%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW473_2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:29:48 PM UTC 2026
% Result : Theorem 2.97s 2.12s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 44 ~; 37 |; 7 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 89 ( 87 usr; 87 prp; 0-2 aty)
% Number of functors : 325 ( 325 usr; 58 con; 0-3 aty)
% Number of variables : 75 ( 0 sgn 75 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
cOMBB_a_fun_a_bool_a: ( fun_a_a * fun_a_fun_a_bool ) > fun_a_fun_a_bool ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(func_def_2,type,
cOMBB_1885489796ol_nat: ( fun_nat_a * fun_a_fun_a_bool ) > fun_nat_fun_a_bool ).
tff(func_def_3,type,
cOMBB_610033911bool_a: ( fun_a_pname * fun_pn800050071e_bool ) > fun_a_fun_pname_bool ).
tff(func_def_4,type,
cOMBB_542850580_pname: ( fun_pname_pname * fun_pn800050071e_bool ) > fun_pn800050071e_bool ).
tff(func_def_5,type,
cOMBB_1212655066ol_nat: ( fun_nat_pname * fun_pn800050071e_bool ) > fun_na936072029e_bool ).
tff(func_def_6,type,
cOMBB_1693087065a_bool: ( fun_fun_a_bool_pname * fun_pn800050071e_bool ) > fun_fu2112074076e_bool ).
tff(func_def_7,type,
cOMBB_598082538e_bool: ( fun_fu1499449723_pname * fun_pn800050071e_bool ) > fun_fu410713561e_bool ).
tff(func_def_8,type,
cOMBB_141086128t_bool: ( fun_fu665170229_pname * fun_pn800050071e_bool ) > fun_fu1492573599e_bool ).
tff(func_def_9,type,
cOMBB_bool_bool_a: ( fun_a_bool * fun_bool_bool ) > fun_a_bool ).
tff(func_def_10,type,
cOMBB_647938656_pname: ( fun_pname_bool * fun_bool_bool ) > fun_pname_bool ).
tff(func_def_11,type,
cOMBB_bool_bool_nat: ( fun_nat_bool * fun_bool_bool ) > fun_nat_bool ).
tff(func_def_12,type,
cOMBB_2140588453a_bool: ( fun_fun_a_bool_bool * fun_bool_bool ) > fun_fun_a_bool_bool ).
tff(func_def_13,type,
cOMBB_307249310e_bool: ( fun_fu1430349052l_bool * fun_bool_bool ) > fun_fu1430349052l_bool ).
tff(func_def_14,type,
cOMBB_238756964t_bool: ( fun_fu425979586l_bool * fun_bool_bool ) > fun_fu425979586l_bool ).
tff(func_def_15,type,
cOMBB_1972296269bool_a: ( fun_a_bool * fun_bo1549164019l_bool ) > fun_a_fun_bool_bool ).
tff(func_def_16,type,
cOMBB_675860798_pname: ( fun_pname_bool * fun_bo1549164019l_bool ) > fun_pn250273176l_bool ).
tff(func_def_17,type,
cOMBB_1015721476ol_nat: ( fun_nat_bool * fun_bo1549164019l_bool ) > fun_na1469252690l_bool ).
tff(func_def_18,type,
cOMBB_338059395a_bool: ( fun_fun_a_bool_bool * fun_bo1549164019l_bool ) > fun_fu554186387l_bool ).
tff(func_def_19,type,
cOMBB_2095475776e_bool: ( fun_fu1430349052l_bool * fun_bo1549164019l_bool ) > fun_fu31783638l_bool ).
tff(func_def_20,type,
cOMBB_444170502t_bool: ( fun_fu425979586l_bool * fun_bo1549164019l_bool ) > fun_fu1016514960l_bool ).
tff(func_def_21,type,
cOMBB_1321347587bool_a: ( fun_a_nat * fun_nat_fun_nat_bool ) > fun_a_fun_nat_bool ).
tff(func_def_22,type,
cOMBB_523834888_pname: ( fun_pname_nat * fun_nat_fun_nat_bool ) > fun_pn406123357t_bool ).
tff(func_def_23,type,
cOMBB_800536526ol_nat: ( fun_nat_nat * fun_nat_fun_nat_bool ) > fun_nat_fun_nat_bool ).
tff(func_def_24,type,
cOMBB_164527437a_bool: ( fun_fun_a_bool_nat * fun_nat_fun_nat_bool ) > fun_fu600484770t_bool ).
tff(func_def_25,type,
cOMBB_1896684278e_bool: ( fun_fu1668467777ol_nat * fun_nat_fun_nat_bool ) > fun_fu900310687t_bool ).
tff(func_def_26,type,
cOMBB_1250273980t_bool: ( fun_fun_nat_bool_nat * fun_nat_fun_nat_bool ) > fun_fu821463397t_bool ).
tff(func_def_27,type,
cOMBB_472261505bool_a: ( fun_a_fun_a_bool * fun_fu1471507361l_bool ) > fun_a_1255737515l_bool ).
tff(func_def_28,type,
cOMBB_392435466_pname: ( fun_pname_fun_a_bool * fun_fu1471507361l_bool ) > fun_pn1038293468l_bool ).
tff(func_def_29,type,
cOMBB_1823939024ol_nat: ( fun_nat_fun_a_bool * fun_fu1471507361l_bool ) > fun_na1632405922l_bool ).
tff(func_def_30,type,
cOMBB_1137537805bool_a: ( fun_a_fun_pname_bool * fun_fu802393907l_bool ) > fun_a_968466022l_bool ).
tff(func_def_31,type,
cOMBB_408569982_pname: ( fun_pn800050071e_bool * fun_fu802393907l_bool ) > fun_pn422929397l_bool ).
tff(func_def_32,type,
cOMBB_2117322052ol_nat: ( fun_na936072029e_bool * fun_fu802393907l_bool ) > fun_na2122364079l_bool ).
tff(func_def_33,type,
cOMBB_743407885bool_a: ( fun_a_fun_nat_bool * fun_fu1217155507l_bool ) > fun_a_762926252l_bool ).
tff(func_def_34,type,
cOMBB_928955006_pname: ( fun_pn406123357t_bool * fun_fu1217155507l_bool ) > fun_pn1165013435l_bool ).
tff(func_def_35,type,
cOMBB_2026977092ol_nat: ( fun_nat_fun_nat_bool * fun_fu1217155507l_bool ) > fun_na1436237685l_bool ).
tff(func_def_36,type,
cOMBC_a_a_bool: fun_a_fun_a_bool > fun_a_fun_a_bool ).
tff(func_def_37,type,
cOMBC_a_pname_bool: fun_a_fun_pname_bool > fun_pname_fun_a_bool ).
tff(func_def_38,type,
cOMBC_a_nat_bool: fun_a_fun_nat_bool > fun_nat_fun_a_bool ).
tff(func_def_39,type,
cOMBC_1355376034l_bool: fun_a_1255737515l_bool > fun_fu1731003005a_bool ).
tff(func_def_40,type,
cOMBC_1834145417l_bool: fun_a_968466022l_bool > fun_fu923319872a_bool ).
tff(func_def_41,type,
cOMBC_777206479l_bool: fun_a_762926252l_bool > fun_fu277003770a_bool ).
tff(func_def_42,type,
cOMBC_pname_a_bool: fun_pname_fun_a_bool > fun_a_fun_pname_bool ).
tff(func_def_43,type,
cOMBC_1149511130e_bool: fun_pn800050071e_bool > fun_pn800050071e_bool ).
tff(func_def_44,type,
cOMBC_pname_nat_bool: fun_pn406123357t_bool > fun_na936072029e_bool ).
tff(func_def_45,type,
cOMBC_445755039l_bool: fun_pn1038293468l_bool > fun_fu2112074076e_bool ).
tff(func_def_46,type,
cOMBC_1058051404l_bool: fun_pn422929397l_bool > fun_fu410713561e_bool ).
tff(func_def_47,type,
cOMBC_267053842l_bool: fun_pn1165013435l_bool > fun_fu1492573599e_bool ).
tff(func_def_48,type,
cOMBC_nat_a_bool: fun_nat_fun_a_bool > fun_a_fun_nat_bool ).
tff(func_def_49,type,
cOMBC_nat_pname_bool: fun_na936072029e_bool > fun_pn406123357t_bool ).
tff(func_def_50,type,
cOMBC_nat_nat_bool: fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).
tff(func_def_51,type,
cOMBC_1928494297l_bool: fun_na1632405922l_bool > fun_fu600484770t_bool ).
tff(func_def_52,type,
cOMBC_386238098l_bool: fun_na2122364079l_bool > fun_fu900310687t_bool ).
tff(func_def_53,type,
cOMBC_226598744l_bool: fun_na1436237685l_bool > fun_fu821463397t_bool ).
tff(func_def_54,type,
cOMBC_1738168533e_bool: fun_fu2112074076e_bool > fun_pn1038293468l_bool ).
tff(func_def_55,type,
cOMBC_619334683t_bool: fun_fu600484770t_bool > fun_na1632405922l_bool ).
tff(func_def_56,type,
cOMBC_1732670874l_bool: fun_fu1471507361l_bool > fun_fu1471507361l_bool ).
tff(func_def_57,type,
cOMBC_1880041174l_bool: fun_fu386216885l_bool > fun_fu911136611l_bool ).
tff(func_def_58,type,
cOMBC_1004116266e_bool: fun_fu410713561e_bool > fun_pn422929397l_bool ).
tff(func_def_59,type,
cOMBC_1666426608t_bool: fun_fu900310687t_bool > fun_na2122364079l_bool ).
tff(func_def_60,type,
cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).
tff(func_def_61,type,
cOMBC_1988546018l_bool: fun_fu931343505l_bool > fun_fu2087345469l_bool ).
tff(func_def_62,type,
cOMBC_615407716e_bool: fun_fu1492573599e_bool > fun_pn1165013435l_bool ).
tff(func_def_63,type,
cOMBC_385542954t_bool: fun_fu821463397t_bool > fun_na1436237685l_bool ).
tff(func_def_64,type,
cOMBC_1693257480l_bool: fun_fu1217155507l_bool > fun_fu1217155507l_bool ).
tff(func_def_65,type,
cOMBC_1245412066l_bool: fun_fu1436348701l_bool > fun_fu616551101l_bool ).
tff(func_def_66,type,
cOMBC_331553030l_bool: fun_fu418465139l_bool > fun_fu418465139l_bool ).
tff(func_def_67,type,
cOMBC_7971162l_bool: fun_fu1911931399l_bool > fun_fu1911931399l_bool ).
tff(func_def_68,type,
cOMBC_595898202l_bool: fun_fu140186515l_bool > fun_fu140186515l_bool ).
tff(func_def_69,type,
cOMBK_a_pname: x_a > fun_pname_a ).
tff(func_def_70,type,
cOMBK_bool_a: bool > fun_a_bool ).
tff(func_def_71,type,
cOMBK_bool_pname: bool > fun_pname_bool ).
tff(func_def_72,type,
cOMBK_bool_nat: bool > fun_nat_bool ).
tff(func_def_73,type,
cOMBK_324466864a_bool: bool > fun_fun_a_bool_bool ).
tff(func_def_74,type,
cOMBK_1857069011e_bool: bool > fun_fu1430349052l_bool ).
tff(func_def_75,type,
cOMBK_1994329625t_bool: bool > fun_fu425979586l_bool ).
tff(func_def_76,type,
cOMBS_a_bool_bool: ( fun_a_bool * fun_a_fun_bool_bool ) > fun_a_bool ).
tff(func_def_77,type,
cOMBS_568398431l_bool: ( fun_pname_bool * fun_pn250273176l_bool ) > fun_pname_bool ).
tff(func_def_78,type,
cOMBS_nat_bool_bool: ( fun_nat_bool * fun_na1469252690l_bool ) > fun_nat_bool ).
tff(func_def_79,type,
cOMBS_1035972772l_bool: ( fun_fun_a_bool_bool * fun_fu554186387l_bool ) > fun_fun_a_bool_bool ).
tff(func_def_80,type,
cOMBS_350070575l_bool: ( fun_fu1430349052l_bool * fun_fu31783638l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_81,type,
cOMBS_1187019125l_bool: ( fun_fu425979586l_bool * fun_fu1016514960l_bool ) > fun_fu425979586l_bool ).
tff(func_def_82,type,
body: pname > option_com ).
tff(func_def_83,type,
finite_card_a: fun_fun_a_bool_nat ).
tff(func_def_84,type,
finite_card_pname: fun_fu1668467777ol_nat ).
tff(func_def_85,type,
finite_card_nat: fun_fun_nat_bool_nat ).
tff(func_def_86,type,
finite1306199131a_bool: fun_fu2020802748ol_nat ).
tff(func_def_87,type,
finite1340463720e_bool: fun_fu1730389579ol_nat ).
tff(func_def_88,type,
finite346522414t_bool: fun_fu411113733ol_nat ).
tff(func_def_89,type,
finite_finite_a: fun_fun_a_bool_bool ).
tff(func_def_90,type,
finite_finite_pname: fun_fu1430349052l_bool ).
tff(func_def_91,type,
finite_finite_nat: fun_fu425979586l_bool ).
tff(func_def_92,type,
finite347923420a_bool: fun_fu885608257l_bool ).
tff(func_def_93,type,
finite595471783e_bool: fun_fu399576434l_bool ).
tff(func_def_94,type,
finite2012431853t_bool: fun_fu814369080l_bool ).
tff(func_def_95,type,
finite1381704300l_bool: fun_fu255076663l_bool ).
tff(func_def_96,type,
finite786885583l_bool: fun_fu1438281908l_bool ).
tff(func_def_97,type,
finite1701474069l_bool: fun_fu61768826l_bool ).
tff(func_def_98,type,
minus_minus_nat: nat > fun_nat_nat ).
tff(func_def_99,type,
one_one_nat: nat ).
tff(func_def_100,type,
plus_plus_nat: nat > fun_nat_nat ).
tff(func_def_101,type,
zero_zero_nat: nat ).
tff(func_def_102,type,
suc: fun_nat_nat ).
tff(func_def_103,type,
nat_case_bool: ( fun_nat_bool * bool ) > fun_nat_bool ).
tff(func_def_104,type,
the_com: option_com > com ).
tff(func_def_105,type,
bot_bot_bool: bool ).
tff(func_def_106,type,
bot_bot_nat: nat ).
tff(func_def_107,type,
bot_bot_fun_a_bool: fun_a_bool ).
tff(func_def_108,type,
bot_bo844097828e_bool: fun_pname_bool ).
tff(func_def_109,type,
bot_bot_fun_nat_bool: fun_nat_bool ).
tff(func_def_110,type,
bot_bo1389914601l_bool: fun_fun_a_bool_bool ).
tff(func_def_111,type,
bot_bo1649642514l_bool: fun_fu1430349052l_bool ).
tff(func_def_112,type,
bot_bo1701429464l_bool: fun_fu425979586l_bool ).
tff(func_def_113,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_114,type,
ord_less_eq_bool: fun_bo1549164019l_bool ).
tff(func_def_115,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_116,type,
ord_le1311769555a_bool: fun_fu1471507361l_bool ).
tff(func_def_117,type,
ord_le313189616e_bool: fun_fu802393907l_bool ).
tff(func_def_118,type,
ord_le1568362934t_bool: fun_fu1217155507l_bool ).
tff(func_def_119,type,
ord_le1375614389l_bool: fun_fu418465139l_bool ).
tff(func_def_120,type,
ord_le675606854l_bool: fun_fu1911931399l_bool ).
tff(func_def_121,type,
ord_le1454342156l_bool: fun_fu140186515l_bool ).
tff(func_def_122,type,
collect_a: fun_a_bool > fun_a_bool ).
tff(func_def_123,type,
collect_pname: fun_pname_bool > fun_pname_bool ).
tff(func_def_124,type,
collect_nat: fun_nat_bool > fun_nat_bool ).
tff(func_def_125,type,
collect_fun_a_bool: fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
tff(func_def_126,type,
collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
tff(func_def_127,type,
collect_fun_nat_bool: fun_fu425979586l_bool > fun_fu425979586l_bool ).
tff(func_def_128,type,
collec707592106l_bool: fun_fu885608257l_bool > fun_fu885608257l_bool ).
tff(func_def_129,type,
collec1613912337l_bool: fun_fu399576434l_bool > fun_fu399576434l_bool ).
tff(func_def_130,type,
collec1015864663l_bool: fun_fu814369080l_bool > fun_fu814369080l_bool ).
tff(func_def_131,type,
image_a_a: ( fun_a_bool * fun_a_a ) > fun_a_bool ).
tff(func_def_132,type,
image_a_pname: ( fun_a_bool * fun_a_pname ) > fun_pname_bool ).
tff(func_def_133,type,
image_a_nat: ( fun_a_bool * fun_a_nat ) > fun_nat_bool ).
tff(func_def_134,type,
image_a_fun_a_bool: ( fun_a_bool * fun_a_fun_a_bool ) > fun_fun_a_bool_bool ).
tff(func_def_135,type,
image_819518260e_bool: ( fun_a_bool * fun_a_fun_pname_bool ) > fun_fu1430349052l_bool ).
tff(func_def_136,type,
image_a_fun_nat_bool: ( fun_a_bool * fun_a_fun_nat_bool ) > fun_fu425979586l_bool ).
tff(func_def_137,type,
image_pname_a: ( fun_pname_bool * fun_pname_a ) > fun_a_bool ).
tff(func_def_138,type,
image_pname_pname: ( fun_pname_bool * fun_pname_pname ) > fun_pname_bool ).
tff(func_def_139,type,
image_pname_nat: ( fun_pname_bool * fun_pname_nat ) > fun_nat_bool ).
tff(func_def_140,type,
image_112932426a_bool: ( fun_pname_bool * fun_pname_fun_a_bool ) > fun_fun_a_bool_bool ).
tff(func_def_141,type,
image_47868345e_bool: ( fun_pname_bool * fun_pn800050071e_bool ) > fun_fu1430349052l_bool ).
tff(func_def_142,type,
image_2129980159t_bool: ( fun_pname_bool * fun_pn406123357t_bool ) > fun_fu425979586l_bool ).
tff(func_def_143,type,
image_nat_a: ( fun_nat_bool * fun_nat_a ) > fun_a_bool ).
tff(func_def_144,type,
image_nat_pname: ( fun_nat_bool * fun_nat_pname ) > fun_pname_bool ).
tff(func_def_145,type,
image_nat_nat: ( fun_nat_bool * fun_nat_nat ) > fun_nat_bool ).
tff(func_def_146,type,
image_nat_fun_a_bool: ( fun_nat_bool * fun_nat_fun_a_bool ) > fun_fun_a_bool_bool ).
tff(func_def_147,type,
image_1655916159e_bool: ( fun_nat_bool * fun_na936072029e_bool ) > fun_fu1430349052l_bool ).
tff(func_def_148,type,
image_26036933t_bool: ( fun_nat_bool * fun_nat_fun_nat_bool ) > fun_fu425979586l_bool ).
tff(func_def_149,type,
image_fun_a_bool_a: ( fun_fun_a_bool_bool * fun_fun_a_bool_a ) > fun_a_bool ).
tff(func_def_150,type,
image_1854862208_pname: ( fun_fun_a_bool_bool * fun_fun_a_bool_pname ) > fun_pname_bool ).
tff(func_def_151,type,
image_fun_a_bool_nat: ( fun_fun_a_bool_bool * fun_fun_a_bool_nat ) > fun_nat_bool ).
tff(func_def_152,type,
image_876012084bool_a: ( fun_fu1430349052l_bool * fun_fun_pname_bool_a ) > fun_a_bool ).
tff(func_def_153,type,
image_1283814551_pname: ( fun_fu1430349052l_bool * fun_fu1499449723_pname ) > fun_pname_bool ).
tff(func_def_154,type,
image_1551609309ol_nat: ( fun_fu1430349052l_bool * fun_fu1668467777ol_nat ) > fun_nat_bool ).
tff(func_def_155,type,
image_fun_nat_bool_a: ( fun_fu425979586l_bool * fun_fun_nat_bool_a ) > fun_a_bool ).
tff(func_def_156,type,
image_1921560913_pname: ( fun_fu425979586l_bool * fun_fu665170229_pname ) > fun_pname_bool ).
tff(func_def_157,type,
image_496248727ol_nat: ( fun_fu425979586l_bool * fun_fun_nat_bool_nat ) > fun_nat_bool ).
tff(func_def_158,type,
insert_a: ( fun_a_bool * x_a ) > fun_a_bool ).
tff(func_def_159,type,
insert_pname: ( fun_pname_bool * pname ) > fun_pname_bool ).
tff(func_def_160,type,
insert_nat: ( fun_nat_bool * nat ) > fun_nat_bool ).
tff(func_def_161,type,
insert_fun_a_bool: ( fun_fun_a_bool_bool * fun_a_bool ) > fun_fun_a_bool_bool ).
tff(func_def_162,type,
insert1325755072e_bool: ( fun_fu1430349052l_bool * fun_pname_bool ) > fun_fu1430349052l_bool ).
tff(func_def_163,type,
insert_fun_nat_bool: ( fun_fu425979586l_bool * fun_nat_bool ) > fun_fu425979586l_bool ).
tff(func_def_164,type,
fFalse: bool ).
tff(func_def_165,type,
fNot: fun_bool_bool ).
tff(func_def_166,type,
fTrue: bool ).
tff(func_def_167,type,
fconj: fun_bo1549164019l_bool ).
tff(func_def_168,type,
fdisj: fun_bo1549164019l_bool ).
tff(func_def_169,type,
fequal_a: fun_a_fun_a_bool ).
tff(func_def_170,type,
fequal_pname: fun_pn800050071e_bool ).
tff(func_def_171,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(func_def_172,type,
fequal_fun_a_bool: fun_fu1471507361l_bool ).
tff(func_def_173,type,
fequal533582459e_bool: fun_fu802393907l_bool ).
tff(func_def_174,type,
fequal_fun_nat_bool: fun_fu1217155507l_bool ).
tff(func_def_175,type,
fimplies: fun_bo1549164019l_bool ).
tff(func_def_176,type,
hAPP_a_a: ( x_a * fun_a_a ) > x_a ).
tff(func_def_177,type,
hAPP_a_pname: ( x_a * fun_a_pname ) > pname ).
tff(func_def_178,type,
hAPP_a_bool: ( x_a * fun_a_bool ) > bool ).
tff(func_def_179,type,
hAPP_a_nat: ( x_a * fun_a_nat ) > nat ).
tff(func_def_180,type,
hAPP_a_fun_a_bool: ( x_a * fun_a_fun_a_bool ) > fun_a_bool ).
tff(func_def_181,type,
hAPP_a93125764e_bool: ( x_a * fun_a_fun_pname_bool ) > fun_pname_bool ).
tff(func_def_182,type,
hAPP_a_fun_bool_bool: ( x_a * fun_a_fun_bool_bool ) > fun_bool_bool ).
tff(func_def_183,type,
hAPP_a_fun_nat_bool: ( x_a * fun_a_fun_nat_bool ) > fun_nat_bool ).
tff(func_def_184,type,
hAPP_a85458249l_bool: ( x_a * fun_a_1255737515l_bool ) > fun_fun_a_bool_bool ).
tff(func_def_185,type,
hAPP_a217006258l_bool: ( x_a * fun_a_968466022l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_186,type,
hAPP_a1392362872l_bool: ( x_a * fun_a_762926252l_bool ) > fun_fu425979586l_bool ).
tff(func_def_187,type,
hAPP_pname_a: ( pname * fun_pname_a ) > x_a ).
tff(func_def_188,type,
hAPP_pname_pname: ( pname * fun_pname_pname ) > pname ).
tff(func_def_189,type,
hAPP_pname_bool: ( pname * fun_pname_bool ) > bool ).
tff(func_def_190,type,
hAPP_pname_nat: ( pname * fun_pname_nat ) > nat ).
tff(func_def_191,type,
hAPP_p1534023578a_bool: ( pname * fun_pname_fun_a_bool ) > fun_a_bool ).
tff(func_def_192,type,
hAPP_p61793385e_bool: ( pname * fun_pn800050071e_bool ) > fun_pname_bool ).
tff(func_def_193,type,
hAPP_p393069232l_bool: ( pname * fun_pn250273176l_bool ) > fun_bool_bool ).
tff(func_def_194,type,
hAPP_p1499970991t_bool: ( pname * fun_pn406123357t_bool ) > fun_nat_bool ).
tff(func_def_195,type,
hAPP_p1824510254l_bool: ( pname * fun_pn1038293468l_bool ) > fun_fun_a_bool_bool ).
tff(func_def_196,type,
hAPP_p338031245l_bool: ( pname * fun_pn422929397l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_197,type,
hAPP_p130839763l_bool: ( pname * fun_pn1165013435l_bool ) > fun_fu425979586l_bool ).
tff(func_def_198,type,
hAPP_bool_bool: ( bool * fun_bool_bool ) > bool ).
tff(func_def_199,type,
hAPP_b589554111l_bool: ( bool * fun_bo1549164019l_bool ) > fun_bool_bool ).
tff(func_def_200,type,
hAPP_nat_a: ( nat * fun_nat_a ) > x_a ).
tff(func_def_201,type,
hAPP_nat_pname: ( nat * fun_nat_pname ) > pname ).
tff(func_def_202,type,
hAPP_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(func_def_203,type,
hAPP_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(func_def_204,type,
hAPP_nat_fun_a_bool: ( nat * fun_nat_fun_a_bool ) > fun_a_bool ).
tff(func_def_205,type,
hAPP_n1025906991e_bool: ( nat * fun_na936072029e_bool ) > fun_pname_bool ).
tff(func_def_206,type,
hAPP_n1006566506l_bool: ( nat * fun_na1469252690l_bool ) > fun_bool_bool ).
tff(func_def_207,type,
hAPP_n1699378549t_bool: ( nat * fun_nat_fun_nat_bool ) > fun_nat_bool ).
tff(func_def_208,type,
hAPP_n1414589940l_bool: ( nat * fun_na1632405922l_bool ) > fun_fun_a_bool_bool ).
tff(func_def_209,type,
hAPP_n850744903l_bool: ( nat * fun_na2122364079l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_210,type,
hAPP_n215258509l_bool: ( nat * fun_na1436237685l_bool ) > fun_fu425979586l_bool ).
tff(func_def_211,type,
hAPP_f1128469712_pname: ( fun_a_bool * fun_fun_a_bool_pname ) > pname ).
tff(func_def_212,type,
hAPP_fun_a_bool_bool: ( fun_a_bool * fun_fun_a_bool_bool ) > bool ).
tff(func_def_213,type,
hAPP_fun_a_bool_nat: ( fun_a_bool * fun_fun_a_bool_nat ) > nat ).
tff(func_def_214,type,
hAPP_f2050579477a_bool: ( fun_a_bool * fun_fu1731003005a_bool ) > fun_a_bool ).
tff(func_def_215,type,
hAPP_f1794073134e_bool: ( fun_a_bool * fun_fu2112074076e_bool ) > fun_pname_bool ).
tff(func_def_216,type,
hAPP_f198738859l_bool: ( fun_a_bool * fun_fu554186387l_bool ) > fun_bool_bool ).
tff(func_def_217,type,
hAPP_f282463732t_bool: ( fun_a_bool * fun_fu600484770t_bool ) > fun_nat_bool ).
tff(func_def_218,type,
hAPP_f1631501043l_bool: ( fun_a_bool * fun_fu1471507361l_bool ) > fun_fun_a_bool_bool ).
tff(func_def_219,type,
hAPP_f285962445l_bool: ( fun_a_bool * fun_fu386216885l_bool ) > fun_fu885608257l_bool ).
tff(func_def_220,type,
hAPP_f1297739591_pname: ( fun_pname_bool * fun_fu1499449723_pname ) > pname ).
tff(func_def_221,type,
hAPP_f1664156314l_bool: ( fun_pname_bool * fun_fu1430349052l_bool ) > bool ).
tff(func_def_222,type,
hAPP_f921600141ol_nat: ( fun_pname_bool * fun_fu1668467777ol_nat ) > nat ).
tff(func_def_223,type,
hAPP_f1051908748a_bool: ( fun_pname_bool * fun_fu923319872a_bool ) > fun_a_bool ).
tff(func_def_224,type,
hAPP_f759274231e_bool: ( fun_pname_bool * fun_fu410713561e_bool ) > fun_pname_bool ).
tff(func_def_225,type,
hAPP_f1476298914l_bool: ( fun_pname_bool * fun_fu31783638l_bool ) > fun_bool_bool ).
tff(func_def_226,type,
hAPP_f1066163005t_bool: ( fun_pname_bool * fun_fu900310687t_bool ) > fun_nat_bool ).
tff(func_def_227,type,
hAPP_f434788991l_bool: ( fun_pname_bool * fun_fu802393907l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_228,type,
hAPP_f556039215l_bool: ( fun_pname_bool * fun_fu931343505l_bool ) > fun_fu399576434l_bool ).
tff(func_def_229,type,
hAPP_f1291551745_pname: ( fun_nat_bool * fun_fu665170229_pname ) > pname ).
tff(func_def_230,type,
hAPP_f54304608l_bool: ( fun_nat_bool * fun_fu425979586l_bool ) > bool ).
tff(func_def_231,type,
hAPP_f22106695ol_nat: ( fun_nat_bool * fun_fun_nat_bool_nat ) > nat ).
tff(func_def_232,type,
hAPP_f1549043526a_bool: ( fun_nat_bool * fun_fu277003770a_bool ) > fun_a_bool ).
tff(func_def_233,type,
hAPP_f654413245e_bool: ( fun_nat_bool * fun_fu1492573599e_bool ) > fun_pname_bool ).
tff(func_def_234,type,
hAPP_f1748468828l_bool: ( fun_nat_bool * fun_fu1016514960l_bool ) > fun_bool_bool ).
tff(func_def_235,type,
hAPP_f800510211t_bool: ( fun_nat_bool * fun_fu821463397t_bool ) > fun_nat_bool ).
tff(func_def_236,type,
hAPP_f103356543l_bool: ( fun_nat_bool * fun_fu1217155507l_bool ) > fun_fu425979586l_bool ).
tff(func_def_237,type,
hAPP_f1951378235l_bool: ( fun_nat_bool * fun_fu1436348701l_bool ) > fun_fu814369080l_bool ).
tff(func_def_238,type,
hAPP_f621171935l_bool: ( fun_fun_a_bool_bool * fun_fu885608257l_bool ) > bool ).
tff(func_def_239,type,
hAPP_f2009550088ol_nat: ( fun_fun_a_bool_bool * fun_fu2020802748ol_nat ) > nat ).
tff(func_def_240,type,
hAPP_f2117159681l_bool: ( fun_fun_a_bool_bool * fun_fu911136611l_bool ) > fun_fun_a_bool_bool ).
tff(func_def_241,type,
hAPP_f1434722111l_bool: ( fun_fun_a_bool_bool * fun_fu418465139l_bool ) > fun_fu885608257l_bool ).
tff(func_def_242,type,
hAPP_f1935102916l_bool: ( fun_fu1430349052l_bool * fun_fu399576434l_bool ) > bool ).
tff(func_def_243,type,
hAPP_f55526627ol_nat: ( fun_fu1430349052l_bool * fun_fu1730389579ol_nat ) > nat ).
tff(func_def_244,type,
hAPP_f559147733l_bool: ( fun_fu1430349052l_bool * fun_fu2087345469l_bool ) > fun_fu1430349052l_bool ).
tff(func_def_245,type,
hAPP_f510955609l_bool: ( fun_fu1430349052l_bool * fun_fu1911931399l_bool ) > fun_fu399576434l_bool ).
tff(func_def_246,type,
hAPP_f1637334154l_bool: ( fun_fu425979586l_bool * fun_fu814369080l_bool ) > bool ).
tff(func_def_247,type,
hAPP_f696928925ol_nat: ( fun_fu425979586l_bool * fun_fu411113733ol_nat ) > nat ).
tff(func_def_248,type,
hAPP_f1246832597l_bool: ( fun_fu425979586l_bool * fun_fu616551101l_bool ) > fun_fu425979586l_bool ).
tff(func_def_249,type,
hAPP_f1772781669l_bool: ( fun_fu425979586l_bool * fun_fu140186515l_bool ) > fun_fu814369080l_bool ).
tff(func_def_250,type,
hAPP_f292226953l_bool: ( fun_fu885608257l_bool * fun_fu255076663l_bool ) > bool ).
tff(func_def_251,type,
hAPP_f389811538l_bool: ( fun_fu399576434l_bool * fun_fu1438281908l_bool ) > bool ).
tff(func_def_252,type,
hAPP_f937997336l_bool: ( fun_fu814369080l_bool * fun_fu61768826l_bool ) > bool ).
tff(func_def_253,type,
member_a: fun_a_1255737515l_bool ).
tff(func_def_254,type,
member_pname: fun_pn422929397l_bool ).
tff(func_def_255,type,
member_nat: fun_na1436237685l_bool ).
tff(func_def_256,type,
member_fun_a_bool: fun_fu386216885l_bool ).
tff(func_def_257,type,
member799430823e_bool: fun_fu931343505l_bool ).
tff(func_def_258,type,
member_fun_nat_bool: fun_fu1436348701l_bool ).
tff(func_def_259,type,
g: fun_a_bool ).
tff(func_def_260,type,
p: fun_a_bool > fun_fun_a_bool_bool ).
tff(func_def_261,type,
u: fun_pname_bool ).
tff(func_def_262,type,
mgt: com > x_a ).
tff(func_def_263,type,
mgt_call: fun_pname_a ).
tff(func_def_264,type,
na: nat ).
tff(func_def_265,type,
pn: pname ).
tff(func_def_266,type,
wt: com > bool ).
tff(func_def_267,type,
sK0: ( fun_a_bool * fun_a_bool ) > x_a ).
tff(func_def_268,type,
sK1: ( fun_pname_bool * ( fun_pname_a * fun_a_bool ) ) > fun_pname_bool ).
tff(func_def_269,type,
sK2: ( fun_a_bool * ( fun_pname_bool * fun_pname_a ) ) > fun_pname_bool ).
tff(func_def_270,type,
sK3: ( nat * nat ) > nat ).
tff(func_def_271,type,
sK4: ( nat * nat ) > nat ).
tff(func_def_272,type,
sK5: ( nat * nat ) > nat ).
tff(func_def_273,type,
sK6: ( nat * fun_nat_bool ) > nat ).
tff(func_def_274,type,
sK7: ( nat * nat ) > nat ).
tff(func_def_275,type,
sK8: nat > nat ).
tff(func_def_276,type,
sK9: fun_nat_nat > nat ).
tff(func_def_277,type,
sK10: fun_nat_fun_nat_bool > nat ).
tff(func_def_278,type,
sK11: fun_nat_bool > nat ).
tff(func_def_279,type,
sK12: ( fun_pname_bool * fun_pname_bool ) > pname ).
tff(func_def_280,type,
sK13: ( fun_pname_bool * ( fun_a_bool * fun_pname_a ) ) > pname ).
tff(func_def_281,type,
sK14: ( fun_pname_bool * ( fun_pname_a * x_a ) ) > pname ).
tff(func_def_282,type,
sK15: ( fun_pname_bool * ( fun_pname_a * x_a ) ) > pname ).
tff(func_def_283,type,
sK16: ( fun_a_bool * fun_fun_a_bool_bool ) > x_a ).
tff(func_def_284,type,
sK17: ( fun_a_bool * fun_fun_a_bool_bool ) > fun_a_bool ).
tff(func_def_285,type,
sK18: fun_a_bool > x_a ).
tff(func_def_286,type,
sK19: fun_a_bool > x_a ).
tff(func_def_287,type,
sK20: ( fun_pname_bool * fun_fu1430349052l_bool ) > pname ).
tff(func_def_288,type,
sK21: ( fun_pname_bool * fun_fu1430349052l_bool ) > fun_pname_bool ).
tff(func_def_289,type,
sK22: fun_pname_bool > pname ).
tff(func_def_290,type,
sK23: fun_pname_bool > pname ).
tff(func_def_291,type,
sK24: ( fun_a_bool * ( fun_a_pname * fun_pname_bool ) ) > fun_a_bool ).
tff(func_def_292,type,
sK25: ( fun_pname_bool * ( fun_a_bool * fun_a_pname ) ) > fun_a_bool ).
tff(func_def_293,type,
sK26: ( fun_a_bool * ( fun_a_nat * fun_nat_bool ) ) > fun_a_bool ).
tff(func_def_294,type,
sK27: ( fun_nat_bool * ( fun_a_bool * fun_a_nat ) ) > fun_a_bool ).
tff(func_def_295,type,
sK28: fun_nat_nat > nat ).
tff(func_def_296,type,
sK29: fun_nat_nat > nat ).
tff(func_def_297,type,
sK30: ( fun_nat_bool * nat ) > nat ).
tff(func_def_298,type,
sK31: fun_nat_nat > nat ).
tff(func_def_299,type,
sK32: fun_nat_nat > nat ).
tff(func_def_300,type,
sK33: ( nat * fun_nat_bool ) > nat ).
tff(func_def_301,type,
sK34: fun_nat_bool > nat ).
tff(func_def_302,type,
sK35: ( nat * nat ) > nat ).
tff(func_def_303,type,
sK36: ( fun_nat_bool * fun_nat_bool ) > nat ).
tff(func_def_304,type,
sK37: ( nat * fun_nat_bool ) > nat ).
tff(func_def_305,type,
sK38: fun_nat_bool > nat ).
tff(func_def_306,type,
sK39: ( fun_nat_bool * ( fun_pname_bool * fun_nat_pname ) ) > nat ).
tff(func_def_307,type,
sK40: ( fun_nat_bool * ( fun_nat_pname * pname ) ) > nat ).
tff(func_def_308,type,
sK41: ( fun_pname_bool * ( fun_nat_bool * fun_nat_pname ) ) > fun_nat_bool ).
tff(func_def_309,type,
sK42: ( fun_pname_bool * ( fun_nat_bool * fun_pname_nat ) ) > pname ).
tff(func_def_310,type,
sK43: ( fun_pname_bool * ( fun_pname_nat * nat ) ) > pname ).
tff(func_def_311,type,
sK44: ( fun_nat_bool * ( fun_pname_bool * fun_pname_nat ) ) > fun_pname_bool ).
tff(func_def_312,type,
sK45: fun_nat_bool > nat ).
tff(func_def_313,type,
sK46: fun_nat_bool > nat ).
tff(func_def_314,type,
sK47: ( fun_nat_bool * fun_fu425979586l_bool ) > nat ).
tff(func_def_315,type,
sK48: ( fun_nat_bool * fun_fu425979586l_bool ) > fun_nat_bool ).
tff(func_def_316,type,
sK49: fun_pname_bool > pname ).
tff(func_def_317,type,
sK50: fun_pname_bool > pname ).
tff(func_def_318,type,
sK51: ( fun_pname_bool * fun_pname_bool ) > pname ).
tff(func_def_319,type,
sK52: fun_nat_bool > nat ).
tff(func_def_320,type,
sK53: fun_nat_bool > nat ).
tff(func_def_321,type,
sK54: ( fun_a_bool * fun_a_bool ) > x_a ).
tff(func_def_322,type,
sK55: ( fun_nat_bool * fun_nat_bool ) > nat ).
tff(func_def_323,type,
sK56: fun_nat_bool > nat ).
tff(func_def_324,type,
sK57: fun_a_bool > x_a ).
tff(func_def_325,type,
sK58: fun_a_bool > x_a ).
tff(f216,axiom,
! [X0: fun_pname_bool,X1: x_a,X2: fun_pname_a,X3: pname] :
( ( X1 = hAPP_pname_a(X2,X3) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_image__eqI) ).
tff(f289,axiom,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
<=> hBOOL(hAPP_pname_bool(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_mem__def) ).
tff(f290,axiom,
! [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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_mem__def) ).
tff(f325,axiom,
! [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)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__subset) ).
tff(f809,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f812,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f814,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
tff(f815,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,[status(cth)],[f814]) ).
tff(f816,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,[],[f815]) ).
tff(f992,plain,
! [X0: fun_pname_bool,X1: x_a,X2: fun_pname_a,X3: pname] :
( ( hAPP_pname_a(X2,X3) != X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0))) ),
inference(ennf_transformation,[],[f216]) ).
tff(f993,plain,
! [X0: fun_pname_bool,X1: x_a,X2: fun_pname_a,X3: pname] :
( ( hAPP_pname_a(X2,X3) != X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0))) ),
inference(flattening,[],[f992]) ).
tff(f1280,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,[],[f325]) ).
tff(f1281,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,[],[f1280]) ).
tff(f1394,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,[],[f289]) ).
tff(f1432,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,[],[f290]) ).
tff(f1436,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f809]) ).
tff(f1439,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f812]) ).
tff(f1441,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,[],[f816]) ).
tff(f1655,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_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,[],[f1281]) ).
tff(f1678,plain,
! [X2: fun_pname_a,X3: pname,X0: fun_pname_bool,X1: x_a] :
( ( hAPP_pname_a(X2,X3) != X1 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0))) ),
inference(cnf_transformation,[],[f993]) ).
tff(f2024,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,[],[f1394]) ).
tff(f2025,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,[],[f1394]) ).
tff(f2117,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,[],[f1432]) ).
tff(f2118,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,[],[f1432]) ).
tff(f2216,plain,
! [X2: fun_pname_a,X3: pname,X0: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X2,X3)),image_pname_a(X2,X0))) ),
inference(equality_resolution,[],[f1678]) ).
tcf(c_50,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1436]) ).
tcf(c_53,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f1439]) ).
tcf(c_55,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(cnf_transformation,[],[f1441]) ).
tcf(c_256,plain,
! [X0_x_a: x_a,X0_fun_a_bool: fun_a_bool,X1_fun_a_bool: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0_x_a,X1_fun_a_bool)),X0_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_fun_a_bool),X0_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_x_a),X0_fun_a_bool)) ),
inference(cnf_transformation,[],[f1655]) ).
tcf(c_281,plain,
! [X0_pname: pname,X0_fun_pname_a: fun_pname_a,X0_fun_pname_bool: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_fun_pname_a,X0_pname)),image_pname_a(X0_fun_pname_a,X0_fun_pname_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_pname),X0_fun_pname_bool)) ),
inference(cnf_transformation,[],[f2216]) ).
tcf(c_607,plain,
! [X0_pname: pname,X0_fun_pname_bool: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_pname),X0_fun_pname_bool))
| ~ hBOOL(hAPP_pname_bool(X0_fun_pname_bool,X0_pname)) ),
inference(cnf_transformation,[],[f2025]) ).
tcf(c_608,plain,
! [X0_pname: pname,X0_fun_pname_bool: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(X0_fun_pname_bool,X0_pname))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_pname),X0_fun_pname_bool)) ),
inference(cnf_transformation,[],[f2024]) ).
tcf(c_700,plain,
! [X0_x_a: x_a,X0_fun_a_bool: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_x_a),X0_fun_a_bool))
| ~ hBOOL(hAPP_a_bool(X0_fun_a_bool,X0_x_a)) ),
inference(cnf_transformation,[],[f2118]) ).
tcf(c_701,plain,
! [X0_x_a: x_a,X0_fun_a_bool: fun_a_bool] :
( hBOOL(hAPP_a_bool(X0_fun_a_bool,X0_x_a))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_x_a),X0_fun_a_bool)) ),
inference(cnf_transformation,[],[f2117]) ).
tcf(c_968,plain,
! [X0_x_a: x_a,X0_fun_a_bool: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_x_a),X0_fun_a_bool))
| ~ hBOOL(hAPP_a_bool(X0_fun_a_bool,X0_x_a)) ),
inference(prop_impl_just,[status(thm)],[c_700]) ).
tcf(c_1294,plain,
! [X0_pname: pname,X0_fun_pname_a: fun_pname_a,X0_fun_pname_bool: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_fun_pname_a,X0_pname)),image_pname_a(X0_fun_pname_a,X0_fun_pname_bool)))
| ~ hBOOL(hAPP_pname_bool(X0_fun_pname_bool,X0_pname)) ),
inference(prop_impl_just,[status(thm)],[c_607,c_281]) ).
tcf(c_2290,plain,
! [X0_x_a: x_a,X0_fun_a_bool: fun_a_bool,X1_fun_a_bool: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0_x_a,X0_fun_a_bool)),X1_fun_a_bool))
| ~ hBOOL(hAPP_a_bool(X1_fun_a_bool,X0_x_a))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_fun_a_bool),X1_fun_a_bool)) ),
inference(bin_hyper_res,[status(thm)],[c_256,c_968]) ).
tcf(c_6503,plain,
! [X0_pname: pname,X0_fun_pname_a: fun_pname_a,X0_fun_pname_bool: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_fun_pname_a,X0_pname)),image_pname_a(X0_fun_pname_a,X0_fun_pname_bool)))
| ~ hBOOL(hAPP_pname_bool(X0_fun_pname_bool,X0_pname)) ),
inference(prop_impl_just,[status(thm)],[c_1294]) ).
tcf(c_14409,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_a_bool(image_pname_a(mgt_call,u),hAPP_pname_a(mgt_call,pn))) ),
inference(superposition,[status(thm)],[c_2290,c_55]) ).
tcf(c_14412,plain,
~ hBOOL(hAPP_a_bool(image_pname_a(mgt_call,u),hAPP_pname_a(mgt_call,pn))),
inference(forward_subsumption_resolution,[status(thm)],[c_14409,c_50]) ).
tcf(c_14612,plain,
hBOOL(hAPP_pname_bool(u,pn)),
inference(superposition,[status(thm)],[c_53,c_608]) ).
tcf(c_14710,plain,
! [X0_pname: pname,X0_fun_pname_a: fun_pname_a,X0_fun_pname_bool: fun_pname_bool] :
( hBOOL(hAPP_a_bool(image_pname_a(X0_fun_pname_a,X0_fun_pname_bool),hAPP_pname_a(X0_fun_pname_a,X0_pname)))
| ~ hBOOL(hAPP_pname_bool(X0_fun_pname_bool,X0_pname)) ),
inference(superposition,[status(thm)],[c_6503,c_701]) ).
tcf(c_15797,plain,
~ hBOOL(hAPP_pname_bool(u,pn)),
inference(superposition,[status(thm)],[c_14710,c_14412]) ).
tcf(c_15798,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15797,c_14612]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473_2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.39 % Computer : n014.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Thu Sep 24 22:33:48 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.43 Running first-order theorem proving
% 0.09/0.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.44
% 0.09/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.44
% 0.09/0.44 % Detected problem language: tptp
% 0.09/0.45 % Proving...
% 2.97/2.12 % SZS status Started for theBenchmark.p
% 2.97/2.12 % SZS status Theorem for theBenchmark.p
% 2.97/2.12
% 2.97/2.12 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.97/2.12
% 2.97/2.12 % ------ iProver source info
% 2.97/2.12
% 2.97/2.12 % git: date: 2026-07-19 20:42:38 +0200
% 2.97/2.12 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.97/2.12 % git: non_committed_changes: false
% 2.97/2.12
% 2.97/2.12 % ------ Parsing...
% 2.97/2.12 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.97/2.12 %
% 2.97/2.12
% 2.97/2.12 % ------ Preprocessing... sup_sim: 95 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 2.97/2.12
% 2.97/2.12 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.97/2.12 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 2.97/2.12 %
% 2.97/2.12
% 2.97/2.12 % ------ Preprocessing...
% 2.97/2.12 % ------ Proving...
% 2.97/2.12 % ------ Problem Properties
% 2.97/2.12
% 2.97/2.12 %
% 2.97/2.12 % clauses 401
% 2.97/2.12 % conjectures 1
% 2.97/2.12 % EPR 0
% 2.97/2.12 % Horn 288
% 2.97/2.12 % unary 82
% 2.97/2.12 % binary 187
% 2.97/2.12 % lits 897
% 2.97/2.12 % lits eq 183
% 2.97/2.12 % fd_pure 0
% 2.97/2.12 % fd_pseudo 0
% 2.97/2.12 % fd_cond 16
% 2.97/2.12 % fd_pseudo_cond 46
% 2.97/2.12 % AC symbols 0
% 2.97/2.12
% 2.97/2.12 % ------ Schedule dynamic 5 is on
% 2.97/2.12
% 2.97/2.12 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.97/2.12
% 2.97/2.12
% 2.97/2.12 % ------
% 2.97/2.12 % Current options:
% 2.97/2.12 % ------
% 2.97/2.12
% 2.97/2.12
% 2.97/2.12 %
% 2.97/2.12
% 2.97/2.12 % ------ Proving...
% 2.97/2.12 %
% 2.97/2.12
% 2.97/2.12 % SZS status Theorem for theBenchmark.p
% 2.97/2.12
% 2.97/2.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.97/2.12
% 2.97/2.12
%------------------------------------------------------------------------------