%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU675^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:02 EDT 2024
% Result : Timeout 300.10s 101.99s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 463
% Syntax : Number of formulae : 510 ( 8 unt; 270 typ; 0 def)
% Number of atoms : 1998 ( 314 equ; 0 cnn)
% Maximal formula atoms : 569 ( 8 avg)
% Number of connectives : 7170 ( 451 ~; 435 |; 343 &;4688 @)
% ( 264 <=>; 989 =>; 0 <=; 0 <~>)
% Maximal formula depth : 763 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 376 ( 376 >; 0 *; 0 +; 0 <<)
% Number of symbols : 273 ( 270 usr; 199 con; 0-4 aty)
% Number of variables : 1823 ( 116 ^1627 !; 80 ?;1823 :)
% 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,
epred1_0: $o ).
thf(decl_250,type,
esk1_2: $i > $i > $i ).
thf(decl_251,type,
esk2_2: $i > $i > $i ).
thf(decl_252,type,
esk3_2: $i > $i > $i ).
thf(decl_253,type,
esk4_1: $i > $i ).
thf(decl_254,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_255,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_256,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_257,type,
esk8_1: $i > $i ).
thf(decl_258,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_259,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_260,type,
esk11_2: $i > $i > $i ).
thf(decl_261,type,
esk12_2: $i > $i > $i ).
thf(decl_262,type,
esk13_1: $i > $i ).
thf(decl_263,type,
esk14_1: $i > $i ).
thf(decl_264,type,
esk15_1: $i > $i ).
thf(decl_265,type,
esk16_2: $i > $i > $i ).
thf(decl_266,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_267,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_268,type,
esk19_1: $i > $i ).
thf(decl_269,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_270,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_271,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_272,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_273,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_274,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_275,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_276,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_277,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_278,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_279,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_280,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_281,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_282,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_283,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_284,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_285,type,
esk36_2: $i > $i > $i ).
thf(decl_286,type,
esk37_2: $i > $i > $i ).
thf(decl_287,type,
esk38_2: $i > $i > $i ).
thf(decl_288,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_289,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_290,type,
esk41_2: $i > $i > $i ).
thf(decl_291,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_292,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_293,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_294,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_295,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_296,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_297,type,
esk48_0: $i ).
thf(decl_298,type,
esk49_0: $i ).
thf(decl_299,type,
esk50_0: $i ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',ex1I) ).
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/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
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/sandbox2/benchmark/theBenchmark.p',exuI1) ).
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/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',apProp) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
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/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(infuncsetfunc,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
=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
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/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).
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/sandbox2/benchmark/theBenchmark.p',app) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
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/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
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/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
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/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
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/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
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/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER) ).
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/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
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/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(funcSet,axiom,
( funcSet
= ( ^ [X4: $i,X5: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X4 @ X5 ) )
@ ^ [X30: $i] : ( func @ X4 @ X5 @ X30 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcSet) ).
thf(c_0_192,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_193,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_194,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_195,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_196,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_197,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_198,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_199,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_200,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_201,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_202,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_203,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_204,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_205,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_206,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_207,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_208,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_209,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_210,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_211,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_212,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_213,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_214,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_215,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_216,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_217,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_218,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_219,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_220,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_221,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_222,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_223,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_224,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_225,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_226,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_227,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_228,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_229,plain,
( epred1_0
<=> ! [X601: $i] :
? [X602: $i] :
( ! [X603: $i] :
( ( in @ X603 @ X602 )
=> ! [X604: $i] :
( ( in @ X604 @ X603 )
=> ( in @ X604 @ X601 ) ) )
& ! [X605: $i,X606: $i] :
( ( ( in @ X605 @ X601 )
& ( in @ X606 @ X601 ) )
=> ( ! [X607: $i] :
( ( in @ X607 @ X602 )
=> ( ( in @ X605 @ X607 )
<=> ( in @ X606 @ X607 ) ) )
=> ( X605 = X606 ) ) )
& ! [X608: $i,X609: $i] :
( ( ( in @ X608 @ X602 )
& ( in @ X609 @ X602 ) )
=> ( ! [X610: $i] :
( ( in @ X610 @ X608 )
=> ( in @ X610 @ X609 ) )
| ! [X611: $i] :
( ( in @ X611 @ X609 )
=> ( in @ X611 @ X608 ) ) ) )
& ! [X612: $i] :
( ( ! [X613: $i] :
( ( in @ X613 @ X612 )
=> ( in @ X613 @ X601 ) )
& ? [X614: $i] : ( in @ X614 @ X612 ) )
=> ? [X615: $i,X616: $i] :
( ( in @ X615 @ X602 )
& ( in @ X616 @ X612 )
& ~ ? [X617: $i] :
( ( in @ X617 @ X615 )
& ( in @ X617 @ X612 ) )
& ! [X618: $i] :
( ( in @ X618 @ X602 )
=> ( ! [X619: $i] :
( ( in @ X619 @ X618 )
=> ( in @ X619 @ X615 ) )
| ( in @ X616 @ X618 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_230,negated_conjecture,
~ ( ! [X574: $i,X575: $i] :
( ! [X576: $i] :
( ( in @ X576 @ X574 )
<=> ( in @ X576 @ X575 ) )
=> ( X574 = X575 ) )
=> ( ! [X577: $i] :
~ ( in @ X577 @ emptyset )
=> ( ! [X578: $i,X579: $i,X580: $i] :
( ( in @ X580 @ ( setadjoin @ X578 @ X579 ) )
<=> ( ( X580 = X578 )
| ( in @ X580 @ X579 ) ) )
=> ( ! [X581: $i,X582: $i] :
( ( in @ X582 @ ( powerset @ X581 ) )
<=> ! [X583: $i] :
( ( in @ X583 @ X582 )
=> ( in @ X583 @ X581 ) ) )
=> ( ! [X584: $i,X585: $i] :
( ( in @ X585 @ ( setunion @ X584 ) )
<=> ? [X586: $i] :
( ( in @ X585 @ X586 )
& ( in @ X586 @ X584 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X587: $i] :
( ( in @ X587 @ omega )
=> ( in @ ( setadjoin @ X587 @ X587 ) @ omega ) )
=> ( ! [X588: $i] :
( ( ( in @ emptyset @ X588 )
& ! [X589: $i] :
( ( ( in @ X589 @ omega )
& ( in @ X589 @ X588 ) )
=> ( in @ ( setadjoin @ X589 @ X589 ) @ X588 ) ) )
=> ! [X590: $i] :
( ( in @ X590 @ omega )
=> ( in @ X590 @ X588 ) ) )
=> ( ! [X591: $i > $i > $o,X592: $i] :
( ! [X593: $i] :
( ( in @ X593 @ X592 )
=> ( exu @ ( X591 @ X593 ) ) )
=> ? [X594: $i] :
! [X595: $i] :
( ( in @ X595 @ X594 )
<=> ? [X596: $i] :
( ( in @ X596 @ X592 )
& ( X591 @ X596 @ X595 ) ) ) )
=> ( ! [X597: $i] :
( ? [X598: $i] : ( in @ X598 @ X597 )
=> ? [X599: $i] :
( ( in @ X599 @ X597 )
& ~ ? [X600: $i] :
( ( in @ X600 @ X599 )
& ( in @ X600 @ X597 ) ) ) )
=> ( epred1_0
=> ( ! [X620: $i > $o] :
( ( exu @ X620 )
=> ( X620
@ ( descr
@ ^ [Z0: $i] : ( X620 @ Z0 ) ) ) )
=> ( ! [X621: $i,X622: $i > $o,X623: $i] :
( ( in @ X623 @ X621 )
=> ( ( X622 @ X623 )
=> ( in @ X623 @ ( dsetconstr @ X621 @ X622 ) ) ) )
=> ( ! [X624: $i,X625: $i > $o,X626: $i] :
( ( in @ X626 @ ( dsetconstr @ X624 @ X625 ) )
=> ( in @ X626 @ X624 ) )
=> ( ! [X627: $i,X628: $i > $o,X629: $i] :
( ( in @ X629 @ ( dsetconstr @ X627 @ X628 ) )
=> ( X628 @ X629 ) )
=> ( ! [X630: $i > $o] :
( ( exu @ X630 )
=> ? [X631: $i] :
( ( X630 @ X631 )
& ! [X632: $i] :
( ( X630 @ X632 )
=> ( X631 = X632 ) ) ) )
=> ( ! [X633: $o,X634: $i] :
( ( in @ X634 @ ( prop2set @ X633 ) )
=> X633 )
=> ( ! [X635: $i] :
( ( in @ X635 @ emptyset )
=> ! [X636: $o] : X636 )
=> ( ! [X637: $i] :
( ( in @ X637 @ emptyset )
=> ~ $true )
=> ( ! [X638: $i] :
~ ( in @ X638 @ emptyset )
=> ( ! [X639: $i > $o] :
( ( exu @ X639 )
=> ? [X640: $i] : ( X639 @ X640 ) )
=> ( ! [X641: $i,X642: $i] :
( ! [X643: $i] :
( ( in @ X643 @ X641 )
=> ( in @ X643 @ X642 ) )
=> ( ! [X644: $i] :
( ( in @ X644 @ X642 )
=> ( in @ X644 @ X641 ) )
=> ( X641 = X642 ) ) )
=> ( ! [X645: $i] :
( ! [X646: $i] :
~ ( in @ X646 @ X645 )
=> ( X645 = emptyset ) )
=> ( ! [X647: $i] :
( ! [X648: $i] :
~ ( in @ X648 @ X647 )
=> ( X647 = emptyset ) )
=> ( ! [X649: $i,X650: $i > $o,X651: $i] :
( ( in @ X651 @ X649 )
=> ( ( in @ X651 @ ( dsetconstr @ X649 @ X650 ) )
<=> ( X650 @ X651 ) ) )
=> ( ! [X652: $i] :
( ( nonempty @ X652 )
=> ? [X653: $i] : ( in @ X653 @ X652 ) )
=> ( ! [X654: $i,X655: $i > $o,X656: $i] :
( ( in @ X656 @ X654 )
=> ( ( X655 @ X656 )
=> ( nonempty @ ( dsetconstr @ X654 @ X655 ) ) ) )
=> ( ! [X657: $i] :
( ? [X658: $i] : ( in @ X658 @ X657 )
=> ( nonempty @ X657 ) )
=> ( ! [X659: $i,X660: $i] : ( in @ X659 @ ( setadjoin @ X659 @ X660 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X661: $i,X662: $i,X663: $i] :
( ( in @ X663 @ X662 )
=> ( in @ X663 @ ( setadjoin @ X661 @ X662 ) ) )
=> ( ! [X664: $i,X665: $i,X666: $i] :
( ( in @ X666 @ ( setadjoin @ X664 @ X665 ) )
=> ! [X667: $o] :
( ( ( X666 = X664 )
=> X667 )
=> ( ( ( in @ X666 @ X665 )
=> X667 )
=> X667 ) ) )
=> ( ! [X668: $i,X669: $i,X670: $i] :
( ( in @ X670 @ ( setadjoin @ X668 @ X669 ) )
=> ( ( X670 = X668 )
| ( in @ X670 @ X669 ) ) )
=> ( ! [X671: $i] :
( ( dsetconstr @ X671
@ ^ [Z0: $i] : $true )
= X671 )
=> ( ! [X672: $i,X673: $i] :
( ! [X674: $i] :
( ( in @ X674 @ X673 )
=> ( in @ X674 @ X672 ) )
=> ( in @ X673 @ ( powerset @ X672 ) ) )
=> ( ! [X675: $i] : ( in @ emptyset @ ( powerset @ X675 ) )
=> ( ! [X676: $i] : ( in @ emptyset @ ( powerset @ X676 ) )
=> ( ! [X677: $i,X678: $i,X679: $i] :
( ( in @ X678 @ ( powerset @ X677 ) )
=> ( ( in @ X679 @ X678 )
=> ( in @ X679 @ X677 ) ) )
=> ( ! [X680: $i,X681: $i,X682: $i] :
( ( in @ X681 @ X682 )
=> ( ( in @ X682 @ X680 )
=> ( in @ X681 @ ( setunion @ X680 ) ) ) )
=> ( ! [X683: $i,X684: $i] :
( ( in @ X684 @ ( setunion @ X683 ) )
=> ! [X685: $o] :
( ! [X686: $i] :
( ( in @ X684 @ X686 )
=> ( ( in @ X686 @ X683 )
=> X685 ) )
=> X685 ) )
=> ( ! [X687: $i,X688: $i] :
( ( in @ X688 @ X687 )
=> ( in @ X688 @ ( powerset @ ( setunion @ X687 ) ) ) )
=> ( ! [X689: $i > $o] :
( ( exu @ X689 )
=> ? [X690: $i] :
! [X691: $i] :
( ( X689 @ X691 )
<=> ( X691 = X690 ) ) )
=> ( ! [X692: $i] :
( ( nonempty @ X692 )
=> ? [X693: $i] :
( ( in @ X693 @ X692 )
& $true ) )
=> ( ! [X694: $i,X695: $i] :
( ( in @ X694 @ ( setadjoin @ X695 @ emptyset ) )
=> ( X694 = X695 ) )
=> ( ! [X696: $i,X697: $i] :
( ( X696 != X697 )
=> ~ ( in @ X697 @ ( setadjoin @ X696 @ emptyset ) ) )
=> ( ! [X698: $i,X699: $i] :
( ( X698 = X699 )
=> ( in @ X698 @ ( setadjoin @ X699 @ emptyset ) ) )
=> ( ! [X700: $i,X701: $i] :
( ( in @ X700 @ ( setadjoin @ X701 @ emptyset ) )
=> ( in @ X701 @ ( setadjoin @ X700 @ emptyset ) ) )
=> ( ! [X702: $i,X703: $i,X704: $i] :
( ( in @ X704 @ ( setadjoin @ X702 @ ( setadjoin @ X703 @ emptyset ) ) )
=> ( ( X704 = X702 )
| ( X704 = X703 ) ) )
=> ( ! [X705: $i,X706: $i] : ( in @ X705 @ ( setadjoin @ X705 @ ( setadjoin @ X706 @ emptyset ) ) )
=> ( ! [X707: $i,X708: $i] : ( in @ X708 @ ( setadjoin @ X707 @ ( setadjoin @ X708 @ emptyset ) ) )
=> ( ! [X709: $i,X710: $i > $o] :
( ? [X711: $i] :
( ( in @ X711 @ X709 )
& ( X710 @ X711 ) )
=> ( ( ( dsetconstr @ X709 @ X710 )
= emptyset )
=> ~ $true ) )
=> ( ! [X712: $i > $o,X713: $i] :
( ( in @ X713 @ emptyset )
=> ( X712 @ X713 ) )
=> ( ! [X714: $i,X715: $i > $o] :
( ~ ! [X716: $i] :
( ( in @ X716 @ X714 )
=> ( X715 @ X716 ) )
=> ? [X717: $i] :
( ( in @ X717 @ X714 )
& ~ ( X715 @ X717 ) ) )
=> ( ! [X718: $i,X719: $i > $o] :
( ! [X720: $i] :
( ( in @ X720 @ X718 )
=> ~ ( X719 @ X720 ) )
=> ~ ? [X721: $i] :
( ( in @ X721 @ X718 )
& ( X719 @ X721 ) ) )
=> ( ! [X722: $i,X723: $i > $o] :
( ~ ? [X724: $i] :
( ( in @ X724 @ X722 )
& ( X723 @ X724 ) )
=> ! [X725: $i] :
( ( in @ X725 @ X722 )
=> ~ ( X723 @ X725 ) ) )
=> ( ! [X726: $i,X727: $i > $o] :
( ? [X728: $i] :
( ( in @ X728 @ X726 )
& ~ ( X727 @ X728 ) )
=> ~ ! [X729: $i] :
( ( in @ X729 @ X726 )
=> ( X727 @ X729 ) ) )
=> ( ! [X730: $o] :
( X730
=> ( in @ emptyset @ ( prop2set @ X730 ) ) )
=> ( prop2set2propI
=> ( ! [X731: $i,X732: $i > $o] :
( ~ ? [X733: $i] :
( ( in @ X733 @ X731 )
& ( X732 @ X733 ) )
=> ! [X734: $i] :
( ( in @ X734 @ X731 )
=> ~ ( X732 @ X734 ) ) )
=> ( ! [X735: $i,X736: $i > $o] :
( ~ ! [X737: $i] :
( ( in @ X737 @ X735 )
=> ( X736 @ X737 ) )
=> ? [X738: $i] :
( ( in @ X738 @ X735 )
& ~ ( X736 @ X738 ) ) )
=> ( ! [X739: $i > $o] :
( ? [X740: $i] :
( ( X739 @ X740 )
& ! [X741: $i] :
( ( X739 @ X741 )
=> ( X740 = X741 ) ) )
=> ( exu @ X739 ) )
=> ( ! [X742: $i > $o] :
( ? [X743: $i] : ( X742 @ X743 )
=> ( ! [X744: $i,X745: $i] :
( ( X742 @ X744 )
=> ( ( X742 @ X745 )
=> ( X744 = X745 ) ) )
=> ( exu @ X742 ) ) )
=> ( ! [X746: $i > $o] :
( ? [X747: $i] :
! [X748: $i] :
( ( X746 @ X748 )
<=> ( X748 = X747 ) )
=> ( exu @ X746 ) )
=> ( ! [X749: $i,X750: $i] :
( ( X749 = X750 )
=> ! [X751: $i,X752: $i] :
( ( X751 = X752 )
=> ( ( in @ X751 @ X749 )
=> ( in @ X752 @ X750 ) ) ) )
=> ( ! [X753: $i,X754: $i] :
( ( X753 = X754 )
=> ! [X755: $i,X756: $i] :
( ( X755 = X756 )
=> ( ( in @ X755 @ X753 )
<=> ( in @ X756 @ X754 ) ) ) )
=> ( ! [X757: $i > $o] :
( ( exu @ X757 )
=> ! [X758: $i,X759: $i] :
( ( X757 @ X758 )
=> ( ( X757 @ X759 )
=> ( X758 = X759 ) ) ) )
=> ( ! [X760: $i > $o,X761: $i > $o] :
( ! [X762: $i,X763: $i] :
( ( X762 = X763 )
=> ( ( X760 @ X762 )
<=> ( X761 @ X763 ) ) )
=> ( ( exu @ X760 )
<=> ( exu @ X761 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X764: $i,X765: $i] :
( ( X764 = X765 )
=> ! [X766: $i,X767: $i] :
( ( X766 = X767 )
=> ( ( setadjoin @ X764 @ X766 )
= ( setadjoin @ X765 @ X767 ) ) ) )
=> ( ! [X768: $i,X769: $i] :
( ( X768 = X769 )
=> ( ( powerset @ X768 )
= ( powerset @ X769 ) ) )
=> ( ! [X770: $i,X771: $i] :
( ( X770 = X771 )
=> ( ( setunion @ X770 )
= ( setunion @ X771 ) ) )
=> ( ( omega = omega )
=> ( ! [X772: $i > $o] :
( ( exu @ X772 )
=> ! [X773: $i,X774: $i] :
( ( X772 @ X773 )
=> ( ( X772 @ X774 )
=> ( X773 = X774 ) ) ) )
=> ( ! [X775: $i > $o,X776: $i > $o] :
( ! [X777: $i,X778: $i] :
( ( X777 = X778 )
=> ( ( X775 @ X777 )
<=> ( X776 @ X778 ) ) )
=> ( ( exu @ X775 )
=> ( ( exu @ X776 )
=> ( ( descr @ X775 )
= ( descr @ X776 ) ) ) ) )
=> ( ! [X779: $i,X780: $i] :
( ( X779 = X780 )
=> ! [X781: $i > $o,X782: $i > $o] :
( ! [X783: $i] :
( ( in @ X783 @ X779 )
=> ! [X784: $i] :
( ( in @ X784 @ X780 )
=> ( ( X783 = X784 )
=> ( ( X781 @ X783 )
<=> ( X782 @ X784 ) ) ) ) )
=> ( ( dsetconstr @ X779 @ X781 )
= ( dsetconstr @ X780 @ X782 ) ) ) )
=> ( ! [X785: $i,X786: $i] :
( ! [X787: $i] :
( ( in @ X787 @ X785 )
=> ( in @ X787 @ X786 ) )
=> ( subset @ X785 @ X786 ) )
=> ( ! [X788: $i,X789: $i] :
( ( X788 = X789 )
=> ( subset @ X789 @ X788 ) )
=> ( ! [X790: $i,X791: $i] :
( ( X790 = X791 )
=> ( subset @ X790 @ X791 ) )
=> ( ! [X792: $i,X793: $i] :
( ! [X794: $i] :
( ( in @ X794 @ X792 )
=> ( in @ X794 @ X793 ) )
=> ( subset @ X792 @ X793 ) )
=> ( ! [X795: $i] : ( subset @ emptyset @ X795 )
=> ( ! [X796: $i,X797: $i,X798: $i] :
( ( subset @ X796 @ X797 )
=> ( ( in @ X798 @ X796 )
=> ( in @ X798 @ X797 ) ) )
=> ( ! [X799: $i,X800: $i,X801: $i] :
( ( subset @ X799 @ X800 )
=> ( ~ ( in @ X801 @ X800 )
=> ~ ( in @ X801 @ X799 ) ) )
=> ( ! [X802: $i,X803: $i,X804: $i] :
( ( in @ X804 @ X802 )
=> ( ~ ( in @ X804 @ X803 )
=> ~ ( subset @ X802 @ X803 ) ) )
=> ( ! [X805: $i,X806: $i] :
( ~ ( subset @ X805 @ X806 )
=> ( X805 != X806 ) )
=> ( ! [X807: $i,X808: $i,X809: $i] :
( ( in @ X809 @ X807 )
=> ( ~ ( in @ X809 @ X808 )
=> ( X807 != X808 ) ) )
=> ( ! [X810: $i] : ( subset @ X810 @ X810 )
=> ( ! [X811: $i,X812: $i,X813: $i] :
( ( subset @ X811 @ X812 )
=> ( ( subset @ X812 @ X813 )
=> ( subset @ X811 @ X813 ) ) )
=> ( ! [X814: $i,X815: $i] : ( subset @ X815 @ ( setadjoin @ X814 @ X815 ) )
=> ( ! [X816: $i,X817: $i,X818: $i] :
( ( subset @ X816 @ X818 )
=> ( subset @ X816 @ ( setadjoin @ X817 @ X818 ) ) )
=> ( ! [X819: $i,X820: $i] :
( ( subset @ X819 @ X820 )
=> ( in @ X819 @ ( powerset @ X820 ) ) )
=> ( ! [X821: $i,X822: $i] :
( ( subset @ X821 @ X822 )
=> ( ( subset @ X822 @ X821 )
=> ( X821 = X822 ) ) )
=> ( ! [X823: $i] :
( ( subset @ X823 @ emptyset )
=> ( X823 = emptyset ) )
=> ( ! [X824: $i,X825: $i] :
( ( subset @ X825 @ X824 )
=> ( in @ X825 @ ( powerset @ X824 ) ) )
=> ( ! [X826: $i,X827: $i] :
( ( in @ X827 @ ( powerset @ X826 ) )
=> ( subset @ X827 @ X826 ) )
=> ( ! [X828: $i] : ( in @ X828 @ ( powerset @ X828 ) )
=> ( ! [X829: $i,X830: $i] :
( ( subset @ X829 @ X830 )
=> ( subset @ ( powerset @ X829 ) @ ( powerset @ X830 ) ) )
=> ( ! [X831: $i,X832: $i > $o] : ( in @ ( dsetconstr @ X831 @ X832 ) @ ( powerset @ X831 ) )
=> ( ! [X833: $i,X834: $i > $o] : ( subset @ ( dsetconstr @ X833 @ X834 ) @ X833 )
=> ( ! [X835: $i,X836: $i,X837: $i] :
( ( in @ X837 @ X835 )
=> ( in @ X837 @ ( binunion @ X835 @ X836 ) ) )
=> ( ! [X838: $i,X839: $i] : ( in @ X839 @ ( setadjoin @ X838 @ ( setadjoin @ X839 @ emptyset ) ) )
=> ( ! [X840: $i,X841: $i,X842: $i] :
( ( in @ X842 @ X841 )
=> ( in @ X842 @ ( binunion @ X840 @ X841 ) ) )
=> ( ! [X843: $i,X844: $i,X845: $i,X846: $o] :
( ( in @ X845 @ ( binunion @ X843 @ X844 ) )
=> ( ( ( in @ X845 @ X843 )
=> X846 )
=> ( ( ( in @ X845 @ X844 )
=> X846 )
=> X846 ) ) )
=> ( ! [X847: $i,X848: $i,X849: $i] :
( ( in @ X849 @ ( binunion @ X847 @ X848 ) )
=> ( ( in @ X849 @ X847 )
| ( in @ X849 @ X848 ) ) )
=> ( ! [X850: $i,X851: $i] : ( subset @ X850 @ ( binunion @ X850 @ X851 ) )
=> ( ! [X852: $i,X853: $i] : ( subset @ X853 @ ( binunion @ X852 @ X853 ) )
=> ( ! [X854: $i,X855: $i,X856: $i] :
( ( in @ X856 @ X854 )
=> ( ( in @ X856 @ X855 )
=> ( in @ X856 @ ( binintersect @ X854 @ X855 ) ) ) )
=> ( ! [X857: $i,X858: $i,X859: $i] :
( ( subset @ X859 @ X857 )
=> ( ( subset @ X859 @ X858 )
=> ( subset @ X859 @ ( binintersect @ X857 @ X858 ) ) ) )
=> ( ! [X860: $i,X861: $i,X862: $i] :
( ( in @ X862 @ ( binintersect @ X860 @ X861 ) )
=> ( in @ X862 @ X860 ) )
=> ( ! [X863: $i,X864: $i] : ( subset @ ( binintersect @ X863 @ X864 ) @ X863 )
=> ( ! [X865: $i,X866: $i] :
( ( subset @ X865 @ X866 )
=> ( ( binintersect @ X865 @ X866 )
= X865 ) )
=> ( ! [X867: $i,X868: $i] :
( ( ( binintersect @ X867 @ X868 )
= X868 )
=> ( subset @ X868 @ X867 ) )
=> ( ! [X869: $i,X870: $i,X871: $i] :
( ( in @ X871 @ ( binintersect @ X869 @ X870 ) )
=> ( in @ X871 @ X870 ) )
=> ( ! [X872: $i,X873: $i] :
( ~ ? [X874: $i] :
( ( in @ X874 @ X872 )
& ( in @ X874 @ X873 ) )
=> ( ( binintersect @ X872 @ X873 )
= emptyset ) )
=> ( ! [X875: $i,X876: $i] : ( subset @ ( binintersect @ X875 @ X876 ) @ X876 )
=> ( ! [X877: $i,X878: $i] :
( ( subset @ X878 @ X877 )
=> ( ( binintersect @ X877 @ X878 )
= X878 ) )
=> ( ! [X879: $i,X880: $i] :
( ( ( binintersect @ X879 @ X880 )
= X879 )
=> ( subset @ X879 @ X880 ) )
=> ( ! [X881: $i,X882: $i,X883: $i] :
( ( binintersect @ X881 @ ( binunion @ X882 @ X883 ) )
= ( binunion @ ( binintersect @ X881 @ X882 ) @ ( binintersect @ X881 @ X883 ) ) )
=> ( ! [X884: $i,X885: $i,X886: $i] :
( ( in @ X886 @ X884 )
=> ( ~ ( in @ X886 @ X885 )
=> ( in @ X886 @ ( setminus @ X884 @ X885 ) ) ) )
=> ( ! [X887: $i,X888: $i,X889: $i] :
( ( in @ X889 @ ( setminus @ X887 @ X888 ) )
=> ( in @ X889 @ X887 ) )
=> ( ! [X890: $i,X891: $i,X892: $i] :
( ( in @ X892 @ ( setminus @ X890 @ X891 ) )
=> ~ ( in @ X892 @ X891 ) )
=> ( ! [X893: $i,X894: $i] :
( ( subset @ X893 @ X894 )
=> ( ( setminus @ X893 @ X894 )
= emptyset ) )
=> ( ! [X895: $i,X896: $i,X897: $i] :
( ~ ( in @ X897 @ ( setminus @ X895 @ X896 ) )
=> ( ( in @ X897 @ X895 )
=> ( in @ X897 @ X896 ) ) )
=> ( ! [X898: $i,X899: $i,X900: $i] :
( ~ ( in @ X900 @ ( setminus @ X898 @ X899 ) )
=> ( ~ ( in @ X900 @ X899 )
=> ~ ( in @ X900 @ X898 ) ) )
=> ( ! [X901: $i,X902: $i,X903: $i] :
( ~ ( in @ X903 @ X901 )
=> ~ ( in @ X903 @ ( setminus @ X901 @ X902 ) ) )
=> ( ! [X904: $i,X905: $i,X906: $i] :
( ( in @ X906 @ X905 )
=> ~ ( in @ X906 @ ( setminus @ X904 @ X905 ) ) )
=> ( ! [X907: $i,X908: $i] : ( subset @ ( setminus @ X907 @ X908 ) @ X907 )
=> ( ! [X909: $i,X910: $i] :
( ( ( setminus @ X909 @ X910 )
= emptyset )
=> ( subset @ X909 @ X910 ) )
=> ( ! [X911: $i,X912: $i,X913: $i] :
( ( in @ X913 @ ( symdiff @ X911 @ X912 ) )
=> ! [X914: $o] :
( ( ( in @ X913 @ X911 )
=> ( ~ ( in @ X913 @ X912 )
=> X914 ) )
=> ( ( ~ ( in @ X913 @ X911 )
=> ( ( in @ X913 @ X912 )
=> X914 ) )
=> X914 ) ) )
=> ( ! [X915: $i,X916: $i,X917: $i] :
( ( in @ X917 @ X915 )
=> ( ~ ( in @ X917 @ X916 )
=> ( in @ X917 @ ( symdiff @ X915 @ X916 ) ) ) )
=> ( ! [X918: $i,X919: $i,X920: $i] :
( ~ ( in @ X920 @ X918 )
=> ( ( in @ X920 @ X919 )
=> ( in @ X920 @ ( symdiff @ X918 @ X919 ) ) ) )
=> ( ! [X921: $i,X922: $i,X923: $i] :
( ( in @ X923 @ X921 )
=> ( ( in @ X923 @ X922 )
=> ~ ( in @ X923 @ ( symdiff @ X921 @ X922 ) ) ) )
=> ( ! [X924: $i,X925: $i,X926: $i] :
( ~ ( in @ X926 @ X924 )
=> ( ~ ( in @ X926 @ X925 )
=> ~ ( in @ X926 @ ( symdiff @ X924 @ X925 ) ) ) )
=> ( ! [X927: $i,X928: $i] : ( in @ X928 @ ( setadjoin @ X927 @ ( setadjoin @ X928 @ emptyset ) ) )
=> ( ! [X929: $i,X930: $i] : ( in @ X929 @ ( setunion @ ( setadjoin @ ( setadjoin @ X929 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X929 @ ( setadjoin @ X930 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X931: $i,X932: $i] : ( in @ X932 @ ( setunion @ ( setadjoin @ ( setadjoin @ X931 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X931 @ ( setadjoin @ X932 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X933: $i,X934: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X933 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X933 @ ( setadjoin @ X934 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X935: $i,X936: $i] : ( iskpair @ ( kpair @ X935 @ X936 ) )
=> ( ! [X937: $i,X938: $i] :
( ( in @ X938 @ X937 )
=> ( subset @ ( setadjoin @ X938 @ emptyset ) @ X937 ) )
=> ( ! [X939: $i,X940: $i] :
( ( in @ X940 @ X939 )
=> ( in @ ( setadjoin @ X940 @ emptyset ) @ ( powerset @ X939 ) ) )
=> ( ! [X941: $i,X942: $i,X943: $i] :
( ( in @ X943 @ X941 )
=> ( in @ ( setadjoin @ X943 @ emptyset ) @ ( powerset @ ( binunion @ X941 @ X942 ) ) ) )
=> ( ! [X944: $i,X945: $i,X946: $i] :
( ( in @ X946 @ ( setadjoin @ X944 @ ( setadjoin @ X945 @ emptyset ) ) )
=> ( ( X946 = X944 )
| ( X946 = X945 ) ) )
=> ( ! [X947: $i,X948: $i,X949: $i] :
( ( in @ X949 @ X947 )
=> ! [X950: $i] :
( ( in @ X950 @ X948 )
=> ( subset @ ( setadjoin @ X949 @ ( setadjoin @ X950 @ emptyset ) ) @ ( binunion @ X947 @ X948 ) ) ) )
=> ( ! [X951: $i,X952: $i,X953: $i] :
( ( in @ X953 @ X951 )
=> ! [X954: $i] :
( ( in @ X954 @ X952 )
=> ( in @ ( setadjoin @ X953 @ ( setadjoin @ X954 @ emptyset ) ) @ ( powerset @ ( binunion @ X951 @ X952 ) ) ) ) )
=> ( ! [X955: $i,X956: $i,X957: $i] :
( ( in @ X957 @ X955 )
=> ! [X958: $i] :
( ( in @ X958 @ X956 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X957 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X957 @ ( setadjoin @ X958 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X955 @ X956 ) ) ) ) )
=> ( ! [X959: $i,X960: $i,X961: $i] :
( ( in @ X961 @ X959 )
=> ! [X962: $i] :
( ( in @ X962 @ X960 )
=> ( in @ ( setadjoin @ ( setadjoin @ X961 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X961 @ ( setadjoin @ X962 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X959 @ X960 ) ) ) ) ) )
=> ( ! [X963: $i,X964: $i,X965: $i] :
( ( in @ X965 @ X963 )
=> ! [X966: $i] :
( ( in @ X966 @ X964 )
=> ( in @ ( kpair @ X965 @ X966 ) @ ( powerset @ ( powerset @ ( binunion @ X963 @ X964 ) ) ) ) ) )
=> ( ! [X967: $i,X968: $i,X969: $i] :
( ( in @ X969 @ X967 )
=> ! [X970: $i] :
( ( in @ X970 @ X968 )
=> ( in @ ( kpair @ X969 @ X970 ) @ ( cartprod @ X967 @ X968 ) ) ) )
=> ( ! [X971: $i,X972: $i,X973: $i] :
( ( in @ X973 @ ( cartprod @ X971 @ X972 ) )
=> ? [X974: $i] :
( ( in @ X974 @ X971 )
& ? [X975: $i] :
( ( in @ X975 @ X972 )
& ( X973
= ( kpair @ X974 @ X975 ) ) ) ) )
=> ( ! [X976: $i,X977: $i,X978: $i] :
( ( in @ X978 @ ( cartprod @ X976 @ X977 ) )
=> ( iskpair @ X978 ) )
=> ( ! [X979: $i,X980: $i] :
( ( in @ X980 @ ( setunion @ X979 ) )
=> ? [X981: $i] :
( ( in @ X981 @ X979 )
& ( in @ X980 @ X981 ) ) )
=> ( ! [X982: $i] : ( subset @ ( setunion @ ( setadjoin @ X982 @ emptyset ) ) @ X982 )
=> ( ! [X983: $i] : ( subset @ X983 @ ( setunion @ ( setadjoin @ X983 @ emptyset ) ) )
=> ( ! [X984: $i] :
( ( setunion @ ( setadjoin @ X984 @ emptyset ) )
= X984 )
=> ( ! [X985: $i,X986: $i > $o] :
( ! [X987: $i] :
( ( in @ X987 @ X985 )
=> ! [X988: $i] :
( ( in @ X988 @ X985 )
=> ( ( X986 @ X987 )
=> ( ( X986 @ X988 )
=> ( X987 = X988 ) ) ) ) )
=> ( ? [X989: $i] :
( ( in @ X989 @ X985 )
& ( X986 @ X989 ) )
=> ( singleton @ ( dsetconstr @ X985 @ X986 ) ) ) )
=> ( ! [X990: $i,X991: $i > $o] :
( ( ex1 @ X990 @ X991 )
=> ? [X992: $i] :
( ( in @ X992 @ X990 )
& ( X991 @ X992 ) ) )
=> ( ! [X993: $i,X994: $i > $o,X995: $i] :
( ( in @ X995 @ X993 )
=> ( ( X994 @ X995 )
=> ( ! [X996: $i] :
( ( in @ X996 @ X993 )
=> ( ( X994 @ X996 )
=> ( X996 = X995 ) ) )
=> ( ex1 @ X993 @ X994 ) ) ) )
=> ( ! [X997: $i,X998: $i > $o] :
( ! [X999: $i] :
( ( in @ X999 @ X997 )
=> ! [X1000: $i] :
( ( in @ X1000 @ X997 )
=> ( ( X998 @ X999 )
=> ( ( X998 @ X1000 )
=> ( X999 = X1000 ) ) ) ) )
=> ( ? [X1001: $i] :
( ( in @ X1001 @ X997 )
& ( X998 @ X1001 ) )
=> ( ex1 @ X997 @ X998 ) ) )
=> ( ! [X1002: $i,X1003: $i] :
( ( ( setadjoin @ X1002 @ emptyset )
= ( setadjoin @ X1003 @ emptyset ) )
=> ( X1002 = X1003 ) )
=> ( ! [X1004: $i,X1005: $i,X1006: $i] :
( ( in @ ( setadjoin @ X1006 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1004 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1004 @ ( setadjoin @ X1005 @ emptyset ) ) @ emptyset ) ) )
=> ( X1004 = X1006 ) )
=> ( ! [X1007: $i] :
( ( iskpair @ X1007 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1007 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1007 ) ) ) )
=> ( ! [X1008: $i] :
( ( singleton @ X1008 )
=> ( in @ ( setunion @ X1008 ) @ X1008 ) )
=> ( ! [X1009: $i,X1010: $i] :
( ( kfst @ ( kpair @ X1009 @ X1010 ) )
= X1009 )
=> ( ! [X1011: $i,X1012: $i,X1013: $i] :
( ( in @ X1013 @ ( cartprod @ X1011 @ X1012 ) )
=> ( in @ ( kfst @ X1013 ) @ X1011 ) )
=> ( ! [X1014: $i,X1015: $i,X1016: $i,X1017: $i] :
( ( ( setadjoin @ ( setadjoin @ X1014 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1014 @ ( setadjoin @ X1015 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1016 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1016 @ ( setadjoin @ X1017 @ emptyset ) ) @ emptyset ) ) )
=> ( X1014 = X1016 ) )
=> ( ! [X1018: $i,X1019: $i,X1020: $i,X1021: $i] :
( ( ( kpair @ X1018 @ X1019 )
= ( kpair @ X1020 @ X1021 ) )
=> ( X1018 = X1020 ) )
=> ( ! [X1022: $i,X1023: $i] :
( ( X1022 = X1023 )
=> ( ( setadjoin @ X1022 @ ( setadjoin @ X1023 @ emptyset ) )
= ( setadjoin @ X1022 @ emptyset ) ) )
=> ( ! [X1024: $i,X1025: $i] :
( ( X1024 = X1025 )
=> ( ( setadjoin @ ( setadjoin @ X1024 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1024 @ ( setadjoin @ X1025 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1024 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1026: $i,X1027: $i,X1028: $i,X1029: $i] :
( ( ( setadjoin @ ( setadjoin @ X1026 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1026 @ ( setadjoin @ X1027 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1028 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1028 @ ( setadjoin @ X1029 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1028 = X1029 )
=> ( X1027 = X1029 ) ) )
=> ( ! [X1030: $i,X1031: $i,X1032: $i] :
( ( ( setadjoin @ X1030 @ ( setadjoin @ X1031 @ emptyset ) )
= ( setadjoin @ X1032 @ emptyset ) )
=> ( X1030 = X1031 ) )
=> ( ! [X1033: $i,X1034: $i,X1035: $i,X1036: $i] :
( ( ( setadjoin @ ( setadjoin @ X1033 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1033 @ ( setadjoin @ X1034 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1035 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1035 @ ( setadjoin @ X1036 @ emptyset ) ) @ emptyset ) ) )
=> ( X1034 = X1036 ) )
=> ( ! [X1037: $i,X1038: $i,X1039: $i,X1040: $i] :
( ( ( kpair @ X1037 @ X1038 )
= ( kpair @ X1039 @ X1040 ) )
=> ( X1038 = X1040 ) )
=> ( ! [X1041: $i] :
( ( iskpair @ X1041 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1041 )
@ ^ [Z0: $i] :
( X1041
= ( kpair @ ( kfst @ X1041 ) @ Z0 ) ) ) ) )
=> ( ! [X1042: $i,X1043: $i] :
( ( ksnd @ ( kpair @ X1042 @ X1043 ) )
= X1043 )
=> ( ! [X1044: $i] :
( ( iskpair @ X1044 )
=> ( ( kpair @ ( kfst @ X1044 ) @ ( ksnd @ X1044 ) )
= X1044 ) )
=> ( ! [X1045: $i,X1046: $i,X1047: $i] :
( ( in @ X1047 @ ( cartprod @ X1045 @ X1046 ) )
=> ( in @ ( ksnd @ X1047 ) @ X1046 ) )
=> ( ! [X1048: $i,X1049: $i,X1050: $i,X1051: $i] :
( ( in @ ( kpair @ X1050 @ X1051 ) @ ( cartprod @ X1048 @ X1049 ) )
=> ( in @ X1050 @ X1048 ) )
=> ( ! [X1052: $i,X1053: $i,X1054: $i,X1055: $i] :
( ( in @ ( kpair @ X1054 @ X1055 ) @ ( cartprod @ X1052 @ X1053 ) )
=> ( in @ X1055 @ X1053 ) )
=> ( ! [X1056: $i,X1057: $i,X1058: $i] :
( ( in @ X1058 @ X1056 )
=> ! [X1059: $i] :
( ( in @ X1059 @ X1057 )
=> ( ( kpair @ X1058 @ X1059 )
= ( kpair @ X1058 @ X1059 ) ) ) )
=> ( ! [X1060: $i,X1061: $i,X1062: $i] :
( ( in @ X1062 @ X1060 )
=> ! [X1063: $i] :
( ( in @ X1063 @ X1061 )
=> ( ( kfst @ ( kpair @ X1062 @ X1063 ) )
= X1062 ) ) )
=> ( ! [X1064: $i,X1065: $i,X1066: $i] :
( ( in @ X1066 @ X1064 )
=> ! [X1067: $i] :
( ( in @ X1067 @ X1065 )
=> ( ( ksnd @ ( kpair @ X1066 @ X1067 ) )
= X1067 ) ) )
=> ( ! [X1068: $i,X1069: $i,X1070: $i] :
( ( in @ X1070 @ ( cartprod @ X1068 @ X1069 ) )
=> ( ( kpair @ ( kfst @ X1070 ) @ ( ksnd @ X1070 ) )
= X1070 ) )
=> ( ! [X1071: $i,X1072: $i,X1073: $i > $i > $o,X1074: $i] :
( ( in @ X1074 @ X1071 )
=> ! [X1075: $i] :
( ( in @ X1075 @ X1072 )
=> ( ( X1073 @ X1074 @ X1075 )
=> ( in @ ( kpair @ X1074 @ X1075 ) @ ( dpsetconstr @ X1071 @ X1072 @ X1073 ) ) ) ) )
=> ( ! [X1076: $i,X1077: $i,X1078: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1076 @ X1077 @ X1078 ) @ ( cartprod @ X1076 @ X1077 ) )
=> ( ! [X1079: $i,X1080: $i,X1081: $i > $i > $o] : ( breln @ X1079 @ X1080 @ ( dpsetconstr @ X1079 @ X1080 @ X1081 ) )
=> ( ! [X1082: $i,X1083: $i,X1084: $i > $i > $o,X1085: $i] :
( ( in @ X1085 @ X1082 )
=> ! [X1086: $i] :
( ( in @ X1086 @ X1083 )
=> ( ( in @ ( kpair @ X1085 @ X1086 ) @ ( dpsetconstr @ X1082 @ X1083 @ X1084 ) )
=> ( X1084 @ X1085 @ X1086 ) ) ) )
=> ( ! [X1087: $i,X1088: $i,X1089: $i > $i > $o,X1090: $i,X1091: $i] :
( ( in @ ( kpair @ X1090 @ X1091 ) @ ( dpsetconstr @ X1087 @ X1088 @ X1089 ) )
=> ( in @ X1090 @ X1087 ) )
=> ( ! [X1092: $i,X1093: $i,X1094: $i > $i > $o,X1095: $i,X1096: $i] :
( ( in @ ( kpair @ X1095 @ X1096 ) @ ( dpsetconstr @ X1092 @ X1093 @ X1094 ) )
=> ( in @ X1096 @ X1093 ) )
=> ( ! [X1097: $i,X1098: $i,X1099: $i > $i > $o,X1100: $i,X1101: $i] :
( ( in @ ( kpair @ X1100 @ X1101 ) @ ( dpsetconstr @ X1097 @ X1098 @ X1099 ) )
=> ( X1099 @ X1100 @ X1101 ) )
=> ( ! [X1102: $i,X1103: $i,X1104: $i] :
( ( func @ X1102 @ X1103 @ X1104 )
=> ! [X1105: $i] :
( ( in @ X1105 @ X1102 )
=> ( singleton
@ ( dsetconstr @ X1103
@ ^ [Z0: $i] : ( in @ ( kpair @ X1105 @ Z0 ) @ X1104 ) ) ) ) )
=> ( ! [X1106: $i,X1107: $i,X1108: $i] :
( ( func @ X1106 @ X1107 @ X1108 )
=> ! [X1109: $i] :
( ( in @ X1109 @ X1106 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1107
@ ^ [Z0: $i] : ( in @ ( kpair @ X1109 @ Z0 ) @ X1108 ) ) )
@ X1107 ) ) )
=> ( ! [X1110: $i,X1111: $i,X1112: $i] :
( ( func @ X1110 @ X1111 @ X1112 )
=> ! [X1113: $i] :
( ( in @ X1113 @ X1110 )
=> ( in @ ( ap @ X1110 @ X1111 @ X1112 @ X1113 ) @ X1111 ) ) )
=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ 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(assume_negation,[status(cth)],[infuncsetfunc]),c_0_192]),setukpairinjR1]),app]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),quantDeMorgan1]),setunionE2]),setunionsingleton1]),quantDeMorgan2]),setunionsingleton2]),setunionsingleton]),quantDeMorgan3]),c_0_193]),c_0_194]),quantDeMorgan4]),c_0_195]),c_0_196]),prop2setI]),singletonsuniq]),setukpairinjL1]),notdexE]),c_0_197]),theprop]),notdallE]),kfstpairEq]),cartprodfstin]),c_0_198]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),c_0_199]),setukpairinjR12]),subsetE]),upairequniteq]),setukpairinjR2]),setukpairinjR]),inCongP]),c_0_200]),ksndpairEq]),in__Cong]),kpairsurjEq]),cartprodsndin]),c_0_201]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),c_0_202]),cartprodsndpairEq]),cartprodpairsurjEq]),emptyset__Cong]),c_0_203]),c_0_204]),setadjoin__Cong]),c_0_205]),c_0_206]),powerset__Cong]),c_0_207]),c_0_208]),setunion__Cong]),c_0_209]),c_0_210]),omega__Cong]),c_0_211]),c_0_212]),c_0_213]),c_0_214]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),bs114d]),setminusI]),setminusEL]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_215]),c_0_216]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),upairsetIR]),binintersectER]),c_0_217]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),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]),vacuousDall]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_218]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_219]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_220]),nonemptyE1]),c_0_221]),noeltsimpempty]),emptyI]),setext]),c_0_222]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_223]),c_0_224]),c_0_225]),c_0_226]),c_0_227]),wellorderingAx]),foundationAx]),c_0_228]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_229]) ).
thf(c_0_231,plain,
! [X1114: $i,X1115: $i] :
( ( funcSet @ X1114 @ X1115 )
= ( dsetconstr @ ( powerset @ ( cartprod @ X1114 @ X1115 ) )
@ ^ [Z0: $i] : ( func @ X1114 @ X1115 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[funcSet])]) ).
thf(c_0_232,negated_conjecture,
! [X1116: $i,X1117: $i,X1119: $i,X1120: $i,X1121: $i,X1122: $i,X1123: $i,X1124: $i,X1125: $i,X1126: $i,X1127: $i,X1129: $i,X1130: $i,X1132: $i,X1133: $i,X1134: $i,X1135: $i,X1136: $i,X1138: $i,X1139: $i > $i > $o,X1140: $i,X1143: $i,X1145: $i,X1146: $i,X1147: $i,X1148: $i,X1150: $i,X1151: $i > $o,X1152: $i,X1153: $i > $o,X1154: $i,X1155: $i,X1156: $i > $o,X1157: $i,X1158: $i,X1159: $i > $o,X1160: $i,X1161: $i > $o,X1163: $i,X1164: $o,X1165: $i,X1166: $i,X1167: $o,X1168: $i,X1169: $i,X1170: $i > $o,X1172: $i,X1173: $i,X1176: $i,X1178: $i,X1180: $i,X1181: $i > $o,X1182: $i,X1183: $i,X1185: $i,X1186: $i > $o,X1187: $i,X1188: $i,X1189: $i,X1190: $i,X1191: $i,X1192: $i,X1193: $i,X1194: $i,X1195: $i,X1196: $i,X1197: $i,X1198: $o,X1199: $i,X1200: $i,X1201: $i,X1202: $i,X1203: $i,X1204: $i,X1206: $i,X1207: $i,X1208: $i,X1209: $i,X1210: $i,X1211: $i,X1212: $i,X1213: $i,X1214: $i,X1215: $i,X1216: $o,X1218: $i,X1219: $i,X1220: $i > $o,X1222: $i,X1223: $i,X1224: $i,X1226: $i,X1227: $i,X1228: $i,X1229: $i,X1230: $i,X1231: $i,X1232: $i,X1233: $i,X1234: $i,X1235: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i,X1240: $i,X1241: $i,X1242: $i > $o,X1243: $i,X1244: $i > $o,X1245: $i,X1246: $i,X1247: $i > $o,X1248: $i,X1250: $i,X1251: $i > $o,X1253: $i,X1254: $i,X1255: $i > $o,X1257: $i,X1258: $i,X1259: $i > $o,X1260: $i,X1262: $o,X1263: $i,X1264: $i > $o,X1266: $i,X1267: $i,X1268: $i > $o,X1269: $i,X1271: $i > $o,X1272: $i,X1274: $i > $o,X1275: $i,X1278: $i > $o,X1279: $i,X1281: $i,X1282: $i,X1283: $i,X1284: $i,X1285: $i,X1286: $i,X1287: $i,X1288: $i,X1289: $i > $o,X1290: $i,X1291: $i,X1292: $i > $o,X1293: $i > $o,X1296: $i,X1297: $i,X1298: $i,X1299: $i,X1300: $i,X1301: $i,X1302: $i,X1303: $i,X1304: $i > $o,X1305: $i,X1306: $i,X1307: $i > $o,X1308: $i > $o,X1311: $i,X1312: $i,X1313: $i > $o,X1314: $i > $o,X1317: $i,X1318: $i,X1320: $i,X1321: $i,X1322: $i,X1323: $i,X1324: $i,X1325: $i,X1327: $i,X1328: $i,X1329: $i,X1330: $i,X1331: $i,X1332: $i,X1333: $i,X1334: $i,X1335: $i,X1336: $i,X1337: $i,X1338: $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,X1356: $i,X1357: $i,X1358: $i,X1359: $i,X1360: $i,X1361: $i,X1362: $i,X1363: $i,X1364: $i > $o,X1365: $i,X1366: $i > $o,X1367: $i,X1368: $i,X1369: $i,X1370: $i,X1371: $i,X1372: $i,X1373: $i,X1374: $i,X1375: $i,X1376: $i,X1377: $i,X1378: $o,X1379: $i,X1380: $i,X1381: $i,X1382: $i,X1383: $i,X1384: $i,X1385: $i,X1386: $i,X1387: $i,X1388: $i,X1389: $i,X1390: $i,X1391: $i,X1392: $i,X1393: $i,X1394: $i,X1395: $i,X1396: $i,X1397: $i,X1398: $i,X1399: $i,X1400: $i,X1401: $i,X1402: $i,X1403: $i,X1404: $i,X1405: $i,X1407: $i,X1408: $i,X1409: $i,X1410: $i,X1411: $i,X1412: $i,X1413: $i,X1414: $i,X1415: $i,X1416: $i,X1417: $i,X1418: $i,X1419: $i,X1420: $i,X1421: $i,X1422: $i,X1423: $i,X1424: $i,X1425: $i,X1426: $i,X1427: $i,X1428: $i,X1429: $i,X1430: $i,X1431: $i,X1432: $i,X1433: $i,X1434: $i,X1435: $i,X1436: $i,X1437: $i,X1438: $i,X1439: $i,X1440: $i,X1441: $i,X1442: $i,X1443: $i,X1444: $i,X1445: $i,X1446: $o,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,X1478: $i,X1479: $i,X1480: $i,X1481: $i,X1482: $i,X1483: $i,X1484: $i,X1485: $i,X1486: $i,X1487: $i,X1488: $i,X1489: $i,X1490: $i,X1491: $i,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,X1508: $i,X1509: $i,X1510: $i,X1511: $i,X1512: $i,X1514: $i,X1515: $i,X1516: $i,X1517: $i,X1518: $i > $o,X1521: $i,X1522: $i,X1523: $i > $o,X1525: $i,X1526: $i > $o,X1527: $i,X1529: $i,X1530: $i > $o,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: $i,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 > $i > $o,X1606: $i,X1607: $i,X1608: $i,X1609: $i,X1610: $i > $i > $o,X1611: $i,X1612: $i,X1613: $i > $i > $o,X1614: $i,X1615: $i,X1616: $i > $i > $o,X1617: $i,X1618: $i,X1619: $i,X1620: $i,X1621: $i > $i > $o,X1622: $i,X1623: $i,X1624: $i,X1625: $i,X1626: $i > $i > $o,X1627: $i,X1628: $i,X1629: $i,X1630: $i,X1631: $i > $i > $o,X1632: $i,X1633: $i,X1634: $i,X1635: $i,X1636: $i,X1637: $i,X1638: $i,X1639: $i,X1640: $i,X1641: $i,X1642: $i,X1643: $i,X1644: $i,X1645: $i] :
( ( ~ ( in @ ( esk1_2 @ X1116 @ X1117 ) @ X1116 )
| ~ ( in @ ( esk1_2 @ X1116 @ X1117 ) @ X1117 )
| ( X1116 = X1117 ) )
& ( ( in @ ( esk1_2 @ X1116 @ X1117 ) @ X1116 )
| ( in @ ( esk1_2 @ X1116 @ X1117 ) @ X1117 )
| ( X1116 = X1117 ) )
& ~ ( in @ X1119 @ emptyset )
& ( ~ ( in @ X1122 @ ( setadjoin @ X1120 @ X1121 ) )
| ( X1122 = X1120 )
| ( in @ X1122 @ X1121 ) )
& ( ( X1122 != X1120 )
| ( in @ X1122 @ ( setadjoin @ X1120 @ X1121 ) ) )
& ( ~ ( in @ X1122 @ X1121 )
| ( in @ X1122 @ ( setadjoin @ X1120 @ X1121 ) ) )
& ( ~ ( in @ X1124 @ ( powerset @ X1123 ) )
| ~ ( in @ X1125 @ X1124 )
| ( in @ X1125 @ X1123 ) )
& ( ( in @ ( esk2_2 @ X1126 @ X1127 ) @ X1127 )
| ( in @ X1127 @ ( powerset @ X1126 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1126 @ X1127 ) @ X1126 )
| ( in @ X1127 @ ( powerset @ X1126 ) ) )
& ( ( in @ X1130 @ ( esk3_2 @ X1129 @ X1130 ) )
| ~ ( in @ X1130 @ ( setunion @ X1129 ) ) )
& ( ( in @ ( esk3_2 @ X1129 @ X1130 ) @ X1129 )
| ~ ( in @ X1130 @ ( setunion @ X1129 ) ) )
& ( ~ ( in @ X1133 @ X1134 )
| ~ ( in @ X1134 @ X1132 )
| ( in @ X1133 @ ( setunion @ X1132 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1135 @ omega )
| ( in @ ( setadjoin @ X1135 @ X1135 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1136 ) @ omega )
| ~ ( in @ emptyset @ X1136 )
| ~ ( in @ X1138 @ omega )
| ( in @ X1138 @ X1136 ) )
& ( ( in @ ( esk4_1 @ X1136 ) @ X1136 )
| ~ ( in @ emptyset @ X1136 )
| ~ ( in @ X1138 @ omega )
| ( in @ X1138 @ X1136 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1136 ) @ ( esk4_1 @ X1136 ) ) @ X1136 )
| ~ ( in @ emptyset @ X1136 )
| ~ ( in @ X1138 @ omega )
| ( in @ X1138 @ X1136 ) )
& ( ( in @ ( esk7_3 @ X1139 @ X1140 @ X1143 ) @ X1140 )
| ~ ( in @ X1143 @ ( esk6_2 @ X1139 @ X1140 ) )
| ( in @ ( esk5_2 @ X1139 @ X1140 ) @ X1140 ) )
& ( ( X1139 @ ( esk7_3 @ X1139 @ X1140 @ X1143 ) @ X1143 )
| ~ ( in @ X1143 @ ( esk6_2 @ X1139 @ X1140 ) )
| ( in @ ( esk5_2 @ X1139 @ X1140 ) @ X1140 ) )
& ( ~ ( in @ X1146 @ X1140 )
| ~ ( X1139 @ X1146 @ X1145 )
| ( in @ X1145 @ ( esk6_2 @ X1139 @ X1140 ) )
| ( in @ ( esk5_2 @ X1139 @ X1140 ) @ X1140 ) )
& ( ( in @ ( esk7_3 @ X1139 @ X1140 @ X1143 ) @ X1140 )
| ~ ( in @ X1143 @ ( esk6_2 @ X1139 @ X1140 ) )
| ~ ( exu @ ( X1139 @ ( esk5_2 @ X1139 @ X1140 ) ) ) )
& ( ( X1139 @ ( esk7_3 @ X1139 @ X1140 @ X1143 ) @ X1143 )
| ~ ( in @ X1143 @ ( esk6_2 @ X1139 @ X1140 ) )
| ~ ( exu @ ( X1139 @ ( esk5_2 @ X1139 @ X1140 ) ) ) )
& ( ~ ( in @ X1146 @ X1140 )
| ~ ( X1139 @ X1146 @ X1145 )
| ( in @ X1145 @ ( esk6_2 @ X1139 @ X1140 ) )
| ~ ( exu @ ( X1139 @ ( esk5_2 @ X1139 @ X1140 ) ) ) )
& ( ( in @ ( esk8_1 @ X1147 ) @ X1147 )
| ~ ( in @ X1148 @ X1147 ) )
& ( ~ ( in @ X1150 @ ( esk8_1 @ X1147 ) )
| ~ ( in @ X1150 @ X1147 )
| ~ ( in @ X1148 @ X1147 ) )
& epred1_0
& ( ~ ( exu @ X1151 )
| ( X1151 @ ( descr @ X1151 ) ) )
& ( ~ ( in @ X1154 @ X1152 )
| ~ ( X1153 @ X1154 )
| ( in @ X1154 @ ( dsetconstr @ X1152 @ X1153 ) ) )
& ( ~ ( in @ X1157 @ ( dsetconstr @ X1155 @ X1156 ) )
| ( in @ X1157 @ X1155 ) )
& ( ~ ( in @ X1160 @ ( dsetconstr @ X1158 @ X1159 ) )
| ( X1159 @ X1160 ) )
& ( ( X1161 @ ( esk9_1 @ X1161 ) )
| ~ ( exu @ X1161 ) )
& ( ~ ( X1161 @ X1163 )
| ( ( esk9_1 @ X1161 )
= X1163 )
| ~ ( exu @ X1161 ) )
& ( ~ ( in @ X1165 @ ( prop2set @ X1164 ) )
| X1164 )
& ( ~ ( in @ X1166 @ emptyset )
| X1167 )
& ( ~ ( in @ X1168 @ emptyset )
| ~ $true )
& ~ ( in @ X1169 @ emptyset )
& ( ~ ( exu @ X1170 )
| ( X1170 @ ( esk10_1 @ X1170 ) ) )
& ( ( in @ ( esk12_2 @ X1172 @ X1173 ) @ X1173 )
| ( X1172 = X1173 )
| ( in @ ( esk11_2 @ X1172 @ X1173 ) @ X1172 ) )
& ( ~ ( in @ ( esk12_2 @ X1172 @ X1173 ) @ X1172 )
| ( X1172 = X1173 )
| ( in @ ( esk11_2 @ X1172 @ X1173 ) @ X1172 ) )
& ( ( in @ ( esk12_2 @ X1172 @ X1173 ) @ X1173 )
| ( X1172 = X1173 )
| ~ ( in @ ( esk11_2 @ X1172 @ X1173 ) @ X1173 ) )
& ( ~ ( in @ ( esk12_2 @ X1172 @ X1173 ) @ X1172 )
| ( X1172 = X1173 )
| ~ ( in @ ( esk11_2 @ X1172 @ X1173 ) @ X1173 ) )
& ( ( in @ ( esk13_1 @ X1176 ) @ X1176 )
| ( X1176 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1178 ) @ X1178 )
| ( X1178 = emptyset ) )
& ( ~ ( in @ X1182 @ ( dsetconstr @ X1180 @ X1181 ) )
| ( X1181 @ X1182 )
| ~ ( in @ X1182 @ X1180 ) )
& ( ~ ( X1181 @ X1182 )
| ( in @ X1182 @ ( dsetconstr @ X1180 @ X1181 ) )
| ~ ( in @ X1182 @ X1180 ) )
& ( ~ ( nonempty @ X1183 )
| ( in @ ( esk15_1 @ X1183 ) @ X1183 ) )
& ( ~ ( in @ X1187 @ X1185 )
| ~ ( X1186 @ X1187 )
| ( nonempty @ ( dsetconstr @ X1185 @ X1186 ) ) )
& ( ~ ( in @ X1189 @ X1188 )
| ( nonempty @ X1188 ) )
& ( in @ X1190 @ ( setadjoin @ X1190 @ X1191 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1194 @ X1193 )
| ( in @ X1194 @ ( setadjoin @ X1192 @ X1193 ) ) )
& ( ( in @ X1197 @ X1196 )
| X1198
| ( X1197 = X1195 )
| ~ ( in @ X1197 @ ( setadjoin @ X1195 @ X1196 ) ) )
& ( ~ X1198
| X1198
| ( X1197 = X1195 )
| ~ ( in @ X1197 @ ( setadjoin @ X1195 @ X1196 ) ) )
& ( ( in @ X1197 @ X1196 )
| X1198
| ~ X1198
| ~ ( in @ X1197 @ ( setadjoin @ X1195 @ X1196 ) ) )
& ( ~ X1198
| X1198
| ~ X1198
| ~ ( in @ X1197 @ ( setadjoin @ X1195 @ X1196 ) ) )
& ( ~ ( in @ X1201 @ ( setadjoin @ X1199 @ X1200 ) )
| ( X1201 = X1199 )
| ( in @ X1201 @ X1200 ) )
& ( ( dsetconstr @ X1202
@ ^ [Z0: $i] : $true )
= X1202 )
& ( ( in @ ( esk16_2 @ X1203 @ X1204 ) @ X1204 )
| ( in @ X1204 @ ( powerset @ X1203 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1203 @ X1204 ) @ X1203 )
| ( in @ X1204 @ ( powerset @ X1203 ) ) )
& ( in @ emptyset @ ( powerset @ X1206 ) )
& ( in @ emptyset @ ( powerset @ X1207 ) )
& ( ~ ( in @ X1209 @ ( powerset @ X1208 ) )
| ~ ( in @ X1210 @ X1209 )
| ( in @ X1210 @ X1208 ) )
& ( ~ ( in @ X1212 @ X1213 )
| ~ ( in @ X1213 @ X1211 )
| ( in @ X1212 @ ( setunion @ X1211 ) ) )
& ( ( in @ X1215 @ ( esk17_3 @ X1214 @ X1215 @ X1216 ) )
| X1216
| ~ ( in @ X1215 @ ( setunion @ X1214 ) ) )
& ( ( in @ ( esk17_3 @ X1214 @ X1215 @ X1216 ) @ X1214 )
| X1216
| ~ ( in @ X1215 @ ( setunion @ X1214 ) ) )
& ( ~ X1216
| X1216
| ~ ( in @ X1215 @ ( setunion @ X1214 ) ) )
& ( ~ ( in @ X1219 @ X1218 )
| ( in @ X1219 @ ( powerset @ ( setunion @ X1218 ) ) ) )
& ( ~ ( X1220 @ X1222 )
| ( X1222
= ( esk18_1 @ X1220 ) )
| ~ ( exu @ X1220 ) )
& ( ( X1223
!= ( esk18_1 @ X1220 ) )
| ( X1220 @ X1223 )
| ~ ( exu @ X1220 ) )
& ( ( in @ ( esk19_1 @ X1224 ) @ X1224 )
| ~ ( nonempty @ X1224 ) )
& ( $true
| ~ ( nonempty @ X1224 ) )
& ( ~ ( in @ X1226 @ ( setadjoin @ X1227 @ emptyset ) )
| ( X1226 = X1227 ) )
& ( ( X1228 = X1229 )
| ~ ( in @ X1229 @ ( setadjoin @ X1228 @ emptyset ) ) )
& ( ( X1230 != X1231 )
| ( in @ X1230 @ ( setadjoin @ X1231 @ emptyset ) ) )
& ( ~ ( in @ X1232 @ ( setadjoin @ X1233 @ emptyset ) )
| ( in @ X1233 @ ( setadjoin @ X1232 @ emptyset ) ) )
& ( ~ ( in @ X1236 @ ( setadjoin @ X1234 @ ( setadjoin @ X1235 @ emptyset ) ) )
| ( X1236 = X1234 )
| ( X1236 = X1235 ) )
& ( in @ X1237 @ ( setadjoin @ X1237 @ ( setadjoin @ X1238 @ emptyset ) ) )
& ( in @ X1240 @ ( setadjoin @ X1239 @ ( setadjoin @ X1240 @ emptyset ) ) )
& ( ~ ( in @ X1243 @ X1241 )
| ~ ( X1242 @ X1243 )
| ( ( dsetconstr @ X1241 @ X1242 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1245 @ emptyset )
| ( X1244 @ X1245 ) )
& ( ( in @ ( esk20_2 @ X1246 @ X1247 ) @ X1246 )
| ~ ( in @ X1248 @ X1246 )
| ( X1247 @ X1248 ) )
& ( ~ ( X1247 @ ( esk20_2 @ X1246 @ X1247 ) )
| ~ ( in @ X1248 @ X1246 )
| ( X1247 @ X1248 ) )
& ( ( in @ ( esk21_2 @ X1250 @ X1251 ) @ X1250 )
| ~ ( in @ X1253 @ X1250 )
| ~ ( X1251 @ X1253 ) )
& ( ( X1251 @ ( esk21_2 @ X1250 @ X1251 ) )
| ~ ( in @ X1253 @ X1250 )
| ~ ( X1251 @ X1253 ) )
& ( ( in @ ( esk22_2 @ X1254 @ X1255 ) @ X1254 )
| ~ ( in @ X1257 @ X1254 )
| ~ ( X1255 @ X1257 ) )
& ( ( X1255 @ ( esk22_2 @ X1254 @ X1255 ) )
| ~ ( in @ X1257 @ X1254 )
| ~ ( X1255 @ X1257 ) )
& ( ( in @ ( esk23_2 @ X1258 @ X1259 ) @ X1258 )
| ~ ( in @ X1260 @ X1258 )
| ( X1259 @ X1260 ) )
& ( ~ ( X1259 @ ( esk23_2 @ X1258 @ X1259 ) )
| ~ ( in @ X1260 @ X1258 )
| ( X1259 @ X1260 ) )
& ( ~ X1262
| ( in @ emptyset @ ( prop2set @ X1262 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1263 @ X1264 ) @ X1263 )
| ~ ( in @ X1266 @ X1263 )
| ~ ( X1264 @ X1266 ) )
& ( ( X1264 @ ( esk24_2 @ X1263 @ X1264 ) )
| ~ ( in @ X1266 @ X1263 )
| ~ ( X1264 @ X1266 ) )
& ( ( in @ ( esk25_2 @ X1267 @ X1268 ) @ X1267 )
| ~ ( in @ X1269 @ X1267 )
| ( X1268 @ X1269 ) )
& ( ~ ( X1268 @ ( esk25_2 @ X1267 @ X1268 ) )
| ~ ( in @ X1269 @ X1267 )
| ( X1268 @ X1269 ) )
& ( ( X1271 @ ( esk26_2 @ X1271 @ X1272 ) )
| ~ ( X1271 @ X1272 )
| ( exu @ X1271 ) )
& ( ( X1272
!= ( esk26_2 @ X1271 @ X1272 ) )
| ~ ( X1271 @ X1272 )
| ( exu @ X1271 ) )
& ( ( X1274 @ ( esk27_1 @ X1274 ) )
| ( exu @ X1274 )
| ~ ( X1274 @ X1275 ) )
& ( ( X1274 @ ( esk28_1 @ X1274 ) )
| ( exu @ X1274 )
| ~ ( X1274 @ X1275 ) )
& ( ( ( esk27_1 @ X1274 )
!= ( esk28_1 @ X1274 ) )
| ( exu @ X1274 )
| ~ ( X1274 @ X1275 ) )
& ( ~ ( X1278 @ ( esk29_2 @ X1278 @ X1279 ) )
| ( ( esk29_2 @ X1278 @ X1279 )
!= X1279 )
| ( exu @ X1278 ) )
& ( ( X1278 @ ( esk29_2 @ X1278 @ X1279 ) )
| ( ( esk29_2 @ X1278 @ X1279 )
= X1279 )
| ( exu @ X1278 ) )
& ( ( X1281 != X1282 )
| ( X1283 != X1284 )
| ~ ( in @ X1283 @ X1281 )
| ( in @ X1284 @ X1282 ) )
& ( ~ ( in @ X1287 @ X1285 )
| ( in @ X1288 @ X1286 )
| ( X1287 != X1288 )
| ( X1285 != X1286 ) )
& ( ~ ( in @ X1288 @ X1286 )
| ( in @ X1287 @ X1285 )
| ( X1287 != X1288 )
| ( X1285 != X1286 ) )
& ( ~ ( exu @ X1289 )
| ~ ( X1289 @ X1290 )
| ~ ( X1289 @ X1291 )
| ( X1290 = X1291 ) )
& ( ~ ( exu @ X1292 )
| ( exu @ X1293 )
| ( ( esk30_2 @ X1292 @ X1293 )
= ( esk31_2 @ X1292 @ X1293 ) ) )
& ( ~ ( exu @ X1293 )
| ( exu @ X1292 )
| ( ( esk30_2 @ X1292 @ X1293 )
= ( esk31_2 @ X1292 @ X1293 ) ) )
& ( ~ ( exu @ X1292 )
| ( exu @ X1293 )
| ~ ( X1292 @ ( esk30_2 @ X1292 @ X1293 ) )
| ~ ( X1293 @ ( esk31_2 @ X1292 @ X1293 ) ) )
& ( ~ ( exu @ X1293 )
| ( exu @ X1292 )
| ~ ( X1292 @ ( esk30_2 @ X1292 @ X1293 ) )
| ~ ( X1293 @ ( esk31_2 @ X1292 @ X1293 ) ) )
& ( ~ ( exu @ X1292 )
| ( exu @ X1293 )
| ( X1292 @ ( esk30_2 @ X1292 @ X1293 ) )
| ( X1293 @ ( esk31_2 @ X1292 @ X1293 ) ) )
& ( ~ ( exu @ X1293 )
| ( exu @ X1292 )
| ( X1292 @ ( esk30_2 @ X1292 @ X1293 ) )
| ( X1293 @ ( esk31_2 @ X1292 @ X1293 ) ) )
& ( emptyset = emptyset )
& ( ( X1296 != X1297 )
| ( X1298 != X1299 )
| ( ( setadjoin @ X1296 @ X1298 )
= ( setadjoin @ X1297 @ X1299 ) ) )
& ( ( X1300 != X1301 )
| ( ( powerset @ X1300 )
= ( powerset @ X1301 ) ) )
& ( ( X1302 != X1303 )
| ( ( setunion @ X1302 )
= ( setunion @ X1303 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1304 )
| ~ ( X1304 @ X1305 )
| ~ ( X1304 @ X1306 )
| ( X1305 = X1306 ) )
& ( ( ( esk32_2 @ X1307 @ X1308 )
= ( esk33_2 @ X1307 @ X1308 ) )
| ~ ( exu @ X1307 )
| ~ ( exu @ X1308 )
| ( ( descr @ X1307 )
= ( descr @ X1308 ) ) )
& ( ~ ( X1307 @ ( esk32_2 @ X1307 @ X1308 ) )
| ~ ( X1308 @ ( esk33_2 @ X1307 @ X1308 ) )
| ~ ( exu @ X1307 )
| ~ ( exu @ X1308 )
| ( ( descr @ X1307 )
= ( descr @ X1308 ) ) )
& ( ( X1307 @ ( esk32_2 @ X1307 @ X1308 ) )
| ( X1308 @ ( esk33_2 @ X1307 @ X1308 ) )
| ~ ( exu @ X1307 )
| ~ ( exu @ X1308 )
| ( ( descr @ X1307 )
= ( descr @ X1308 ) ) )
& ( ( in @ ( esk34_4 @ X1311 @ X1312 @ X1313 @ X1314 ) @ X1311 )
| ( ( dsetconstr @ X1311 @ X1313 )
= ( dsetconstr @ X1312 @ X1314 ) )
| ( X1311 != X1312 ) )
& ( ( in @ ( esk35_4 @ X1311 @ X1312 @ X1313 @ X1314 ) @ X1312 )
| ( ( dsetconstr @ X1311 @ X1313 )
= ( dsetconstr @ X1312 @ X1314 ) )
| ( X1311 != X1312 ) )
& ( ( ( esk34_4 @ X1311 @ X1312 @ X1313 @ X1314 )
= ( esk35_4 @ X1311 @ X1312 @ X1313 @ X1314 ) )
| ( ( dsetconstr @ X1311 @ X1313 )
= ( dsetconstr @ X1312 @ X1314 ) )
| ( X1311 != X1312 ) )
& ( ~ ( X1313 @ ( esk34_4 @ X1311 @ X1312 @ X1313 @ X1314 ) )
| ~ ( X1314 @ ( esk35_4 @ X1311 @ X1312 @ X1313 @ X1314 ) )
| ( ( dsetconstr @ X1311 @ X1313 )
= ( dsetconstr @ X1312 @ X1314 ) )
| ( X1311 != X1312 ) )
& ( ( X1313 @ ( esk34_4 @ X1311 @ X1312 @ X1313 @ X1314 ) )
| ( X1314 @ ( esk35_4 @ X1311 @ X1312 @ X1313 @ X1314 ) )
| ( ( dsetconstr @ X1311 @ X1313 )
= ( dsetconstr @ X1312 @ X1314 ) )
| ( X1311 != X1312 ) )
& ( ( in @ ( esk36_2 @ X1317 @ X1318 ) @ X1317 )
| ( subset @ X1317 @ X1318 ) )
& ( ~ ( in @ ( esk36_2 @ X1317 @ X1318 ) @ X1318 )
| ( subset @ X1317 @ X1318 ) )
& ( ( X1320 != X1321 )
| ( subset @ X1321 @ X1320 ) )
& ( ( X1322 != X1323 )
| ( subset @ X1322 @ X1323 ) )
& ( ( in @ ( esk37_2 @ X1324 @ X1325 ) @ X1324 )
| ( subset @ X1324 @ X1325 ) )
& ( ~ ( in @ ( esk37_2 @ X1324 @ X1325 ) @ X1325 )
| ( subset @ X1324 @ X1325 ) )
& ( subset @ emptyset @ X1327 )
& ( ~ ( subset @ X1328 @ X1329 )
| ~ ( in @ X1330 @ X1328 )
| ( in @ X1330 @ X1329 ) )
& ( ~ ( subset @ X1331 @ X1332 )
| ( in @ X1333 @ X1332 )
| ~ ( in @ X1333 @ X1331 ) )
& ( ~ ( in @ X1336 @ X1334 )
| ( in @ X1336 @ X1335 )
| ~ ( subset @ X1334 @ X1335 ) )
& ( ( subset @ X1337 @ X1338 )
| ( X1337 != X1338 ) )
& ( ~ ( in @ X1341 @ X1339 )
| ( in @ X1341 @ X1340 )
| ( X1339 != X1340 ) )
& ( subset @ X1342 @ X1342 )
& ( ~ ( subset @ X1343 @ X1344 )
| ~ ( subset @ X1344 @ X1345 )
| ( subset @ X1343 @ X1345 ) )
& ( subset @ X1347 @ ( setadjoin @ X1346 @ X1347 ) )
& ( ~ ( subset @ X1348 @ X1350 )
| ( subset @ X1348 @ ( setadjoin @ X1349 @ X1350 ) ) )
& ( ~ ( subset @ X1351 @ X1352 )
| ( in @ X1351 @ ( powerset @ X1352 ) ) )
& ( ~ ( subset @ X1353 @ X1354 )
| ~ ( subset @ X1354 @ X1353 )
| ( X1353 = X1354 ) )
& ( ~ ( subset @ X1355 @ emptyset )
| ( X1355 = emptyset ) )
& ( ~ ( subset @ X1357 @ X1356 )
| ( in @ X1357 @ ( powerset @ X1356 ) ) )
& ( ~ ( in @ X1359 @ ( powerset @ X1358 ) )
| ( subset @ X1359 @ X1358 ) )
& ( in @ X1360 @ ( powerset @ X1360 ) )
& ( ~ ( subset @ X1361 @ X1362 )
| ( subset @ ( powerset @ X1361 ) @ ( powerset @ X1362 ) ) )
& ( in @ ( dsetconstr @ X1363 @ X1364 ) @ ( powerset @ X1363 ) )
& ( subset @ ( dsetconstr @ X1365 @ X1366 ) @ X1365 )
& ( ~ ( in @ X1369 @ X1367 )
| ( in @ X1369 @ ( binunion @ X1367 @ X1368 ) ) )
& ( in @ X1371 @ ( setadjoin @ X1370 @ ( setadjoin @ X1371 @ emptyset ) ) )
& ( ~ ( in @ X1374 @ X1373 )
| ( in @ X1374 @ ( binunion @ X1372 @ X1373 ) ) )
& ( ( in @ X1377 @ X1376 )
| X1378
| ( in @ X1377 @ X1375 )
| ~ ( in @ X1377 @ ( binunion @ X1375 @ X1376 ) ) )
& ( ~ X1378
| X1378
| ( in @ X1377 @ X1375 )
| ~ ( in @ X1377 @ ( binunion @ X1375 @ X1376 ) ) )
& ( ( in @ X1377 @ X1376 )
| X1378
| ~ X1378
| ~ ( in @ X1377 @ ( binunion @ X1375 @ X1376 ) ) )
& ( ~ X1378
| X1378
| ~ X1378
| ~ ( in @ X1377 @ ( binunion @ X1375 @ X1376 ) ) )
& ( ~ ( in @ X1381 @ ( binunion @ X1379 @ X1380 ) )
| ( in @ X1381 @ X1379 )
| ( in @ X1381 @ X1380 ) )
& ( subset @ X1382 @ ( binunion @ X1382 @ X1383 ) )
& ( subset @ X1385 @ ( binunion @ X1384 @ X1385 ) )
& ( ~ ( in @ X1388 @ X1386 )
| ~ ( in @ X1388 @ X1387 )
| ( in @ X1388 @ ( binintersect @ X1386 @ X1387 ) ) )
& ( ~ ( subset @ X1391 @ X1389 )
| ~ ( subset @ X1391 @ X1390 )
| ( subset @ X1391 @ ( binintersect @ X1389 @ X1390 ) ) )
& ( ~ ( in @ X1394 @ ( binintersect @ X1392 @ X1393 ) )
| ( in @ X1394 @ X1392 ) )
& ( subset @ ( binintersect @ X1395 @ X1396 ) @ X1395 )
& ( ~ ( subset @ X1397 @ X1398 )
| ( ( binintersect @ X1397 @ X1398 )
= X1397 ) )
& ( ( ( binintersect @ X1399 @ X1400 )
!= X1400 )
| ( subset @ X1400 @ X1399 ) )
& ( ~ ( in @ X1403 @ ( binintersect @ X1401 @ X1402 ) )
| ( in @ X1403 @ X1402 ) )
& ( ( in @ ( esk38_2 @ X1404 @ X1405 ) @ X1404 )
| ( ( binintersect @ X1404 @ X1405 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1404 @ X1405 ) @ X1405 )
| ( ( binintersect @ X1404 @ X1405 )
= emptyset ) )
& ( subset @ ( binintersect @ X1407 @ X1408 ) @ X1408 )
& ( ~ ( subset @ X1410 @ X1409 )
| ( ( binintersect @ X1409 @ X1410 )
= X1410 ) )
& ( ( ( binintersect @ X1411 @ X1412 )
!= X1411 )
| ( subset @ X1411 @ X1412 ) )
& ( ( binintersect @ X1413 @ ( binunion @ X1414 @ X1415 ) )
= ( binunion @ ( binintersect @ X1413 @ X1414 ) @ ( binintersect @ X1413 @ X1415 ) ) )
& ( ~ ( in @ X1418 @ X1416 )
| ( in @ X1418 @ X1417 )
| ( in @ X1418 @ ( setminus @ X1416 @ X1417 ) ) )
& ( ~ ( in @ X1421 @ ( setminus @ X1419 @ X1420 ) )
| ( in @ X1421 @ X1419 ) )
& ( ~ ( in @ X1424 @ ( setminus @ X1422 @ X1423 ) )
| ~ ( in @ X1424 @ X1423 ) )
& ( ~ ( subset @ X1425 @ X1426 )
| ( ( setminus @ X1425 @ X1426 )
= emptyset ) )
& ( ( in @ X1429 @ ( setminus @ X1427 @ X1428 ) )
| ~ ( in @ X1429 @ X1427 )
| ( in @ X1429 @ X1428 ) )
& ( ( in @ X1432 @ ( setminus @ X1430 @ X1431 ) )
| ( in @ X1432 @ X1431 )
| ~ ( in @ X1432 @ X1430 ) )
& ( ( in @ X1435 @ X1433 )
| ~ ( in @ X1435 @ ( setminus @ X1433 @ X1434 ) ) )
& ( ~ ( in @ X1438 @ X1437 )
| ~ ( in @ X1438 @ ( setminus @ X1436 @ X1437 ) ) )
& ( subset @ ( setminus @ X1439 @ X1440 ) @ X1439 )
& ( ( ( setminus @ X1441 @ X1442 )
!= emptyset )
| ( subset @ X1441 @ X1442 ) )
& ( ~ ( in @ X1445 @ X1443 )
| X1446
| ( in @ X1445 @ X1443 )
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ( in @ X1445 @ X1444 )
| X1446
| ( in @ X1445 @ X1443 )
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ~ X1446
| X1446
| ( in @ X1445 @ X1443 )
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ~ ( in @ X1445 @ X1443 )
| X1446
| ~ ( in @ X1445 @ X1444 )
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ( in @ X1445 @ X1444 )
| X1446
| ~ ( in @ X1445 @ X1444 )
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ~ X1446
| X1446
| ~ ( in @ X1445 @ X1444 )
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ~ ( in @ X1445 @ X1443 )
| X1446
| ~ X1446
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ( in @ X1445 @ X1444 )
| X1446
| ~ X1446
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ~ X1446
| X1446
| ~ X1446
| ~ ( in @ X1445 @ ( symdiff @ X1443 @ X1444 ) ) )
& ( ~ ( in @ X1449 @ X1447 )
| ( in @ X1449 @ X1448 )
| ( in @ X1449 @ ( symdiff @ X1447 @ X1448 ) ) )
& ( ( in @ X1452 @ X1450 )
| ~ ( in @ X1452 @ X1451 )
| ( in @ X1452 @ ( symdiff @ X1450 @ X1451 ) ) )
& ( ~ ( in @ X1455 @ X1453 )
| ~ ( in @ X1455 @ X1454 )
| ~ ( in @ X1455 @ ( symdiff @ X1453 @ X1454 ) ) )
& ( ( in @ X1458 @ X1456 )
| ( in @ X1458 @ X1457 )
| ~ ( in @ X1458 @ ( symdiff @ X1456 @ X1457 ) ) )
& ( in @ X1460 @ ( setadjoin @ X1459 @ ( setadjoin @ X1460 @ emptyset ) ) )
& ( in @ X1461 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1461 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1461 @ ( setadjoin @ X1462 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1464 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1463 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1463 @ ( setadjoin @ X1464 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1465 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1465 @ ( setadjoin @ X1466 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1467 @ X1468 ) )
& ( ~ ( in @ X1470 @ X1469 )
| ( subset @ ( setadjoin @ X1470 @ emptyset ) @ X1469 ) )
& ( ~ ( in @ X1472 @ X1471 )
| ( in @ ( setadjoin @ X1472 @ emptyset ) @ ( powerset @ X1471 ) ) )
& ( ~ ( in @ X1475 @ X1473 )
| ( in @ ( setadjoin @ X1475 @ emptyset ) @ ( powerset @ ( binunion @ X1473 @ X1474 ) ) ) )
& ( ~ ( in @ X1478 @ ( setadjoin @ X1476 @ ( setadjoin @ X1477 @ emptyset ) ) )
| ( X1478 = X1476 )
| ( X1478 = X1477 ) )
& ( ~ ( in @ X1481 @ X1479 )
| ~ ( in @ X1482 @ X1480 )
| ( subset @ ( setadjoin @ X1481 @ ( setadjoin @ X1482 @ emptyset ) ) @ ( binunion @ X1479 @ X1480 ) ) )
& ( ~ ( in @ X1485 @ X1483 )
| ~ ( in @ X1486 @ X1484 )
| ( in @ ( setadjoin @ X1485 @ ( setadjoin @ X1486 @ emptyset ) ) @ ( powerset @ ( binunion @ X1483 @ X1484 ) ) ) )
& ( ~ ( in @ X1489 @ X1487 )
| ~ ( in @ X1490 @ X1488 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1489 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1489 @ ( setadjoin @ X1490 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1487 @ X1488 ) ) ) )
& ( ~ ( in @ X1493 @ X1491 )
| ~ ( in @ X1494 @ X1492 )
| ( in @ ( setadjoin @ ( setadjoin @ X1493 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1493 @ ( setadjoin @ X1494 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1491 @ X1492 ) ) ) ) )
& ( ~ ( in @ X1497 @ X1495 )
| ~ ( in @ X1498 @ X1496 )
| ( in @ ( kpair @ X1497 @ X1498 ) @ ( powerset @ ( powerset @ ( binunion @ X1495 @ X1496 ) ) ) ) )
& ( ~ ( in @ X1501 @ X1499 )
| ~ ( in @ X1502 @ X1500 )
| ( in @ ( kpair @ X1501 @ X1502 ) @ ( cartprod @ X1499 @ X1500 ) ) )
& ( ( in @ ( esk39_3 @ X1503 @ X1504 @ X1505 ) @ X1503 )
| ~ ( in @ X1505 @ ( cartprod @ X1503 @ X1504 ) ) )
& ( ( in @ ( esk40_3 @ X1503 @ X1504 @ X1505 ) @ X1504 )
| ~ ( in @ X1505 @ ( cartprod @ X1503 @ X1504 ) ) )
& ( ( X1505
= ( kpair @ ( esk39_3 @ X1503 @ X1504 @ X1505 ) @ ( esk40_3 @ X1503 @ X1504 @ X1505 ) ) )
| ~ ( in @ X1505 @ ( cartprod @ X1503 @ X1504 ) ) )
& ( ~ ( in @ X1510 @ ( cartprod @ X1508 @ X1509 ) )
| ( iskpair @ X1510 ) )
& ( ( in @ ( esk41_2 @ X1511 @ X1512 ) @ X1511 )
| ~ ( in @ X1512 @ ( setunion @ X1511 ) ) )
& ( ( in @ X1512 @ ( esk41_2 @ X1511 @ X1512 ) )
| ~ ( in @ X1512 @ ( setunion @ X1511 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1514 @ emptyset ) ) @ X1514 )
& ( subset @ X1515 @ ( setunion @ ( setadjoin @ X1515 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1516 @ emptyset ) )
= X1516 )
& ( ( in @ ( esk42_2 @ X1517 @ X1518 ) @ X1517 )
| ~ ( in @ X1521 @ X1517 )
| ~ ( X1518 @ X1521 )
| ( singleton @ ( dsetconstr @ X1517 @ X1518 ) ) )
& ( ( in @ ( esk43_2 @ X1517 @ X1518 ) @ X1517 )
| ~ ( in @ X1521 @ X1517 )
| ~ ( X1518 @ X1521 )
| ( singleton @ ( dsetconstr @ X1517 @ X1518 ) ) )
& ( ( X1518 @ ( esk42_2 @ X1517 @ X1518 ) )
| ~ ( in @ X1521 @ X1517 )
| ~ ( X1518 @ X1521 )
| ( singleton @ ( dsetconstr @ X1517 @ X1518 ) ) )
& ( ( X1518 @ ( esk43_2 @ X1517 @ X1518 ) )
| ~ ( in @ X1521 @ X1517 )
| ~ ( X1518 @ X1521 )
| ( singleton @ ( dsetconstr @ X1517 @ X1518 ) ) )
& ( ( ( esk42_2 @ X1517 @ X1518 )
!= ( esk43_2 @ X1517 @ X1518 ) )
| ~ ( in @ X1521 @ X1517 )
| ~ ( X1518 @ X1521 )
| ( singleton @ ( dsetconstr @ X1517 @ X1518 ) ) )
& ( ( in @ ( esk44_2 @ X1522 @ X1523 ) @ X1522 )
| ~ ( ex1 @ X1522 @ X1523 ) )
& ( ( X1523 @ ( esk44_2 @ X1522 @ X1523 ) )
| ~ ( ex1 @ X1522 @ X1523 ) )
& ( ( in @ ( esk45_3 @ X1525 @ X1526 @ X1527 ) @ X1525 )
| ( ex1 @ X1525 @ X1526 )
| ~ ( X1526 @ X1527 )
| ~ ( in @ X1527 @ X1525 ) )
& ( ( X1526 @ ( esk45_3 @ X1525 @ X1526 @ X1527 ) )
| ( ex1 @ X1525 @ X1526 )
| ~ ( X1526 @ X1527 )
| ~ ( in @ X1527 @ X1525 ) )
& ( ( ( esk45_3 @ X1525 @ X1526 @ X1527 )
!= X1527 )
| ( ex1 @ X1525 @ X1526 )
| ~ ( X1526 @ X1527 )
| ~ ( in @ X1527 @ X1525 ) )
& ( ( in @ ( esk46_2 @ X1529 @ X1530 ) @ X1529 )
| ~ ( in @ X1533 @ X1529 )
| ~ ( X1530 @ X1533 )
| ( ex1 @ X1529 @ X1530 ) )
& ( ( in @ ( esk47_2 @ X1529 @ X1530 ) @ X1529 )
| ~ ( in @ X1533 @ X1529 )
| ~ ( X1530 @ X1533 )
| ( ex1 @ X1529 @ X1530 ) )
& ( ( X1530 @ ( esk46_2 @ X1529 @ X1530 ) )
| ~ ( in @ X1533 @ X1529 )
| ~ ( X1530 @ X1533 )
| ( ex1 @ X1529 @ X1530 ) )
& ( ( X1530 @ ( esk47_2 @ X1529 @ X1530 ) )
| ~ ( in @ X1533 @ X1529 )
| ~ ( X1530 @ X1533 )
| ( ex1 @ X1529 @ X1530 ) )
& ( ( ( esk46_2 @ X1529 @ X1530 )
!= ( esk47_2 @ X1529 @ X1530 ) )
| ~ ( in @ X1533 @ X1529 )
| ~ ( X1530 @ X1533 )
| ( ex1 @ X1529 @ X1530 ) )
& ( ( ( setadjoin @ X1534 @ emptyset )
!= ( setadjoin @ X1535 @ emptyset ) )
| ( X1534 = X1535 ) )
& ( ~ ( in @ ( setadjoin @ X1538 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1536 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1536 @ ( setadjoin @ X1537 @ emptyset ) ) @ emptyset ) ) )
| ( X1536 = X1538 ) )
& ( ~ ( iskpair @ X1539 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1539 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1539 ) ) ) )
& ( ~ ( singleton @ X1540 )
| ( in @ ( setunion @ X1540 ) @ X1540 ) )
& ( ( kfst @ ( kpair @ X1541 @ X1542 ) )
= X1541 )
& ( ~ ( in @ X1545 @ ( cartprod @ X1543 @ X1544 ) )
| ( in @ ( kfst @ X1545 ) @ X1543 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1546 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1546 @ ( setadjoin @ X1547 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1548 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1548 @ ( setadjoin @ X1549 @ emptyset ) ) @ emptyset ) ) )
| ( X1546 = X1548 ) )
& ( ( ( kpair @ X1550 @ X1551 )
!= ( kpair @ X1552 @ X1553 ) )
| ( X1550 = X1552 ) )
& ( ( X1554 != X1555 )
| ( ( setadjoin @ X1554 @ ( setadjoin @ X1555 @ emptyset ) )
= ( setadjoin @ X1554 @ emptyset ) ) )
& ( ( X1556 != X1557 )
| ( ( setadjoin @ ( setadjoin @ X1556 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1556 @ ( setadjoin @ X1557 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1556 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1558 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1558 @ ( setadjoin @ X1559 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1560 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1560 @ ( setadjoin @ X1561 @ emptyset ) ) @ emptyset ) ) )
| ( X1560 != X1561 )
| ( X1559 = X1561 ) )
& ( ( ( setadjoin @ X1562 @ ( setadjoin @ X1563 @ emptyset ) )
!= ( setadjoin @ X1564 @ emptyset ) )
| ( X1562 = X1563 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1565 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1565 @ ( setadjoin @ X1566 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1567 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1567 @ ( setadjoin @ X1568 @ emptyset ) ) @ emptyset ) ) )
| ( X1566 = X1568 ) )
& ( ( ( kpair @ X1569 @ X1570 )
!= ( kpair @ X1571 @ X1572 ) )
| ( X1570 = X1572 ) )
& ( ~ ( iskpair @ X1573 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1573 )
@ ^ [Z0: $i] :
( X1573
= ( kpair @ ( kfst @ X1573 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X1574 @ X1575 ) )
= X1575 )
& ( ~ ( iskpair @ X1576 )
| ( ( kpair @ ( kfst @ X1576 ) @ ( ksnd @ X1576 ) )
= X1576 ) )
& ( ~ ( in @ X1579 @ ( cartprod @ X1577 @ X1578 ) )
| ( in @ ( ksnd @ X1579 ) @ X1578 ) )
& ( ~ ( in @ ( kpair @ X1582 @ X1583 ) @ ( cartprod @ X1580 @ X1581 ) )
| ( in @ X1582 @ X1580 ) )
& ( ~ ( in @ ( kpair @ X1586 @ X1587 ) @ ( cartprod @ X1584 @ X1585 ) )
| ( in @ X1587 @ X1585 ) )
& ( ~ ( in @ X1590 @ X1588 )
| ~ ( in @ X1591 @ X1589 )
| ( ( kpair @ X1590 @ X1591 )
= ( kpair @ X1590 @ X1591 ) ) )
& ( ~ ( in @ X1594 @ X1592 )
| ~ ( in @ X1595 @ X1593 )
| ( ( kfst @ ( kpair @ X1594 @ X1595 ) )
= X1594 ) )
& ( ~ ( in @ X1598 @ X1596 )
| ~ ( in @ X1599 @ X1597 )
| ( ( ksnd @ ( kpair @ X1598 @ X1599 ) )
= X1599 ) )
& ( ~ ( in @ X1602 @ ( cartprod @ X1600 @ X1601 ) )
| ( ( kpair @ ( kfst @ X1602 ) @ ( ksnd @ X1602 ) )
= X1602 ) )
& ( ~ ( in @ X1606 @ X1603 )
| ~ ( in @ X1607 @ X1604 )
| ~ ( X1605 @ X1606 @ X1607 )
| ( in @ ( kpair @ X1606 @ X1607 ) @ ( dpsetconstr @ X1603 @ X1604 @ X1605 ) ) )
& ( subset @ ( dpsetconstr @ X1608 @ X1609 @ X1610 ) @ ( cartprod @ X1608 @ X1609 ) )
& ( breln @ X1611 @ X1612 @ ( dpsetconstr @ X1611 @ X1612 @ X1613 ) )
& ( ~ ( in @ X1617 @ X1614 )
| ~ ( in @ X1618 @ X1615 )
| ~ ( in @ ( kpair @ X1617 @ X1618 ) @ ( dpsetconstr @ X1614 @ X1615 @ X1616 ) )
| ( X1616 @ X1617 @ X1618 ) )
& ( ~ ( in @ ( kpair @ X1622 @ X1623 ) @ ( dpsetconstr @ X1619 @ X1620 @ X1621 ) )
| ( in @ X1622 @ X1619 ) )
& ( ~ ( in @ ( kpair @ X1627 @ X1628 ) @ ( dpsetconstr @ X1624 @ X1625 @ X1626 ) )
| ( in @ X1628 @ X1625 ) )
& ( ~ ( in @ ( kpair @ X1632 @ X1633 ) @ ( dpsetconstr @ X1629 @ X1630 @ X1631 ) )
| ( X1631 @ X1632 @ X1633 ) )
& ( ~ ( func @ X1634 @ X1635 @ X1636 )
| ~ ( in @ X1637 @ X1634 )
| ( singleton
@ ( dsetconstr @ X1635
@ ^ [Z0: $i] : ( in @ ( kpair @ X1637 @ Z0 ) @ X1636 ) ) ) )
& ( ~ ( func @ X1638 @ X1639 @ X1640 )
| ~ ( in @ X1641 @ X1638 )
| ( in
@ ( setunion
@ ( dsetconstr @ X1639
@ ^ [Z0: $i] : ( in @ ( kpair @ X1641 @ Z0 ) @ X1640 ) ) )
@ X1639 ) )
& ( ~ ( func @ X1642 @ X1643 @ X1644 )
| ~ ( in @ X1645 @ X1642 )
| ( in @ ( ap @ X1642 @ X1643 @ X1644 @ X1645 ) @ X1643 ) )
& ( in @ esk50_0 @ ( funcSet @ esk48_0 @ esk49_0 ) )
& ~ ( func @ esk48_0 @ esk49_0 @ esk50_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_230])])])])])])]) ).
thf(c_0_233,plain,
! [X1649: $i,X1650: $i] :
( ( funcSet @ X1649 @ X1650 )
= ( dsetconstr @ ( powerset @ ( cartprod @ X1649 @ X1650 ) )
@ ^ [Z0: $i] : ( func @ X1649 @ X1650 @ Z0 ) ) ),
inference(variable_rename,[status(thm)],[c_0_231]) ).
thf(c_0_234,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( X1 @ X2 )
| ~ ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
thf(c_0_235,plain,
! [X2: $i,X3: $i] :
( ( funcSet @ X2 @ X3 )
= ( dsetconstr @ ( powerset @ ( cartprod @ X2 @ X3 ) ) @ ( func @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
thf(c_0_236,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( func @ X2 @ X3 @ X4 )
| ~ ( in @ X4 @ ( funcSet @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
thf(c_0_237,negated_conjecture,
in @ esk50_0 @ ( funcSet @ esk48_0 @ esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
thf(c_0_238,negated_conjecture,
~ ( func @ esk48_0 @ esk49_0 @ esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
thf(c_0_239,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_237]),c_0_238]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU675^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 15:37:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running higher-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 300.10/101.99 # Version: 3.1.0-ho
% 300.10/101.99 # Preprocessing class: HSLMSLSSLLLCHFA.
% 300.10/101.99 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 300.10/101.99 # Starting ehoh_best5 with 300s (1) cores
% 300.10/101.99 # Starting almost_fo_3_lam with 300s (1) cores
% 300.10/101.99 # Starting new_bool_5 with 300s (1) cores
% 300.10/101.99 # Starting pre_casc_3 with 300s (1) cores
% 300.10/101.99 # Starting ho_unfolding_8 with 300s (1) cores
% 300.10/101.99 # Starting new_ho_10_cnf2 with 300s (1) cores
% 300.10/101.99 # Starting new_bool_3 with 300s (1) cores
% 300.10/101.99 # Starting new_ho_5 with 300s (1) cores
% 300.10/101.99 # new_bool_5 with pid 18891 completed with status 0
% 300.10/101.99 # Result found by new_bool_5
% 300.10/101.99 # Preprocessing class: HSLMSLSSLLLCHFA.
% 300.10/101.99 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 300.10/101.99 # Starting ehoh_best5 with 300s (1) cores
% 300.10/101.99 # Starting almost_fo_3_lam with 300s (1) cores
% 300.10/101.99 # Starting new_bool_5 with 300s (1) cores
% 300.10/101.99 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 300.10/101.99 # Search class: HGHSM-FSLM31-MHFMMSBN
% 300.10/101.99 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 300.10/101.99 # Starting new_ho_10_cnf2 with 163s (1) cores
% 300.10/101.99 # new_ho_10_cnf2 with pid 18899 completed with status 0
% 300.10/101.99 # Result found by new_ho_10_cnf2
% 300.10/101.99 # Preprocessing class: HSLMSLSSLLLCHFA.
% 300.10/101.99 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 300.10/101.99 # Starting ehoh_best5 with 300s (1) cores
% 300.10/101.99 # Starting almost_fo_3_lam with 300s (1) cores
% 300.10/101.99 # Starting new_bool_5 with 300s (1) cores
% 300.10/101.99 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 300.10/101.99 # Search class: HGHSM-FSLM31-MHFMMSBN
% 300.10/101.99 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 300.10/101.99 # Starting new_ho_10_cnf2 with 163s (1) cores
% 300.10/101.99 # Preprocessing time : 0.005 s
% 300.10/101.99 # Presaturation interreduction done
% 300.10/101.99
% 300.10/101.99 # Proof found!
% 300.10/101.99 # SZS status Theorem
% 300.10/101.99 # SZS output start CNFRefutation
% See solution above
% 300.10/101.99 # Parsed axioms : 427
% 300.10/101.99 # Removed by relevancy pruning/SinE : 235
% 300.10/101.99 # Initial clauses : 293
% 300.10/101.99 # Removed in clause preprocessing : 26
% 300.10/101.99 # Initial clauses in saturation : 267
% 300.10/101.99 # Processed clauses : 1637
% 300.10/101.99 # ...of these trivial : 25
% 300.10/101.99 # ...subsumed : 517
% 300.10/101.99 # ...remaining for further processing : 1095
% 300.10/101.99 # Other redundant clauses eliminated : 62
% 300.10/101.99 # Clauses deleted for lack of memory : 0
% 300.10/101.99 # Backward-subsumed : 21
% 300.10/101.99 # Backward-rewritten : 16
% 300.10/101.99 # Generated clauses : 26886
% 300.10/101.99 # ...of the previous two non-redundant : 25955
% 300.10/101.99 # ...aggressively subsumed : 0
% 300.10/101.99 # Contextual simplify-reflections : 0
% 300.10/101.99 # Paramodulations : 26817
% 300.10/101.99 # Factorizations : 2
% 300.10/101.99 # NegExts : 0
% 300.10/101.99 # Equation resolutions : 67
% 300.10/101.99 # Disequality decompositions : 0
% 300.10/101.99 # Total rewrite steps : 1198
% 300.10/101.99 # ...of those cached : 1021
% 300.10/101.99 # Propositional unsat checks : 0
% 300.10/101.99 # Propositional check models : 0
% 300.10/101.99 # Propositional check unsatisfiable : 0
% 300.10/101.99 # Propositional clauses : 0
% 300.10/101.99 # Propositional clauses after purity: 0
% 300.10/101.99 # Propositional unsat core size : 0
% 300.10/101.99 # Propositional preprocessing time : 0.000
% 300.10/101.99 # Propositional encoding time : 0.000
% 300.10/101.99 # Propositional solver time : 0.000
% 300.10/101.99 # Success case prop preproc time : 0.000
% 300.10/101.99 # Success case prop encoding time : 0.000
% 300.10/101.99 # Success case prop solver time : 0.000
% 300.10/101.99 # Current number of processed clauses : 819
% 300.10/101.99 # Positive orientable unit clauses : 80
% 300.10/101.99 # Positive unorientable unit clauses: 0
% 300.10/101.99 # Negative unit clauses : 16
% 300.10/101.99 # Non-unit-clauses : 723
% 300.10/101.99 # Current number of unprocessed clauses: 24561
% 300.10/101.99 # ...number of literals in the above : 78527
% 300.10/101.99 # Current number of archived formulas : 0
% 300.10/101.99 # Current number of archived clauses : 263
% 300.10/101.99 # Clause-clause subsumption calls (NU) : 50256
% 300.10/101.99 # Rec. Clause-clause subsumption calls : 39228
% 300.10/101.99 # Non-unit clause-clause subsumptions : 298
% 300.10/101.99 # Unit Clause-clause subsumption calls : 1113
% 300.10/101.99 # Rewrite failures with RHS unbound : 0
% 300.10/101.99 # BW rewrite match attempts : 32
% 300.10/101.99 # BW rewrite match successes : 13
% 300.10/101.99 # Condensation attempts : 1637
% 300.10/101.99 # Condensation successes : 15
% 300.10/101.99 # Termbank termtop insertions : 441746
% 300.10/101.99 # Search garbage collected termcells : 16925
% 300.10/101.99
% 300.10/101.99 # -------------------------------------------------
% 300.10/101.99 # User time : 0.464 s
% 300.10/101.99 # System time : 0.021 s
% 300.10/101.99 # Total time : 0.485 s
% 300.10/101.99 # Maximum resident set size: 6116 pages
% 300.10/101.99
% 300.10/101.99 # -------------------------------------------------
% 300.10/101.99 # User time : 0.473 s
% 300.10/101.99 # System time : 0.025 s
% 300.10/101.99 # Total time : 0.498 s
% 300.10/101.99 # Maximum resident set size: 2208 pages
% 300.10/101.99 % E---3.1 exiting
% 300.10/101.99 Cputime limit exceeded (core dumped)
% 300.10/101.99 % E exiting
%------------------------------------------------------------------------------