%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU687^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 : Mon Jun 24 15:10:05 EDT 2024
% Result : Theorem 243.67s 31.46s
% Output : CNFRefutation 243.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 204
% Syntax : Number of formulae : 259 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 2208 ( 326 equ; 0 cnn)
% Maximal formula atoms : 633 ( 8 avg)
% Number of connectives : 8119 ( 498 ~; 491 |; 369 &;5375 @)
% ( 280 <=>;1106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 832 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 215 ( 215 >; 0 *; 0 +; 0 <<)
% Number of symbols : 297 ( 293 usr; 215 con; 0-4 aty)
% Number of variables : 2008 ( 124 ^1804 !; 80 ?;2008 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
epred1_0: $o ).
thf(decl_263,type,
esk1_2: $i > $i > $i ).
thf(decl_264,type,
esk2_2: $i > $i > $i ).
thf(decl_265,type,
esk3_2: $i > $i > $i ).
thf(decl_266,type,
esk4_1: $i > $i ).
thf(decl_267,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_268,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_269,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_270,type,
esk8_1: $i > $i ).
thf(decl_271,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_272,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_273,type,
esk11_2: $i > $i > $i ).
thf(decl_274,type,
esk12_2: $i > $i > $i ).
thf(decl_275,type,
esk13_1: $i > $i ).
thf(decl_276,type,
esk14_1: $i > $i ).
thf(decl_277,type,
esk15_1: $i > $i ).
thf(decl_278,type,
esk16_2: $i > $i > $i ).
thf(decl_279,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_280,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_281,type,
esk19_1: $i > $i ).
thf(decl_282,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_283,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_284,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_285,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_286,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_287,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_288,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_289,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_290,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_291,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_292,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_293,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_294,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_295,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_296,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_297,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_298,type,
esk36_2: $i > $i > $i ).
thf(decl_299,type,
esk37_2: $i > $i > $i ).
thf(decl_300,type,
esk38_2: $i > $i > $i ).
thf(decl_301,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_302,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_303,type,
esk41_2: $i > $i > $i ).
thf(decl_304,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_305,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_306,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_307,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_308,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_309,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_310,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_311,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_312,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_313,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_314,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_315,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_316,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_317,type,
esk55_0: $i ).
thf(decl_318,type,
esk56_0: $i ).
thf(decl_319,type,
esk57_0: $i ).
thf(decl_320,type,
esk58_0: $i ).
thf(decl_321,type,
esk59_0: $i ).
thf(decl_322,type,
esk60_0: $i ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',kfstsingleton) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setoftrueEq) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ksndsingleton) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exuI3) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',apProp) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptyE1) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X31 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X33 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X34 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ex1E2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exuI1) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',descr__Cong) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',sepSubset) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ex1I) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',replAx) ).
thf(funcextLem,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X35: $i] :
( ( func @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',funcextLem) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',powersetI) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodmempaircEq) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X30 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',funcGraphProp2) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairinjL1) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',powersetE) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',theprop) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setunionI) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairinjL2) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setunionE) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairinjR11) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subPowSU) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairinjR) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',nonemptyImpWitness) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodsndin) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',uniqinunit) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodpairmemER) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',notinsingleton) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodpairsurjEq) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',upairsetIL) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',app) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',upairsetIR) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X30 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',funcinfuncset) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',vacuousDall) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X29 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',brelnall1) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',quantDeMorgan1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X29 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',brelnall2) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X30 @ X2 ) ) @ X30 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X30 @ X2 ) ) @ X30 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',funcGraphProp3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',prop2setI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',notdallE) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',powersetE1) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',powerset__Cong) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptyinPowerset) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',subsetemptysetimpeq) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',disjointsetsI1) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptyInPowerset) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setunionsingleton) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p',setextAx) ).
thf(c_0_203,plain,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_204,plain,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_205,plain,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE2]) ).
thf(c_0_206,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_207,plain,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ksndsingleton]) ).
thf(c_0_208,plain,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI3]) ).
thf(c_0_209,plain,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X22 @ Z0 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrI]) ).
thf(c_0_210,plain,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X23 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrSub]) ).
thf(c_0_211,plain,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[setOfPairsIsBReln]) ).
thf(c_0_212,plain,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X25 @ Z0 @ Z1 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrERa]) ).
thf(c_0_213,plain,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X26 @ Z0 @ Z1 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL1]) ).
thf(c_0_214,plain,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X27 @ Z0 @ Z1 ) ) )
=> ( in @ X3 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL2]) ).
thf(c_0_215,plain,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X28 @ Z0 @ Z1 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrER]) ).
thf(c_0_216,plain,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_217,plain,
( apProp
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
@ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[apProp]) ).
thf(c_0_218,plain,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= emptyset )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[emptyE1]) ).
thf(c_0_219,plain,
( lamProp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X31 @ Z0 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamProp]) ).
thf(c_0_220,plain,
( lamp
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_221,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X34 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_222,plain,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E2]) ).
thf(c_0_223,plain,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI1]) ).
thf(c_0_224,plain,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI2]) ).
thf(c_0_225,plain,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE3u]) ).
thf(c_0_226,plain,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
<=> ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu__Cong]) ).
thf(c_0_227,plain,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuEu]) ).
thf(c_0_228,plain,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descr__Cong]) ).
thf(c_0_229,plain,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( dsetconstr @ X5
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).
thf(c_0_230,plain,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ ( powerset @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[sepInPowerset]) ).
thf(c_0_231,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_232,plain,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singletonprop]) ).
thf(c_0_233,plain,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E1]) ).
thf(c_0_234,plain,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I]) ).
thf(c_0_235,plain,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[nonemptyI]) ).
thf(c_0_236,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_237,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_238,plain,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE1]) ).
thf(c_0_239,plain,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_240,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_241,plain,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_242,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_243,plain,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[replAx]) ).
thf(c_0_244,plain,
( epred1_0
<=> ! [X663: $i] :
? [X664: $i] :
( ! [X665: $i] :
( ( in @ X665 @ X664 )
=> ! [X666: $i] :
( ( in @ X666 @ X665 )
=> ( in @ X666 @ X663 ) ) )
& ! [X667: $i,X668: $i] :
( ( ( in @ X667 @ X663 )
& ( in @ X668 @ X663 ) )
=> ( ! [X669: $i] :
( ( in @ X669 @ X664 )
=> ( ( in @ X667 @ X669 )
<=> ( in @ X668 @ X669 ) ) )
=> ( X667 = X668 ) ) )
& ! [X670: $i,X671: $i] :
( ( ( in @ X670 @ X664 )
& ( in @ X671 @ X664 ) )
=> ( ! [X672: $i] :
( ( in @ X672 @ X670 )
=> ( in @ X672 @ X671 ) )
| ! [X673: $i] :
( ( in @ X673 @ X671 )
=> ( in @ X673 @ X670 ) ) ) )
& ! [X674: $i] :
( ( ! [X675: $i] :
( ( in @ X675 @ X674 )
=> ( in @ X675 @ X663 ) )
& ? [X676: $i] : ( in @ X676 @ X674 ) )
=> ? [X677: $i,X678: $i] :
( ( in @ X677 @ X664 )
& ( in @ X678 @ X674 )
& ~ ? [X679: $i] :
( ( in @ X679 @ X677 )
& ( in @ X679 @ X674 ) )
& ! [X680: $i] :
( ( in @ X680 @ X664 )
=> ( ! [X681: $i] :
( ( in @ X681 @ X680 )
=> ( in @ X681 @ X677 ) )
| ( in @ X678 @ X680 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_245,negated_conjecture,
~ ( ! [X636: $i,X637: $i] :
( ! [X638: $i] :
( ( in @ X638 @ X636 )
<=> ( in @ X638 @ X637 ) )
=> ( X636 = X637 ) )
=> ( ! [X639: $i] :
~ ( in @ X639 @ emptyset )
=> ( ! [X640: $i,X641: $i,X642: $i] :
( ( in @ X642 @ ( setadjoin @ X640 @ X641 ) )
<=> ( ( X642 = X640 )
| ( in @ X642 @ X641 ) ) )
=> ( ! [X643: $i,X644: $i] :
( ( in @ X644 @ ( powerset @ X643 ) )
<=> ! [X645: $i] :
( ( in @ X645 @ X644 )
=> ( in @ X645 @ X643 ) ) )
=> ( ! [X646: $i,X647: $i] :
( ( in @ X647 @ ( setunion @ X646 ) )
<=> ? [X648: $i] :
( ( in @ X647 @ X648 )
& ( in @ X648 @ X646 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X649: $i] :
( ( in @ X649 @ omega )
=> ( in @ ( setadjoin @ X649 @ X649 ) @ omega ) )
=> ( ! [X650: $i] :
( ( ( in @ emptyset @ X650 )
& ! [X651: $i] :
( ( ( in @ X651 @ omega )
& ( in @ X651 @ X650 ) )
=> ( in @ ( setadjoin @ X651 @ X651 ) @ X650 ) ) )
=> ! [X652: $i] :
( ( in @ X652 @ omega )
=> ( in @ X652 @ X650 ) ) )
=> ( ! [X653: $i > $i > $o,X654: $i] :
( ! [X655: $i] :
( ( in @ X655 @ X654 )
=> ( exu @ ( X653 @ X655 ) ) )
=> ? [X656: $i] :
! [X657: $i] :
( ( in @ X657 @ X656 )
<=> ? [X658: $i] :
( ( in @ X658 @ X654 )
& ( X653 @ X658 @ X657 ) ) ) )
=> ( ! [X659: $i] :
( ? [X660: $i] : ( in @ X660 @ X659 )
=> ? [X661: $i] :
( ( in @ X661 @ X659 )
& ~ ? [X662: $i] :
( ( in @ X662 @ X661 )
& ( in @ X662 @ X659 ) ) ) )
=> ( epred1_0
=> ( ! [X682: $i > $o] :
( ( exu @ X682 )
=> ( X682
@ ( descr
@ ^ [Z0: $i] : ( X682 @ Z0 ) ) ) )
=> ( ! [X683: $i,X684: $i > $o,X685: $i] :
( ( in @ X685 @ X683 )
=> ( ( X684 @ X685 )
=> ( in @ X685 @ ( dsetconstr @ X683 @ X684 ) ) ) )
=> ( ! [X686: $i,X687: $i > $o,X688: $i] :
( ( in @ X688 @ ( dsetconstr @ X686 @ X687 ) )
=> ( in @ X688 @ X686 ) )
=> ( ! [X689: $i,X690: $i > $o,X691: $i] :
( ( in @ X691 @ ( dsetconstr @ X689 @ X690 ) )
=> ( X690 @ X691 ) )
=> ( ! [X692: $i > $o] :
( ( exu @ X692 )
=> ? [X693: $i] :
( ( X692 @ X693 )
& ! [X694: $i] :
( ( X692 @ X694 )
=> ( X693 = X694 ) ) ) )
=> ( ! [X695: $o,X696: $i] :
( ( in @ X696 @ ( prop2set @ X695 ) )
=> X695 )
=> ( ! [X697: $i] :
( ( in @ X697 @ emptyset )
=> ! [X698: $o] : X698 )
=> ( ! [X699: $i] :
( ( in @ X699 @ emptyset )
=> ~ $true )
=> ( ! [X700: $i] :
~ ( in @ X700 @ emptyset )
=> ( ! [X701: $i > $o] :
( ( exu @ X701 )
=> ? [X702: $i] : ( X701 @ X702 ) )
=> ( ! [X703: $i,X704: $i] :
( ! [X705: $i] :
( ( in @ X705 @ X703 )
=> ( in @ X705 @ X704 ) )
=> ( ! [X706: $i] :
( ( in @ X706 @ X704 )
=> ( in @ X706 @ X703 ) )
=> ( X703 = X704 ) ) )
=> ( ! [X707: $i] :
( ! [X708: $i] :
~ ( in @ X708 @ X707 )
=> ( X707 = emptyset ) )
=> ( ! [X709: $i] :
( ! [X710: $i] :
~ ( in @ X710 @ X709 )
=> ( X709 = emptyset ) )
=> ( ! [X711: $i,X712: $i > $o,X713: $i] :
( ( in @ X713 @ X711 )
=> ( ( in @ X713 @ ( dsetconstr @ X711 @ X712 ) )
<=> ( X712 @ X713 ) ) )
=> ( ! [X714: $i] :
( ( nonempty @ X714 )
=> ? [X715: $i] : ( in @ X715 @ X714 ) )
=> ( ! [X716: $i,X717: $i > $o,X718: $i] :
( ( in @ X718 @ X716 )
=> ( ( X717 @ X718 )
=> ( nonempty @ ( dsetconstr @ X716 @ X717 ) ) ) )
=> ( ! [X719: $i] :
( ? [X720: $i] : ( in @ X720 @ X719 )
=> ( nonempty @ X719 ) )
=> ( ! [X721: $i,X722: $i] : ( in @ X721 @ ( setadjoin @ X721 @ X722 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X723: $i,X724: $i,X725: $i] :
( ( in @ X725 @ X724 )
=> ( in @ X725 @ ( setadjoin @ X723 @ X724 ) ) )
=> ( ! [X726: $i,X727: $i,X728: $i] :
( ( in @ X728 @ ( setadjoin @ X726 @ X727 ) )
=> ! [X729: $o] :
( ( ( X728 = X726 )
=> X729 )
=> ( ( ( in @ X728 @ X727 )
=> X729 )
=> X729 ) ) )
=> ( ! [X730: $i,X731: $i,X732: $i] :
( ( in @ X732 @ ( setadjoin @ X730 @ X731 ) )
=> ( ( X732 = X730 )
| ( in @ X732 @ X731 ) ) )
=> ( ! [X733: $i] :
( ( dsetconstr @ X733
@ ^ [Z0: $i] : $true )
= X733 )
=> ( ! [X734: $i,X735: $i] :
( ! [X736: $i] :
( ( in @ X736 @ X735 )
=> ( in @ X736 @ X734 ) )
=> ( in @ X735 @ ( powerset @ X734 ) ) )
=> ( ! [X737: $i] : ( in @ emptyset @ ( powerset @ X737 ) )
=> ( ! [X738: $i] : ( in @ emptyset @ ( powerset @ X738 ) )
=> ( ! [X739: $i,X740: $i,X741: $i] :
( ( in @ X740 @ ( powerset @ X739 ) )
=> ( ( in @ X741 @ X740 )
=> ( in @ X741 @ X739 ) ) )
=> ( ! [X742: $i,X743: $i,X744: $i] :
( ( in @ X743 @ X744 )
=> ( ( in @ X744 @ X742 )
=> ( in @ X743 @ ( setunion @ X742 ) ) ) )
=> ( ! [X745: $i,X746: $i] :
( ( in @ X746 @ ( setunion @ X745 ) )
=> ! [X747: $o] :
( ! [X748: $i] :
( ( in @ X746 @ X748 )
=> ( ( in @ X748 @ X745 )
=> X747 ) )
=> X747 ) )
=> ( ! [X749: $i,X750: $i] :
( ( in @ X750 @ X749 )
=> ( in @ X750 @ ( powerset @ ( setunion @ X749 ) ) ) )
=> ( ! [X751: $i > $o] :
( ( exu @ X751 )
=> ? [X752: $i] :
! [X753: $i] :
( ( X751 @ X753 )
<=> ( X753 = X752 ) ) )
=> ( ! [X754: $i] :
( ( nonempty @ X754 )
=> ? [X755: $i] :
( ( in @ X755 @ X754 )
& $true ) )
=> ( ! [X756: $i,X757: $i] :
( ( in @ X756 @ ( setadjoin @ X757 @ emptyset ) )
=> ( X756 = X757 ) )
=> ( ! [X758: $i,X759: $i] :
( ( X758 != X759 )
=> ~ ( in @ X759 @ ( setadjoin @ X758 @ emptyset ) ) )
=> ( ! [X760: $i,X761: $i] :
( ( X760 = X761 )
=> ( in @ X760 @ ( setadjoin @ X761 @ emptyset ) ) )
=> ( ! [X762: $i,X763: $i] :
( ( in @ X762 @ ( setadjoin @ X763 @ emptyset ) )
=> ( in @ X763 @ ( setadjoin @ X762 @ emptyset ) ) )
=> ( ! [X764: $i,X765: $i,X766: $i] :
( ( in @ X766 @ ( setadjoin @ X764 @ ( setadjoin @ X765 @ emptyset ) ) )
=> ( ( X766 = X764 )
| ( X766 = X765 ) ) )
=> ( ! [X767: $i,X768: $i] : ( in @ X767 @ ( setadjoin @ X767 @ ( setadjoin @ X768 @ emptyset ) ) )
=> ( ! [X769: $i,X770: $i] : ( in @ X770 @ ( setadjoin @ X769 @ ( setadjoin @ X770 @ emptyset ) ) )
=> ( ! [X771: $i,X772: $i > $o] :
( ? [X773: $i] :
( ( in @ X773 @ X771 )
& ( X772 @ X773 ) )
=> ( ( ( dsetconstr @ X771 @ X772 )
= emptyset )
=> ~ $true ) )
=> ( ! [X774: $i > $o,X775: $i] :
( ( in @ X775 @ emptyset )
=> ( X774 @ X775 ) )
=> ( ! [X776: $i,X777: $i > $o] :
( ~ ! [X778: $i] :
( ( in @ X778 @ X776 )
=> ( X777 @ X778 ) )
=> ? [X779: $i] :
( ( in @ X779 @ X776 )
& ~ ( X777 @ X779 ) ) )
=> ( ! [X780: $i,X781: $i > $o] :
( ! [X782: $i] :
( ( in @ X782 @ X780 )
=> ~ ( X781 @ X782 ) )
=> ~ ? [X783: $i] :
( ( in @ X783 @ X780 )
& ( X781 @ X783 ) ) )
=> ( ! [X784: $i,X785: $i > $o] :
( ~ ? [X786: $i] :
( ( in @ X786 @ X784 )
& ( X785 @ X786 ) )
=> ! [X787: $i] :
( ( in @ X787 @ X784 )
=> ~ ( X785 @ X787 ) ) )
=> ( ! [X788: $i,X789: $i > $o] :
( ? [X790: $i] :
( ( in @ X790 @ X788 )
& ~ ( X789 @ X790 ) )
=> ~ ! [X791: $i] :
( ( in @ X791 @ X788 )
=> ( X789 @ X791 ) ) )
=> ( ! [X792: $o] :
( X792
=> ( in @ emptyset @ ( prop2set @ X792 ) ) )
=> ( prop2set2propI
=> ( ! [X793: $i,X794: $i > $o] :
( ~ ? [X795: $i] :
( ( in @ X795 @ X793 )
& ( X794 @ X795 ) )
=> ! [X796: $i] :
( ( in @ X796 @ X793 )
=> ~ ( X794 @ X796 ) ) )
=> ( ! [X797: $i,X798: $i > $o] :
( ~ ! [X799: $i] :
( ( in @ X799 @ X797 )
=> ( X798 @ X799 ) )
=> ? [X800: $i] :
( ( in @ X800 @ X797 )
& ~ ( X798 @ X800 ) ) )
=> ( ! [X801: $i > $o] :
( ? [X802: $i] :
( ( X801 @ X802 )
& ! [X803: $i] :
( ( X801 @ X803 )
=> ( X802 = X803 ) ) )
=> ( exu @ X801 ) )
=> ( ! [X804: $i > $o] :
( ? [X805: $i] : ( X804 @ X805 )
=> ( ! [X806: $i,X807: $i] :
( ( X804 @ X806 )
=> ( ( X804 @ X807 )
=> ( X806 = X807 ) ) )
=> ( exu @ X804 ) ) )
=> ( ! [X808: $i > $o] :
( ? [X809: $i] :
! [X810: $i] :
( ( X808 @ X810 )
<=> ( X810 = X809 ) )
=> ( exu @ X808 ) )
=> ( ! [X811: $i,X812: $i] :
( ( X811 = X812 )
=> ! [X813: $i,X814: $i] :
( ( X813 = X814 )
=> ( ( in @ X813 @ X811 )
=> ( in @ X814 @ X812 ) ) ) )
=> ( ! [X815: $i,X816: $i] :
( ( X815 = X816 )
=> ! [X817: $i,X818: $i] :
( ( X817 = X818 )
=> ( ( in @ X817 @ X815 )
<=> ( in @ X818 @ X816 ) ) ) )
=> ( ! [X819: $i > $o] :
( ( exu @ X819 )
=> ! [X820: $i,X821: $i] :
( ( X819 @ X820 )
=> ( ( X819 @ X821 )
=> ( X820 = X821 ) ) ) )
=> ( ! [X822: $i > $o,X823: $i > $o] :
( ! [X824: $i,X825: $i] :
( ( X824 = X825 )
=> ( ( X822 @ X824 )
<=> ( X823 @ X825 ) ) )
=> ( ( exu @ X822 )
<=> ( exu @ X823 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X826: $i,X827: $i] :
( ( X826 = X827 )
=> ! [X828: $i,X829: $i] :
( ( X828 = X829 )
=> ( ( setadjoin @ X826 @ X828 )
= ( setadjoin @ X827 @ X829 ) ) ) )
=> ( ! [X830: $i,X831: $i] :
( ( X830 = X831 )
=> ( ( powerset @ X830 )
= ( powerset @ X831 ) ) )
=> ( ! [X832: $i,X833: $i] :
( ( X832 = X833 )
=> ( ( setunion @ X832 )
= ( setunion @ X833 ) ) )
=> ( ( omega = omega )
=> ( ! [X834: $i > $o] :
( ( exu @ X834 )
=> ! [X835: $i,X836: $i] :
( ( X834 @ X835 )
=> ( ( X834 @ X836 )
=> ( X835 = X836 ) ) ) )
=> ( ! [X837: $i > $o,X838: $i > $o] :
( ! [X839: $i,X840: $i] :
( ( X839 = X840 )
=> ( ( X837 @ X839 )
<=> ( X838 @ X840 ) ) )
=> ( ( exu @ X837 )
=> ( ( exu @ X838 )
=> ( ( descr @ X837 )
= ( descr @ X838 ) ) ) ) )
=> ( ! [X841: $i,X842: $i] :
( ( X841 = X842 )
=> ! [X843: $i > $o,X844: $i > $o] :
( ! [X845: $i] :
( ( in @ X845 @ X841 )
=> ! [X846: $i] :
( ( in @ X846 @ X842 )
=> ( ( X845 = X846 )
=> ( ( X843 @ X845 )
<=> ( X844 @ X846 ) ) ) ) )
=> ( ( dsetconstr @ X841 @ X843 )
= ( dsetconstr @ X842 @ X844 ) ) ) )
=> ( ! [X847: $i,X848: $i] :
( ! [X849: $i] :
( ( in @ X849 @ X847 )
=> ( in @ X849 @ X848 ) )
=> ( subset @ X847 @ X848 ) )
=> ( ! [X850: $i,X851: $i] :
( ( X850 = X851 )
=> ( subset @ X851 @ X850 ) )
=> ( ! [X852: $i,X853: $i] :
( ( X852 = X853 )
=> ( subset @ X852 @ X853 ) )
=> ( ! [X854: $i,X855: $i] :
( ! [X856: $i] :
( ( in @ X856 @ X854 )
=> ( in @ X856 @ X855 ) )
=> ( subset @ X854 @ X855 ) )
=> ( ! [X857: $i] : ( subset @ emptyset @ X857 )
=> ( ! [X858: $i,X859: $i,X860: $i] :
( ( subset @ X858 @ X859 )
=> ( ( in @ X860 @ X858 )
=> ( in @ X860 @ X859 ) ) )
=> ( ! [X861: $i,X862: $i,X863: $i] :
( ( subset @ X861 @ X862 )
=> ( ~ ( in @ X863 @ X862 )
=> ~ ( in @ X863 @ X861 ) ) )
=> ( ! [X864: $i,X865: $i,X866: $i] :
( ( in @ X866 @ X864 )
=> ( ~ ( in @ X866 @ X865 )
=> ~ ( subset @ X864 @ X865 ) ) )
=> ( ! [X867: $i,X868: $i] :
( ~ ( subset @ X867 @ X868 )
=> ( X867 != X868 ) )
=> ( ! [X869: $i,X870: $i,X871: $i] :
( ( in @ X871 @ X869 )
=> ( ~ ( in @ X871 @ X870 )
=> ( X869 != X870 ) ) )
=> ( ! [X872: $i] : ( subset @ X872 @ X872 )
=> ( ! [X873: $i,X874: $i,X875: $i] :
( ( subset @ X873 @ X874 )
=> ( ( subset @ X874 @ X875 )
=> ( subset @ X873 @ X875 ) ) )
=> ( ! [X876: $i,X877: $i] : ( subset @ X877 @ ( setadjoin @ X876 @ X877 ) )
=> ( ! [X878: $i,X879: $i,X880: $i] :
( ( subset @ X878 @ X880 )
=> ( subset @ X878 @ ( setadjoin @ X879 @ X880 ) ) )
=> ( ! [X881: $i,X882: $i] :
( ( subset @ X881 @ X882 )
=> ( in @ X881 @ ( powerset @ X882 ) ) )
=> ( ! [X883: $i,X884: $i] :
( ( subset @ X883 @ X884 )
=> ( ( subset @ X884 @ X883 )
=> ( X883 = X884 ) ) )
=> ( ! [X885: $i] :
( ( subset @ X885 @ emptyset )
=> ( X885 = emptyset ) )
=> ( ! [X886: $i,X887: $i] :
( ( subset @ X887 @ X886 )
=> ( in @ X887 @ ( powerset @ X886 ) ) )
=> ( ! [X888: $i,X889: $i] :
( ( in @ X889 @ ( powerset @ X888 ) )
=> ( subset @ X889 @ X888 ) )
=> ( ! [X890: $i] : ( in @ X890 @ ( powerset @ X890 ) )
=> ( ! [X891: $i,X892: $i] :
( ( subset @ X891 @ X892 )
=> ( subset @ ( powerset @ X891 ) @ ( powerset @ X892 ) ) )
=> ( ! [X893: $i,X894: $i > $o] : ( in @ ( dsetconstr @ X893 @ X894 ) @ ( powerset @ X893 ) )
=> ( ! [X895: $i,X896: $i > $o] : ( subset @ ( dsetconstr @ X895 @ X896 ) @ X895 )
=> ( ! [X897: $i,X898: $i,X899: $i] :
( ( in @ X899 @ X897 )
=> ( in @ X899 @ ( binunion @ X897 @ X898 ) ) )
=> ( ! [X900: $i,X901: $i] : ( in @ X901 @ ( setadjoin @ X900 @ ( setadjoin @ X901 @ emptyset ) ) )
=> ( ! [X902: $i,X903: $i,X904: $i] :
( ( in @ X904 @ X903 )
=> ( in @ X904 @ ( binunion @ X902 @ X903 ) ) )
=> ( ! [X905: $i,X906: $i,X907: $i,X908: $o] :
( ( in @ X907 @ ( binunion @ X905 @ X906 ) )
=> ( ( ( in @ X907 @ X905 )
=> X908 )
=> ( ( ( in @ X907 @ X906 )
=> X908 )
=> X908 ) ) )
=> ( ! [X909: $i,X910: $i,X911: $i] :
( ( in @ X911 @ ( binunion @ X909 @ X910 ) )
=> ( ( in @ X911 @ X909 )
| ( in @ X911 @ X910 ) ) )
=> ( ! [X912: $i,X913: $i] : ( subset @ X912 @ ( binunion @ X912 @ X913 ) )
=> ( ! [X914: $i,X915: $i] : ( subset @ X915 @ ( binunion @ X914 @ X915 ) )
=> ( ! [X916: $i,X917: $i,X918: $i] :
( ( in @ X918 @ X916 )
=> ( ( in @ X918 @ X917 )
=> ( in @ X918 @ ( binintersect @ X916 @ X917 ) ) ) )
=> ( ! [X919: $i,X920: $i,X921: $i] :
( ( subset @ X921 @ X919 )
=> ( ( subset @ X921 @ X920 )
=> ( subset @ X921 @ ( binintersect @ X919 @ X920 ) ) ) )
=> ( ! [X922: $i,X923: $i,X924: $i] :
( ( in @ X924 @ ( binintersect @ X922 @ X923 ) )
=> ( in @ X924 @ X922 ) )
=> ( ! [X925: $i,X926: $i] : ( subset @ ( binintersect @ X925 @ X926 ) @ X925 )
=> ( ! [X927: $i,X928: $i] :
( ( subset @ X927 @ X928 )
=> ( ( binintersect @ X927 @ X928 )
= X927 ) )
=> ( ! [X929: $i,X930: $i] :
( ( ( binintersect @ X929 @ X930 )
= X930 )
=> ( subset @ X930 @ X929 ) )
=> ( ! [X931: $i,X932: $i,X933: $i] :
( ( in @ X933 @ ( binintersect @ X931 @ X932 ) )
=> ( in @ X933 @ X932 ) )
=> ( ! [X934: $i,X935: $i] :
( ~ ? [X936: $i] :
( ( in @ X936 @ X934 )
& ( in @ X936 @ X935 ) )
=> ( ( binintersect @ X934 @ X935 )
= emptyset ) )
=> ( ! [X937: $i,X938: $i] : ( subset @ ( binintersect @ X937 @ X938 ) @ X938 )
=> ( ! [X939: $i,X940: $i] :
( ( subset @ X940 @ X939 )
=> ( ( binintersect @ X939 @ X940 )
= X940 ) )
=> ( ! [X941: $i,X942: $i] :
( ( ( binintersect @ X941 @ X942 )
= X941 )
=> ( subset @ X941 @ X942 ) )
=> ( ! [X943: $i,X944: $i,X945: $i] :
( ( binintersect @ X943 @ ( binunion @ X944 @ X945 ) )
= ( binunion @ ( binintersect @ X943 @ X944 ) @ ( binintersect @ X943 @ X945 ) ) )
=> ( ! [X946: $i,X947: $i,X948: $i] :
( ( in @ X948 @ X946 )
=> ( ~ ( in @ X948 @ X947 )
=> ( in @ X948 @ ( setminus @ X946 @ X947 ) ) ) )
=> ( ! [X949: $i,X950: $i,X951: $i] :
( ( in @ X951 @ ( setminus @ X949 @ X950 ) )
=> ( in @ X951 @ X949 ) )
=> ( ! [X952: $i,X953: $i,X954: $i] :
( ( in @ X954 @ ( setminus @ X952 @ X953 ) )
=> ~ ( in @ X954 @ X953 ) )
=> ( ! [X955: $i,X956: $i] :
( ( subset @ X955 @ X956 )
=> ( ( setminus @ X955 @ X956 )
= emptyset ) )
=> ( ! [X957: $i,X958: $i,X959: $i] :
( ~ ( in @ X959 @ ( setminus @ X957 @ X958 ) )
=> ( ( in @ X959 @ X957 )
=> ( in @ X959 @ X958 ) ) )
=> ( ! [X960: $i,X961: $i,X962: $i] :
( ~ ( in @ X962 @ ( setminus @ X960 @ X961 ) )
=> ( ~ ( in @ X962 @ X961 )
=> ~ ( in @ X962 @ X960 ) ) )
=> ( ! [X963: $i,X964: $i,X965: $i] :
( ~ ( in @ X965 @ X963 )
=> ~ ( in @ X965 @ ( setminus @ X963 @ X964 ) ) )
=> ( ! [X966: $i,X967: $i,X968: $i] :
( ( in @ X968 @ X967 )
=> ~ ( in @ X968 @ ( setminus @ X966 @ X967 ) ) )
=> ( ! [X969: $i,X970: $i] : ( subset @ ( setminus @ X969 @ X970 ) @ X969 )
=> ( ! [X971: $i,X972: $i] :
( ( ( setminus @ X971 @ X972 )
= emptyset )
=> ( subset @ X971 @ X972 ) )
=> ( ! [X973: $i,X974: $i,X975: $i] :
( ( in @ X975 @ ( symdiff @ X973 @ X974 ) )
=> ! [X976: $o] :
( ( ( in @ X975 @ X973 )
=> ( ~ ( in @ X975 @ X974 )
=> X976 ) )
=> ( ( ~ ( in @ X975 @ X973 )
=> ( ( in @ X975 @ X974 )
=> X976 ) )
=> X976 ) ) )
=> ( ! [X977: $i,X978: $i,X979: $i] :
( ( in @ X979 @ X977 )
=> ( ~ ( in @ X979 @ X978 )
=> ( in @ X979 @ ( symdiff @ X977 @ X978 ) ) ) )
=> ( ! [X980: $i,X981: $i,X982: $i] :
( ~ ( in @ X982 @ X980 )
=> ( ( in @ X982 @ X981 )
=> ( in @ X982 @ ( symdiff @ X980 @ X981 ) ) ) )
=> ( ! [X983: $i,X984: $i,X985: $i] :
( ( in @ X985 @ X983 )
=> ( ( in @ X985 @ X984 )
=> ~ ( in @ X985 @ ( symdiff @ X983 @ X984 ) ) ) )
=> ( ! [X986: $i,X987: $i,X988: $i] :
( ~ ( in @ X988 @ X986 )
=> ( ~ ( in @ X988 @ X987 )
=> ~ ( in @ X988 @ ( symdiff @ X986 @ X987 ) ) ) )
=> ( ! [X989: $i,X990: $i] : ( in @ X990 @ ( setadjoin @ X989 @ ( setadjoin @ X990 @ emptyset ) ) )
=> ( ! [X991: $i,X992: $i] : ( in @ X991 @ ( setunion @ ( setadjoin @ ( setadjoin @ X991 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X991 @ ( setadjoin @ X992 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X993: $i,X994: $i] : ( in @ X994 @ ( setunion @ ( setadjoin @ ( setadjoin @ X993 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X993 @ ( setadjoin @ X994 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X995: $i,X996: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X995 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X995 @ ( setadjoin @ X996 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X997: $i,X998: $i] : ( iskpair @ ( kpair @ X997 @ X998 ) )
=> ( ! [X999: $i,X1000: $i] :
( ( in @ X1000 @ X999 )
=> ( subset @ ( setadjoin @ X1000 @ emptyset ) @ X999 ) )
=> ( ! [X1001: $i,X1002: $i] :
( ( in @ X1002 @ X1001 )
=> ( in @ ( setadjoin @ X1002 @ emptyset ) @ ( powerset @ X1001 ) ) )
=> ( ! [X1003: $i,X1004: $i,X1005: $i] :
( ( in @ X1005 @ X1003 )
=> ( in @ ( setadjoin @ X1005 @ emptyset ) @ ( powerset @ ( binunion @ X1003 @ X1004 ) ) ) )
=> ( ! [X1006: $i,X1007: $i,X1008: $i] :
( ( in @ X1008 @ ( setadjoin @ X1006 @ ( setadjoin @ X1007 @ emptyset ) ) )
=> ( ( X1008 = X1006 )
| ( X1008 = X1007 ) ) )
=> ( ! [X1009: $i,X1010: $i,X1011: $i] :
( ( in @ X1011 @ X1009 )
=> ! [X1012: $i] :
( ( in @ X1012 @ X1010 )
=> ( subset @ ( setadjoin @ X1011 @ ( setadjoin @ X1012 @ emptyset ) ) @ ( binunion @ X1009 @ X1010 ) ) ) )
=> ( ! [X1013: $i,X1014: $i,X1015: $i] :
( ( in @ X1015 @ X1013 )
=> ! [X1016: $i] :
( ( in @ X1016 @ X1014 )
=> ( in @ ( setadjoin @ X1015 @ ( setadjoin @ X1016 @ emptyset ) ) @ ( powerset @ ( binunion @ X1013 @ X1014 ) ) ) ) )
=> ( ! [X1017: $i,X1018: $i,X1019: $i] :
( ( in @ X1019 @ X1017 )
=> ! [X1020: $i] :
( ( in @ X1020 @ X1018 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1019 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1019 @ ( setadjoin @ X1020 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1017 @ X1018 ) ) ) ) )
=> ( ! [X1021: $i,X1022: $i,X1023: $i] :
( ( in @ X1023 @ X1021 )
=> ! [X1024: $i] :
( ( in @ X1024 @ X1022 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1023 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1023 @ ( setadjoin @ X1024 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1021 @ X1022 ) ) ) ) ) )
=> ( ! [X1025: $i,X1026: $i,X1027: $i] :
( ( in @ X1027 @ X1025 )
=> ! [X1028: $i] :
( ( in @ X1028 @ X1026 )
=> ( in @ ( kpair @ X1027 @ X1028 ) @ ( powerset @ ( powerset @ ( binunion @ X1025 @ X1026 ) ) ) ) ) )
=> ( ! [X1029: $i,X1030: $i,X1031: $i] :
( ( in @ X1031 @ X1029 )
=> ! [X1032: $i] :
( ( in @ X1032 @ X1030 )
=> ( in @ ( kpair @ X1031 @ X1032 ) @ ( cartprod @ X1029 @ X1030 ) ) ) )
=> ( ! [X1033: $i,X1034: $i,X1035: $i] :
( ( in @ X1035 @ ( cartprod @ X1033 @ X1034 ) )
=> ? [X1036: $i] :
( ( in @ X1036 @ X1033 )
& ? [X1037: $i] :
( ( in @ X1037 @ X1034 )
& ( X1035
= ( kpair @ X1036 @ X1037 ) ) ) ) )
=> ( ! [X1038: $i,X1039: $i,X1040: $i] :
( ( in @ X1040 @ ( cartprod @ X1038 @ X1039 ) )
=> ( iskpair @ X1040 ) )
=> ( ! [X1041: $i,X1042: $i] :
( ( in @ X1042 @ ( setunion @ X1041 ) )
=> ? [X1043: $i] :
( ( in @ X1043 @ X1041 )
& ( in @ X1042 @ X1043 ) ) )
=> ( ! [X1044: $i] : ( subset @ ( setunion @ ( setadjoin @ X1044 @ emptyset ) ) @ X1044 )
=> ( ! [X1045: $i] : ( subset @ X1045 @ ( setunion @ ( setadjoin @ X1045 @ emptyset ) ) )
=> ( ! [X1046: $i] :
( ( setunion @ ( setadjoin @ X1046 @ emptyset ) )
= X1046 )
=> ( ! [X1047: $i,X1048: $i > $o] :
( ! [X1049: $i] :
( ( in @ X1049 @ X1047 )
=> ! [X1050: $i] :
( ( in @ X1050 @ X1047 )
=> ( ( X1048 @ X1049 )
=> ( ( X1048 @ X1050 )
=> ( X1049 = X1050 ) ) ) ) )
=> ( ? [X1051: $i] :
( ( in @ X1051 @ X1047 )
& ( X1048 @ X1051 ) )
=> ( singleton @ ( dsetconstr @ X1047 @ X1048 ) ) ) )
=> ( ! [X1052: $i,X1053: $i > $o] :
( ( ex1 @ X1052 @ X1053 )
=> ? [X1054: $i] :
( ( in @ X1054 @ X1052 )
& ( X1053 @ X1054 ) ) )
=> ( ! [X1055: $i,X1056: $i > $o,X1057: $i] :
( ( in @ X1057 @ X1055 )
=> ( ( X1056 @ X1057 )
=> ( ! [X1058: $i] :
( ( in @ X1058 @ X1055 )
=> ( ( X1056 @ X1058 )
=> ( X1058 = X1057 ) ) )
=> ( ex1 @ X1055 @ X1056 ) ) ) )
=> ( ! [X1059: $i,X1060: $i > $o] :
( ! [X1061: $i] :
( ( in @ X1061 @ X1059 )
=> ! [X1062: $i] :
( ( in @ X1062 @ X1059 )
=> ( ( X1060 @ X1061 )
=> ( ( X1060 @ X1062 )
=> ( X1061 = X1062 ) ) ) ) )
=> ( ? [X1063: $i] :
( ( in @ X1063 @ X1059 )
& ( X1060 @ X1063 ) )
=> ( ex1 @ X1059 @ X1060 ) ) )
=> ( ! [X1064: $i,X1065: $i] :
( ( ( setadjoin @ X1064 @ emptyset )
= ( setadjoin @ X1065 @ emptyset ) )
=> ( X1064 = X1065 ) )
=> ( ! [X1066: $i,X1067: $i,X1068: $i] :
( ( in @ ( setadjoin @ X1068 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1066 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1066 @ ( setadjoin @ X1067 @ emptyset ) ) @ emptyset ) ) )
=> ( X1066 = X1068 ) )
=> ( ! [X1069: $i] :
( ( iskpair @ X1069 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1069 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1069 ) ) ) )
=> ( ! [X1070: $i] :
( ( singleton @ X1070 )
=> ( in @ ( setunion @ X1070 ) @ X1070 ) )
=> ( ! [X1071: $i,X1072: $i] :
( ( kfst @ ( kpair @ X1071 @ X1072 ) )
= X1071 )
=> ( ! [X1073: $i,X1074: $i,X1075: $i] :
( ( in @ X1075 @ ( cartprod @ X1073 @ X1074 ) )
=> ( in @ ( kfst @ X1075 ) @ X1073 ) )
=> ( ! [X1076: $i,X1077: $i,X1078: $i,X1079: $i] :
( ( ( setadjoin @ ( setadjoin @ X1076 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1076 @ ( setadjoin @ X1077 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1078 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1078 @ ( setadjoin @ X1079 @ emptyset ) ) @ emptyset ) ) )
=> ( X1076 = X1078 ) )
=> ( ! [X1080: $i,X1081: $i,X1082: $i,X1083: $i] :
( ( ( kpair @ X1080 @ X1081 )
= ( kpair @ X1082 @ X1083 ) )
=> ( X1080 = X1082 ) )
=> ( ! [X1084: $i,X1085: $i] :
( ( X1084 = X1085 )
=> ( ( setadjoin @ X1084 @ ( setadjoin @ X1085 @ emptyset ) )
= ( setadjoin @ X1084 @ emptyset ) ) )
=> ( ! [X1086: $i,X1087: $i] :
( ( X1086 = X1087 )
=> ( ( setadjoin @ ( setadjoin @ X1086 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1086 @ ( setadjoin @ X1087 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1086 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1088: $i,X1089: $i,X1090: $i,X1091: $i] :
( ( ( setadjoin @ ( setadjoin @ X1088 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1088 @ ( setadjoin @ X1089 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1090 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1090 @ ( setadjoin @ X1091 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1090 = X1091 )
=> ( X1089 = X1091 ) ) )
=> ( ! [X1092: $i,X1093: $i,X1094: $i] :
( ( ( setadjoin @ X1092 @ ( setadjoin @ X1093 @ emptyset ) )
= ( setadjoin @ X1094 @ emptyset ) )
=> ( X1092 = X1093 ) )
=> ( ! [X1095: $i,X1096: $i,X1097: $i,X1098: $i] :
( ( ( setadjoin @ ( setadjoin @ X1095 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1095 @ ( setadjoin @ X1096 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1097 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1097 @ ( setadjoin @ X1098 @ emptyset ) ) @ emptyset ) ) )
=> ( X1096 = X1098 ) )
=> ( ! [X1099: $i,X1100: $i,X1101: $i,X1102: $i] :
( ( ( kpair @ X1099 @ X1100 )
= ( kpair @ X1101 @ X1102 ) )
=> ( X1100 = X1102 ) )
=> ( ! [X1103: $i] :
( ( iskpair @ X1103 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1103 )
@ ^ [Z0: $i] :
( X1103
= ( kpair @ ( kfst @ X1103 ) @ Z0 ) ) ) ) )
=> ( ! [X1104: $i,X1105: $i] :
( ( ksnd @ ( kpair @ X1104 @ X1105 ) )
= X1105 )
=> ( ! [X1106: $i] :
( ( iskpair @ X1106 )
=> ( ( kpair @ ( kfst @ X1106 ) @ ( ksnd @ X1106 ) )
= X1106 ) )
=> ( ! [X1107: $i,X1108: $i,X1109: $i] :
( ( in @ X1109 @ ( cartprod @ X1107 @ X1108 ) )
=> ( in @ ( ksnd @ X1109 ) @ X1108 ) )
=> ( ! [X1110: $i,X1111: $i,X1112: $i,X1113: $i] :
( ( in @ ( kpair @ X1112 @ X1113 ) @ ( cartprod @ X1110 @ X1111 ) )
=> ( in @ X1112 @ X1110 ) )
=> ( ! [X1114: $i,X1115: $i,X1116: $i,X1117: $i] :
( ( in @ ( kpair @ X1116 @ X1117 ) @ ( cartprod @ X1114 @ X1115 ) )
=> ( in @ X1117 @ X1115 ) )
=> ( ! [X1118: $i,X1119: $i,X1120: $i] :
( ( in @ X1120 @ X1118 )
=> ! [X1121: $i] :
( ( in @ X1121 @ X1119 )
=> ( ( kpair @ X1120 @ X1121 )
= ( kpair @ X1120 @ X1121 ) ) ) )
=> ( ! [X1122: $i,X1123: $i,X1124: $i] :
( ( in @ X1124 @ X1122 )
=> ! [X1125: $i] :
( ( in @ X1125 @ X1123 )
=> ( ( kfst @ ( kpair @ X1124 @ X1125 ) )
= X1124 ) ) )
=> ( ! [X1126: $i,X1127: $i,X1128: $i] :
( ( in @ X1128 @ X1126 )
=> ! [X1129: $i] :
( ( in @ X1129 @ X1127 )
=> ( ( ksnd @ ( kpair @ X1128 @ X1129 ) )
= X1129 ) ) )
=> ( ! [X1130: $i,X1131: $i,X1132: $i] :
( ( in @ X1132 @ ( cartprod @ X1130 @ X1131 ) )
=> ( ( kpair @ ( kfst @ X1132 ) @ ( ksnd @ X1132 ) )
= X1132 ) )
=> ( ! [X1133: $i,X1134: $i,X1135: $i > $i > $o,X1136: $i] :
( ( in @ X1136 @ X1133 )
=> ! [X1137: $i] :
( ( in @ X1137 @ X1134 )
=> ( ( X1135 @ X1136 @ X1137 )
=> ( in @ ( kpair @ X1136 @ X1137 ) @ ( dpsetconstr @ X1133 @ X1134 @ X1135 ) ) ) ) )
=> ( ! [X1138: $i,X1139: $i,X1140: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1138 @ X1139 @ X1140 ) @ ( cartprod @ X1138 @ X1139 ) )
=> ( ! [X1141: $i,X1142: $i,X1143: $i > $i > $o] : ( breln @ X1141 @ X1142 @ ( dpsetconstr @ X1141 @ X1142 @ X1143 ) )
=> ( ! [X1144: $i,X1145: $i,X1146: $i > $i > $o,X1147: $i] :
( ( in @ X1147 @ X1144 )
=> ! [X1148: $i] :
( ( in @ X1148 @ X1145 )
=> ( ( in @ ( kpair @ X1147 @ X1148 ) @ ( dpsetconstr @ X1144 @ X1145 @ X1146 ) )
=> ( X1146 @ X1147 @ X1148 ) ) ) )
=> ( ! [X1149: $i,X1150: $i,X1151: $i > $i > $o,X1152: $i,X1153: $i] :
( ( in @ ( kpair @ X1152 @ X1153 ) @ ( dpsetconstr @ X1149 @ X1150 @ X1151 ) )
=> ( in @ X1152 @ X1149 ) )
=> ( ! [X1154: $i,X1155: $i,X1156: $i > $i > $o,X1157: $i,X1158: $i] :
( ( in @ ( kpair @ X1157 @ X1158 ) @ ( dpsetconstr @ X1154 @ X1155 @ X1156 ) )
=> ( in @ X1158 @ X1155 ) )
=> ( ! [X1159: $i,X1160: $i,X1161: $i > $i > $o,X1162: $i,X1163: $i] :
( ( in @ ( kpair @ X1162 @ X1163 ) @ ( dpsetconstr @ X1159 @ X1160 @ X1161 ) )
=> ( X1161 @ X1162 @ X1163 ) )
=> ( ! [X1164: $i,X1165: $i,X1166: $i] :
( ( func @ X1164 @ X1165 @ X1166 )
=> ! [X1167: $i] :
( ( in @ X1167 @ X1164 )
=> ( singleton
@ ( dsetconstr @ X1165
@ ^ [Z0: $i] : ( in @ ( kpair @ X1167 @ Z0 ) @ X1166 ) ) ) ) )
=> ( ! [X1168: $i,X1169: $i,X1170: $i] :
( ( func @ X1168 @ X1169 @ X1170 )
=> ! [X1171: $i] :
( ( in @ X1171 @ X1168 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1169
@ ^ [Z0: $i] : ( in @ ( kpair @ X1171 @ Z0 ) @ X1170 ) ) )
@ X1169 ) ) )
=> ( ! [X1172: $i,X1173: $i,X1174: $i] :
( ( func @ X1172 @ X1173 @ X1174 )
=> ! [X1175: $i] :
( ( in @ X1175 @ X1172 )
=> ( in @ ( ap @ X1172 @ X1173 @ X1174 @ X1175 ) @ X1173 ) ) )
=> ( ! [X1176: $i,X1177: $i,X1178: $i] :
( ( in @ X1178 @ ( funcSet @ X1176 @ X1177 ) )
=> ( func @ X1176 @ X1177 @ X1178 ) )
=> ( ! [X1179: $i,X1180: $i,X1181: $i] :
( ( in @ X1181 @ ( funcSet @ X1179 @ X1180 ) )
=> ! [X1182: $i] :
( ( in @ X1182 @ X1179 )
=> ( in @ ( ap @ X1179 @ X1180 @ X1181 @ X1182 ) @ X1180 ) ) )
=> ( ! [X1183: $i,X1184: $i,X1185: $i] :
( ( func @ X1183 @ X1184 @ X1185 )
=> ( in @ X1185 @ ( funcSet @ X1183 @ X1184 ) ) )
=> ( ! [X1186: $i,X1187: $i,X1188: $i > $i] :
( ! [X1189: $i] :
( ( in @ X1189 @ X1186 )
=> ( in @ ( X1188 @ X1189 ) @ X1187 ) )
=> ( func @ X1186 @ X1187
@ ( dpsetconstr @ X1186 @ X1187
@ ^ [Z0: $i] : ( $eq @ ( X1188 @ Z0 ) ) ) ) )
=> ( ! [X1190: $i,X1191: $i,X1192: $i > $i] :
( ! [X1193: $i] :
( ( in @ X1193 @ X1190 )
=> ( in @ ( X1192 @ X1193 ) @ X1191 ) )
=> ( func @ X1190 @ X1191 @ ( lam @ X1190 @ X1191 @ X1192 ) ) )
=> ( ! [X1194: $i,X1195: $i,X1196: $i > $i] :
( ! [X1197: $i] :
( ( in @ X1197 @ X1194 )
=> ( in @ ( X1196 @ X1197 ) @ X1195 ) )
=> ( in @ ( lam @ X1194 @ X1195 @ X1196 ) @ ( funcSet @ X1194 @ X1195 ) ) )
=> ( ! [X1198: $i,X1199: $i,X1200: $i] :
( ( breln @ X1198 @ X1199 @ X1200 )
=> ! [X1201: $i > $o] :
( ! [X1202: $i] :
( ( in @ X1202 @ X1198 )
=> ! [X1203: $i] :
( ( in @ X1203 @ X1199 )
=> ( ( in @ ( kpair @ X1202 @ X1203 ) @ X1200 )
=> ( X1201 @ ( kpair @ X1202 @ X1203 ) ) ) ) )
=> ! [X1204: $i] :
( ( in @ X1204 @ X1200 )
=> ( X1201 @ X1204 ) ) ) )
=> ( ! [X1205: $i,X1206: $i,X1207: $i] :
( ( breln @ X1205 @ X1206 @ X1207 )
=> ! [X1208: $i > $o] :
( ! [X1209: $i] :
( ( in @ X1209 @ X1205 )
=> ! [X1210: $i] :
( ( in @ X1210 @ X1206 )
=> ( ( in @ ( kpair @ X1209 @ X1210 ) @ X1207 )
=> ( X1208 @ ( kpair @ X1209 @ X1210 ) ) ) ) )
=> ! [X1211: $i] :
( ( in @ X1211 @ X1207 )
=> ( X1208 @ X1211 ) ) ) )
=> ( ! [X1212: $i,X1213: $i > $o] :
( ( ex1 @ X1212 @ X1213 )
=> ! [X1214: $i] :
( ( in @ X1214 @ X1212 )
=> ! [X1215: $i] :
( ( in @ X1215 @ X1212 )
=> ( ( X1213 @ X1214 )
=> ( ( X1213 @ X1215 )
=> ( X1214 = X1215 ) ) ) ) ) )
=> ( ! [X1216: $i,X1217: $i,X1218: $i] :
( ( func @ X1216 @ X1217 @ X1218 )
=> ! [X1219: $i] :
( ( in @ X1219 @ X1216 )
=> ( in @ ( kpair @ X1219 @ ( ap @ X1216 @ X1217 @ X1218 @ X1219 ) ) @ X1218 ) ) )
=> ( ! [X1220: $i,X1221: $i,X1222: $i] :
( ( in @ X1222 @ ( funcSet @ X1220 @ X1221 ) )
=> ! [X1223: $i] :
( ( in @ X1223 @ X1220 )
=> ( in @ ( kpair @ X1223 @ ( ap @ X1220 @ X1221 @ X1222 @ X1223 ) ) @ X1222 ) ) )
=> ( ! [X1224: $i,X1225: $i,X1226: $i] :
( ( func @ X1224 @ X1225 @ X1226 )
=> ! [X1227: $i] :
( ( in @ X1227 @ X1224 )
=> ! [X1228: $i] :
( ( in @ X1228 @ X1225 )
=> ( ( in @ ( kpair @ X1227 @ X1228 ) @ X1226 )
=> ( ( ap @ X1224 @ X1225 @ X1226 @ X1227 )
= X1228 ) ) ) ) )
=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X35: $i] :
( ( func @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[funcextLem]),powersetI]),cartprodmempaircEq]),funcGraphProp2]),c_0_203]),singletonsuniq]),setukpairinjL1]),powersetE]),c_0_204]),theprop]),setunionI]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setunionE]),setukpairinjL]),setukpairinjR11]),subPowSU]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),c_0_205]),setukpairinjR2]),setukpairinjR]),c_0_206]),c_0_207]),nonemptyImpWitness]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),uniqinunit]),cartprodpairmemEL]),cartprodpairmemER]),c_0_208]),notinsingleton]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),eqinunit]),c_0_209]),c_0_210]),singletonsswitch]),c_0_211]),c_0_212]),c_0_213]),upairsetE]),c_0_214]),c_0_215]),upairsetIL]),c_0_216]),c_0_217]),app]),upairsetIR]),infuncsetfunc]),ap2p]),c_0_218]),funcinfuncset]),c_0_219]),c_0_220]),vacuousDall]),c_0_221]),brelnall1]),quantDeMorgan1]),brelnall2]),c_0_222]),funcGraphProp1]),funcGraphProp3]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_223]),powersetI1]),powersetE1]),c_0_224]),inCongP]),in__Cong]),c_0_225]),c_0_226]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),emptyinPowerset]),setunion__Cong]),omega__Cong]),c_0_227]),c_0_228]),c_0_229]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),inPowerset]),powersetsubset]),c_0_230]),c_0_231]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),emptyInPowerset]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_232]),c_0_233]),c_0_234]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_235]),nonemptyE1]),c_0_236]),noeltsimpempty]),emptyI]),setext]),c_0_237]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_238]),c_0_239]),c_0_240]),c_0_241]),c_0_242]),wellorderingAx]),foundationAx]),c_0_243]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_244]) ).
thf(c_0_246,negated_conjecture,
! [X1229: $i,X1230: $i,X1232: $i,X1233: $i,X1234: $i,X1235: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i,X1240: $i,X1242: $i,X1243: $i,X1245: $i,X1246: $i,X1247: $i,X1248: $i,X1249: $i,X1251: $i,X1252: $i > $i > $o,X1253: $i,X1256: $i,X1258: $i,X1259: $i,X1260: $i,X1261: $i,X1263: $i,X1264: $i > $o,X1265: $i,X1266: $i > $o,X1267: $i,X1268: $i,X1269: $i > $o,X1270: $i,X1271: $i,X1272: $i > $o,X1273: $i,X1274: $i > $o,X1276: $i,X1277: $o,X1278: $i,X1279: $i,X1280: $o,X1281: $i,X1282: $i,X1283: $i > $o,X1285: $i,X1286: $i,X1289: $i,X1291: $i,X1293: $i,X1294: $i > $o,X1295: $i,X1296: $i,X1298: $i,X1299: $i > $o,X1300: $i,X1301: $i,X1302: $i,X1303: $i,X1304: $i,X1305: $i,X1306: $i,X1307: $i,X1308: $i,X1309: $i,X1310: $i,X1311: $o,X1312: $i,X1313: $i,X1314: $i,X1315: $i,X1316: $i,X1317: $i,X1319: $i,X1320: $i,X1321: $i,X1322: $i,X1323: $i,X1324: $i,X1325: $i,X1326: $i,X1327: $i,X1328: $i,X1329: $o,X1331: $i,X1332: $i,X1333: $i > $o,X1335: $i,X1336: $i,X1337: $i,X1339: $i,X1340: $i,X1341: $i,X1342: $i,X1343: $i,X1344: $i,X1345: $i,X1346: $i,X1347: $i,X1348: $i,X1349: $i,X1350: $i,X1351: $i,X1352: $i,X1353: $i,X1354: $i,X1355: $i > $o,X1356: $i,X1357: $i > $o,X1358: $i,X1359: $i,X1360: $i > $o,X1361: $i,X1363: $i,X1364: $i > $o,X1366: $i,X1367: $i,X1368: $i > $o,X1370: $i,X1371: $i,X1372: $i > $o,X1373: $i,X1375: $o,X1376: $i,X1377: $i > $o,X1379: $i,X1380: $i,X1381: $i > $o,X1382: $i,X1384: $i > $o,X1385: $i,X1387: $i > $o,X1388: $i,X1391: $i > $o,X1392: $i,X1394: $i,X1395: $i,X1396: $i,X1397: $i,X1398: $i,X1399: $i,X1400: $i,X1401: $i,X1402: $i > $o,X1403: $i,X1404: $i,X1405: $i > $o,X1406: $i > $o,X1409: $i,X1410: $i,X1411: $i,X1412: $i,X1413: $i,X1414: $i,X1415: $i,X1416: $i,X1417: $i > $o,X1418: $i,X1419: $i,X1420: $i > $o,X1421: $i > $o,X1424: $i,X1425: $i,X1426: $i > $o,X1427: $i > $o,X1430: $i,X1431: $i,X1433: $i,X1434: $i,X1435: $i,X1436: $i,X1437: $i,X1438: $i,X1440: $i,X1441: $i,X1442: $i,X1443: $i,X1444: $i,X1445: $i,X1446: $i,X1447: $i,X1448: $i,X1449: $i,X1450: $i,X1451: $i,X1452: $i,X1453: $i,X1454: $i,X1455: $i,X1456: $i,X1457: $i,X1458: $i,X1459: $i,X1460: $i,X1461: $i,X1462: $i,X1463: $i,X1464: $i,X1465: $i,X1466: $i,X1467: $i,X1468: $i,X1469: $i,X1470: $i,X1471: $i,X1472: $i,X1473: $i,X1474: $i,X1475: $i,X1476: $i,X1477: $i > $o,X1478: $i,X1479: $i > $o,X1480: $i,X1481: $i,X1482: $i,X1483: $i,X1484: $i,X1485: $i,X1486: $i,X1487: $i,X1488: $i,X1489: $i,X1490: $i,X1491: $o,X1492: $i,X1493: $i,X1494: $i,X1495: $i,X1496: $i,X1497: $i,X1498: $i,X1499: $i,X1500: $i,X1501: $i,X1502: $i,X1503: $i,X1504: $i,X1505: $i,X1506: $i,X1507: $i,X1508: $i,X1509: $i,X1510: $i,X1511: $i,X1512: $i,X1513: $i,X1514: $i,X1515: $i,X1516: $i,X1517: $i,X1518: $i,X1520: $i,X1521: $i,X1522: $i,X1523: $i,X1524: $i,X1525: $i,X1526: $i,X1527: $i,X1528: $i,X1529: $i,X1530: $i,X1531: $i,X1532: $i,X1533: $i,X1534: $i,X1535: $i,X1536: $i,X1537: $i,X1538: $i,X1539: $i,X1540: $i,X1541: $i,X1542: $i,X1543: $i,X1544: $i,X1545: $i,X1546: $i,X1547: $i,X1548: $i,X1549: $i,X1550: $i,X1551: $i,X1552: $i,X1553: $i,X1554: $i,X1555: $i,X1556: $i,X1557: $i,X1558: $i,X1559: $o,X1560: $i,X1561: $i,X1562: $i,X1563: $i,X1564: $i,X1565: $i,X1566: $i,X1567: $i,X1568: $i,X1569: $i,X1570: $i,X1571: $i,X1572: $i,X1573: $i,X1574: $i,X1575: $i,X1576: $i,X1577: $i,X1578: $i,X1579: $i,X1580: $i,X1581: $i,X1582: $i,X1583: $i,X1584: $i,X1585: $i,X1586: $i,X1587: $i,X1588: $i,X1589: $i,X1590: $i,X1591: $i,X1592: $i,X1593: $i,X1594: $i,X1595: $i,X1596: $i,X1597: $i,X1598: $i,X1599: $i,X1600: $i,X1601: $i,X1602: $i,X1603: $i,X1604: $i,X1605: $i,X1606: $i,X1607: $i,X1608: $i,X1609: $i,X1610: $i,X1611: $i,X1612: $i,X1613: $i,X1614: $i,X1615: $i,X1616: $i,X1617: $i,X1618: $i,X1621: $i,X1622: $i,X1623: $i,X1624: $i,X1625: $i,X1627: $i,X1628: $i,X1629: $i,X1630: $i,X1631: $i > $o,X1634: $i,X1635: $i,X1636: $i > $o,X1638: $i,X1639: $i > $o,X1640: $i,X1642: $i,X1643: $i > $o,X1646: $i,X1647: $i,X1648: $i,X1649: $i,X1650: $i,X1651: $i,X1652: $i,X1653: $i,X1654: $i,X1655: $i,X1656: $i,X1657: $i,X1658: $i,X1659: $i,X1660: $i,X1661: $i,X1662: $i,X1663: $i,X1664: $i,X1665: $i,X1666: $i,X1667: $i,X1668: $i,X1669: $i,X1670: $i,X1671: $i,X1672: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i,X1678: $i,X1679: $i,X1680: $i,X1681: $i,X1682: $i,X1683: $i,X1684: $i,X1685: $i,X1686: $i,X1687: $i,X1688: $i,X1689: $i,X1690: $i,X1691: $i,X1692: $i,X1693: $i,X1694: $i,X1695: $i,X1696: $i,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i,X1702: $i,X1703: $i,X1704: $i,X1705: $i,X1706: $i,X1707: $i,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i,X1713: $i,X1714: $i,X1715: $i,X1716: $i,X1717: $i,X1718: $i > $i > $o,X1719: $i,X1720: $i,X1721: $i,X1722: $i,X1723: $i > $i > $o,X1724: $i,X1725: $i,X1726: $i > $i > $o,X1727: $i,X1728: $i,X1729: $i > $i > $o,X1730: $i,X1731: $i,X1732: $i,X1733: $i,X1734: $i > $i > $o,X1735: $i,X1736: $i,X1737: $i,X1738: $i,X1739: $i > $i > $o,X1740: $i,X1741: $i,X1742: $i,X1743: $i,X1744: $i > $i > $o,X1745: $i,X1746: $i,X1747: $i,X1748: $i,X1749: $i,X1750: $i,X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1756: $i,X1757: $i,X1758: $i,X1759: $i,X1760: $i,X1761: $i,X1762: $i,X1763: $i,X1764: $i,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1769: $i,X1770: $i,X1771: $i > $i,X1773: $i,X1774: $i,X1775: $i > $i,X1777: $i,X1778: $i,X1779: $i > $i,X1781: $i,X1782: $i,X1783: $i,X1784: $i > $o,X1787: $i,X1788: $i,X1789: $i,X1790: $i,X1791: $i > $o,X1794: $i,X1795: $i,X1796: $i > $o,X1797: $i,X1798: $i,X1799: $i,X1800: $i,X1801: $i,X1802: $i,X1803: $i,X1804: $i,X1805: $i,X1806: $i,X1807: $i,X1808: $i,X1809: $i,X1810: $i,X1811: $i,X1816: $i] :
( ( ~ ( in @ ( esk1_2 @ X1229 @ X1230 ) @ X1229 )
| ~ ( in @ ( esk1_2 @ X1229 @ X1230 ) @ X1230 )
| ( X1229 = X1230 ) )
& ( ( in @ ( esk1_2 @ X1229 @ X1230 ) @ X1229 )
| ( in @ ( esk1_2 @ X1229 @ X1230 ) @ X1230 )
| ( X1229 = X1230 ) )
& ~ ( in @ X1232 @ emptyset )
& ( ~ ( in @ X1235 @ ( setadjoin @ X1233 @ X1234 ) )
| ( X1235 = X1233 )
| ( in @ X1235 @ X1234 ) )
& ( ( X1235 != X1233 )
| ( in @ X1235 @ ( setadjoin @ X1233 @ X1234 ) ) )
& ( ~ ( in @ X1235 @ X1234 )
| ( in @ X1235 @ ( setadjoin @ X1233 @ X1234 ) ) )
& ( ~ ( in @ X1237 @ ( powerset @ X1236 ) )
| ~ ( in @ X1238 @ X1237 )
| ( in @ X1238 @ X1236 ) )
& ( ( in @ ( esk2_2 @ X1239 @ X1240 ) @ X1240 )
| ( in @ X1240 @ ( powerset @ X1239 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1239 @ X1240 ) @ X1239 )
| ( in @ X1240 @ ( powerset @ X1239 ) ) )
& ( ( in @ X1243 @ ( esk3_2 @ X1242 @ X1243 ) )
| ~ ( in @ X1243 @ ( setunion @ X1242 ) ) )
& ( ( in @ ( esk3_2 @ X1242 @ X1243 ) @ X1242 )
| ~ ( in @ X1243 @ ( setunion @ X1242 ) ) )
& ( ~ ( in @ X1246 @ X1247 )
| ~ ( in @ X1247 @ X1245 )
| ( in @ X1246 @ ( setunion @ X1245 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1248 @ omega )
| ( in @ ( setadjoin @ X1248 @ X1248 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1249 ) @ omega )
| ~ ( in @ emptyset @ X1249 )
| ~ ( in @ X1251 @ omega )
| ( in @ X1251 @ X1249 ) )
& ( ( in @ ( esk4_1 @ X1249 ) @ X1249 )
| ~ ( in @ emptyset @ X1249 )
| ~ ( in @ X1251 @ omega )
| ( in @ X1251 @ X1249 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1249 ) @ ( esk4_1 @ X1249 ) ) @ X1249 )
| ~ ( in @ emptyset @ X1249 )
| ~ ( in @ X1251 @ omega )
| ( in @ X1251 @ X1249 ) )
& ( ( in @ ( esk7_3 @ X1252 @ X1253 @ X1256 ) @ X1253 )
| ~ ( in @ X1256 @ ( esk6_2 @ X1252 @ X1253 ) )
| ( in @ ( esk5_2 @ X1252 @ X1253 ) @ X1253 ) )
& ( ( X1252 @ ( esk7_3 @ X1252 @ X1253 @ X1256 ) @ X1256 )
| ~ ( in @ X1256 @ ( esk6_2 @ X1252 @ X1253 ) )
| ( in @ ( esk5_2 @ X1252 @ X1253 ) @ X1253 ) )
& ( ~ ( in @ X1259 @ X1253 )
| ~ ( X1252 @ X1259 @ X1258 )
| ( in @ X1258 @ ( esk6_2 @ X1252 @ X1253 ) )
| ( in @ ( esk5_2 @ X1252 @ X1253 ) @ X1253 ) )
& ( ( in @ ( esk7_3 @ X1252 @ X1253 @ X1256 ) @ X1253 )
| ~ ( in @ X1256 @ ( esk6_2 @ X1252 @ X1253 ) )
| ~ ( exu @ ( X1252 @ ( esk5_2 @ X1252 @ X1253 ) ) ) )
& ( ( X1252 @ ( esk7_3 @ X1252 @ X1253 @ X1256 ) @ X1256 )
| ~ ( in @ X1256 @ ( esk6_2 @ X1252 @ X1253 ) )
| ~ ( exu @ ( X1252 @ ( esk5_2 @ X1252 @ X1253 ) ) ) )
& ( ~ ( in @ X1259 @ X1253 )
| ~ ( X1252 @ X1259 @ X1258 )
| ( in @ X1258 @ ( esk6_2 @ X1252 @ X1253 ) )
| ~ ( exu @ ( X1252 @ ( esk5_2 @ X1252 @ X1253 ) ) ) )
& ( ( in @ ( esk8_1 @ X1260 ) @ X1260 )
| ~ ( in @ X1261 @ X1260 ) )
& ( ~ ( in @ X1263 @ ( esk8_1 @ X1260 ) )
| ~ ( in @ X1263 @ X1260 )
| ~ ( in @ X1261 @ X1260 ) )
& epred1_0
& ( ~ ( exu @ X1264 )
| ( X1264 @ ( descr @ X1264 ) ) )
& ( ~ ( in @ X1267 @ X1265 )
| ~ ( X1266 @ X1267 )
| ( in @ X1267 @ ( dsetconstr @ X1265 @ X1266 ) ) )
& ( ~ ( in @ X1270 @ ( dsetconstr @ X1268 @ X1269 ) )
| ( in @ X1270 @ X1268 ) )
& ( ~ ( in @ X1273 @ ( dsetconstr @ X1271 @ X1272 ) )
| ( X1272 @ X1273 ) )
& ( ( X1274 @ ( esk9_1 @ X1274 ) )
| ~ ( exu @ X1274 ) )
& ( ~ ( X1274 @ X1276 )
| ( ( esk9_1 @ X1274 )
= X1276 )
| ~ ( exu @ X1274 ) )
& ( ~ ( in @ X1278 @ ( prop2set @ X1277 ) )
| X1277 )
& ( ~ ( in @ X1279 @ emptyset )
| X1280 )
& ( ~ ( in @ X1281 @ emptyset )
| ~ $true )
& ~ ( in @ X1282 @ emptyset )
& ( ~ ( exu @ X1283 )
| ( X1283 @ ( esk10_1 @ X1283 ) ) )
& ( ( in @ ( esk12_2 @ X1285 @ X1286 ) @ X1286 )
| ( X1285 = X1286 )
| ( in @ ( esk11_2 @ X1285 @ X1286 ) @ X1285 ) )
& ( ~ ( in @ ( esk12_2 @ X1285 @ X1286 ) @ X1285 )
| ( X1285 = X1286 )
| ( in @ ( esk11_2 @ X1285 @ X1286 ) @ X1285 ) )
& ( ( in @ ( esk12_2 @ X1285 @ X1286 ) @ X1286 )
| ( X1285 = X1286 )
| ~ ( in @ ( esk11_2 @ X1285 @ X1286 ) @ X1286 ) )
& ( ~ ( in @ ( esk12_2 @ X1285 @ X1286 ) @ X1285 )
| ( X1285 = X1286 )
| ~ ( in @ ( esk11_2 @ X1285 @ X1286 ) @ X1286 ) )
& ( ( in @ ( esk13_1 @ X1289 ) @ X1289 )
| ( X1289 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1291 ) @ X1291 )
| ( X1291 = emptyset ) )
& ( ~ ( in @ X1295 @ ( dsetconstr @ X1293 @ X1294 ) )
| ( X1294 @ X1295 )
| ~ ( in @ X1295 @ X1293 ) )
& ( ~ ( X1294 @ X1295 )
| ( in @ X1295 @ ( dsetconstr @ X1293 @ X1294 ) )
| ~ ( in @ X1295 @ X1293 ) )
& ( ~ ( nonempty @ X1296 )
| ( in @ ( esk15_1 @ X1296 ) @ X1296 ) )
& ( ~ ( in @ X1300 @ X1298 )
| ~ ( X1299 @ X1300 )
| ( nonempty @ ( dsetconstr @ X1298 @ X1299 ) ) )
& ( ~ ( in @ X1302 @ X1301 )
| ( nonempty @ X1301 ) )
& ( in @ X1303 @ ( setadjoin @ X1303 @ X1304 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1307 @ X1306 )
| ( in @ X1307 @ ( setadjoin @ X1305 @ X1306 ) ) )
& ( ( in @ X1310 @ X1309 )
| X1311
| ( X1310 = X1308 )
| ~ ( in @ X1310 @ ( setadjoin @ X1308 @ X1309 ) ) )
& ( ~ X1311
| X1311
| ( X1310 = X1308 )
| ~ ( in @ X1310 @ ( setadjoin @ X1308 @ X1309 ) ) )
& ( ( in @ X1310 @ X1309 )
| X1311
| ~ X1311
| ~ ( in @ X1310 @ ( setadjoin @ X1308 @ X1309 ) ) )
& ( ~ X1311
| X1311
| ~ X1311
| ~ ( in @ X1310 @ ( setadjoin @ X1308 @ X1309 ) ) )
& ( ~ ( in @ X1314 @ ( setadjoin @ X1312 @ X1313 ) )
| ( X1314 = X1312 )
| ( in @ X1314 @ X1313 ) )
& ( ( dsetconstr @ X1315
@ ^ [Z0: $i] : $true )
= X1315 )
& ( ( in @ ( esk16_2 @ X1316 @ X1317 ) @ X1317 )
| ( in @ X1317 @ ( powerset @ X1316 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1316 @ X1317 ) @ X1316 )
| ( in @ X1317 @ ( powerset @ X1316 ) ) )
& ( in @ emptyset @ ( powerset @ X1319 ) )
& ( in @ emptyset @ ( powerset @ X1320 ) )
& ( ~ ( in @ X1322 @ ( powerset @ X1321 ) )
| ~ ( in @ X1323 @ X1322 )
| ( in @ X1323 @ X1321 ) )
& ( ~ ( in @ X1325 @ X1326 )
| ~ ( in @ X1326 @ X1324 )
| ( in @ X1325 @ ( setunion @ X1324 ) ) )
& ( ( in @ X1328 @ ( esk17_3 @ X1327 @ X1328 @ X1329 ) )
| X1329
| ~ ( in @ X1328 @ ( setunion @ X1327 ) ) )
& ( ( in @ ( esk17_3 @ X1327 @ X1328 @ X1329 ) @ X1327 )
| X1329
| ~ ( in @ X1328 @ ( setunion @ X1327 ) ) )
& ( ~ X1329
| X1329
| ~ ( in @ X1328 @ ( setunion @ X1327 ) ) )
& ( ~ ( in @ X1332 @ X1331 )
| ( in @ X1332 @ ( powerset @ ( setunion @ X1331 ) ) ) )
& ( ~ ( X1333 @ X1335 )
| ( X1335
= ( esk18_1 @ X1333 ) )
| ~ ( exu @ X1333 ) )
& ( ( X1336
!= ( esk18_1 @ X1333 ) )
| ( X1333 @ X1336 )
| ~ ( exu @ X1333 ) )
& ( ( in @ ( esk19_1 @ X1337 ) @ X1337 )
| ~ ( nonempty @ X1337 ) )
& ( $true
| ~ ( nonempty @ X1337 ) )
& ( ~ ( in @ X1339 @ ( setadjoin @ X1340 @ emptyset ) )
| ( X1339 = X1340 ) )
& ( ( X1341 = X1342 )
| ~ ( in @ X1342 @ ( setadjoin @ X1341 @ emptyset ) ) )
& ( ( X1343 != X1344 )
| ( in @ X1343 @ ( setadjoin @ X1344 @ emptyset ) ) )
& ( ~ ( in @ X1345 @ ( setadjoin @ X1346 @ emptyset ) )
| ( in @ X1346 @ ( setadjoin @ X1345 @ emptyset ) ) )
& ( ~ ( in @ X1349 @ ( setadjoin @ X1347 @ ( setadjoin @ X1348 @ emptyset ) ) )
| ( X1349 = X1347 )
| ( X1349 = X1348 ) )
& ( in @ X1350 @ ( setadjoin @ X1350 @ ( setadjoin @ X1351 @ emptyset ) ) )
& ( in @ X1353 @ ( setadjoin @ X1352 @ ( setadjoin @ X1353 @ emptyset ) ) )
& ( ~ ( in @ X1356 @ X1354 )
| ~ ( X1355 @ X1356 )
| ( ( dsetconstr @ X1354 @ X1355 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1358 @ emptyset )
| ( X1357 @ X1358 ) )
& ( ( in @ ( esk20_2 @ X1359 @ X1360 ) @ X1359 )
| ~ ( in @ X1361 @ X1359 )
| ( X1360 @ X1361 ) )
& ( ~ ( X1360 @ ( esk20_2 @ X1359 @ X1360 ) )
| ~ ( in @ X1361 @ X1359 )
| ( X1360 @ X1361 ) )
& ( ( in @ ( esk21_2 @ X1363 @ X1364 ) @ X1363 )
| ~ ( in @ X1366 @ X1363 )
| ~ ( X1364 @ X1366 ) )
& ( ( X1364 @ ( esk21_2 @ X1363 @ X1364 ) )
| ~ ( in @ X1366 @ X1363 )
| ~ ( X1364 @ X1366 ) )
& ( ( in @ ( esk22_2 @ X1367 @ X1368 ) @ X1367 )
| ~ ( in @ X1370 @ X1367 )
| ~ ( X1368 @ X1370 ) )
& ( ( X1368 @ ( esk22_2 @ X1367 @ X1368 ) )
| ~ ( in @ X1370 @ X1367 )
| ~ ( X1368 @ X1370 ) )
& ( ( in @ ( esk23_2 @ X1371 @ X1372 ) @ X1371 )
| ~ ( in @ X1373 @ X1371 )
| ( X1372 @ X1373 ) )
& ( ~ ( X1372 @ ( esk23_2 @ X1371 @ X1372 ) )
| ~ ( in @ X1373 @ X1371 )
| ( X1372 @ X1373 ) )
& ( ~ X1375
| ( in @ emptyset @ ( prop2set @ X1375 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1376 @ X1377 ) @ X1376 )
| ~ ( in @ X1379 @ X1376 )
| ~ ( X1377 @ X1379 ) )
& ( ( X1377 @ ( esk24_2 @ X1376 @ X1377 ) )
| ~ ( in @ X1379 @ X1376 )
| ~ ( X1377 @ X1379 ) )
& ( ( in @ ( esk25_2 @ X1380 @ X1381 ) @ X1380 )
| ~ ( in @ X1382 @ X1380 )
| ( X1381 @ X1382 ) )
& ( ~ ( X1381 @ ( esk25_2 @ X1380 @ X1381 ) )
| ~ ( in @ X1382 @ X1380 )
| ( X1381 @ X1382 ) )
& ( ( X1384 @ ( esk26_2 @ X1384 @ X1385 ) )
| ~ ( X1384 @ X1385 )
| ( exu @ X1384 ) )
& ( ( X1385
!= ( esk26_2 @ X1384 @ X1385 ) )
| ~ ( X1384 @ X1385 )
| ( exu @ X1384 ) )
& ( ( X1387 @ ( esk27_1 @ X1387 ) )
| ( exu @ X1387 )
| ~ ( X1387 @ X1388 ) )
& ( ( X1387 @ ( esk28_1 @ X1387 ) )
| ( exu @ X1387 )
| ~ ( X1387 @ X1388 ) )
& ( ( ( esk27_1 @ X1387 )
!= ( esk28_1 @ X1387 ) )
| ( exu @ X1387 )
| ~ ( X1387 @ X1388 ) )
& ( ~ ( X1391 @ ( esk29_2 @ X1391 @ X1392 ) )
| ( ( esk29_2 @ X1391 @ X1392 )
!= X1392 )
| ( exu @ X1391 ) )
& ( ( X1391 @ ( esk29_2 @ X1391 @ X1392 ) )
| ( ( esk29_2 @ X1391 @ X1392 )
= X1392 )
| ( exu @ X1391 ) )
& ( ( X1394 != X1395 )
| ( X1396 != X1397 )
| ~ ( in @ X1396 @ X1394 )
| ( in @ X1397 @ X1395 ) )
& ( ~ ( in @ X1400 @ X1398 )
| ( in @ X1401 @ X1399 )
| ( X1400 != X1401 )
| ( X1398 != X1399 ) )
& ( ~ ( in @ X1401 @ X1399 )
| ( in @ X1400 @ X1398 )
| ( X1400 != X1401 )
| ( X1398 != X1399 ) )
& ( ~ ( exu @ X1402 )
| ~ ( X1402 @ X1403 )
| ~ ( X1402 @ X1404 )
| ( X1403 = X1404 ) )
& ( ~ ( exu @ X1405 )
| ( exu @ X1406 )
| ( ( esk30_2 @ X1405 @ X1406 )
= ( esk31_2 @ X1405 @ X1406 ) ) )
& ( ~ ( exu @ X1406 )
| ( exu @ X1405 )
| ( ( esk30_2 @ X1405 @ X1406 )
= ( esk31_2 @ X1405 @ X1406 ) ) )
& ( ~ ( exu @ X1405 )
| ( exu @ X1406 )
| ~ ( X1405 @ ( esk30_2 @ X1405 @ X1406 ) )
| ~ ( X1406 @ ( esk31_2 @ X1405 @ X1406 ) ) )
& ( ~ ( exu @ X1406 )
| ( exu @ X1405 )
| ~ ( X1405 @ ( esk30_2 @ X1405 @ X1406 ) )
| ~ ( X1406 @ ( esk31_2 @ X1405 @ X1406 ) ) )
& ( ~ ( exu @ X1405 )
| ( exu @ X1406 )
| ( X1405 @ ( esk30_2 @ X1405 @ X1406 ) )
| ( X1406 @ ( esk31_2 @ X1405 @ X1406 ) ) )
& ( ~ ( exu @ X1406 )
| ( exu @ X1405 )
| ( X1405 @ ( esk30_2 @ X1405 @ X1406 ) )
| ( X1406 @ ( esk31_2 @ X1405 @ X1406 ) ) )
& ( emptyset = emptyset )
& ( ( X1409 != X1410 )
| ( X1411 != X1412 )
| ( ( setadjoin @ X1409 @ X1411 )
= ( setadjoin @ X1410 @ X1412 ) ) )
& ( ( X1413 != X1414 )
| ( ( powerset @ X1413 )
= ( powerset @ X1414 ) ) )
& ( ( X1415 != X1416 )
| ( ( setunion @ X1415 )
= ( setunion @ X1416 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1417 )
| ~ ( X1417 @ X1418 )
| ~ ( X1417 @ X1419 )
| ( X1418 = X1419 ) )
& ( ( ( esk32_2 @ X1420 @ X1421 )
= ( esk33_2 @ X1420 @ X1421 ) )
| ~ ( exu @ X1420 )
| ~ ( exu @ X1421 )
| ( ( descr @ X1420 )
= ( descr @ X1421 ) ) )
& ( ~ ( X1420 @ ( esk32_2 @ X1420 @ X1421 ) )
| ~ ( X1421 @ ( esk33_2 @ X1420 @ X1421 ) )
| ~ ( exu @ X1420 )
| ~ ( exu @ X1421 )
| ( ( descr @ X1420 )
= ( descr @ X1421 ) ) )
& ( ( X1420 @ ( esk32_2 @ X1420 @ X1421 ) )
| ( X1421 @ ( esk33_2 @ X1420 @ X1421 ) )
| ~ ( exu @ X1420 )
| ~ ( exu @ X1421 )
| ( ( descr @ X1420 )
= ( descr @ X1421 ) ) )
& ( ( in @ ( esk34_4 @ X1424 @ X1425 @ X1426 @ X1427 ) @ X1424 )
| ( ( dsetconstr @ X1424 @ X1426 )
= ( dsetconstr @ X1425 @ X1427 ) )
| ( X1424 != X1425 ) )
& ( ( in @ ( esk35_4 @ X1424 @ X1425 @ X1426 @ X1427 ) @ X1425 )
| ( ( dsetconstr @ X1424 @ X1426 )
= ( dsetconstr @ X1425 @ X1427 ) )
| ( X1424 != X1425 ) )
& ( ( ( esk34_4 @ X1424 @ X1425 @ X1426 @ X1427 )
= ( esk35_4 @ X1424 @ X1425 @ X1426 @ X1427 ) )
| ( ( dsetconstr @ X1424 @ X1426 )
= ( dsetconstr @ X1425 @ X1427 ) )
| ( X1424 != X1425 ) )
& ( ~ ( X1426 @ ( esk34_4 @ X1424 @ X1425 @ X1426 @ X1427 ) )
| ~ ( X1427 @ ( esk35_4 @ X1424 @ X1425 @ X1426 @ X1427 ) )
| ( ( dsetconstr @ X1424 @ X1426 )
= ( dsetconstr @ X1425 @ X1427 ) )
| ( X1424 != X1425 ) )
& ( ( X1426 @ ( esk34_4 @ X1424 @ X1425 @ X1426 @ X1427 ) )
| ( X1427 @ ( esk35_4 @ X1424 @ X1425 @ X1426 @ X1427 ) )
| ( ( dsetconstr @ X1424 @ X1426 )
= ( dsetconstr @ X1425 @ X1427 ) )
| ( X1424 != X1425 ) )
& ( ( in @ ( esk36_2 @ X1430 @ X1431 ) @ X1430 )
| ( subset @ X1430 @ X1431 ) )
& ( ~ ( in @ ( esk36_2 @ X1430 @ X1431 ) @ X1431 )
| ( subset @ X1430 @ X1431 ) )
& ( ( X1433 != X1434 )
| ( subset @ X1434 @ X1433 ) )
& ( ( X1435 != X1436 )
| ( subset @ X1435 @ X1436 ) )
& ( ( in @ ( esk37_2 @ X1437 @ X1438 ) @ X1437 )
| ( subset @ X1437 @ X1438 ) )
& ( ~ ( in @ ( esk37_2 @ X1437 @ X1438 ) @ X1438 )
| ( subset @ X1437 @ X1438 ) )
& ( subset @ emptyset @ X1440 )
& ( ~ ( subset @ X1441 @ X1442 )
| ~ ( in @ X1443 @ X1441 )
| ( in @ X1443 @ X1442 ) )
& ( ~ ( subset @ X1444 @ X1445 )
| ( in @ X1446 @ X1445 )
| ~ ( in @ X1446 @ X1444 ) )
& ( ~ ( in @ X1449 @ X1447 )
| ( in @ X1449 @ X1448 )
| ~ ( subset @ X1447 @ X1448 ) )
& ( ( subset @ X1450 @ X1451 )
| ( X1450 != X1451 ) )
& ( ~ ( in @ X1454 @ X1452 )
| ( in @ X1454 @ X1453 )
| ( X1452 != X1453 ) )
& ( subset @ X1455 @ X1455 )
& ( ~ ( subset @ X1456 @ X1457 )
| ~ ( subset @ X1457 @ X1458 )
| ( subset @ X1456 @ X1458 ) )
& ( subset @ X1460 @ ( setadjoin @ X1459 @ X1460 ) )
& ( ~ ( subset @ X1461 @ X1463 )
| ( subset @ X1461 @ ( setadjoin @ X1462 @ X1463 ) ) )
& ( ~ ( subset @ X1464 @ X1465 )
| ( in @ X1464 @ ( powerset @ X1465 ) ) )
& ( ~ ( subset @ X1466 @ X1467 )
| ~ ( subset @ X1467 @ X1466 )
| ( X1466 = X1467 ) )
& ( ~ ( subset @ X1468 @ emptyset )
| ( X1468 = emptyset ) )
& ( ~ ( subset @ X1470 @ X1469 )
| ( in @ X1470 @ ( powerset @ X1469 ) ) )
& ( ~ ( in @ X1472 @ ( powerset @ X1471 ) )
| ( subset @ X1472 @ X1471 ) )
& ( in @ X1473 @ ( powerset @ X1473 ) )
& ( ~ ( subset @ X1474 @ X1475 )
| ( subset @ ( powerset @ X1474 ) @ ( powerset @ X1475 ) ) )
& ( in @ ( dsetconstr @ X1476 @ X1477 ) @ ( powerset @ X1476 ) )
& ( subset @ ( dsetconstr @ X1478 @ X1479 ) @ X1478 )
& ( ~ ( in @ X1482 @ X1480 )
| ( in @ X1482 @ ( binunion @ X1480 @ X1481 ) ) )
& ( in @ X1484 @ ( setadjoin @ X1483 @ ( setadjoin @ X1484 @ emptyset ) ) )
& ( ~ ( in @ X1487 @ X1486 )
| ( in @ X1487 @ ( binunion @ X1485 @ X1486 ) ) )
& ( ( in @ X1490 @ X1489 )
| X1491
| ( in @ X1490 @ X1488 )
| ~ ( in @ X1490 @ ( binunion @ X1488 @ X1489 ) ) )
& ( ~ X1491
| X1491
| ( in @ X1490 @ X1488 )
| ~ ( in @ X1490 @ ( binunion @ X1488 @ X1489 ) ) )
& ( ( in @ X1490 @ X1489 )
| X1491
| ~ X1491
| ~ ( in @ X1490 @ ( binunion @ X1488 @ X1489 ) ) )
& ( ~ X1491
| X1491
| ~ X1491
| ~ ( in @ X1490 @ ( binunion @ X1488 @ X1489 ) ) )
& ( ~ ( in @ X1494 @ ( binunion @ X1492 @ X1493 ) )
| ( in @ X1494 @ X1492 )
| ( in @ X1494 @ X1493 ) )
& ( subset @ X1495 @ ( binunion @ X1495 @ X1496 ) )
& ( subset @ X1498 @ ( binunion @ X1497 @ X1498 ) )
& ( ~ ( in @ X1501 @ X1499 )
| ~ ( in @ X1501 @ X1500 )
| ( in @ X1501 @ ( binintersect @ X1499 @ X1500 ) ) )
& ( ~ ( subset @ X1504 @ X1502 )
| ~ ( subset @ X1504 @ X1503 )
| ( subset @ X1504 @ ( binintersect @ X1502 @ X1503 ) ) )
& ( ~ ( in @ X1507 @ ( binintersect @ X1505 @ X1506 ) )
| ( in @ X1507 @ X1505 ) )
& ( subset @ ( binintersect @ X1508 @ X1509 ) @ X1508 )
& ( ~ ( subset @ X1510 @ X1511 )
| ( ( binintersect @ X1510 @ X1511 )
= X1510 ) )
& ( ( ( binintersect @ X1512 @ X1513 )
!= X1513 )
| ( subset @ X1513 @ X1512 ) )
& ( ~ ( in @ X1516 @ ( binintersect @ X1514 @ X1515 ) )
| ( in @ X1516 @ X1515 ) )
& ( ( in @ ( esk38_2 @ X1517 @ X1518 ) @ X1517 )
| ( ( binintersect @ X1517 @ X1518 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1517 @ X1518 ) @ X1518 )
| ( ( binintersect @ X1517 @ X1518 )
= emptyset ) )
& ( subset @ ( binintersect @ X1520 @ X1521 ) @ X1521 )
& ( ~ ( subset @ X1523 @ X1522 )
| ( ( binintersect @ X1522 @ X1523 )
= X1523 ) )
& ( ( ( binintersect @ X1524 @ X1525 )
!= X1524 )
| ( subset @ X1524 @ X1525 ) )
& ( ( binintersect @ X1526 @ ( binunion @ X1527 @ X1528 ) )
= ( binunion @ ( binintersect @ X1526 @ X1527 ) @ ( binintersect @ X1526 @ X1528 ) ) )
& ( ~ ( in @ X1531 @ X1529 )
| ( in @ X1531 @ X1530 )
| ( in @ X1531 @ ( setminus @ X1529 @ X1530 ) ) )
& ( ~ ( in @ X1534 @ ( setminus @ X1532 @ X1533 ) )
| ( in @ X1534 @ X1532 ) )
& ( ~ ( in @ X1537 @ ( setminus @ X1535 @ X1536 ) )
| ~ ( in @ X1537 @ X1536 ) )
& ( ~ ( subset @ X1538 @ X1539 )
| ( ( setminus @ X1538 @ X1539 )
= emptyset ) )
& ( ( in @ X1542 @ ( setminus @ X1540 @ X1541 ) )
| ~ ( in @ X1542 @ X1540 )
| ( in @ X1542 @ X1541 ) )
& ( ( in @ X1545 @ ( setminus @ X1543 @ X1544 ) )
| ( in @ X1545 @ X1544 )
| ~ ( in @ X1545 @ X1543 ) )
& ( ( in @ X1548 @ X1546 )
| ~ ( in @ X1548 @ ( setminus @ X1546 @ X1547 ) ) )
& ( ~ ( in @ X1551 @ X1550 )
| ~ ( in @ X1551 @ ( setminus @ X1549 @ X1550 ) ) )
& ( subset @ ( setminus @ X1552 @ X1553 ) @ X1552 )
& ( ( ( setminus @ X1554 @ X1555 )
!= emptyset )
| ( subset @ X1554 @ X1555 ) )
& ( ~ ( in @ X1558 @ X1556 )
| X1559
| ( in @ X1558 @ X1556 )
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ( in @ X1558 @ X1557 )
| X1559
| ( in @ X1558 @ X1556 )
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ~ X1559
| X1559
| ( in @ X1558 @ X1556 )
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ~ ( in @ X1558 @ X1556 )
| X1559
| ~ ( in @ X1558 @ X1557 )
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ( in @ X1558 @ X1557 )
| X1559
| ~ ( in @ X1558 @ X1557 )
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ~ X1559
| X1559
| ~ ( in @ X1558 @ X1557 )
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ~ ( in @ X1558 @ X1556 )
| X1559
| ~ X1559
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ( in @ X1558 @ X1557 )
| X1559
| ~ X1559
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ~ X1559
| X1559
| ~ X1559
| ~ ( in @ X1558 @ ( symdiff @ X1556 @ X1557 ) ) )
& ( ~ ( in @ X1562 @ X1560 )
| ( in @ X1562 @ X1561 )
| ( in @ X1562 @ ( symdiff @ X1560 @ X1561 ) ) )
& ( ( in @ X1565 @ X1563 )
| ~ ( in @ X1565 @ X1564 )
| ( in @ X1565 @ ( symdiff @ X1563 @ X1564 ) ) )
& ( ~ ( in @ X1568 @ X1566 )
| ~ ( in @ X1568 @ X1567 )
| ~ ( in @ X1568 @ ( symdiff @ X1566 @ X1567 ) ) )
& ( ( in @ X1571 @ X1569 )
| ( in @ X1571 @ X1570 )
| ~ ( in @ X1571 @ ( symdiff @ X1569 @ X1570 ) ) )
& ( in @ X1573 @ ( setadjoin @ X1572 @ ( setadjoin @ X1573 @ emptyset ) ) )
& ( in @ X1574 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1574 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1574 @ ( setadjoin @ X1575 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1577 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1576 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1576 @ ( setadjoin @ X1577 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1578 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1578 @ ( setadjoin @ X1579 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1580 @ X1581 ) )
& ( ~ ( in @ X1583 @ X1582 )
| ( subset @ ( setadjoin @ X1583 @ emptyset ) @ X1582 ) )
& ( ~ ( in @ X1585 @ X1584 )
| ( in @ ( setadjoin @ X1585 @ emptyset ) @ ( powerset @ X1584 ) ) )
& ( ~ ( in @ X1588 @ X1586 )
| ( in @ ( setadjoin @ X1588 @ emptyset ) @ ( powerset @ ( binunion @ X1586 @ X1587 ) ) ) )
& ( ~ ( in @ X1591 @ ( setadjoin @ X1589 @ ( setadjoin @ X1590 @ emptyset ) ) )
| ( X1591 = X1589 )
| ( X1591 = X1590 ) )
& ( ~ ( in @ X1594 @ X1592 )
| ~ ( in @ X1595 @ X1593 )
| ( subset @ ( setadjoin @ X1594 @ ( setadjoin @ X1595 @ emptyset ) ) @ ( binunion @ X1592 @ X1593 ) ) )
& ( ~ ( in @ X1598 @ X1596 )
| ~ ( in @ X1599 @ X1597 )
| ( in @ ( setadjoin @ X1598 @ ( setadjoin @ X1599 @ emptyset ) ) @ ( powerset @ ( binunion @ X1596 @ X1597 ) ) ) )
& ( ~ ( in @ X1602 @ X1600 )
| ~ ( in @ X1603 @ X1601 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1602 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1602 @ ( setadjoin @ X1603 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1600 @ X1601 ) ) ) )
& ( ~ ( in @ X1606 @ X1604 )
| ~ ( in @ X1607 @ X1605 )
| ( in @ ( setadjoin @ ( setadjoin @ X1606 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1606 @ ( setadjoin @ X1607 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1604 @ X1605 ) ) ) ) )
& ( ~ ( in @ X1610 @ X1608 )
| ~ ( in @ X1611 @ X1609 )
| ( in @ ( kpair @ X1610 @ X1611 ) @ ( powerset @ ( powerset @ ( binunion @ X1608 @ X1609 ) ) ) ) )
& ( ~ ( in @ X1614 @ X1612 )
| ~ ( in @ X1615 @ X1613 )
| ( in @ ( kpair @ X1614 @ X1615 ) @ ( cartprod @ X1612 @ X1613 ) ) )
& ( ( in @ ( esk39_3 @ X1616 @ X1617 @ X1618 ) @ X1616 )
| ~ ( in @ X1618 @ ( cartprod @ X1616 @ X1617 ) ) )
& ( ( in @ ( esk40_3 @ X1616 @ X1617 @ X1618 ) @ X1617 )
| ~ ( in @ X1618 @ ( cartprod @ X1616 @ X1617 ) ) )
& ( ( X1618
= ( kpair @ ( esk39_3 @ X1616 @ X1617 @ X1618 ) @ ( esk40_3 @ X1616 @ X1617 @ X1618 ) ) )
| ~ ( in @ X1618 @ ( cartprod @ X1616 @ X1617 ) ) )
& ( ~ ( in @ X1623 @ ( cartprod @ X1621 @ X1622 ) )
| ( iskpair @ X1623 ) )
& ( ( in @ ( esk41_2 @ X1624 @ X1625 ) @ X1624 )
| ~ ( in @ X1625 @ ( setunion @ X1624 ) ) )
& ( ( in @ X1625 @ ( esk41_2 @ X1624 @ X1625 ) )
| ~ ( in @ X1625 @ ( setunion @ X1624 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1627 @ emptyset ) ) @ X1627 )
& ( subset @ X1628 @ ( setunion @ ( setadjoin @ X1628 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1629 @ emptyset ) )
= X1629 )
& ( ( in @ ( esk42_2 @ X1630 @ X1631 ) @ X1630 )
| ~ ( in @ X1634 @ X1630 )
| ~ ( X1631 @ X1634 )
| ( singleton @ ( dsetconstr @ X1630 @ X1631 ) ) )
& ( ( in @ ( esk43_2 @ X1630 @ X1631 ) @ X1630 )
| ~ ( in @ X1634 @ X1630 )
| ~ ( X1631 @ X1634 )
| ( singleton @ ( dsetconstr @ X1630 @ X1631 ) ) )
& ( ( X1631 @ ( esk42_2 @ X1630 @ X1631 ) )
| ~ ( in @ X1634 @ X1630 )
| ~ ( X1631 @ X1634 )
| ( singleton @ ( dsetconstr @ X1630 @ X1631 ) ) )
& ( ( X1631 @ ( esk43_2 @ X1630 @ X1631 ) )
| ~ ( in @ X1634 @ X1630 )
| ~ ( X1631 @ X1634 )
| ( singleton @ ( dsetconstr @ X1630 @ X1631 ) ) )
& ( ( ( esk42_2 @ X1630 @ X1631 )
!= ( esk43_2 @ X1630 @ X1631 ) )
| ~ ( in @ X1634 @ X1630 )
| ~ ( X1631 @ X1634 )
| ( singleton @ ( dsetconstr @ X1630 @ X1631 ) ) )
& ( ( in @ ( esk44_2 @ X1635 @ X1636 ) @ X1635 )
| ~ ( ex1 @ X1635 @ X1636 ) )
& ( ( X1636 @ ( esk44_2 @ X1635 @ X1636 ) )
| ~ ( ex1 @ X1635 @ X1636 ) )
& ( ( in @ ( esk45_3 @ X1638 @ X1639 @ X1640 ) @ X1638 )
| ( ex1 @ X1638 @ X1639 )
| ~ ( X1639 @ X1640 )
| ~ ( in @ X1640 @ X1638 ) )
& ( ( X1639 @ ( esk45_3 @ X1638 @ X1639 @ X1640 ) )
| ( ex1 @ X1638 @ X1639 )
| ~ ( X1639 @ X1640 )
| ~ ( in @ X1640 @ X1638 ) )
& ( ( ( esk45_3 @ X1638 @ X1639 @ X1640 )
!= X1640 )
| ( ex1 @ X1638 @ X1639 )
| ~ ( X1639 @ X1640 )
| ~ ( in @ X1640 @ X1638 ) )
& ( ( in @ ( esk46_2 @ X1642 @ X1643 ) @ X1642 )
| ~ ( in @ X1646 @ X1642 )
| ~ ( X1643 @ X1646 )
| ( ex1 @ X1642 @ X1643 ) )
& ( ( in @ ( esk47_2 @ X1642 @ X1643 ) @ X1642 )
| ~ ( in @ X1646 @ X1642 )
| ~ ( X1643 @ X1646 )
| ( ex1 @ X1642 @ X1643 ) )
& ( ( X1643 @ ( esk46_2 @ X1642 @ X1643 ) )
| ~ ( in @ X1646 @ X1642 )
| ~ ( X1643 @ X1646 )
| ( ex1 @ X1642 @ X1643 ) )
& ( ( X1643 @ ( esk47_2 @ X1642 @ X1643 ) )
| ~ ( in @ X1646 @ X1642 )
| ~ ( X1643 @ X1646 )
| ( ex1 @ X1642 @ X1643 ) )
& ( ( ( esk46_2 @ X1642 @ X1643 )
!= ( esk47_2 @ X1642 @ X1643 ) )
| ~ ( in @ X1646 @ X1642 )
| ~ ( X1643 @ X1646 )
| ( ex1 @ X1642 @ X1643 ) )
& ( ( ( setadjoin @ X1647 @ emptyset )
!= ( setadjoin @ X1648 @ emptyset ) )
| ( X1647 = X1648 ) )
& ( ~ ( in @ ( setadjoin @ X1651 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1649 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1649 @ ( setadjoin @ X1650 @ emptyset ) ) @ emptyset ) ) )
| ( X1649 = X1651 ) )
& ( ~ ( iskpair @ X1652 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1652 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1652 ) ) ) )
& ( ~ ( singleton @ X1653 )
| ( in @ ( setunion @ X1653 ) @ X1653 ) )
& ( ( kfst @ ( kpair @ X1654 @ X1655 ) )
= X1654 )
& ( ~ ( in @ X1658 @ ( cartprod @ X1656 @ X1657 ) )
| ( in @ ( kfst @ X1658 ) @ X1656 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1659 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1659 @ ( setadjoin @ X1660 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1661 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1661 @ ( setadjoin @ X1662 @ emptyset ) ) @ emptyset ) ) )
| ( X1659 = X1661 ) )
& ( ( ( kpair @ X1663 @ X1664 )
!= ( kpair @ X1665 @ X1666 ) )
| ( X1663 = X1665 ) )
& ( ( X1667 != X1668 )
| ( ( setadjoin @ X1667 @ ( setadjoin @ X1668 @ emptyset ) )
= ( setadjoin @ X1667 @ emptyset ) ) )
& ( ( X1669 != X1670 )
| ( ( setadjoin @ ( setadjoin @ X1669 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1669 @ ( setadjoin @ X1670 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1669 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1671 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1671 @ ( setadjoin @ X1672 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1673 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1673 @ ( setadjoin @ X1674 @ emptyset ) ) @ emptyset ) ) )
| ( X1673 != X1674 )
| ( X1672 = X1674 ) )
& ( ( ( setadjoin @ X1675 @ ( setadjoin @ X1676 @ emptyset ) )
!= ( setadjoin @ X1677 @ emptyset ) )
| ( X1675 = X1676 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1678 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1678 @ ( setadjoin @ X1679 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1680 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1680 @ ( setadjoin @ X1681 @ emptyset ) ) @ emptyset ) ) )
| ( X1679 = X1681 ) )
& ( ( ( kpair @ X1682 @ X1683 )
!= ( kpair @ X1684 @ X1685 ) )
| ( X1683 = X1685 ) )
& ( ~ ( iskpair @ X1686 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1686 )
@ ^ [Z0: $i] :
( X1686
= ( kpair @ ( kfst @ X1686 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X1687 @ X1688 ) )
= X1688 )
& ( ~ ( iskpair @ X1689 )
| ( ( kpair @ ( kfst @ X1689 ) @ ( ksnd @ X1689 ) )
= X1689 ) )
& ( ~ ( in @ X1692 @ ( cartprod @ X1690 @ X1691 ) )
| ( in @ ( ksnd @ X1692 ) @ X1691 ) )
& ( ~ ( in @ ( kpair @ X1695 @ X1696 ) @ ( cartprod @ X1693 @ X1694 ) )
| ( in @ X1695 @ X1693 ) )
& ( ~ ( in @ ( kpair @ X1699 @ X1700 ) @ ( cartprod @ X1697 @ X1698 ) )
| ( in @ X1700 @ X1698 ) )
& ( ~ ( in @ X1703 @ X1701 )
| ~ ( in @ X1704 @ X1702 )
| ( ( kpair @ X1703 @ X1704 )
= ( kpair @ X1703 @ X1704 ) ) )
& ( ~ ( in @ X1707 @ X1705 )
| ~ ( in @ X1708 @ X1706 )
| ( ( kfst @ ( kpair @ X1707 @ X1708 ) )
= X1707 ) )
& ( ~ ( in @ X1711 @ X1709 )
| ~ ( in @ X1712 @ X1710 )
| ( ( ksnd @ ( kpair @ X1711 @ X1712 ) )
= X1712 ) )
& ( ~ ( in @ X1715 @ ( cartprod @ X1713 @ X1714 ) )
| ( ( kpair @ ( kfst @ X1715 ) @ ( ksnd @ X1715 ) )
= X1715 ) )
& ( ~ ( in @ X1719 @ X1716 )
| ~ ( in @ X1720 @ X1717 )
| ~ ( X1718 @ X1719 @ X1720 )
| ( in @ ( kpair @ X1719 @ X1720 ) @ ( dpsetconstr @ X1716 @ X1717 @ X1718 ) ) )
& ( subset @ ( dpsetconstr @ X1721 @ X1722 @ X1723 ) @ ( cartprod @ X1721 @ X1722 ) )
& ( breln @ X1724 @ X1725 @ ( dpsetconstr @ X1724 @ X1725 @ X1726 ) )
& ( ~ ( in @ X1730 @ X1727 )
| ~ ( in @ X1731 @ X1728 )
| ~ ( in @ ( kpair @ X1730 @ X1731 ) @ ( dpsetconstr @ X1727 @ X1728 @ X1729 ) )
| ( X1729 @ X1730 @ X1731 ) )
& ( ~ ( in @ ( kpair @ X1735 @ X1736 ) @ ( dpsetconstr @ X1732 @ X1733 @ X1734 ) )
| ( in @ X1735 @ X1732 ) )
& ( ~ ( in @ ( kpair @ X1740 @ X1741 ) @ ( dpsetconstr @ X1737 @ X1738 @ X1739 ) )
| ( in @ X1741 @ X1738 ) )
& ( ~ ( in @ ( kpair @ X1745 @ X1746 ) @ ( dpsetconstr @ X1742 @ X1743 @ X1744 ) )
| ( X1744 @ X1745 @ X1746 ) )
& ( ~ ( func @ X1747 @ X1748 @ X1749 )
| ~ ( in @ X1750 @ X1747 )
| ( singleton
@ ( dsetconstr @ X1748
@ ^ [Z0: $i] : ( in @ ( kpair @ X1750 @ Z0 ) @ X1749 ) ) ) )
& ( ~ ( func @ X1751 @ X1752 @ X1753 )
| ~ ( in @ X1754 @ X1751 )
| ( in
@ ( setunion
@ ( dsetconstr @ X1752
@ ^ [Z0: $i] : ( in @ ( kpair @ X1754 @ Z0 ) @ X1753 ) ) )
@ X1752 ) )
& ( ~ ( func @ X1755 @ X1756 @ X1757 )
| ~ ( in @ X1758 @ X1755 )
| ( in @ ( ap @ X1755 @ X1756 @ X1757 @ X1758 ) @ X1756 ) )
& ( ~ ( in @ X1761 @ ( funcSet @ X1759 @ X1760 ) )
| ( func @ X1759 @ X1760 @ X1761 ) )
& ( ~ ( in @ X1764 @ ( funcSet @ X1762 @ X1763 ) )
| ~ ( in @ X1765 @ X1762 )
| ( in @ ( ap @ X1762 @ X1763 @ X1764 @ X1765 ) @ X1763 ) )
& ( ~ ( func @ X1766 @ X1767 @ X1768 )
| ( in @ X1768 @ ( funcSet @ X1766 @ X1767 ) ) )
& ( ( in @ ( esk48_3 @ X1769 @ X1770 @ X1771 ) @ X1769 )
| ( func @ X1769 @ X1770
@ ( dpsetconstr @ X1769 @ X1770
@ ^ [Z0: $i] : ( $eq @ ( X1771 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X1771 @ ( esk48_3 @ X1769 @ X1770 @ X1771 ) ) @ X1770 )
| ( func @ X1769 @ X1770
@ ( dpsetconstr @ X1769 @ X1770
@ ^ [Z0: $i] : ( $eq @ ( X1771 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X1773 @ X1774 @ X1775 ) @ X1773 )
| ( func @ X1773 @ X1774 @ ( lam @ X1773 @ X1774 @ X1775 ) ) )
& ( ~ ( in @ ( X1775 @ ( esk49_3 @ X1773 @ X1774 @ X1775 ) ) @ X1774 )
| ( func @ X1773 @ X1774 @ ( lam @ X1773 @ X1774 @ X1775 ) ) )
& ( ( in @ ( esk50_3 @ X1777 @ X1778 @ X1779 ) @ X1777 )
| ( in @ ( lam @ X1777 @ X1778 @ X1779 ) @ ( funcSet @ X1777 @ X1778 ) ) )
& ( ~ ( in @ ( X1779 @ ( esk50_3 @ X1777 @ X1778 @ X1779 ) ) @ X1778 )
| ( in @ ( lam @ X1777 @ X1778 @ X1779 ) @ ( funcSet @ X1777 @ X1778 ) ) )
& ( ( in @ ( esk51_4 @ X1781 @ X1782 @ X1783 @ X1784 ) @ X1781 )
| ~ ( in @ X1787 @ X1783 )
| ( X1784 @ X1787 )
| ~ ( breln @ X1781 @ X1782 @ X1783 ) )
& ( ( in @ ( esk52_4 @ X1781 @ X1782 @ X1783 @ X1784 ) @ X1782 )
| ~ ( in @ X1787 @ X1783 )
| ( X1784 @ X1787 )
| ~ ( breln @ X1781 @ X1782 @ X1783 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X1781 @ X1782 @ X1783 @ X1784 ) @ ( esk52_4 @ X1781 @ X1782 @ X1783 @ X1784 ) ) @ X1783 )
| ~ ( in @ X1787 @ X1783 )
| ( X1784 @ X1787 )
| ~ ( breln @ X1781 @ X1782 @ X1783 ) )
& ( ~ ( X1784 @ ( kpair @ ( esk51_4 @ X1781 @ X1782 @ X1783 @ X1784 ) @ ( esk52_4 @ X1781 @ X1782 @ X1783 @ X1784 ) ) )
| ~ ( in @ X1787 @ X1783 )
| ( X1784 @ X1787 )
| ~ ( breln @ X1781 @ X1782 @ X1783 ) )
& ( ( in @ ( esk53_4 @ X1788 @ X1789 @ X1790 @ X1791 ) @ X1788 )
| ~ ( in @ X1794 @ X1790 )
| ( X1791 @ X1794 )
| ~ ( breln @ X1788 @ X1789 @ X1790 ) )
& ( ( in @ ( esk54_4 @ X1788 @ X1789 @ X1790 @ X1791 ) @ X1789 )
| ~ ( in @ X1794 @ X1790 )
| ( X1791 @ X1794 )
| ~ ( breln @ X1788 @ X1789 @ X1790 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X1788 @ X1789 @ X1790 @ X1791 ) @ ( esk54_4 @ X1788 @ X1789 @ X1790 @ X1791 ) ) @ X1790 )
| ~ ( in @ X1794 @ X1790 )
| ( X1791 @ X1794 )
| ~ ( breln @ X1788 @ X1789 @ X1790 ) )
& ( ~ ( X1791 @ ( kpair @ ( esk53_4 @ X1788 @ X1789 @ X1790 @ X1791 ) @ ( esk54_4 @ X1788 @ X1789 @ X1790 @ X1791 ) ) )
| ~ ( in @ X1794 @ X1790 )
| ( X1791 @ X1794 )
| ~ ( breln @ X1788 @ X1789 @ X1790 ) )
& ( ~ ( ex1 @ X1795 @ X1796 )
| ~ ( in @ X1797 @ X1795 )
| ~ ( in @ X1798 @ X1795 )
| ~ ( X1796 @ X1797 )
| ~ ( X1796 @ X1798 )
| ( X1797 = X1798 ) )
& ( ~ ( func @ X1799 @ X1800 @ X1801 )
| ~ ( in @ X1802 @ X1799 )
| ( in @ ( kpair @ X1802 @ ( ap @ X1799 @ X1800 @ X1801 @ X1802 ) ) @ X1801 ) )
& ( ~ ( in @ X1805 @ ( funcSet @ X1803 @ X1804 ) )
| ~ ( in @ X1806 @ X1803 )
| ( in @ ( kpair @ X1806 @ ( ap @ X1803 @ X1804 @ X1805 @ X1806 ) ) @ X1805 ) )
& ( ~ ( func @ X1807 @ X1808 @ X1809 )
| ~ ( in @ X1810 @ X1807 )
| ~ ( in @ X1811 @ X1808 )
| ~ ( in @ ( kpair @ X1810 @ X1811 ) @ X1809 )
| ( ( ap @ X1807 @ X1808 @ X1809 @ X1810 )
= X1811 ) )
& ( func @ esk55_0 @ esk56_0 @ esk57_0 )
& ( func @ esk55_0 @ esk56_0 @ esk58_0 )
& ( ~ ( in @ X1816 @ esk55_0 )
| ( ( ap @ esk55_0 @ esk56_0 @ esk57_0 @ X1816 )
= ( ap @ esk55_0 @ esk56_0 @ esk58_0 @ X1816 ) ) )
& ( in @ esk59_0 @ esk55_0 )
& ( in @ esk60_0 @ esk56_0 )
& ( in @ ( kpair @ esk59_0 @ esk60_0 ) @ esk58_0 )
& ~ ( in @ ( kpair @ esk59_0 @ esk60_0 ) @ esk57_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[c_0_245])])])])])])]) ).
thf(c_0_247,negated_conjecture,
! [X2: $i,X3: $i,X7: $i,X5: $i,X4: $i] :
( ( ( ap @ X2 @ X3 @ X4 @ X5 )
= X7 )
| ~ ( func @ X2 @ X3 @ X4 )
| ~ ( in @ X5 @ X2 )
| ~ ( in @ X7 @ X3 )
| ~ ( in @ ( kpair @ X5 @ X7 ) @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_248,negated_conjecture,
in @ ( kpair @ esk59_0 @ esk60_0 ) @ esk58_0,
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_249,negated_conjecture,
! [X2: $i] :
( ( ( ap @ esk55_0 @ esk56_0 @ esk57_0 @ X2 )
= ( ap @ esk55_0 @ esk56_0 @ esk58_0 @ X2 ) )
| ~ ( in @ X2 @ esk55_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_250,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( ap @ X2 @ X3 @ esk58_0 @ esk59_0 )
= esk60_0 )
| ~ ( func @ X2 @ X3 @ esk58_0 )
| ~ ( in @ esk60_0 @ X3 )
| ~ ( in @ esk59_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_247,c_0_248]) ).
thf(c_0_251,negated_conjecture,
in @ esk59_0 @ esk55_0,
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_252,negated_conjecture,
func @ esk55_0 @ esk56_0 @ esk58_0,
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_253,negated_conjecture,
in @ esk60_0 @ esk56_0,
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_254,negated_conjecture,
! [X3: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( kpair @ X5 @ ( ap @ X2 @ X3 @ X4 @ X5 ) ) @ X4 )
| ~ ( func @ X2 @ X3 @ X4 )
| ~ ( in @ X5 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_255,negated_conjecture,
( ( ap @ esk55_0 @ esk56_0 @ esk57_0 @ esk59_0 )
= esk60_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_251]),c_0_252]),c_0_253])]) ).
thf(c_0_256,negated_conjecture,
func @ esk55_0 @ esk56_0 @ esk57_0,
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_257,negated_conjecture,
~ ( in @ ( kpair @ esk59_0 @ esk60_0 ) @ esk57_0 ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
thf(c_0_258,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_256]),c_0_251])]),c_0_257]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU687^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 : Fri Jun 21 12:21:09 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.22/0.57 Running higher-order theorem proving
% 0.22/0.57 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.JbjehVMOIt/E---3.1_26855.p
% 243.67/31.46 # Version: 3.2.0-ho
% 243.67/31.46 # Preprocessing class: HSLMSLSSLLLCHFA.
% 243.67/31.46 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 243.67/31.46 # Starting ehoh_best5 with 300s (1) cores
% 243.67/31.46 # Starting almost_fo_3_lam with 300s (1) cores
% 243.67/31.46 # Starting new_bool_5 with 300s (1) cores
% 243.67/31.46 # Starting pre_casc_3 with 300s (1) cores
% 243.67/31.46 # Starting ho_unfolding_8 with 300s (1) cores
% 243.67/31.46 # Starting new_ho_10_cnf2 with 300s (1) cores
% 243.67/31.46 # Starting new_bool_3 with 300s (1) cores
% 243.67/31.46 # Starting new_ho_5 with 300s (1) cores
% 243.67/31.46 # new_bool_5 with pid 26966 completed with status 0
% 243.67/31.46 # Result found by new_bool_5
% 243.67/31.46 # Preprocessing class: HSLMSLSSLLLCHFA.
% 243.67/31.46 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 243.67/31.46 # Starting ehoh_best5 with 300s (1) cores
% 243.67/31.46 # Starting almost_fo_3_lam with 300s (1) cores
% 243.67/31.46 # Starting new_bool_5 with 300s (1) cores
% 243.67/31.46 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 243.67/31.46 # Search class: HGHSM-FSLM32-MHFMMSBN
% 243.67/31.46 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 243.67/31.46 # Starting ho_unfolding_8 with 55s (1) cores
% 243.67/31.46 # ho_unfolding_8 with pid 26974 completed with status 0
% 243.67/31.46 # Result found by ho_unfolding_8
% 243.67/31.46 # Preprocessing class: HSLMSLSSLLLCHFA.
% 243.67/31.46 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 243.67/31.46 # Starting ehoh_best5 with 300s (1) cores
% 243.67/31.46 # Starting almost_fo_3_lam with 300s (1) cores
% 243.67/31.46 # Starting new_bool_5 with 300s (1) cores
% 243.67/31.46 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 243.67/31.46 # Search class: HGHSM-FSLM32-MHFMMSBN
% 243.67/31.46 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 243.67/31.46 # Starting ho_unfolding_8 with 55s (1) cores
% 243.67/31.46 # Preprocessing time : 0.053 s
% 243.67/31.46 # Presaturation interreduction done
% 243.67/31.46
% 243.67/31.46 # Proof found!
% 243.67/31.46 # SZS status Theorem
% 243.67/31.46 # SZS output start CNFRefutation
% See solution above
% 243.67/31.46 # Parsed axioms : 451
% 243.67/31.46 # Removed by relevancy pruning/SinE : 248
% 243.67/31.46 # Initial clauses : 319
% 243.67/31.46 # Removed in clause preprocessing : 26
% 243.67/31.46 # Initial clauses in saturation : 293
% 243.67/31.46 # Processed clauses : 11821
% 243.67/31.46 # ...of these trivial : 36
% 243.67/31.46 # ...subsumed : 6881
% 243.67/31.46 # ...remaining for further processing : 4904
% 243.67/31.46 # Other redundant clauses eliminated : 160
% 243.67/31.46 # Clauses deleted for lack of memory : 0
% 243.67/31.46 # Backward-subsumed : 135
% 243.67/31.46 # Backward-rewritten : 11
% 243.67/31.46 # Generated clauses : 827032
% 243.67/31.46 # ...of the previous two non-redundant : 823099
% 243.67/31.46 # ...aggressively subsumed : 0
% 243.67/31.46 # Contextual simplify-reflections : 30
% 243.67/31.46 # Paramodulations : 826711
% 243.67/31.46 # Factorizations : 118
% 243.67/31.46 # NegExts : 11
% 243.67/31.46 # Equation resolutions : 184
% 243.67/31.46 # Disequality decompositions : 0
% 243.67/31.46 # Total rewrite steps : 12406
% 243.67/31.46 # ...of those cached : 11734
% 243.67/31.46 # Propositional unsat checks : 0
% 243.67/31.46 # Propositional check models : 0
% 243.67/31.46 # Propositional check unsatisfiable : 0
% 243.67/31.46 # Propositional clauses : 0
% 243.67/31.46 # Propositional clauses after purity: 0
% 243.67/31.46 # Propositional unsat core size : 0
% 243.67/31.46 # Propositional preprocessing time : 0.000
% 243.67/31.46 # Propositional encoding time : 0.000
% 243.67/31.46 # Propositional solver time : 0.000
% 243.67/31.46 # Success case prop preproc time : 0.000
% 243.67/31.46 # Success case prop encoding time : 0.000
% 243.67/31.46 # Success case prop solver time : 0.000
% 243.67/31.46 # Current number of processed clauses : 4492
% 243.67/31.46 # Positive orientable unit clauses : 83
% 243.67/31.46 # Positive unorientable unit clauses: 0
% 243.67/31.46 # Negative unit clauses : 195
% 243.67/31.46 # Non-unit-clauses : 4214
% 243.67/31.46 # Current number of unprocessed clauses: 811306
% 243.67/31.46 # ...number of literals in the above : 3578030
% 243.67/31.46 # Current number of archived formulas : 0
% 243.67/31.46 # Current number of archived clauses : 399
% 243.67/31.46 # Clause-clause subsumption calls (NU) : 1418078
% 243.67/31.46 # Rec. Clause-clause subsumption calls : 761344
% 243.67/31.46 # Non-unit clause-clause subsumptions : 5042
% 243.67/31.46 # Unit Clause-clause subsumption calls : 30423
% 243.67/31.46 # Rewrite failures with RHS unbound : 0
% 243.67/31.46 # BW rewrite match attempts : 40
% 243.67/31.46 # BW rewrite match successes : 10
% 243.67/31.46 # Condensation attempts : 0
% 243.67/31.46 # Condensation successes : 0
% 243.67/31.46 # Termbank termtop insertions : 18346892
% 243.67/31.46 # Search garbage collected termcells : 18641
% 243.67/31.46
% 243.67/31.46 # -------------------------------------------------
% 243.67/31.46 # User time : 29.477 s
% 243.67/31.46 # System time : 0.817 s
% 243.67/31.46 # Total time : 30.295 s
% 243.67/31.46 # Maximum resident set size: 6524 pages
% 243.67/31.46
% 243.67/31.46 # -------------------------------------------------
% 243.67/31.46 # User time : 29.489 s
% 243.67/31.46 # System time : 0.823 s
% 243.67/31.46 # Total time : 30.311 s
% 243.67/31.46 # Maximum resident set size: 2344 pages
% 243.67/31.46 % E---3.1 exiting
% 243.80/31.47 % E exiting
%------------------------------------------------------------------------------