformation,[],[f1037]) ).
tff(f1037,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1))) ) ),
inference(nnf_transformation,[],[f603]) ).
tff(f603,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(rectify,[],[f141]) ).
tff(f141,axiom,
! [X5: fun_a_bool,X2: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X5,X2)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_140_finite__insert) ).
tff(f2100,plain,
spl17_109,
inference(avatar_split_clause,[],[f1378,f2098]) ).
tff(f2098,plain,
( spl17_109
<=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_109])]) ).
tff(f1378,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1))) ),
inference(cnf_transformation,[],[f1036]) ).
tff(f1036,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1))) ) ),
inference(nnf_transformation,[],[f602]) ).
tff(f602,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rectify,[],[f139]) ).
tff(f139,axiom,
! [X5: fun_nat_bool,X2: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X5,X2)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_138_finite__insert) ).
tff(f2096,plain,
spl17_108,
inference(avatar_split_clause,[],[f1345,f2094]) ).
tff(f2094,plain,
( spl17_108
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_108])]) ).
tff(f1345,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ),
inference(cnf_transformation,[],[f910]) ).
tff(f910,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ),
inference(ennf_transformation,[],[f585]) ).
tff(f585,plain,
! [X0: nat,X1: nat] :
( ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f120]) ).
tff(f120,axiom,
! [X15: nat,X16: nat] :
( ( hAPP_nat_nat(suc,X15) = hAPP_nat_nat(suc,X16) )
=> ( X15 = X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_119_Suc__inject) ).
tff(f2092,plain,
spl17_107,
inference(avatar_split_clause,[],[f1314,f2090]) ).
tff(f2090,plain,
( spl17_107
<=> ! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_107])]) ).
tff(f1314,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f866]) ).
tff(f866,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f556]) ).
tff(f556,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X0,X1))) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X5: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_47_finite_OinsertI) ).
tff(f2088,plain,
spl17_106,
inference(avatar_split_clause,[],[f1313,f2086]) ).
tff(f2086,plain,
( spl17_106
<=> ! [X0: fun_pname_pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_106])]) ).
tff(f1313,plain,
! [X0: fun_pname_pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f865]) ).
tff(f865,plain,
! [X0: fun_pname_pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f555]) ).
tff(f555,plain,
! [X0: fun_pname_pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X0,X1))) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X3: fun_pname_pname,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_38_finite__imageI) ).
tff(f2084,plain,
spl17_105,
inference(avatar_split_clause,[],[f1312,f2082]) ).
tff(f2082,plain,
( spl17_105
<=> ! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_105])]) ).
tff(f1312,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f864]) ).
tff(f864,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f554]) ).
tff(f554,plain,
! [X0: fun_pname_a,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1))) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X3: fun_pname_a,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_10_finite__imageI) ).
tff(f2080,plain,
spl17_104,
inference(avatar_split_clause,[],[f1311,f2078]) ).
tff(f2078,plain,
( spl17_104
<=> ! [X0: fun_pname_nat,X1: fun_pname_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_104])]) ).
tff(f1311,plain,
! [X0: fun_pname_nat,X1: fun_pname_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f863]) ).
tff(f863,plain,
! [X0: fun_pname_nat,X1: fun_pname_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f553]) ).
tff(f553,plain,
! [X0: fun_pname_nat,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X0,X1))) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X3: fun_pname_nat,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_43_finite__imageI) ).
tff(f2076,plain,
spl17_103,
inference(avatar_split_clause,[],[f1310,f2074]) ).
tff(f2074,plain,
( spl17_103
<=> ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_103])]) ).
tff(f1310,plain,
! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f862]) ).
tff(f862,plain,
! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f552]) ).
tff(f552,plain,
! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1))) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X3: fun_pn406123357t_bool,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_37_finite__imageI) ).
tff(f2072,plain,
( spl17_102
| ~ spl17_41 ),
inference(avatar_split_clause,[],[f1873,f1804,f2070]) ).
tff(f2070,plain,
( spl17_102
<=> ! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_102])]) ).
tff(f1804,plain,
( spl17_41
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).
tff(f1873,plain,
( ! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X0))
| ~ spl17_41 ),
inference(equality_resolution,[],[f1805]) ).
tff(f1805,plain,
( ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 != X1 )
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1)) )
| ~ spl17_41 ),
inference(avatar_component_clause,[],[f1804]) ).
tff(f2068,plain,
spl17_101,
inference(avatar_split_clause,[],[f1309,f2066]) ).
tff(f2066,plain,
( spl17_101
<=> ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_101])]) ).
tff(f1309,plain,
! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f861]) ).
tff(f861,plain,
! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f551]) ).
tff(f551,plain,
! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1))) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X3: fun_pn800050071e_bool,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_36_finite__imageI) ).
tff(f2064,plain,
spl17_100,
inference(avatar_split_clause,[],[f1308,f2062]) ).
tff(f2062,plain,
( spl17_100
<=> ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_100])]) ).
tff(f1308,plain,
! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f860]) ).
tff(f860,plain,
! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f550]) ).
tff(f550,plain,
! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1))) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X3: fun_pname_fun_a_bool,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_35_finite__imageI) ).
tff(f2060,plain,
spl17_99,
inference(avatar_split_clause,[],[f1307,f2058]) ).
tff(f2058,plain,
( spl17_99
<=> ! [X0: fun_pn422929397l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_99])]) ).
tff(f1307,plain,
! [X0: fun_pn422929397l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f859]) ).
tff(f859,plain,
! [X0: fun_pn422929397l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f549]) ).
tff(f549,plain,
! [X0: fun_pn422929397l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X0,X1))) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X3: fun_pn422929397l_bool,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_33_finite__imageI) ).
tff(f2056,plain,
spl17_98,
inference(avatar_split_clause,[],[f1306,f2054]) ).
tff(f2054,plain,
( spl17_98
<=> ! [X0: fun_pn1165013435l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_98])]) ).
tff(f1306,plain,
! [X0: fun_pn1165013435l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f858]) ).
tff(f858,plain,
! [X0: fun_pn1165013435l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f548]) ).
tff(f548,plain,
! [X0: fun_pn1165013435l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X0,X1))) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X3: fun_pn1165013435l_bool,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_32_finite__imageI) ).
tff(f2052,plain,
spl17_97,
inference(avatar_split_clause,[],[f1305,f2050]) ).
tff(f2050,plain,
( spl17_97
<=> ! [X0: fun_pn1038293468l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_97])]) ).
tff(f1305,plain,
! [X0: fun_pn1038293468l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(cnf_transformation,[],[f857]) ).
tff(f857,plain,
! [X0: fun_pn1038293468l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X0,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(ennf_transformation,[],[f547]) ).
tff(f547,plain,
! [X0: fun_pn1038293468l_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X0,X1))) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X3: fun_pn1038293468l_bool,X4: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_34_finite__imageI) ).
tff(f2048,plain,
spl17_96,
inference(avatar_split_clause,[],[f1294,f2046]) ).
tff(f2046,plain,
( spl17_96
<=> ! [X0: fun_a_pname,X1: fun_a_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_96])]) ).
tff(f1294,plain,
! [X0: fun_a_pname,X1: fun_a_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f843]) ).
tff(f843,plain,
! [X0: fun_a_pname,X1: fun_a_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f537]) ).
tff(f537,plain,
! [X0: fun_a_pname,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1))) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X3: fun_a_pname,X4: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_24_finite__imageI) ).
tff(f2044,plain,
spl17_95,
inference(avatar_split_clause,[],[f1293,f2042]) ).
tff(f2042,plain,
( spl17_95
<=> ! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_95])]) ).
tff(f1293,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f842]) ).
tff(f842,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f536]) ).
tff(f536,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X0,X1))) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X5: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_45_finite_OinsertI) ).
tff(f2040,plain,
spl17_94,
inference(avatar_split_clause,[],[f1292,f2038]) ).
tff(f2038,plain,
( spl17_94
<=> ! [X0: fun_a_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_94])]) ).
tff(f1292,plain,
! [X0: fun_a_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f841]) ).
tff(f841,plain,
! [X0: fun_a_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f535]) ).
tff(f535,plain,
! [X0: fun_a_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X0,X1))) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X3: fun_a_a,X4: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_39_finite__imageI) ).
tff(f2036,plain,
spl17_93,
inference(avatar_split_clause,[],[f1291,f2034]) ).
tff(f2034,plain,
( spl17_93
<=> ! [X0: fun_a_nat,X1: fun_a_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_93])]) ).
tff(f1291,plain,
! [X0: fun_a_nat,X1: fun_a_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(cnf_transformation,[],[f840]) ).
tff(f840,plain,
! [X0: fun_a_nat,X1: fun_a_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(ennf_transformation,[],[f534]) ).
tff(f534,plain,
! [X0: fun_a_nat,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1))) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X3: fun_a_nat,X4: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_17_finite__imageI) ).
tff(f2032,plain,
spl17_92,
inference(avatar_split_clause,[],[f1278,f2030]) ).
tff(f2030,plain,
( spl17_92
<=> ! [X0: fun_nat_pname,X1: fun_nat_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_92])]) ).
tff(f1278,plain,
! [X0: fun_nat_pname,X1: fun_nat_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f824]) ).
tff(f824,plain,
! [X0: fun_nat_pname,X1: fun_nat_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f522]) ).
tff(f522,plain,
! [X0: fun_nat_pname,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X0,X1))) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X3: fun_nat_pname,X4: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_44_finite__imageI) ).
tff(f2028,plain,
( spl17_91
| ~ spl17_40 ),
inference(avatar_split_clause,[],[f1872,f1800,f2026]) ).
tff(f2026,plain,
( spl17_91
<=> ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_91])]) ).
tff(f1800,plain,
( spl17_40
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).
tff(f1872,plain,
( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X0))
| ~ spl17_40 ),
inference(equality_resolution,[],[f1801]) ).
tff(f1801,plain,
( ! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 != X1 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1)) )
| ~ spl17_40 ),
inference(avatar_component_clause,[],[f1800]) ).
tff(f2024,plain,
spl17_90,
inference(avatar_split_clause,[],[f1277,f2022]) ).
tff(f2022,plain,
( spl17_90
<=> ! [X0: fun_nat_a,X1: fun_nat_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_90])]) ).
tff(f1277,plain,
! [X0: fun_nat_a,X1: fun_nat_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f823]) ).
tff(f823,plain,
! [X0: fun_nat_a,X1: fun_nat_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f521]) ).
tff(f521,plain,
! [X0: fun_nat_a,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1))) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X3: fun_nat_a,X4: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_31_finite__imageI) ).
tff(f2020,plain,
spl17_89,
inference(avatar_split_clause,[],[f1276,f2018]) ).
tff(f2018,plain,
( spl17_89
<=> ! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_89])]) ).
tff(f1276,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f822]) ).
tff(f822,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f520]) ).
tff(f520,plain,
! [X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X0,X1))) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X5: nat,X2: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_46_finite_OinsertI) ).
tff(f2016,plain,
spl17_88,
inference(avatar_split_clause,[],[f1275,f2014]) ).
tff(f2014,plain,
( spl17_88
<=> ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_88])]) ).
tff(f1275,plain,
! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f821]) ).
tff(f821,plain,
! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f519]) ).
tff(f519,plain,
! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1))) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X3: fun_nat_fun_a_bool,X4: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_28_finite__imageI) ).
tff(f2012,plain,
spl17_87,
inference(avatar_split_clause,[],[f1274,f2010]) ).
tff(f2010,plain,
( spl17_87
<=> ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_87])]) ).
tff(f1274,plain,
! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f820]) ).
tff(f820,plain,
! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f518]) ).
tff(f518,plain,
! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1))) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X3: fun_na936072029e_bool,X4: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_29_finite__imageI) ).
tff(f2008,plain,
spl17_86,
inference(avatar_split_clause,[],[f1273,f2006]) ).
tff(f2006,plain,
( spl17_86
<=> ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_86])]) ).
tff(f1273,plain,
! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f819]) ).
tff(f819,plain,
! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f517]) ).
tff(f517,plain,
! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1))) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X3: fun_nat_fun_nat_bool,X4: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_30_finite__imageI) ).
tff(f2004,plain,
spl17_85,
inference(avatar_split_clause,[],[f1272,f2002]) ).
tff(f2002,plain,
( spl17_85
<=> ! [X0: fun_na1632405922l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_85])]) ).
tff(f1272,plain,
! [X0: fun_na1632405922l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f818]) ).
tff(f818,plain,
! [X0: fun_na1632405922l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f516]) ).
tff(f516,plain,
! [X0: fun_na1632405922l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X0,X1))) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X3: fun_na1632405922l_bool,X4: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_27_finite__imageI) ).
tff(f2000,plain,
spl17_84,
inference(avatar_split_clause,[],[f1271,f1998]) ).
tff(f1998,plain,
( spl17_84
<=> ! [X0: fun_na1436237685l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_84])]) ).
tff(f1271,plain,
! [X0: fun_na1436237685l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f817]) ).
tff(f817,plain,
! [X0: fun_na1436237685l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f515]) ).
tff(f515,plain,
! [X0: fun_na1436237685l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X0,X1))) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X3: fun_na1436237685l_bool,X4: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_25_finite__imageI) ).
tff(f1996,plain,
spl17_83,
inference(avatar_split_clause,[],[f1270,f1994]) ).
tff(f1994,plain,
( spl17_83
<=> ! [X0: fun_na2122364079l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_83])]) ).
tff(f1270,plain,
! [X0: fun_na2122364079l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(cnf_transformation,[],[f816]) ).
tff(f816,plain,
! [X0: fun_na2122364079l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X0,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(ennf_transformation,[],[f514]) ).
tff(f514,plain,
! [X0: fun_na2122364079l_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X0,X1))) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X3: fun_na2122364079l_bool,X4: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_26_finite__imageI) ).
tff(f1992,plain,
spl17_82,
inference(avatar_split_clause,[],[f1239,f1990]) ).
tff(f1990,plain,
( spl17_82
<=> ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_82])]) ).
tff(f1239,plain,
! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f776]) ).
tff(f776,plain,
! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f486]) ).
tff(f486,plain,
! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1))) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X3: fun_fu1499449723_pname,X4: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_22_finite__imageI) ).
tff(f1988,plain,
spl17_81,
inference(avatar_split_clause,[],[f1238,f1986]) ).
tff(f1986,plain,
( spl17_81
<=> ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_81])]) ).
tff(f1238,plain,
! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f775]) ).
tff(f775,plain,
! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f485]) ).
tff(f485,plain,
! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1))) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X3: fun_fun_a_bool_pname,X4: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_21_finite__imageI) ).
tff(f1984,plain,
( spl17_80
| ~ spl17_39 ),
inference(avatar_split_clause,[],[f1871,f1796,f1982]) ).
tff(f1982,plain,
( spl17_80
<=> ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_80])]) ).
tff(f1796,plain,
( spl17_39
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).
tff(f1871,plain,
( ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X0))
| ~ spl17_39 ),
inference(equality_resolution,[],[f1797]) ).
tff(f1797,plain,
( ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 != X1 )
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) )
| ~ spl17_39 ),
inference(avatar_component_clause,[],[f1796]) ).
tff(f1980,plain,
spl17_79,
inference(avatar_split_clause,[],[f1237,f1978]) ).
tff(f1978,plain,
( spl17_79
<=> ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_79])]) ).
tff(f1237,plain,
! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f774]) ).
tff(f774,plain,
! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f484]) ).
tff(f484,plain,
! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1))) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X3: fun_fu665170229_pname,X4: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_23_finite__imageI) ).
tff(f1976,plain,
spl17_78,
inference(avatar_split_clause,[],[f1236,f1974]) ).
tff(f1974,plain,
( spl17_78
<=> ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_78])]) ).
tff(f1236,plain,
! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f773]) ).
tff(f773,plain,
! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f483]) ).
tff(f483,plain,
! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X0,X1))) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X3: fun_fun_a_bool_a,X4: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_42_finite__imageI) ).
tff(f1972,plain,
spl17_77,
inference(avatar_split_clause,[],[f1235,f1970]) ).
tff(f1970,plain,
( spl17_77
<=> ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_77])]) ).
tff(f1235,plain,
! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f772]) ).
tff(f772,plain,
! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f482]) ).
tff(f482,plain,
! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X0,X1))) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X3: fun_fun_pname_bool_a,X4: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_41_finite__imageI) ).
tff(f1968,plain,
spl17_76,
inference(avatar_split_clause,[],[f1234,f1966]) ).
tff(f1966,plain,
( spl17_76
<=> ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_76])]) ).
tff(f1234,plain,
! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f771]) ).
tff(f771,plain,
! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f481]) ).
tff(f481,plain,
! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X0,X1))) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X3: fun_fun_nat_bool_a,X4: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_40_finite__imageI) ).
tff(f1964,plain,
spl17_75,
inference(avatar_split_clause,[],[f1233,f1962]) ).
tff(f1962,plain,
( spl17_75
<=> ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_75])]) ).
tff(f1233,plain,
! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f770]) ).
tff(f770,plain,
! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f480]) ).
tff(f480,plain,
! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1))) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X3: fun_fun_nat_bool_nat,X4: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_16_finite__imageI) ).
tff(f1960,plain,
spl17_74,
inference(avatar_split_clause,[],[f1232,f1958]) ).
tff(f1958,plain,
( spl17_74
<=> ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_74])]) ).
tff(f1232,plain,
! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f769]) ).
tff(f769,plain,
! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f479]) ).
tff(f479,plain,
! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1))) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X3: fun_fu1668467777ol_nat,X4: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_15_finite__imageI) ).
tff(f1956,plain,
spl17_73,
inference(avatar_split_clause,[],[f1231,f1954]) ).
tff(f1954,plain,
( spl17_73
<=> ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_73])]) ).
tff(f1231,plain,
! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f768]) ).
tff(f768,plain,
! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f478]) ).
tff(f478,plain,
! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1))) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X3: fun_fun_a_bool_nat,X4: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_14_finite__imageI) ).
tff(f1952,plain,
spl17_72,
inference(avatar_split_clause,[],[f1230,f1950]) ).
tff(f1950,plain,
( spl17_72
<=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_72])]) ).
tff(f1230,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(cnf_transformation,[],[f767]) ).
tff(f767,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(ennf_transformation,[],[f477]) ).
tff(f477,plain,
! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X0,X1))) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X5: fun_nat_bool,X2: fun_fu425979586l_bool] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_53_finite_OinsertI) ).
tff(f1948,plain,
spl17_71,
inference(avatar_split_clause,[],[f1229,f1946]) ).
tff(f1946,plain,
( spl17_71
<=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_71])]) ).
tff(f1229,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(cnf_transformation,[],[f766]) ).
tff(f766,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(ennf_transformation,[],[f476]) ).
tff(f476,plain,
! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X0,X1))) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X5: fun_pname_bool,X2: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_52_finite_OinsertI) ).
tff(f1944,plain,
spl17_70,
inference(avatar_split_clause,[],[f1228,f1942]) ).
tff(f1942,plain,
( spl17_70
<=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_70])]) ).
tff(f1228,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(cnf_transformation,[],[f765]) ).
tff(f765,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(ennf_transformation,[],[f475]) ).
tff(f475,plain,
! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X0,X1))) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X5: fun_a_bool,X2: fun_fun_a_bool_bool] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_51_finite_OinsertI) ).
tff(f1940,plain,
( spl17_69
| ~ spl17_38 ),
inference(avatar_split_clause,[],[f1870,f1792,f1938]) ).
tff(f1792,plain,
( spl17_38
<=> ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).
tff(f1870,plain,
( ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X0))
| ~ spl17_38 ),
inference(equality_resolution,[],[f1793]) ).
tff(f1793,plain,
( ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) )
| ~ spl17_38 ),
inference(avatar_component_clause,[],[f1792]) ).
tff(f1936,plain,
spl17_68,
inference(avatar_split_clause,[],[f1224,f1934]) ).
tff(f1934,plain,
( spl17_68
<=> ! [X0: fun_fu1664106117_pname,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_68])]) ).
tff(f1224,plain,
! [X0: fun_fu1664106117_pname,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(cnf_transformation,[],[f761]) ).
tff(f761,plain,
! [X0: fun_fu1664106117_pname,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(ennf_transformation,[],[f471]) ).
tff(f471,plain,
! [X0: fun_fu1664106117_pname,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X0,X1))) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X3: fun_fu1664106117_pname,X4: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_19_finite__imageI) ).
tff(f1932,plain,
spl17_67,
inference(avatar_split_clause,[],[f1223,f1930]) ).
tff(f1930,plain,
( spl17_67
<=> ! [X0: fun_fu1175941238_pname,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_67])]) ).
tff(f1223,plain,
! [X0: fun_fu1175941238_pname,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(cnf_transformation,[],[f760]) ).
tff(f760,plain,
! [X0: fun_fu1175941238_pname,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(ennf_transformation,[],[f470]) ).
tff(f470,plain,
! [X0: fun_fu1175941238_pname,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X0,X1))) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X3: fun_fu1175941238_pname,X4: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_20_finite__imageI) ).
tff(f1928,plain,
spl17_66,
inference(avatar_split_clause,[],[f1222,f1926]) ).
tff(f1926,plain,
( spl17_66
<=> ! [X0: fun_fu881587263_pname,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_66])]) ).
tff(f1222,plain,
! [X0: fun_fu881587263_pname,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(cnf_transformation,[],[f759]) ).
tff(f759,plain,
! [X0: fun_fu881587263_pname,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(ennf_transformation,[],[f469]) ).
tff(f469,plain,
! [X0: fun_fu881587263_pname,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X0,X1))) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X3: fun_fu881587263_pname,X4: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X4))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_18_finite__imageI) ).
tff(f1924,plain,
spl17_65,
inference(avatar_split_clause,[],[f1221,f1922]) ).
tff(f1922,plain,
( spl17_65
<=> ! [X0: fun_fu2020802748ol_nat,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_65])]) ).
tff(f1221,plain,
! [X0: fun_fu2020802748ol_nat,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(cnf_transformation,[],[f758]) ).
tff(f758,plain,
! [X0: fun_fu2020802748ol_nat,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(ennf_transformation,[],[f468]) ).
tff(f468,plain,
! [X0: fun_fu2020802748ol_nat,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X0,X1))) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X3: fun_fu2020802748ol_nat,X4: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_13_finite__imageI) ).
tff(f1920,plain,
spl17_64,
inference(avatar_split_clause,[],[f1220,f1918]) ).
tff(f1918,plain,
( spl17_64
<=> ! [X0: fun_fu1730389579ol_nat,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_64])]) ).
tff(f1220,plain,
! [X0: fun_fu1730389579ol_nat,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(cnf_transformation,[],[f757]) ).
tff(f757,plain,
! [X0: fun_fu1730389579ol_nat,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(ennf_transformation,[],[f467]) ).
tff(f467,plain,
! [X0: fun_fu1730389579ol_nat,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X0,X1))) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X3: fun_fu1730389579ol_nat,X4: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_12_finite__imageI) ).
tff(f1916,plain,
spl17_63,
inference(avatar_split_clause,[],[f1219,f1914]) ).
tff(f1914,plain,
( spl17_63
<=> ! [X0: fun_fu411113733ol_nat,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_63])]) ).
tff(f1219,plain,
! [X0: fun_fu411113733ol_nat,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(cnf_transformation,[],[f756]) ).
tff(f756,plain,
! [X0: fun_fu411113733ol_nat,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(ennf_transformation,[],[f466]) ).
tff(f466,plain,
! [X0: fun_fu411113733ol_nat,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X0,X1))) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X3: fun_fu411113733ol_nat,X4: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X4))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X3,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_11_finite__imageI) ).
tff(f1912,plain,
spl17_62,
inference(avatar_split_clause,[],[f1218,f1910]) ).
tff(f1910,plain,
( spl17_62
<=> ! [X0: fun_fu425979586l_bool,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_62])]) ).
tff(f1218,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(cnf_transformation,[],[f755]) ).
tff(f755,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X0,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(ennf_transformation,[],[f465]) ).
tff(f465,plain,
! [X0: fun_fu425979586l_bool,X1: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X0,X1))) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X5: fun_fu425979586l_bool,X2: fun_fu814369080l_bool] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X2))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_48_finite_OinsertI) ).
tff(f1908,plain,
spl17_61,
inference(avatar_split_clause,[],[f1217,f1906]) ).
tff(f1906,plain,
( spl17_61
<=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_61])]) ).
tff(f1217,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(cnf_transformation,[],[f754]) ).
tff(f754,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X0,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(ennf_transformation,[],[f464]) ).
tff(f464,plain,
! [X0: fun_fu1430349052l_bool,X1: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X0,X1))) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X5: fun_fu1430349052l_bool,X2: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X2))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_49_finite_OinsertI) ).
tff(f1904,plain,
spl17_60,
inference(avatar_split_clause,[],[f1216,f1902]) ).
tff(f1902,plain,
( spl17_60
<=> ! [X0: fun_fun_a_bool_bool,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_60])]) ).
tff(f1216,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(cnf_transformation,[],[f753]) ).
tff(f753,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X0,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(ennf_transformation,[],[f463]) ).
tff(f463,plain,
! [X0: fun_fun_a_bool_bool,X1: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X0,X1))) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X5: fun_fun_a_bool_bool,X2: fun_fu885608257l_bool] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X2))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X5,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_50_finite_OinsertI) ).
tff(f1900,plain,
spl17_59,
inference(avatar_split_clause,[],[f1195,f1898]) ).
tff(f1898,plain,
( spl17_59
<=> ! [X0: bool,X1: bool] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_59])]) ).
tff(f1195,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
inference(cnf_transformation,[],[f446]) ).
tff(f446,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
inference(rectify,[],[f308]) ).
tff(f308,axiom,
! [X41: bool,X42: bool] :
( hBOOL(X42)
| hBOOL(X41)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X41),X42)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fdisj_3_1_U) ).
tff(f1896,plain,
( spl17_58
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f1869,f1788,f1894]) ).
tff(f1788,plain,
( spl17_37
<=> ! [X0: x_a,X1: x_a] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).
tff(f1869,plain,
( ! [X0: x_a] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X0))
| ~ spl17_37 ),
inference(equality_resolution,[],[f1789]) ).
tff(f1789,plain,
( ! [X0: x_a,X1: x_a] :
( ( X0 != X1 )
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) )
| ~ spl17_37 ),
inference(avatar_component_clause,[],[f1788]) ).
tff(f1892,plain,
spl17_57,
inference(avatar_split_clause,[],[f1192,f1890]) ).
tff(f1890,plain,
( spl17_57
<=> ! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_57])]) ).
tff(f1192,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
inference(cnf_transformation,[],[f443]) ).
tff(f443,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
inference(rectify,[],[f311]) ).
tff(f311,axiom,
! [X41: bool,X42: bool] :
( hBOOL(X42)
| ~ hBOOL(X41)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X41),X42)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fimplies_3_1_U) ).
tff(f1888,plain,
spl17_56,
inference(avatar_split_clause,[],[f1179,f1886]) ).
tff(f1886,plain,
( spl17_56
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_56])]) ).
tff(f1179,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f430]) ).
tff(f430,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f303]) ).
tff(f303,axiom,
! [X42: bool,X41: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X41),X42))
| ~ hBOOL(X42)
| ~ hBOOL(X41) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fconj_1_1_U) ).
tff(f1877,plain,
( spl17_55
| ~ spl17_36 ),
inference(avatar_split_clause,[],[f1868,f1784,f1875]) ).
tff(f1875,plain,
( spl17_55
<=> ! [X0: pname] : hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_55])]) ).
tff(f1784,plain,
( spl17_36
<=> ! [X0: pname,X1: pname] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
tff(f1868,plain,
( ! [X0: pname] : hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X0))
| ~ spl17_36 ),
inference(equality_resolution,[],[f1785]) ).
tff(f1785,plain,
( ! [X0: pname,X1: pname] :
( ( X0 != X1 )
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) )
| ~ spl17_36 ),
inference(avatar_component_clause,[],[f1784]) ).
tff(f1858,plain,
spl17_54,
inference(avatar_split_clause,[],[f1542,f1856]) ).
tff(f1542,plain,
! [X2: nat,X0: nat,X1: fun_nat_bool] :
( hBOOL(hAPP_nat_bool(insert_nat(X0,X1),X2))
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f1090]) ).
tff(f1854,plain,
spl17_53,
inference(avatar_split_clause,[],[f1539,f1852]) ).
tff(f1539,plain,
! [X2: x_a,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(insert_a(X0,X1),X2))
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f1088]) ).
tff(f1850,plain,
spl17_52,
inference(avatar_split_clause,[],[f1536,f1848]) ).
tff(f1536,plain,
! [X2: pname,X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(insert_pname(X0,X1),X2))
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f1086]) ).
tff(f1846,plain,
spl17_51,
inference(avatar_split_clause,[],[f1206,f1844]) ).
tff(f1844,plain,
( spl17_51
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_51])]) ).
tff(f1206,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f746]) ).
tff(f746,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f457]) ).
tff(f457,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 = X1 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1)) ),
inference(rectify,[],[f233]) ).
tff(f233,axiom,
! [X2: fun_pname_bool,X7: fun_pname_bool] :
( ( X2 = X7 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_232_equalityD1) ).
tff(f1842,plain,
spl17_50,
inference(avatar_split_clause,[],[f1204,f1840]) ).
tff(f1840,plain,
( spl17_50
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).
tff(f1204,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f744]) ).
tff(f744,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f455]) ).
tff(f455,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 = X1 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ),
inference(rectify,[],[f237]) ).
tff(f237,axiom,
! [X2: fun_a_bool,X7: fun_a_bool] :
( ( X2 = X7 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_236_equalityD2) ).
tff(f1838,plain,
spl17_49,
inference(avatar_split_clause,[],[f1202,f1836]) ).
tff(f1836,plain,
( spl17_49
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).
tff(f1202,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f742]) ).
tff(f742,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f453]) ).
tff(f453,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 = X1 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
inference(rectify,[],[f232]) ).
tff(f232,axiom,
! [X2: fun_nat_bool,X7: fun_nat_bool] :
( ( X2 = X7 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_231_equalityD1) ).
tff(f1834,plain,
spl17_48,
inference(avatar_split_clause,[],[f1201,f1832]) ).
tff(f1832,plain,
( spl17_48
<=> ! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
tff(f1201,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f741]) ).
tff(f741,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f452]) ).
tff(f452,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f126]) ).
tff(f126,axiom,
! [X12: nat,X11: nat] :
( ( X11 = X12 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_125_eq__imp__le) ).
tff(f1830,plain,
spl17_47,
inference(avatar_split_clause,[],[f1199,f1828]) ).
tff(f1828,plain,
( spl17_47
<=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
tff(f1199,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1)) ),
inference(cnf_transformation,[],[f450]) ).
tff(f450,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1)) ),
inference(rectify,[],[f326]) ).
tff(f326,axiom,
! [X15: fun_pname_bool,X16: fun_pname_bool] :
( ( X15 = X16 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X15),X16)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
tff(f1826,plain,
spl17_46,
inference(avatar_split_clause,[],[f1198,f1824]) ).
tff(f1824,plain,
( spl17_46
<=> ! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
tff(f1198,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1)) ),
inference(cnf_transformation,[],[f449]) ).
tff(f449,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1)) ),
inference(rectify,[],[f319]) ).
tff(f319,axiom,
! [X15: fun_a_bool,X16: fun_a_bool] :
( ( X15 = X16 )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X15),X16)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
tff(f1822,plain,
spl17_45,
inference(avatar_split_clause,[],[f1197,f1820]) ).
tff(f1820,plain,
( spl17_45
<=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
tff(f1197,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ),
inference(cnf_transformation,[],[f448]) ).
tff(f448,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ),
inference(rectify,[],[f324]) ).
tff(f324,axiom,
! [X15: fun_nat_bool,X16: fun_nat_bool] :
( ( X15 = X16 )
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X15),X16)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
tff(f1818,plain,
spl17_44,
inference(avatar_split_clause,[],[f1196,f1816]) ).
tff(f1816,plain,
( spl17_44
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).
tff(f1196,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ),
inference(cnf_transformation,[],[f447]) ).
tff(f447,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ),
inference(rectify,[],[f314]) ).
tff(f314,axiom,
! [X15: nat,X16: nat] :
( ( X15 = X16 )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X15),X16)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
tff(f1814,plain,
spl17_43,
inference(avatar_split_clause,[],[f1191,f1812]) ).
tff(f1812,plain,
( spl17_43
<=> ! [X0: x_a,X1: x_a] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).
tff(f1191,plain,
! [X0: x_a,X1: x_a] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ),
inference(cnf_transformation,[],[f442]) ).
tff(f442,plain,
! [X0: x_a,X1: x_a] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ),
inference(rectify,[],[f312]) ).
tff(f312,axiom,
! [X15: x_a,X16: x_a] :
( ( X15 = X16 )
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X15),X16)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_1_1_fequal_000t__a_T) ).
tff(f1810,plain,
spl17_42,
inference(avatar_split_clause,[],[f1190,f1808]) ).
tff(f1808,plain,
( spl17_42
<=> ! [X0: pname,X1: pname] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).
tff(f1190,plain,
! [X0: pname,X1: pname] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) ),
inference(cnf_transformation,[],[f441]) ).
tff(f441,plain,
! [X0: pname,X1: pname] :
( ( X0 = X1 )
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) ),
inference(rectify,[],[f316]) ).
tff(f316,axiom,
! [X15: pname,X16: pname] :
( ( X15 = X16 )
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X15),X16)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
tff(f1806,plain,
spl17_41,
inference(avatar_split_clause,[],[f1189,f1804]) ).
tff(f1189,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f440]) ).
tff(f440,plain,
! [X0: fun_pname_bool,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f327]) ).
tff(f327,axiom,
! [X15: fun_pname_bool,X16: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X15),X16))
| ( X15 != X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
tff(f1802,plain,
spl17_40,
inference(avatar_split_clause,[],[f1188,f1800]) ).
tff(f1188,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f439]) ).
tff(f439,plain,
! [X0: fun_a_bool,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f320]) ).
tff(f320,axiom,
! [X15: fun_a_bool,X16: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X15),X16))
| ( X15 != X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
tff(f1798,plain,
spl17_39,
inference(avatar_split_clause,[],[f1187,f1796]) ).
tff(f1187,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f438]) ).
tff(f438,plain,
! [X0: fun_nat_bool,X1: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f325]) ).
tff(f325,axiom,
! [X15: fun_nat_bool,X16: fun_nat_bool] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X15),X16))
| ( X15 != X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
tff(f1794,plain,
spl17_38,
inference(avatar_split_clause,[],[f1186,f1792]) ).
tff(f1186,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f437]) ).
tff(f437,plain,
! [X0: nat,X1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f315]) ).
tff(f315,axiom,
! [X15: nat,X16: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X15),X16))
| ( X15 != X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
tff(f1790,plain,
spl17_37,
inference(avatar_split_clause,[],[f1185,f1788]) ).
tff(f1185,plain,
! [X0: x_a,X1: x_a] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f436]) ).
tff(f436,plain,
! [X0: x_a,X1: x_a] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f313]) ).
tff(f313,axiom,
! [X15: x_a,X16: x_a] :
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X15),X16))
| ( X15 != X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_2_1_fequal_000t__a_T) ).
tff(f1786,plain,
spl17_36,
inference(avatar_split_clause,[],[f1184,f1784]) ).
tff(f1184,plain,
! [X0: pname,X1: pname] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f435]) ).
tff(f435,plain,
! [X0: pname,X1: pname] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
| ( X0 != X1 ) ),
inference(rectify,[],[f317]) ).
tff(f317,axiom,
! [X15: pname,X16: pname] :
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X15),X16))
| ( X15 != X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
tff(f1782,plain,
spl17_35,
inference(avatar_split_clause,[],[f1159,f1780]) ).
tff(f1780,plain,
( spl17_35
<=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
tff(f1159,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)),
inference(cnf_transformation,[],[f410]) ).
tff(f410,plain,
! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X0),X1)),X0)),
inference(rectify,[],[f169]) ).
tff(f169,axiom,
! [X12: nat,X11: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X12),X11)),X12)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_168_diff__le__self) ).
tff(f1778,plain,
spl17_34,
inference(avatar_split_clause,[],[f1158,f1776]) ).
tff(f1776,plain,
( spl17_34
<=> ! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,X1) = insert_a(X0,insert_a(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).
tff(f1158,plain,
! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,X1) = insert_a(X0,insert_a(X0,X1)) ),
inference(cnf_transformation,[],[f409]) ).
tff(f409,plain,
! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,X1) = insert_a(X0,insert_a(X0,X1)) ),
inference(rectify,[],[f207]) ).
tff(f207,axiom,
! [X8: x_a,X2: fun_a_bool] : ( insert_a(X8,X2) = insert_a(X8,insert_a(X8,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_206_insert__absorb2) ).
tff(f1774,plain,
spl17_33,
inference(avatar_split_clause,[],[f1157,f1772]) ).
tff(f1772,plain,
( spl17_33
<=> ! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,X1) = insert_pname(X0,insert_pname(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).
tff(f1157,plain,
! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,X1) = insert_pname(X0,insert_pname(X0,X1)) ),
inference(cnf_transformation,[],[f408]) ).
tff(f408,plain,
! [X0: pname,X1: fun_pname_bool] : ( insert_pname(X0,X1) = insert_pname(X0,insert_pname(X0,X1)) ),
inference(rectify,[],[f206]) ).
tff(f206,axiom,
! [X8: pname,X2: fun_pname_bool] : ( insert_pname(X8,X2) = insert_pname(X8,insert_pname(X8,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_205_insert__absorb2) ).
tff(f1770,plain,
spl17_32,
inference(avatar_split_clause,[],[f1156,f1768]) ).
tff(f1768,plain,
( spl17_32
<=> ! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,X1) = insert_nat(X0,insert_nat(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).
tff(f1156,plain,
! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,X1) = insert_nat(X0,insert_nat(X0,X1)) ),
inference(cnf_transformation,[],[f407]) ).
tff(f407,plain,
! [X0: nat,X1: fun_nat_bool] : ( insert_nat(X0,X1) = insert_nat(X0,insert_nat(X0,X1)) ),
inference(rectify,[],[f205]) ).
tff(f205,axiom,
! [X8: nat,X2: fun_nat_bool] : ( insert_nat(X8,X2) = insert_nat(X8,insert_nat(X8,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_204_insert__absorb2) ).
tff(f1766,plain,
spl17_31,
inference(avatar_split_clause,[],[f1194,f1764]) ).
tff(f1764,plain,
( spl17_31
<=> ! [X0: bool,X1: bool] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).
tff(f1194,plain,
! [X0: bool,X1: bool] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(cnf_transformation,[],[f445]) ).
tff(f445,plain,
! [X0: bool,X1: bool] :
( hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(rectify,[],[f304]) ).
tff(f304,axiom,
! [X41: bool,X42: bool] :
( hBOOL(X41)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X41),X42)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fconj_2_1_U) ).
tff(f1762,plain,
spl17_30,
inference(avatar_split_clause,[],[f1193,f1760]) ).
tff(f1760,plain,
( spl17_30
<=> ! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).
tff(f1193,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(cnf_transformation,[],[f444]) ).
tff(f444,plain,
! [X0: bool,X1: bool] :
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
inference(rectify,[],[f305]) ).
tff(f305,axiom,
! [X41: bool,X42: bool] :
( hBOOL(X42)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X41),X42)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fconj_3_1_U) ).
tff(f1758,plain,
spl17_29,
inference(avatar_split_clause,[],[f1183,f1756]) ).
tff(f1756,plain,
( spl17_29
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).
tff(f1183,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f434]) ).
tff(f434,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f309]) ).
tff(f309,axiom,
! [X42: bool,X41: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X41),X42))
| hBOOL(X41) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fimplies_1_1_U) ).
tff(f1754,plain,
spl17_28,
inference(avatar_split_clause,[],[f1182,f1752]) ).
tff(f1752,plain,
( spl17_28
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).
tff(f1182,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f433]) ).
tff(f433,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f307]) ).
tff(f307,axiom,
! [X41: bool,X42: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X41),X42))
| ~ hBOOL(X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fdisj_2_1_U) ).
tff(f1750,plain,
spl17_27,
inference(avatar_split_clause,[],[f1181,f1748]) ).
tff(f1748,plain,
( spl17_27
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).
tff(f1181,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f432]) ).
tff(f432,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f306]) ).
tff(f306,axiom,
! [X42: bool,X41: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X41),X42))
| ~ hBOOL(X41) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fdisj_1_1_U) ).
tff(f1746,plain,
spl17_26,
inference(avatar_split_clause,[],[f1180,f1744]) ).
tff(f1744,plain,
( spl17_26
<=> ! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
tff(f1180,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f431]) ).
tff(f431,plain,
! [X0: bool,X1: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f310]) ).
tff(f310,axiom,
! [X41: bool,X42: bool] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X41),X42))
| ~ hBOOL(X42) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fimplies_2_1_U) ).
tff(f1742,plain,
spl17_25,
inference(avatar_split_clause,[],[f1155,f1740]) ).
tff(f1740,plain,
( spl17_25
<=> ! [X0: fun_pname_bool,X1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),insert_pname(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
tff(f1155,plain,
! [X0: fun_pname_bool,X1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),insert_pname(X1,X0))),
inference(cnf_transformation,[],[f406]) ).
tff(f406,plain,
! [X0: fun_pname_bool,X1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),insert_pname(X1,X0))),
inference(rectify,[],[f271]) ).
tff(f271,axiom,
! [X7: fun_pname_bool,X5: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),insert_pname(X5,X7))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_270_subset__insertI) ).
tff(f1738,plain,
spl17_24,
inference(avatar_split_clause,[],[f1154,f1736]) ).
tff(f1154,plain,
! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X0,X1))),
inference(cnf_transformation,[],[f405]) ).
tff(f405,plain,
! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),insert_pname(X0,X1))),
inference(rectify,[],[f191]) ).
tff(f191,axiom,
! [X5: pname,X7: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),insert_pname(X5,X7))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_190_insertI1) ).
tff(f1734,plain,
spl17_23,
inference(avatar_split_clause,[],[f1153,f1732]) ).
tff(f1153,plain,
! [X0: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),insert_a(X1,X0))),
inference(cnf_transformation,[],[f404]) ).
tff(f404,plain,
! [X0: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),insert_a(X1,X0))),
inference(rectify,[],[f272]) ).
tff(f272,axiom,
! [X7: fun_a_bool,X5: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),insert_a(X5,X7))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_271_subset__insertI) ).
tff(f1730,plain,
spl17_22,
inference(avatar_split_clause,[],[f1152,f1728]) ).
tff(f1728,plain,
( spl17_22
<=> ! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).
tff(f1152,plain,
! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X0,X1))),
inference(cnf_transformation,[],[f403]) ).
tff(f403,plain,
! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),insert_a(X0,X1))),
inference(rectify,[],[f192]) ).
tff(f192,axiom,
! [X5: x_a,X7: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),insert_a(X5,X7))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_191_insertI1) ).
tff(f1726,plain,
spl17_21,
inference(avatar_split_clause,[],[f1151,f1724]) ).
tff(f1724,plain,
( spl17_21
<=> ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),insert_nat(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).
tff(f1151,plain,
! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),insert_nat(X1,X0))),
inference(cnf_transformation,[],[f402]) ).
tff(f402,plain,
! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),insert_nat(X1,X0))),
inference(rectify,[],[f270]) ).
tff(f270,axiom,
! [X7: fun_nat_bool,X5: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),insert_nat(X5,X7))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_269_subset__insertI) ).
tff(f1722,plain,
spl17_20,
inference(avatar_split_clause,[],[f1150,f1720]) ).
tff(f1720,plain,
( spl17_20
<=> ! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
tff(f1150,plain,
! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X0,X1))),
inference(cnf_transformation,[],[f401]) ).
tff(f401,plain,
! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),insert_nat(X0,X1))),
inference(rectify,[],[f190]) ).
tff(f190,axiom,
! [X5: nat,X7: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),insert_nat(X5,X7))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_189_insertI1) ).
tff(f1718,plain,
spl17_19,
inference(avatar_split_clause,[],[f1133,f1716]) ).
tff(f1133,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)),
inference(cnf_transformation,[],[f386]) ).
tff(f386,plain,
! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)),
inference(rectify,[],[f160]) ).
tff(f160,axiom,
! [X11: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X11)),X11)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_159_Suc__n__not__le__n) ).
tff(f1714,plain,
spl17_18,
inference(avatar_split_clause,[],[f1115,f1711]) ).
tff(f1115,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f363]) ).
tff(f363,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',conj_1) ).
tff(f1709,plain,
~ spl17_17,
inference(avatar_split_clause,[],[f1114,f1706]) ).
tff(f1114,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
inference(cnf_transformation,[],[f367]) ).
tff(f367,axiom,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',conj_5) ).
tff(f1704,plain,
spl17_16,
inference(avatar_split_clause,[],[f1570,f1702]) ).
tff(f1702,plain,
( spl17_16
<=> ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
tff(f1570,plain,
! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))),
inference(forward_demodulation,[],[f1134,f1122]) ).
tff(f1134,plain,
! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),
inference(cnf_transformation,[],[f387]) ).
tff(f387,plain,
! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),
inference(rectify,[],[f118]) ).
tff(f118,axiom,
! [X13: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X13)))),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_117_finite__Collect__le__nat) ).
tff(f1699,plain,
spl17_15,
inference(avatar_split_clause,[],[f1137,f1697]) ).
tff(f1697,plain,
( spl17_15
<=> ! [X0: bool] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
tff(f1137,plain,
! [X0: bool] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
inference(cnf_transformation,[],[f390]) ).
tff(f390,plain,
! [X0: bool] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
inference(rectify,[],[f301]) ).
tff(f301,axiom,
! [X41: bool] :
( ~ hBOOL(X41)
| ~ hBOOL(hAPP_bool_bool(fNot,X41)) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fNot_1_1_U) ).
tff(f1695,plain,
spl17_14,
inference(avatar_split_clause,[],[f1136,f1693]) ).
tff(f1693,plain,
( spl17_14
<=> ! [X0: bool] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
tff(f1136,plain,
! [X0: bool] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f389]) ).
tff(f389,plain,
! [X0: bool] :
( hBOOL(hAPP_bool_bool(fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f302]) ).
tff(f302,axiom,
! [X41: bool] :
( hBOOL(hAPP_bool_bool(fNot,X41))
| hBOOL(X41) ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',help_fNot_2_1_U) ).
tff(f1691,plain,
spl17_13,
inference(avatar_split_clause,[],[f1131,f1689]) ).
tff(f1689,plain,
( spl17_13
<=> ! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
tff(f1131,plain,
! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0)),
inference(cnf_transformation,[],[f384]) ).
tff(f384,plain,
! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0)),
inference(rectify,[],[f227]) ).
tff(f227,axiom,
! [X2: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X2)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_226_subset__refl) ).
tff(f1687,plain,
spl17_12,
inference(avatar_split_clause,[],[f1129,f1685]) ).
tff(f1129,plain,
! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
inference(cnf_transformation,[],[f382]) ).
tff(f382,plain,
! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
inference(rectify,[],[f228]) ).
tff(f228,axiom,
! [X2: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X2)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_227_subset__refl) ).
tff(f1683,plain,
spl17_11,
inference(avatar_split_clause,[],[f1127,f1681]) ).
tff(f1681,plain,
( spl17_11
<=> ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
tff(f1127,plain,
! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)),
inference(cnf_transformation,[],[f380]) ).
tff(f380,plain,
! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)),
inference(rectify,[],[f226]) ).
tff(f226,axiom,
! [X2: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X2)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_225_subset__refl) ).
tff(f1679,plain,
spl17_10,
inference(avatar_split_clause,[],[f1125,f1677]) ).
tff(f1125,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(cnf_transformation,[],[f378]) ).
tff(f378,plain,
! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(rectify,[],[f128]) ).
tff(f128,axiom,
! [X11: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X11)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_127_le__refl) ).
tff(f1675,plain,
spl17_9,
inference(avatar_split_clause,[],[f1113,f1672]) ).
tff(f1113,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f366]) ).
tff(f366,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',conj_4) ).
tff(f1670,plain,
spl17_8,
inference(avatar_split_clause,[],[f1123,f1668]) ).
tff(f1668,plain,
( spl17_8
<=> ! [X0: nat] : ( hAPP_nat_nat(suc,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
tff(f1123,plain,
! [X0: nat] : ( hAPP_nat_nat(suc,X0) != X0 ),
inference(cnf_transformation,[],[f376]) ).
tff(f376,plain,
! [X0: nat] : ( hAPP_nat_nat(suc,X0) != X0 ),
inference(rectify,[],[f123]) ).
tff(f123,axiom,
! [X11: nat] : ( hAPP_nat_nat(suc,X11) != X11 ),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',fact_122_n__not__Suc__n) ).
tff(f1666,plain,
spl17_7,
inference(avatar_split_clause,[],[f1122,f1664]) ).
tff(f1664,plain,
( spl17_7
<=> ! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
tff(f1662,plain,
spl17_6,
inference(avatar_split_clause,[],[f1121,f1660]) ).
tff(f1660,plain,
( spl17_6
<=> ! [X0: fun_fu425979586l_bool] : ( collect_fun_nat_bool(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
tff(f1658,plain,
spl17_5,
inference(avatar_split_clause,[],[f1120,f1656]) ).
tff(f1656,plain,
( spl17_5
<=> ! [X0: fun_fun_a_bool_bool] : ( collect_fun_a_bool(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
tff(f1654,plain,
spl17_4,
inference(avatar_split_clause,[],[f1119,f1652]) ).
tff(f1652,plain,
( spl17_4
<=> ! [X0: fun_fu1430349052l_bool] : ( collec1974731493e_bool(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
tff(f1650,plain,
spl17_3,
inference(avatar_split_clause,[],[f1118,f1648]) ).
tff(f1648,plain,
( spl17_3
<=> ! [X0: fun_pname_bool] : ( collect_pname(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
tff(f1646,plain,
spl17_2,
inference(avatar_split_clause,[],[f1112,f1643]) ).
tff(f1112,plain,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
inference(cnf_transformation,[],[f362]) ).
tff(f362,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
file('/export/starexec/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',conj_0) ).
tff(f1641,plain,
~ spl17_1,
inference(avatar_split_clause,[],[f1111,f1638]) ).
tff(f1111,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(cnf_transformation,[],[f370]) ).
tff(f370,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(flattening,[],[f369]) ).
tff(f369,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))),
inference(negated_conjecture,[],[f368]) ).
tff(f368,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/sandbox/tmp/tmp.0KgqldTZEk/Vampire---4.8_5197',conj_6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19 % Problem : SWW473_1 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.21 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.22/0.42 % Computer : n018.cluster.edu
% 0.22/0.42 % Model : x86_64 x86_64
% 0.22/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.42 % Memory : 8042.1875MB
% 0.22/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.22/0.42 % CPULimit : 300
% 0.22/0.42 % WCLimit : 300
% 0.22/0.42 % DateTime : Wed Aug 30 16:52:34 EDT 2023
% 0.28/0.43 % CPUTime :
% 0.28/0.48 % (5481)Running in auto input_syntax mode. Trying TPTP
% 0.28/0.51 % (5523)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.28/0.51 % (5525)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.28/0.51 % (5522)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.28/0.51 % (5524)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.28/0.51 % (5527)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.28/0.51 % (5529)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.28/0.51 % (5528)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.28/0.62 % (5527)First to succeed.
% 0.28/0.65 % (5527)Refutation found. Thanks to Tanya!
% 0.28/0.65 % SZS status Theorem for Vampire---4
% 0.28/0.65 % SZS output start Proof for Vampire---4
% See solution above
% 0.28/0.67 % (5527)------------------------------
% 0.28/0.67 % (5527)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.28/0.67 % (5527)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.28/0.67 % (5527)Termination reason: Refutation
% 0.28/0.67
% 0.28/0.67 % (5527)Memory used [KB]: 9466
% 0.28/0.67 % (5527)Time elapsed: 0.140 s
% 0.28/0.67 % (5527)------------------------------
% 0.28/0.67 % (5527)------------------------------
% 0.28/0.67 % (5481)Success in time 0.237 s
% 0.28/0.67 % Vampire---4.8 exiting
%------------------------------------------------------------------------------