TSTP Solution File: SWW473+2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 : Fri Sep 1 00:18:01 EDT 2023
% Result : Theorem 30.50s 30.57s
% Output : CNFRefutation 30.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 456
% Syntax : Number of formulae : 572 ( 78 unt; 419 typ; 0 def)
% Number of atoms : 274 ( 87 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 219 ( 98 ~; 89 |; 13 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 693 ( 358 >; 335 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 411 ( 411 usr; 61 con; 0-3 aty)
% Number of variables : 218 ( 24 sgn; 114 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
is_fun_a_bool: $i > $o ).
tff(decl_23,type,
cOMBB_bool_bool_a: ( $i * $i ) > $i ).
tff(decl_24,type,
is_fun_pname_bool: $i > $o ).
tff(decl_25,type,
cOMBB_647938656_pname: ( $i * $i ) > $i ).
tff(decl_26,type,
is_fun949378684l_bool: $i > $o ).
tff(decl_27,type,
cOMBB_2140588453a_bool: ( $i * $i ) > $i ).
tff(decl_28,type,
is_fun1661590463l_bool: $i > $o ).
tff(decl_29,type,
cOMBB_307249310e_bool: ( $i * $i ) > $i ).
tff(decl_30,type,
is_bool: $i > $o ).
tff(decl_31,type,
cOMBK_bool_a: $i > $i ).
tff(decl_32,type,
cOMBK_bool_pname: $i > $i ).
tff(decl_33,type,
cOMBK_324466864a_bool: $i > $i ).
tff(decl_34,type,
cOMBK_1857069011e_bool: $i > $i ).
tff(decl_35,type,
cOMBS_a_bool_bool: ( $i * $i ) > $i ).
tff(decl_36,type,
cOMBS_568398431l_bool: ( $i * $i ) > $i ).
tff(decl_37,type,
cOMBS_1035972772l_bool: ( $i * $i ) > $i ).
tff(decl_38,type,
cOMBS_350070575l_bool: ( $i * $i ) > $i ).
tff(decl_39,type,
finite_finite_a: $i ).
tff(decl_40,type,
finite_finite_pname: $i ).
tff(decl_41,type,
x_a: $i ).
tff(decl_42,type,
undefined_a: $i > $i ).
tff(decl_43,type,
is_a: $i > $o ).
tff(decl_44,type,
pname: $i ).
tff(decl_45,type,
undefined_pname: $i > $i ).
tff(decl_46,type,
is_pname: $i > $o ).
tff(decl_47,type,
bool: $i ).
tff(decl_48,type,
fun: ( $i * $i ) > $i ).
tff(decl_49,type,
undefined_fun_a_bool: $i > $i ).
tff(decl_50,type,
undefi17486888e_bool: $i > $i ).
tff(decl_51,type,
undefi1699038445l_bool: $i > $i ).
tff(decl_52,type,
undefi64961550l_bool: $i > $i ).
tff(decl_53,type,
bot_bot_bool: $i ).
tff(decl_54,type,
bot_bot_fun_a_bool: $i ).
tff(decl_55,type,
bot_bo844097828e_bool: $i ).
tff(decl_56,type,
bot_bo1389914601l_bool: $i ).
tff(decl_57,type,
bot_bo1649642514l_bool: $i ).
tff(decl_58,type,
collect_a: $i > $i ).
tff(decl_59,type,
collect_pname: $i > $i ).
tff(decl_60,type,
collect_fun_a_bool: $i > $i ).
tff(decl_61,type,
collec1974731493e_bool: $i > $i ).
tff(decl_62,type,
image_a_a: ( $i * $i ) > $i ).
tff(decl_63,type,
image_a_pname: ( $i * $i ) > $i ).
tff(decl_64,type,
image_a_fun_a_bool: ( $i * $i ) > $i ).
tff(decl_65,type,
image_819518260e_bool: ( $i * $i ) > $i ).
tff(decl_66,type,
image_pname_a: ( $i * $i ) > $i ).
tff(decl_67,type,
image_pname_pname: ( $i * $i ) > $i ).
tff(decl_68,type,
image_112932426a_bool: ( $i * $i ) > $i ).
tff(decl_69,type,
image_47868345e_bool: ( $i * $i ) > $i ).
tff(decl_70,type,
image_nat_a: ( $i * $i ) > $i ).
tff(decl_71,type,
image_nat_pname: ( $i * $i ) > $i ).
tff(decl_72,type,
image_nat_fun_a_bool: ( $i * $i ) > $i ).
tff(decl_73,type,
image_1655916159e_bool: ( $i * $i ) > $i ).
tff(decl_74,type,
image_fun_a_bool_a: ( $i * $i ) > $i ).
tff(decl_75,type,
image_1854862208_pname: ( $i * $i ) > $i ).
tff(decl_76,type,
image_876012084bool_a: ( $i * $i ) > $i ).
tff(decl_77,type,
image_1283814551_pname: ( $i * $i ) > $i ).
tff(decl_78,type,
image_fun_nat_bool_a: ( $i * $i ) > $i ).
tff(decl_79,type,
image_1921560913_pname: ( $i * $i ) > $i ).
tff(decl_80,type,
insert_a: ( $i * $i ) > $i ).
tff(decl_81,type,
insert_pname: ( $i * $i ) > $i ).
tff(decl_82,type,
insert_fun_a_bool: ( $i * $i ) > $i ).
tff(decl_83,type,
insert1325755072e_bool: ( $i * $i ) > $i ).
tff(decl_84,type,
fFalse: $i ).
tff(decl_85,type,
fTrue: $i ).
tff(decl_86,type,
hAPP_a_a: ( $i * $i ) > $i ).
tff(decl_87,type,
hAPP_a_pname: ( $i * $i ) > $i ).
tff(decl_88,type,
hAPP_a_bool: ( $i * $i ) > $i ).
tff(decl_89,type,
hAPP_a_fun_a_bool: ( $i * $i ) > $i ).
tff(decl_90,type,
hAPP_a93125764e_bool: ( $i * $i ) > $i ).
tff(decl_91,type,
hAPP_a85458249l_bool: ( $i * $i ) > $i ).
tff(decl_92,type,
hAPP_a217006258l_bool: ( $i * $i ) > $i ).
tff(decl_93,type,
hAPP_pname_a: ( $i * $i ) > $i ).
tff(decl_94,type,
hAPP_pname_pname: ( $i * $i ) > $i ).
tff(decl_95,type,
hAPP_pname_bool: ( $i * $i ) > $i ).
tff(decl_96,type,
hAPP_p1534023578a_bool: ( $i * $i ) > $i ).
tff(decl_97,type,
hAPP_p61793385e_bool: ( $i * $i ) > $i ).
tff(decl_98,type,
hAPP_p1824510254l_bool: ( $i * $i ) > $i ).
tff(decl_99,type,
hAPP_p338031245l_bool: ( $i * $i ) > $i ).
tff(decl_100,type,
hAPP_bool_bool: ( $i * $i ) > $i ).
tff(decl_101,type,
hAPP_nat_a: ( $i * $i ) > $i ).
tff(decl_102,type,
hAPP_nat_pname: ( $i * $i ) > $i ).
tff(decl_103,type,
hAPP_nat_bool: ( $i * $i ) > $i ).
tff(decl_104,type,
hAPP_nat_fun_a_bool: ( $i * $i ) > $i ).
tff(decl_105,type,
hAPP_n1025906991e_bool: ( $i * $i ) > $i ).
tff(decl_106,type,
hAPP_n1414589940l_bool: ( $i * $i ) > $i ).
tff(decl_107,type,
hAPP_n850744903l_bool: ( $i * $i ) > $i ).
tff(decl_108,type,
hAPP_f1128469712_pname: ( $i * $i ) > $i ).
tff(decl_109,type,
hAPP_fun_a_bool_bool: ( $i * $i ) > $i ).
tff(decl_110,type,
hAPP_f2050579477a_bool: ( $i * $i ) > $i ).
tff(decl_111,type,
hAPP_f1794073134e_bool: ( $i * $i ) > $i ).
tff(decl_112,type,
hAPP_f1631501043l_bool: ( $i * $i ) > $i ).
tff(decl_113,type,
hAPP_f1297739591_pname: ( $i * $i ) > $i ).
tff(decl_114,type,
hAPP_f1664156314l_bool: ( $i * $i ) > $i ).
tff(decl_115,type,
hAPP_f1051908748a_bool: ( $i * $i ) > $i ).
tff(decl_116,type,
hAPP_f759274231e_bool: ( $i * $i ) > $i ).
tff(decl_117,type,
hAPP_f434788991l_bool: ( $i * $i ) > $i ).
tff(decl_118,type,
hAPP_f1291551745_pname: ( $i * $i ) > $i ).
tff(decl_119,type,
hAPP_f54304608l_bool: ( $i * $i ) > $i ).
tff(decl_120,type,
hAPP_f1549043526a_bool: ( $i * $i ) > $i ).
tff(decl_121,type,
hAPP_f654413245e_bool: ( $i * $i ) > $i ).
tff(decl_122,type,
hAPP_f621171935l_bool: ( $i * $i ) > $i ).
tff(decl_123,type,
hAPP_f2117159681l_bool: ( $i * $i ) > $i ).
tff(decl_124,type,
hAPP_f1935102916l_bool: ( $i * $i ) > $i ).
tff(decl_125,type,
hAPP_f559147733l_bool: ( $i * $i ) > $i ).
tff(decl_126,type,
hAPP_f1637334154l_bool: ( $i * $i ) > $i ).
tff(decl_127,type,
hAPP_f292226953l_bool: ( $i * $i ) > $i ).
tff(decl_128,type,
hAPP_f389811538l_bool: ( $i * $i ) > $i ).
tff(decl_129,type,
hAPP_f937997336l_bool: ( $i * $i ) > $i ).
tff(decl_130,type,
g: $i ).
tff(decl_131,type,
p: $i > $i ).
tff(decl_132,type,
u: $i ).
tff(decl_133,type,
mgt: $i > $i ).
tff(decl_134,type,
pn: $i ).
tff(decl_135,type,
wt: $i > $i ).
tff(decl_136,type,
ord_le1311769555a_bool: $i ).
tff(decl_137,type,
hBOOL: $i > $o ).
tff(decl_138,type,
finite2012431853t_bool: $i ).
tff(decl_139,type,
finite1701474069l_bool: $i ).
tff(decl_140,type,
ord_le1454342156l_bool: $i ).
tff(decl_141,type,
cOMBC_595898202l_bool: $i > $i ).
tff(decl_142,type,
hAPP_f1772781669l_bool: ( $i * $i ) > $i ).
tff(decl_143,type,
collec1015864663l_bool: $i > $i ).
tff(decl_144,type,
finite595471783e_bool: $i ).
tff(decl_145,type,
finite786885583l_bool: $i ).
tff(decl_146,type,
ord_le675606854l_bool: $i ).
tff(decl_147,type,
cOMBC_7971162l_bool: $i > $i ).
tff(decl_148,type,
hAPP_f510955609l_bool: ( $i * $i ) > $i ).
tff(decl_149,type,
collec1613912337l_bool: $i > $i ).
tff(decl_150,type,
finite347923420a_bool: $i ).
tff(decl_151,type,
finite1381704300l_bool: $i ).
tff(decl_152,type,
ord_le1375614389l_bool: $i ).
tff(decl_153,type,
cOMBC_331553030l_bool: $i > $i ).
tff(decl_154,type,
hAPP_f1434722111l_bool: ( $i * $i ) > $i ).
tff(decl_155,type,
collec707592106l_bool: $i > $i ).
tff(decl_156,type,
cOMBC_1732670874l_bool: $i > $i ).
tff(decl_157,type,
ord_le313189616e_bool: $i ).
tff(decl_158,type,
cOMBC_1284144636l_bool: $i > $i ).
tff(decl_159,type,
finite_finite_nat: $i ).
tff(decl_160,type,
ord_le1568362934t_bool: $i ).
tff(decl_161,type,
cOMBC_1693257480l_bool: $i > $i ).
tff(decl_162,type,
hAPP_f103356543l_bool: ( $i * $i ) > $i ).
tff(decl_163,type,
collect_fun_nat_bool: $i > $i ).
tff(decl_164,type,
image_2129980159t_bool: ( $i * $i ) > $i ).
tff(decl_165,type,
image_26036933t_bool: ( $i * $i ) > $i ).
tff(decl_166,type,
image_a_nat: ( $i * $i ) > $i ).
tff(decl_167,type,
image_496248727ol_nat: ( $i * $i ) > $i ).
tff(decl_168,type,
image_1551609309ol_nat: ( $i * $i ) > $i ).
tff(decl_169,type,
image_fun_a_bool_nat: ( $i * $i ) > $i ).
tff(decl_170,type,
insert_fun_nat_bool: ( $i * $i ) > $i ).
tff(decl_171,type,
insert_nat: ( $i * $i ) > $i ).
tff(decl_172,type,
ord_less_eq_nat: $i ).
tff(decl_173,type,
finite_card_pname: $i ).
tff(decl_174,type,
hAPP_f921600141ol_nat: ( $i * $i ) > $i ).
tff(decl_175,type,
hAPP_n1699378549t_bool: ( $i * $i ) > $i ).
tff(decl_176,type,
finite_card_a: $i ).
tff(decl_177,type,
hAPP_fun_a_bool_nat: ( $i * $i ) > $i ).
tff(decl_178,type,
finite346522414t_bool: $i ).
tff(decl_179,type,
hAPP_f696928925ol_nat: ( $i * $i ) > $i ).
tff(decl_180,type,
finite1340463720e_bool: $i ).
tff(decl_181,type,
hAPP_f55526627ol_nat: ( $i * $i ) > $i ).
tff(decl_182,type,
finite1306199131a_bool: $i ).
tff(decl_183,type,
hAPP_f2009550088ol_nat: ( $i * $i ) > $i ).
tff(decl_184,type,
finite_card_nat: $i ).
tff(decl_185,type,
image_pname_nat: ( $i * $i ) > $i ).
tff(decl_186,type,
hAPP_f22106695ol_nat: ( $i * $i ) > $i ).
tff(decl_187,type,
member_fun_nat_bool: $i ).
tff(decl_188,type,
hAPP_f1951378235l_bool: ( $i * $i ) > $i ).
tff(decl_189,type,
suc: $i ).
tff(decl_190,type,
hAPP_nat_nat: ( $i * $i ) > $i ).
tff(decl_191,type,
member799430823e_bool: $i ).
tff(decl_192,type,
hAPP_f556039215l_bool: ( $i * $i ) > $i ).
tff(decl_193,type,
member_fun_a_bool: $i ).
tff(decl_194,type,
hAPP_f285962445l_bool: ( $i * $i ) > $i ).
tff(decl_195,type,
member_nat: $i ).
tff(decl_196,type,
hAPP_n215258509l_bool: ( $i * $i ) > $i ).
tff(decl_197,type,
member_pname: $i ).
tff(decl_198,type,
member_a: $i ).
tff(decl_199,type,
fconj: $i ).
tff(decl_200,type,
cOMBB_1972296269bool_a: ( $i * $i ) > $i ).
tff(decl_201,type,
cOMBB_444170502t_bool: ( $i * $i ) > $i ).
tff(decl_202,type,
cOMBS_1187019125l_bool: ( $i * $i ) > $i ).
tff(decl_203,type,
cOMBB_2095475776e_bool: ( $i * $i ) > $i ).
tff(decl_204,type,
cOMBB_338059395a_bool: ( $i * $i ) > $i ).
tff(decl_205,type,
cOMBB_675860798_pname: ( $i * $i ) > $i ).
tff(decl_206,type,
collect_nat: $i > $i ).
tff(decl_207,type,
cOMBB_1015721476ol_nat: ( $i * $i ) > $i ).
tff(decl_208,type,
cOMBS_nat_bool_bool: ( $i * $i ) > $i ).
tff(decl_209,type,
minus_minus_nat: $i > $i ).
tff(decl_210,type,
cOMBC_nat_nat_bool: $i > $i ).
tff(decl_211,type,
fdisj: $i ).
tff(decl_212,type,
image_nat_nat: ( $i * $i ) > $i ).
tff(decl_213,type,
image_a_fun_nat_bool: ( $i * $i ) > $i ).
tff(decl_214,type,
ord_less_eq_bool: $i ).
tff(decl_215,type,
hAPP_b589554111l_bool: ( $i * $i ) > $i ).
tff(decl_216,type,
cOMBC_226598744l_bool: $i > $i ).
tff(decl_217,type,
hAPP_f800510211t_bool: ( $i * $i ) > $i ).
tff(decl_218,type,
fequal_pname: $i ).
tff(decl_219,type,
cOMBB_1212655066ol_nat: ( $i * $i ) > $i ).
tff(decl_220,type,
cOMBC_nat_pname_bool: $i > $i ).
tff(decl_221,type,
hAPP_p1499970991t_bool: ( $i * $i ) > $i ).
tff(decl_222,type,
cOMBC_1355376034l_bool: $i > $i ).
tff(decl_223,type,
cOMBB_610033911bool_a: ( $i * $i ) > $i ).
tff(decl_224,type,
cOMBC_a_pname_bool: $i > $i ).
tff(decl_225,type,
cOMBC_1058051404l_bool: $i > $i ).
tff(decl_226,type,
cOMBB_542850580_pname: ( $i * $i ) > $i ).
tff(decl_227,type,
cOMBC_1149511130e_bool: $i > $i ).
tff(decl_228,type,
cOMBC_1245412066l_bool: $i > $i ).
tff(decl_229,type,
hAPP_f1246832597l_bool: ( $i * $i ) > $i ).
tff(decl_230,type,
cOMBB_141086128t_bool: ( $i * $i ) > $i ).
tff(decl_231,type,
cOMBC_615407716e_bool: $i > $i ).
tff(decl_232,type,
hAPP_p130839763l_bool: ( $i * $i ) > $i ).
tff(decl_233,type,
cOMBC_1988546018l_bool: $i > $i ).
tff(decl_234,type,
cOMBB_598082538e_bool: ( $i * $i ) > $i ).
tff(decl_235,type,
cOMBC_1004116266e_bool: $i > $i ).
tff(decl_236,type,
cOMBC_1880041174l_bool: $i > $i ).
tff(decl_237,type,
cOMBB_1693087065a_bool: ( $i * $i ) > $i ).
tff(decl_238,type,
cOMBC_1738168533e_bool: $i > $i ).
tff(decl_239,type,
fequal_nat: $i ).
tff(decl_240,type,
cOMBB_800536526ol_nat: ( $i * $i ) > $i ).
tff(decl_241,type,
cOMBB_1321347587bool_a: ( $i * $i ) > $i ).
tff(decl_242,type,
cOMBC_a_nat_bool: $i > $i ).
tff(decl_243,type,
hAPP_a_nat: ( $i * $i ) > $i ).
tff(decl_244,type,
cOMBB_523834888_pname: ( $i * $i ) > $i ).
tff(decl_245,type,
cOMBC_pname_nat_bool: $i > $i ).
tff(decl_246,type,
hAPP_pname_nat: ( $i * $i ) > $i ).
tff(decl_247,type,
cOMBB_1250273980t_bool: ( $i * $i ) > $i ).
tff(decl_248,type,
cOMBC_385542954t_bool: $i > $i ).
tff(decl_249,type,
cOMBB_1896684278e_bool: ( $i * $i ) > $i ).
tff(decl_250,type,
cOMBC_1666426608t_bool: $i > $i ).
tff(decl_251,type,
cOMBB_164527437a_bool: ( $i * $i ) > $i ).
tff(decl_252,type,
cOMBC_619334683t_bool: $i > $i ).
tff(decl_253,type,
fequal_a: $i ).
tff(decl_254,type,
cOMBB_1885489796ol_nat: ( $i * $i ) > $i ).
tff(decl_255,type,
cOMBC_nat_a_bool: $i > $i ).
tff(decl_256,type,
hAPP_a_fun_nat_bool: ( $i * $i ) > $i ).
tff(decl_257,type,
fequal_fun_nat_bool: $i ).
tff(decl_258,type,
cOMBB_2026977092ol_nat: ( $i * $i ) > $i ).
tff(decl_259,type,
fequal533582459e_bool: $i ).
tff(decl_260,type,
cOMBB_2117322052ol_nat: ( $i * $i ) > $i ).
tff(decl_261,type,
cOMBC_386238098l_bool: $i > $i ).
tff(decl_262,type,
hAPP_f1066163005t_bool: ( $i * $i ) > $i ).
tff(decl_263,type,
fequal_fun_a_bool: $i ).
tff(decl_264,type,
cOMBB_1823939024ol_nat: ( $i * $i ) > $i ).
tff(decl_265,type,
cOMBC_1928494297l_bool: $i > $i ).
tff(decl_266,type,
hAPP_f282463732t_bool: ( $i * $i ) > $i ).
tff(decl_267,type,
cOMBB_928955006_pname: ( $i * $i ) > $i ).
tff(decl_268,type,
cOMBC_267053842l_bool: $i > $i ).
tff(decl_269,type,
cOMBB_408569982_pname: ( $i * $i ) > $i ).
tff(decl_270,type,
cOMBB_392435466_pname: ( $i * $i ) > $i ).
tff(decl_271,type,
cOMBC_445755039l_bool: $i > $i ).
tff(decl_272,type,
cOMBB_a_fun_a_bool_a: ( $i * $i ) > $i ).
tff(decl_273,type,
cOMBC_a_a_bool: $i > $i ).
tff(decl_274,type,
cOMBB_743407885bool_a: ( $i * $i ) > $i ).
tff(decl_275,type,
cOMBC_777206479l_bool: $i > $i ).
tff(decl_276,type,
cOMBB_1137537805bool_a: ( $i * $i ) > $i ).
tff(decl_277,type,
cOMBC_1834145417l_bool: $i > $i ).
tff(decl_278,type,
cOMBB_472261505bool_a: ( $i * $i ) > $i ).
tff(decl_279,type,
cOMBB_1897541054_pname: ( $i * $i ) > $i ).
tff(decl_280,type,
cOMBC_pname_a_bool: $i > $i ).
tff(decl_281,type,
fimplies: $i ).
tff(decl_282,type,
fNot: $i ).
tff(decl_283,type,
cOMBB_238756964t_bool: ( $i * $i ) > $i ).
tff(decl_284,type,
cOMBB_bool_bool_nat: ( $i * $i ) > $i ).
tff(decl_285,type,
mgt_call: $i ).
tff(decl_286,type,
bot_bot_fun_nat_bool: $i ).
tff(decl_287,type,
bot_bo1701429464l_bool: $i ).
tff(decl_288,type,
cOMBK_1994329625t_bool: $i > $i ).
tff(decl_289,type,
cOMBK_bool_nat: $i > $i ).
tff(decl_290,type,
bot_bot_nat: $i ).
tff(decl_291,type,
cOMBK_a_pname: $i > $i ).
tff(decl_292,type,
body: $i > $i ).
tff(decl_293,type,
the_com: $i > $i ).
tff(decl_294,type,
one_one_nat: $i ).
tff(decl_295,type,
nat_case_bool: ( $i * $i ) > $i ).
tff(decl_296,type,
plus_plus_nat: $i > $i ).
tff(decl_297,type,
ord_less_nat: $i ).
tff(decl_298,type,
zero_zero_nat: $i ).
tff(decl_299,type,
hAPP_a_fun_bool_bool: ( $i * $i ) > $i ).
tff(decl_300,type,
hAPP_n1006566506l_bool: ( $i * $i ) > $i ).
tff(decl_301,type,
hAPP_p393069232l_bool: ( $i * $i ) > $i ).
tff(decl_302,type,
hAPP_a1392362872l_bool: ( $i * $i ) > $i ).
tff(decl_303,type,
hAPP_f198738859l_bool: ( $i * $i ) > $i ).
tff(decl_304,type,
hAPP_f1748468828l_bool: ( $i * $i ) > $i ).
tff(decl_305,type,
hAPP_f1476298914l_bool: ( $i * $i ) > $i ).
tff(decl_306,type,
na: $i ).
tff(decl_307,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_308,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_309,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_310,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_311,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_312,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_313,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_314,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_315,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_316,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_317,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_318,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_319,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_320,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_321,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_322,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_323,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_324,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_325,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_326,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_327,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_328,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_329,type,
esk23_3: ( $i * $i * $i ) > $i ).
tff(decl_330,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_331,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_332,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_333,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_334,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_335,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_336,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_337,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_338,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_339,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_340,type,
esk34_2: ( $i * $i ) > $i ).
tff(decl_341,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_342,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_343,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_344,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_345,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_346,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_347,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_348,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_349,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_350,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_351,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_352,type,
esk46_2: ( $i * $i ) > $i ).
tff(decl_353,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_354,type,
esk48_2: ( $i * $i ) > $i ).
tff(decl_355,type,
esk49_2: ( $i * $i ) > $i ).
tff(decl_356,type,
esk50_2: ( $i * $i ) > $i ).
tff(decl_357,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_358,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_359,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_360,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_361,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_362,type,
esk56_2: ( $i * $i ) > $i ).
tff(decl_363,type,
esk57_3: ( $i * $i * $i ) > $i ).
tff(decl_364,type,
esk58_2: ( $i * $i ) > $i ).
tff(decl_365,type,
esk59_3: ( $i * $i * $i ) > $i ).
tff(decl_366,type,
esk60_3: ( $i * $i * $i ) > $i ).
tff(decl_367,type,
esk61_3: ( $i * $i * $i ) > $i ).
tff(decl_368,type,
esk62_3: ( $i * $i * $i ) > $i ).
tff(decl_369,type,
esk63_3: ( $i * $i * $i ) > $i ).
tff(decl_370,type,
esk64_3: ( $i * $i * $i ) > $i ).
tff(decl_371,type,
esk65_3: ( $i * $i * $i ) > $i ).
tff(decl_372,type,
esk66_3: ( $i * $i * $i ) > $i ).
tff(decl_373,type,
esk67_3: ( $i * $i * $i ) > $i ).
tff(decl_374,type,
esk68_3: ( $i * $i * $i ) > $i ).
tff(decl_375,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_376,type,
esk70_2: ( $i * $i ) > $i ).
tff(decl_377,type,
esk71_2: ( $i * $i ) > $i ).
tff(decl_378,type,
esk72_3: ( $i * $i * $i ) > $i ).
tff(decl_379,type,
esk73_3: ( $i * $i * $i ) > $i ).
tff(decl_380,type,
esk74_3: ( $i * $i * $i ) > $i ).
tff(decl_381,type,
esk75_3: ( $i * $i * $i ) > $i ).
tff(decl_382,type,
esk76_3: ( $i * $i * $i ) > $i ).
tff(decl_383,type,
esk77_3: ( $i * $i * $i ) > $i ).
tff(decl_384,type,
esk78_3: ( $i * $i * $i ) > $i ).
tff(decl_385,type,
esk79_1: $i > $i ).
tff(decl_386,type,
esk80_2: ( $i * $i ) > $i ).
tff(decl_387,type,
esk81_2: ( $i * $i ) > $i ).
tff(decl_388,type,
esk82_2: ( $i * $i ) > $i ).
tff(decl_389,type,
esk83_2: ( $i * $i ) > $i ).
tff(decl_390,type,
esk84_2: ( $i * $i ) > $i ).
tff(decl_391,type,
esk85_1: $i > $i ).
tff(decl_392,type,
esk86_1: $i > $i ).
tff(decl_393,type,
esk87_1: $i > $i ).
tff(decl_394,type,
esk88_1: $i > $i ).
tff(decl_395,type,
esk89_1: $i > $i ).
tff(decl_396,type,
esk90_1: $i > $i ).
tff(decl_397,type,
esk91_1: $i > $i ).
tff(decl_398,type,
esk92_1: $i > $i ).
tff(decl_399,type,
esk93_1: $i > $i ).
tff(decl_400,type,
esk94_1: $i > $i ).
tff(decl_401,type,
esk95_1: $i > $i ).
tff(decl_402,type,
esk96_1: $i > $i ).
tff(decl_403,type,
esk97_1: $i > $i ).
tff(decl_404,type,
esk98_1: $i > $i ).
tff(decl_405,type,
esk99_1: $i > $i ).
tff(decl_406,type,
esk100_1: $i > $i ).
tff(decl_407,type,
esk101_1: $i > $i ).
tff(decl_408,type,
esk102_1: $i > $i ).
tff(decl_409,type,
esk103_3: ( $i * $i * $i ) > $i ).
tff(decl_410,type,
esk104_3: ( $i * $i * $i ) > $i ).
tff(decl_411,type,
esk105_3: ( $i * $i * $i ) > $i ).
tff(decl_412,type,
esk106_3: ( $i * $i * $i ) > $i ).
tff(decl_413,type,
esk107_3: ( $i * $i * $i ) > $i ).
tff(decl_414,type,
esk108_3: ( $i * $i * $i ) > $i ).
tff(decl_415,type,
esk109_3: ( $i * $i * $i ) > $i ).
tff(decl_416,type,
esk110_3: ( $i * $i * $i ) > $i ).
tff(decl_417,type,
esk111_3: ( $i * $i * $i ) > $i ).
tff(decl_418,type,
esk112_3: ( $i * $i * $i ) > $i ).
tff(decl_419,type,
esk113_3: ( $i * $i * $i ) > $i ).
tff(decl_420,type,
esk114_3: ( $i * $i * $i ) > $i ).
tff(decl_421,type,
esk115_2: ( $i * $i ) > $i ).
tff(decl_422,type,
esk116_2: ( $i * $i ) > $i ).
tff(decl_423,type,
esk117_2: ( $i * $i ) > $i ).
tff(decl_424,type,
esk118_2: ( $i * $i ) > $i ).
tff(decl_425,type,
esk119_2: ( $i * $i ) > $i ).
tff(decl_426,type,
esk120_2: ( $i * $i ) > $i ).
tff(decl_427,type,
esk121_2: ( $i * $i ) > $i ).
tff(decl_428,type,
esk122_2: ( $i * $i ) > $i ).
tff(decl_429,type,
esk123_1: $i > $i ).
tff(decl_430,type,
esk124_2: ( $i * $i ) > $i ).
tff(decl_431,type,
esk125_2: ( $i * $i ) > $i ).
tff(decl_432,type,
esk126_3: ( $i * $i * $i ) > $i ).
tff(decl_433,type,
esk127_3: ( $i * $i * $i ) > $i ).
tff(decl_434,type,
esk128_3: ( $i * $i * $i ) > $i ).
tff(decl_435,type,
esk129_2: ( $i * $i ) > $i ).
tff(decl_436,type,
esk130_2: ( $i * $i ) > $i ).
tff(decl_437,type,
esk131_3: ( $i * $i * $i ) > $i ).
tff(decl_438,type,
esk132_3: ( $i * $i * $i ) > $i ).
tff(decl_439,type,
esk133_2: ( $i * $i ) > $i ).
tff(decl_440,type,
esk134_2: ( $i * $i ) > $i ).
fof(fact_403_Collect__empty__eq,axiom,
! [X13] :
( collect_nat(X13) = bot_bot_fun_nat_bool
<=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Collect__empty__eq) ).
fof(help_fFalse_1_1_T,axiom,
! [X92] :
( is_bool(X92)
=> ( X92 = fTrue
| X92 = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [X1,X2] : is_bool(hAPP_f54304608l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(fact_295_Collect__def,axiom,
! [X13] : collect_nat(X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Collect__def) ).
fof(fact_391_finite_OemptyI,axiom,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_finite_OemptyI) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(fact_426_bot__fun__def,axiom,
! [X30] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X30))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_bot__fun__def) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,hypothesis,
! [X1,X2] : is_bool(hAPP_nat_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
is_bool(bot_bot_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).
fof(fact_416_all__not__in__conv,axiom,
! [X5] :
( ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
<=> X5 = bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_all__not__in__conv) ).
fof(fact_383_emptyE,axiom,
! [X8] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_emptyE) ).
fof(fact_287_mem__def,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
<=> hBOOL(hAPP_nat_bool(X5,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_mem__def) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [X92,X93] :
( is_bool(X92)
=> hAPP_nat_bool(cOMBK_bool_nat(X92),X93) = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
fof(fact_484_singleton__conv,axiom,
! [X8] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)) = insert_a(X8,bot_bot_fun_a_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_singleton__conv) ).
fof(fact_238_insert__compr,axiom,
! [X8,X10] : insert_a(X8,X10) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_insert__compr) ).
fof(fact_490_singleton__conv2,axiom,
! [X8] : collect_a(hAPP_a_fun_a_bool(fequal_a,X8)) = insert_a(X8,bot_bot_fun_a_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_singleton__conv2) ).
fof(fact_307_imageI,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X9,X11)),image_pname_a(X9,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_imageI) ).
fof(fact_302_image__iff,axiom,
! [X38,X9,X5] :
( is_a(X38)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X38),image_pname_a(X9,X5)))
<=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& X38 = hAPP_pname_a(X9,X30) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_image__iff) ).
fof(conj_4,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(fact_290_Collect__def,axiom,
! [X13] :
( is_fun_a_bool(X13)
=> collect_a(X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Collect__def) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,axiom,
! [X92,X93,X94] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X92,X93),X94) = hAPP_a_fun_a_bool(X92,hAPP_pname_a(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000t__a,hypothesis,
! [X1,X2] :
( is_pname(X2)
=> is_a(hAPP_pname_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
fof(fact_337_image__insert,axiom,
! [X9,X8,X10] : image_pname_a(X9,insert_pname(X8,X10)) = insert_a(hAPP_pname_a(X9,X8),image_pname_a(X9,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_image__insert) ).
fof(fact_237_insert__compr,axiom,
! [X8,X10] : insert_pname(X8,X10) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_insert__compr) ).
fof(fact_489_singleton__conv2,axiom,
! [X8] : collect_pname(hAPP_p61793385e_bool(fequal_pname,X8)) = insert_pname(X8,bot_bo844097828e_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_singleton__conv2) ).
fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
! [X1,X2] :
( ( is_fun949378684l_bool(X1)
& is_fun_a_bool(X2) )
=> is_bool(hAPP_fun_a_bool_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(conj_6,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) ).
fof(gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_a(X2)
=> is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_v_pn,hypothesis,
is_pname(pn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_pn) ).
fof(fact_468_image__empty,axiom,
! [X9] : image_pname_a(X9,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_image__empty) ).
fof(fact_324_insert__subset,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X11,X5)),X10))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__subset) ).
fof(conj_1,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL,hypothesis,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun949378684l_bool(hAPP_f1631501043l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).
fof(gsy_v_G,hypothesis,
is_fun_a_bool(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_G) ).
fof(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,hypothesis,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_a_bool(image_pname_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).
fof(gsy_v_U,hypothesis,
is_fun_pname_bool(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_U) ).
fof(c_0_37,plain,
! [X13] :
( collect_nat(X13) = bot_bot_fun_nat_bool
<=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_403_Collect__empty__eq]) ).
fof(c_0_38,plain,
! [X1995] :
( ~ is_bool(X1995)
| X1995 = fTrue
| X1995 = fFalse ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])]) ).
fof(c_0_39,plain,
! [X229,X230] : is_bool(hAPP_f54304608l_bool(X229,X230)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).
fof(c_0_40,plain,
! [X1312,X1313,X1314] :
( ( collect_nat(X1312) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X1312,X1313)) )
& ( hBOOL(hAPP_nat_bool(X1314,esk90_1(X1314)))
| collect_nat(X1314) = bot_bot_fun_nat_bool ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])]) ).
fof(c_0_41,plain,
! [X990] : collect_nat(X990) = X990,
inference(variable_rename,[status(thm)],[fact_295_Collect__def]) ).
cnf(c_0_42,plain,
( X1 = fTrue
| X1 = fFalse
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
is_bool(hAPP_f54304608l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
( collect_nat(X1) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
collect_nat(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[fact_391_finite_OemptyI]) ).
cnf(c_0_47,plain,
( hAPP_f54304608l_bool(X1,X2) = fTrue
| hAPP_f54304608l_bool(X1,X2) = fFalse ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_48,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
fof(c_0_49,plain,
! [X1364] :
( ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1364))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1364)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_426_bot__fun__def])]) ).
cnf(c_0_50,plain,
( X1 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_51,hypothesis,
! [X197,X198] : is_bool(hAPP_nat_bool(X197,X198)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).
cnf(c_0_52,plain,
( hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool) = fFalse
| hBOOL(fTrue) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,plain,
is_bool(bot_bot_bool),
inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool]) ).
cnf(c_0_55,plain,
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)),
inference(er,[status(thm)],[c_0_50]) ).
fof(c_0_57,plain,
! [X5] :
( ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
<=> X5 = bot_bot_fun_nat_bool ),
inference(fof_simplification,[status(thm)],[fact_416_all__not__in__conv]) ).
cnf(c_0_58,hypothesis,
is_bool(hAPP_nat_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
hBOOL(fTrue),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_52]),c_0_53]) ).
cnf(c_0_60,plain,
( fTrue = bot_bot_bool
| fFalse = bot_bot_bool ),
inference(spm,[status(thm)],[c_0_42,c_0_54]) ).
cnf(c_0_61,plain,
~ hBOOL(bot_bot_bool),
inference(sr,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_62,plain,
! [X8] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),bot_bot_fun_nat_bool)),
inference(fof_simplification,[status(thm)],[fact_383_emptyE]) ).
fof(c_0_63,plain,
! [X979,X980] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X979),X980))
| hBOOL(hAPP_nat_bool(X980,X979)) )
& ( ~ hBOOL(hAPP_nat_bool(X980,X979))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X979),X980)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_287_mem__def])]) ).
fof(c_0_64,plain,
! [X1353,X1355,X1356] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk100_1(X1353)),X1353))
| X1353 = bot_bot_fun_nat_bool )
& ( X1355 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1356),X1355)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])])]) ).
fof(c_0_65,plain,
! [X2021,X2022] :
( ~ is_bool(X2021)
| hAPP_nat_bool(cOMBK_bool_nat(X2021),X2022) = X2021 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U])]) ).
cnf(c_0_66,hypothesis,
( hAPP_nat_bool(X1,X2) = fTrue
| hAPP_nat_bool(X1,X2) = fFalse ),
inference(spm,[status(thm)],[c_0_42,c_0_58]) ).
cnf(c_0_67,plain,
fFalse = bot_bot_bool,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
fof(c_0_68,plain,
! [X1280] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1280),bot_bot_fun_nat_bool)),
inference(variable_rename,[status(thm)],[c_0_62]) ).
fof(c_0_69,plain,
! [X1460] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1460)) = insert_a(X1460,bot_bot_fun_a_bool),
inference(variable_rename,[status(thm)],[fact_484_singleton__conv]) ).
fof(c_0_70,plain,
! [X860,X861] : insert_a(X860,X861) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X860)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X861))),
inference(variable_rename,[status(thm)],[fact_238_insert__compr]) ).
fof(c_0_71,plain,
! [X1466] : collect_a(hAPP_a_fun_a_bool(fequal_a,X1466)) = insert_a(X1466,bot_bot_fun_a_bool),
inference(variable_rename,[status(thm)],[fact_490_singleton__conv2]) ).
fof(c_0_72,plain,
! [X1025,X1026,X1027] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1026),X1027))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1025,X1026)),image_pname_a(X1025,X1027))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_307_imageI])]) ).
cnf(c_0_73,plain,
( hBOOL(hAPP_nat_bool(X2,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_74,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk100_1(X1)),X1))
| X1 = bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_75,plain,
( hAPP_nat_bool(cOMBK_bool_nat(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,hypothesis,
( hAPP_nat_bool(X1,X2) = bot_bot_bool
| hAPP_nat_bool(X1,X2) = fTrue ),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_77,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_78,plain,
collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = insert_a(X1,bot_bot_fun_a_bool),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,plain,
insert_a(X1,X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = insert_a(X1,bot_bot_fun_a_bool),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_81,plain,
! [X1006,X1007,X1008,X1010,X1011,X1012] :
( ( is_pname(esk59_3(X1006,X1007,X1008))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1006),image_pname_a(X1007,X1008)))
| ~ is_a(X1006) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk59_3(X1006,X1007,X1008)),X1008))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1006),image_pname_a(X1007,X1008)))
| ~ is_a(X1006) )
& ( X1006 = hAPP_pname_a(X1007,esk59_3(X1006,X1007,X1008))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1006),image_pname_a(X1007,X1008)))
| ~ is_a(X1006) )
& ( ~ is_pname(X1012)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1012),X1011))
| X1006 != hAPP_pname_a(X1010,X1012)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1006),image_pname_a(X1010,X1011)))
| ~ is_a(X1006) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_302_image__iff])])])])])]) ).
cnf(c_0_82,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X3,X1)),image_pname_a(X3,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_83,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]) ).
cnf(c_0_84,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_85,plain,
( X1 = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X1,esk100_1(X1))) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_86,hypothesis,
( hAPP_nat_bool(cOMBK_bool_nat(X1),X2) = bot_bot_bool
| fTrue = X1
| ~ is_bool(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,plain,
( hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool) = fFalse
| ~ hBOOL(fTrue) ),
inference(spm,[status(thm)],[c_0_77,c_0_47]) ).
cnf(c_0_88,plain,
collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))),
inference(rw,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_89,plain,
collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))),
inference(rw,[status(thm)],[c_0_80,c_0_79]) ).
fof(c_0_90,plain,
! [X985] :
( ~ is_fun_a_bool(X985)
| collect_a(X985) = X985 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_290_Collect__def])]) ).
fof(c_0_91,plain,
! [X183,X184] :
( ~ is_pname(X184)
| is_fun_a_bool(hAPP_p1534023578a_bool(X183,X184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(c_0_92,plain,
! [X2090,X2091,X2092] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X2090,X2091),X2092) = hAPP_a_fun_a_bool(X2090,hAPP_pname_a(X2091,X2092)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna]) ).
cnf(c_0_93,plain,
( X1 = hAPP_pname_a(X2,esk59_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_94,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,pn)),image_pname_a(X1,u))),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
fof(c_0_95,hypothesis,
! [X177,X178] :
( ~ is_pname(X178)
| is_a(hAPP_pname_a(X177,X178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000t__a])]) ).
cnf(c_0_96,plain,
( is_pname(esk59_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_97,plain,
! [X1111,X1112,X1113] : image_pname_a(X1111,insert_pname(X1112,X1113)) = insert_a(hAPP_pname_a(X1111,X1112),image_pname_a(X1111,X1113)),
inference(variable_rename,[status(thm)],[fact_337_image__insert]) ).
fof(c_0_98,plain,
! [X858,X859] : insert_pname(X858,X859) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X858)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X859))),
inference(variable_rename,[status(thm)],[fact_237_insert__compr]) ).
fof(c_0_99,plain,
! [X1465] : collect_pname(hAPP_p61793385e_bool(fequal_pname,X1465)) = insert_pname(X1465,bot_bo844097828e_bool),
inference(variable_rename,[status(thm)],[fact_489_singleton__conv2]) ).
cnf(c_0_100,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBK_bool_nat(X2)))
| ~ hBOOL(X2)
| ~ is_bool(X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_75]) ).
cnf(c_0_101,hypothesis,
( cOMBK_bool_nat(X1) = bot_bot_fun_nat_bool
| fTrue = X1
| ~ is_bool(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_61]) ).
cnf(c_0_102,plain,
hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool) = bot_bot_bool,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_59])]),c_0_67]) ).
fof(c_0_103,hypothesis,
! [X209,X210] :
( ~ is_fun949378684l_bool(X209)
| ~ is_fun_a_bool(X210)
| is_bool(hAPP_fun_a_bool_bool(X209,X210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool])]) ).
fof(c_0_104,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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_6])]) ).
cnf(c_0_105,plain,
collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1)),
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_106,plain,
( collect_a(X1) = X1
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
fof(c_0_107,plain,
! [X169,X170] :
( ~ is_a(X170)
| is_fun_a_bool(hAPP_a_fun_a_bool(X169,X170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
cnf(c_0_108,plain,
( is_fun_a_bool(hAPP_p1534023578a_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_109,plain,
hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_110,hypothesis,
( hAPP_pname_a(X1,esk59_3(hAPP_pname_a(X1,pn),X1,u)) = hAPP_pname_a(X1,pn)
| ~ is_a(hAPP_pname_a(X1,pn)) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_111,hypothesis,
( is_a(hAPP_pname_a(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_112,hypothesis,
is_pname(pn),
inference(split_conjunct,[status(thm)],[gsy_v_pn]) ).
cnf(c_0_113,hypothesis,
( is_pname(esk59_3(hAPP_pname_a(X1,pn),X1,u))
| ~ is_a(hAPP_pname_a(X1,pn)) ),
inference(spm,[status(thm)],[c_0_96,c_0_94]) ).
cnf(c_0_114,plain,
image_pname_a(X1,insert_pname(X2,X3)) = insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_115,plain,
insert_pname(X1,X2) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
fof(c_0_116,plain,
! [X1431] : image_pname_a(X1431,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
inference(variable_rename,[status(thm)],[fact_468_image__empty]) ).
cnf(c_0_117,plain,
collect_pname(hAPP_p61793385e_bool(fequal_pname,X1)) = insert_pname(X1,bot_bo844097828e_bool),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_118,hypothesis,
( fTrue = X1
| ~ hBOOL(X1)
| ~ is_bool(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_61]) ).
cnf(c_0_119,hypothesis,
( is_bool(hAPP_fun_a_bool_bool(X1,X2))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_120,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(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_121,plain,
( hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| ~ is_fun_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_122,plain,
( is_fun_a_bool(hAPP_a_fun_a_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
fof(c_0_123,plain,
! [X1072,X1073,X1074] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1072),X1074))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1072,X1073)),X1074)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1073),X1074))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1072,X1073)),X1074)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1072),X1074))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1073),X1074))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1072,X1073)),X1074)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_324_insert__subset])])]) ).
cnf(c_0_124,plain,
( is_fun_a_bool(hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,X3)))
| ~ is_pname(X3) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_125,hypothesis,
hAPP_pname_a(X1,esk59_3(hAPP_pname_a(X1,pn),X1,u)) = hAPP_pname_a(X1,pn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]) ).
cnf(c_0_126,hypothesis,
is_pname(esk59_3(hAPP_pname_a(X1,pn),X1,u)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_111]),c_0_112])]) ).
cnf(c_0_127,plain,
image_pname_a(X1,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3)))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X1,X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_79]),c_0_115]) ).
cnf(c_0_128,plain,
image_pname_a(X1,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_129,plain,
collect_pname(hAPP_p61793385e_bool(fequal_pname,X1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool))),
inference(rw,[status(thm)],[c_0_117,c_0_115]) ).
cnf(c_0_130,hypothesis,
( hAPP_fun_a_bool_bool(X1,X2) = fTrue
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X2) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_131,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[conj_1]) ).
fof(c_0_132,hypothesis,
! [X215,X216] :
( ~ is_fun_a_bool(X216)
| is_fun949378684l_bool(hAPP_f1631501043l_bool(X215,X216)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL])]) ).
cnf(c_0_133,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
inference(rw,[status(thm)],[c_0_120,c_0_79]) ).
cnf(c_0_134,plain,
( hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
| ~ is_a(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_135,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X3)),X2))
| ~ 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,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_136,hypothesis,
is_fun_a_bool(hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,pn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126])]) ).
cnf(c_0_137,plain,
collect_a(hAPP_a_fun_a_bool(fequal_a,hAPP_pname_a(X1,X2))) = image_pname_a(X1,collect_pname(hAPP_p61793385e_bool(fequal_pname,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_89]),c_0_129]) ).
cnf(c_0_138,hypothesis,
( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)) = fTrue
| ~ is_fun949378684l_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g))
| ~ is_fun_a_bool(image_pname_a(mgt_call,u)) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_139,hypothesis,
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_140,hypothesis,
is_fun_a_bool(g),
inference(split_conjunct,[status(thm)],[gsy_v_G]) ).
fof(c_0_141,hypothesis,
! [X127,X128] :
( ~ is_fun_pname_bool(X128)
| is_fun_a_bool(image_pname_a(X127,X128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000t__a])]) ).
cnf(c_0_142,negated_conjecture,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,collect_a(hAPP_a_fun_a_bool(fequal_a,hAPP_pname_a(mgt_call,pn)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u)))
| ~ is_a(hAPP_pname_a(mgt_call,pn)) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_143,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))),X2))
| ~ 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,X3),X2)) ),
inference(rw,[status(thm)],[c_0_135,c_0_79]) ).
cnf(c_0_144,hypothesis,
hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X1,pn)) = image_pname_a(X1,collect_pname(hAPP_p61793385e_bool(fequal_pname,pn))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_136]),c_0_137]) ).
cnf(c_0_145,hypothesis,
( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)) = fTrue
| ~ is_fun_a_bool(image_pname_a(mgt_call,u)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140])]) ).
cnf(c_0_146,hypothesis,
( is_fun_a_bool(image_pname_a(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_147,hypothesis,
is_fun_pname_bool(u),
inference(split_conjunct,[status(thm)],[gsy_v_U]) ).
cnf(c_0_148,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,collect_a(hAPP_a_fun_a_bool(fequal_a,hAPP_pname_a(mgt_call,pn)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_111]),c_0_112])]) ).
cnf(c_0_149,hypothesis,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,image_pname_a(X1,collect_pname(hAPP_p61793385e_bool(fequal_pname,pn)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),image_pname_a(X1,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X1,u))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_94]),c_0_144]) ).
cnf(c_0_150,hypothesis,
hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)) = fTrue,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147])]) ).
cnf(c_0_151,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,image_pname_a(mgt_call,collect_pname(hAPP_p61793385e_bool(fequal_pname,pn)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
inference(spm,[status(thm)],[c_0_148,c_0_137]) ).
cnf(c_0_152,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_59])]),c_0_151]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 22:13:44 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 30.50/30.57 % Version : CSE_E---1.5
% 30.50/30.57 % Problem : theBenchmark.p
% 30.50/30.57 % Proof found
% 30.50/30.57 % SZS status Theorem for theBenchmark.p
% 30.50/30.57 % SZS output start Proof
% See solution above
% 30.59/30.60 % Total time : 30.002000 s
% 30.59/30.60 % SZS output end Proof
% 30.59/30.60 % Total time : 30.022000 s
%------------------------------------------------------------------------------