%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU685^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:08 EDT 2024
% Result : Theorem 1.90s 0.77s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 491
% Syntax : Number of formulae : 541 ( 5 unt; 289 typ; 0 def)
% Number of atoms : 2153 ( 316 equ; 0 cnn)
% Maximal formula atoms : 620 ( 8 avg)
% Number of connectives : 7894 ( 484 ~; 477 |; 363 &;5212 @)
% ( 278 <=>;1080 =>; 0 <=; 0 <~>)
% Maximal formula depth : 819 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 433 ( 433 >; 0 *; 0 +; 0 <<)
% Number of symbols : 293 ( 289 usr; 211 con; 0-4 aty)
% Number of variables : 1969 ( 124 ^1765 !; 80 ?;1969 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
epred1_0: $o ).
thf(decl_261,type,
esk1_2: $i > $i > $i ).
thf(decl_262,type,
esk2_2: $i > $i > $i ).
thf(decl_263,type,
esk3_2: $i > $i > $i ).
thf(decl_264,type,
esk4_1: $i > $i ).
thf(decl_265,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_266,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_267,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_268,type,
esk8_1: $i > $i ).
thf(decl_269,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_270,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_271,type,
esk11_2: $i > $i > $i ).
thf(decl_272,type,
esk12_2: $i > $i > $i ).
thf(decl_273,type,
esk13_1: $i > $i ).
thf(decl_274,type,
esk14_1: $i > $i ).
thf(decl_275,type,
esk15_1: $i > $i ).
thf(decl_276,type,
esk16_2: $i > $i > $i ).
thf(decl_277,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_278,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_279,type,
esk19_1: $i > $i ).
thf(decl_280,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_281,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_282,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_283,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_284,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_285,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_286,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_287,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_288,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_289,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_290,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_291,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_292,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_293,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_294,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_295,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_296,type,
esk36_2: $i > $i > $i ).
thf(decl_297,type,
esk37_2: $i > $i > $i ).
thf(decl_298,type,
esk38_2: $i > $i > $i ).
thf(decl_299,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_300,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_301,type,
esk41_2: $i > $i > $i ).
thf(decl_302,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_303,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_304,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_305,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_306,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_307,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_308,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_309,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_310,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_311,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_312,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_313,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_314,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_315,type,
esk55_0: $i ).
thf(decl_316,type,
esk56_0: $i ).
thf(decl_317,type,
esk57_0: $i ).
thf(decl_318,type,
esk58_0: $i ).
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(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(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(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X31 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X33 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp) ).
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(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X34 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).
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(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(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(funcGraphProp3,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X30 @ X2 ) ) @ X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp3) ).
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(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X30 @ X2 ) ) @ X30 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
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(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
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(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
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(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(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(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(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(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(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(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
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(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(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(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
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(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(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(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X29 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1) ).
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(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X29 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2) ).
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(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(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(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(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(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(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(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(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(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
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(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/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(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(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(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(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(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(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
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(c_0_201,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_202,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_203,plain,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_204,plain,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_205,plain,
( 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_206,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_207,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_208,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_209,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_210,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_211,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_212,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_213,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_214,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_215,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_216,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_217,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_218,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_219,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_220,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_221,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_222,plain,
( lamProp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X31 @ Z0 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamProp]) ).
thf(c_0_223,plain,
( lamp
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_224,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_225,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X34 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_226,plain,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E2]) ).
thf(c_0_227,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_228,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_229,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_230,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_231,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_232,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_233,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_234,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_235,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_236,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_237,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_238,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_239,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_240,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_241,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_242,plain,
( epred1_0
<=> ! [X650: $i] :
? [X651: $i] :
( ! [X652: $i] :
( ( in @ X652 @ X651 )
=> ! [X653: $i] :
( ( in @ X653 @ X652 )
=> ( in @ X653 @ X650 ) ) )
& ! [X654: $i,X655: $i] :
( ( ( in @ X654 @ X650 )
& ( in @ X655 @ X650 ) )
=> ( ! [X656: $i] :
( ( in @ X656 @ X651 )
=> ( ( in @ X654 @ X656 )
<=> ( in @ X655 @ X656 ) ) )
=> ( X654 = X655 ) ) )
& ! [X657: $i,X658: $i] :
( ( ( in @ X657 @ X651 )
& ( in @ X658 @ X651 ) )
=> ( ! [X659: $i] :
( ( in @ X659 @ X657 )
=> ( in @ X659 @ X658 ) )
| ! [X660: $i] :
( ( in @ X660 @ X658 )
=> ( in @ X660 @ X657 ) ) ) )
& ! [X661: $i] :
( ( ! [X662: $i] :
( ( in @ X662 @ X661 )
=> ( in @ X662 @ X650 ) )
& ? [X663: $i] : ( in @ X663 @ X661 ) )
=> ? [X664: $i,X665: $i] :
( ( in @ X664 @ X651 )
& ( in @ X665 @ X661 )
& ~ ? [X666: $i] :
( ( in @ X666 @ X664 )
& ( in @ X666 @ X661 ) )
& ! [X667: $i] :
( ( in @ X667 @ X651 )
=> ( ! [X668: $i] :
( ( in @ X668 @ X667 )
=> ( in @ X668 @ X664 ) )
| ( in @ X665 @ X667 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_243,negated_conjecture,
~ ( ! [X623: $i,X624: $i] :
( ! [X625: $i] :
( ( in @ X625 @ X623 )
<=> ( in @ X625 @ X624 ) )
=> ( X623 = X624 ) )
=> ( ! [X626: $i] :
~ ( in @ X626 @ emptyset )
=> ( ! [X627: $i,X628: $i,X629: $i] :
( ( in @ X629 @ ( setadjoin @ X627 @ X628 ) )
<=> ( ( X629 = X627 )
| ( in @ X629 @ X628 ) ) )
=> ( ! [X630: $i,X631: $i] :
( ( in @ X631 @ ( powerset @ X630 ) )
<=> ! [X632: $i] :
( ( in @ X632 @ X631 )
=> ( in @ X632 @ X630 ) ) )
=> ( ! [X633: $i,X634: $i] :
( ( in @ X634 @ ( setunion @ X633 ) )
<=> ? [X635: $i] :
( ( in @ X634 @ X635 )
& ( in @ X635 @ X633 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X636: $i] :
( ( in @ X636 @ omega )
=> ( in @ ( setadjoin @ X636 @ X636 ) @ omega ) )
=> ( ! [X637: $i] :
( ( ( in @ emptyset @ X637 )
& ! [X638: $i] :
( ( ( in @ X638 @ omega )
& ( in @ X638 @ X637 ) )
=> ( in @ ( setadjoin @ X638 @ X638 ) @ X637 ) ) )
=> ! [X639: $i] :
( ( in @ X639 @ omega )
=> ( in @ X639 @ X637 ) ) )
=> ( ! [X640: $i > $i > $o,X641: $i] :
( ! [X642: $i] :
( ( in @ X642 @ X641 )
=> ( exu @ ( X640 @ X642 ) ) )
=> ? [X643: $i] :
! [X644: $i] :
( ( in @ X644 @ X643 )
<=> ? [X645: $i] :
( ( in @ X645 @ X641 )
& ( X640 @ X645 @ X644 ) ) ) )
=> ( ! [X646: $i] :
( ? [X647: $i] : ( in @ X647 @ X646 )
=> ? [X648: $i] :
( ( in @ X648 @ X646 )
& ~ ? [X649: $i] :
( ( in @ X649 @ X648 )
& ( in @ X649 @ X646 ) ) ) )
=> ( epred1_0
=> ( ! [X669: $i > $o] :
( ( exu @ X669 )
=> ( X669
@ ( descr
@ ^ [Z0: $i] : ( X669 @ Z0 ) ) ) )
=> ( ! [X670: $i,X671: $i > $o,X672: $i] :
( ( in @ X672 @ X670 )
=> ( ( X671 @ X672 )
=> ( in @ X672 @ ( dsetconstr @ X670 @ X671 ) ) ) )
=> ( ! [X673: $i,X674: $i > $o,X675: $i] :
( ( in @ X675 @ ( dsetconstr @ X673 @ X674 ) )
=> ( in @ X675 @ X673 ) )
=> ( ! [X676: $i,X677: $i > $o,X678: $i] :
( ( in @ X678 @ ( dsetconstr @ X676 @ X677 ) )
=> ( X677 @ X678 ) )
=> ( ! [X679: $i > $o] :
( ( exu @ X679 )
=> ? [X680: $i] :
( ( X679 @ X680 )
& ! [X681: $i] :
( ( X679 @ X681 )
=> ( X680 = X681 ) ) ) )
=> ( ! [X682: $o,X683: $i] :
( ( in @ X683 @ ( prop2set @ X682 ) )
=> X682 )
=> ( ! [X684: $i] :
( ( in @ X684 @ emptyset )
=> ! [X685: $o] : X685 )
=> ( ! [X686: $i] :
( ( in @ X686 @ emptyset )
=> ~ $true )
=> ( ! [X687: $i] :
~ ( in @ X687 @ emptyset )
=> ( ! [X688: $i > $o] :
( ( exu @ X688 )
=> ? [X689: $i] : ( X688 @ X689 ) )
=> ( ! [X690: $i,X691: $i] :
( ! [X692: $i] :
( ( in @ X692 @ X690 )
=> ( in @ X692 @ X691 ) )
=> ( ! [X693: $i] :
( ( in @ X693 @ X691 )
=> ( in @ X693 @ X690 ) )
=> ( X690 = X691 ) ) )
=> ( ! [X694: $i] :
( ! [X695: $i] :
~ ( in @ X695 @ X694 )
=> ( X694 = emptyset ) )
=> ( ! [X696: $i] :
( ! [X697: $i] :
~ ( in @ X697 @ X696 )
=> ( X696 = emptyset ) )
=> ( ! [X698: $i,X699: $i > $o,X700: $i] :
( ( in @ X700 @ X698 )
=> ( ( in @ X700 @ ( dsetconstr @ X698 @ X699 ) )
<=> ( X699 @ X700 ) ) )
=> ( ! [X701: $i] :
( ( nonempty @ X701 )
=> ? [X702: $i] : ( in @ X702 @ X701 ) )
=> ( ! [X703: $i,X704: $i > $o,X705: $i] :
( ( in @ X705 @ X703 )
=> ( ( X704 @ X705 )
=> ( nonempty @ ( dsetconstr @ X703 @ X704 ) ) ) )
=> ( ! [X706: $i] :
( ? [X707: $i] : ( in @ X707 @ X706 )
=> ( nonempty @ X706 ) )
=> ( ! [X708: $i,X709: $i] : ( in @ X708 @ ( setadjoin @ X708 @ X709 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X710: $i,X711: $i,X712: $i] :
( ( in @ X712 @ X711 )
=> ( in @ X712 @ ( setadjoin @ X710 @ X711 ) ) )
=> ( ! [X713: $i,X714: $i,X715: $i] :
( ( in @ X715 @ ( setadjoin @ X713 @ X714 ) )
=> ! [X716: $o] :
( ( ( X715 = X713 )
=> X716 )
=> ( ( ( in @ X715 @ X714 )
=> X716 )
=> X716 ) ) )
=> ( ! [X717: $i,X718: $i,X719: $i] :
( ( in @ X719 @ ( setadjoin @ X717 @ X718 ) )
=> ( ( X719 = X717 )
| ( in @ X719 @ X718 ) ) )
=> ( ! [X720: $i] :
( ( dsetconstr @ X720
@ ^ [Z0: $i] : $true )
= X720 )
=> ( ! [X721: $i,X722: $i] :
( ! [X723: $i] :
( ( in @ X723 @ X722 )
=> ( in @ X723 @ X721 ) )
=> ( in @ X722 @ ( powerset @ X721 ) ) )
=> ( ! [X724: $i] : ( in @ emptyset @ ( powerset @ X724 ) )
=> ( ! [X725: $i] : ( in @ emptyset @ ( powerset @ X725 ) )
=> ( ! [X726: $i,X727: $i,X728: $i] :
( ( in @ X727 @ ( powerset @ X726 ) )
=> ( ( in @ X728 @ X727 )
=> ( in @ X728 @ X726 ) ) )
=> ( ! [X729: $i,X730: $i,X731: $i] :
( ( in @ X730 @ X731 )
=> ( ( in @ X731 @ X729 )
=> ( in @ X730 @ ( setunion @ X729 ) ) ) )
=> ( ! [X732: $i,X733: $i] :
( ( in @ X733 @ ( setunion @ X732 ) )
=> ! [X734: $o] :
( ! [X735: $i] :
( ( in @ X733 @ X735 )
=> ( ( in @ X735 @ X732 )
=> X734 ) )
=> X734 ) )
=> ( ! [X736: $i,X737: $i] :
( ( in @ X737 @ X736 )
=> ( in @ X737 @ ( powerset @ ( setunion @ X736 ) ) ) )
=> ( ! [X738: $i > $o] :
( ( exu @ X738 )
=> ? [X739: $i] :
! [X740: $i] :
( ( X738 @ X740 )
<=> ( X740 = X739 ) ) )
=> ( ! [X741: $i] :
( ( nonempty @ X741 )
=> ? [X742: $i] :
( ( in @ X742 @ X741 )
& $true ) )
=> ( ! [X743: $i,X744: $i] :
( ( in @ X743 @ ( setadjoin @ X744 @ emptyset ) )
=> ( X743 = X744 ) )
=> ( ! [X745: $i,X746: $i] :
( ( X745 != X746 )
=> ~ ( in @ X746 @ ( setadjoin @ X745 @ emptyset ) ) )
=> ( ! [X747: $i,X748: $i] :
( ( X747 = X748 )
=> ( in @ X747 @ ( setadjoin @ X748 @ emptyset ) ) )
=> ( ! [X749: $i,X750: $i] :
( ( in @ X749 @ ( setadjoin @ X750 @ emptyset ) )
=> ( in @ X750 @ ( setadjoin @ X749 @ emptyset ) ) )
=> ( ! [X751: $i,X752: $i,X753: $i] :
( ( in @ X753 @ ( setadjoin @ X751 @ ( setadjoin @ X752 @ emptyset ) ) )
=> ( ( X753 = X751 )
| ( X753 = X752 ) ) )
=> ( ! [X754: $i,X755: $i] : ( in @ X754 @ ( setadjoin @ X754 @ ( setadjoin @ X755 @ emptyset ) ) )
=> ( ! [X756: $i,X757: $i] : ( in @ X757 @ ( setadjoin @ X756 @ ( setadjoin @ X757 @ emptyset ) ) )
=> ( ! [X758: $i,X759: $i > $o] :
( ? [X760: $i] :
( ( in @ X760 @ X758 )
& ( X759 @ X760 ) )
=> ( ( ( dsetconstr @ X758 @ X759 )
= emptyset )
=> ~ $true ) )
=> ( ! [X761: $i > $o,X762: $i] :
( ( in @ X762 @ emptyset )
=> ( X761 @ X762 ) )
=> ( ! [X763: $i,X764: $i > $o] :
( ~ ! [X765: $i] :
( ( in @ X765 @ X763 )
=> ( X764 @ X765 ) )
=> ? [X766: $i] :
( ( in @ X766 @ X763 )
& ~ ( X764 @ X766 ) ) )
=> ( ! [X767: $i,X768: $i > $o] :
( ! [X769: $i] :
( ( in @ X769 @ X767 )
=> ~ ( X768 @ X769 ) )
=> ~ ? [X770: $i] :
( ( in @ X770 @ X767 )
& ( X768 @ X770 ) ) )
=> ( ! [X771: $i,X772: $i > $o] :
( ~ ? [X773: $i] :
( ( in @ X773 @ X771 )
& ( X772 @ X773 ) )
=> ! [X774: $i] :
( ( in @ X774 @ X771 )
=> ~ ( X772 @ X774 ) ) )
=> ( ! [X775: $i,X776: $i > $o] :
( ? [X777: $i] :
( ( in @ X777 @ X775 )
& ~ ( X776 @ X777 ) )
=> ~ ! [X778: $i] :
( ( in @ X778 @ X775 )
=> ( X776 @ X778 ) ) )
=> ( ! [X779: $o] :
( X779
=> ( in @ emptyset @ ( prop2set @ X779 ) ) )
=> ( prop2set2propI
=> ( ! [X780: $i,X781: $i > $o] :
( ~ ? [X782: $i] :
( ( in @ X782 @ X780 )
& ( X781 @ X782 ) )
=> ! [X783: $i] :
( ( in @ X783 @ X780 )
=> ~ ( X781 @ X783 ) ) )
=> ( ! [X784: $i,X785: $i > $o] :
( ~ ! [X786: $i] :
( ( in @ X786 @ X784 )
=> ( X785 @ X786 ) )
=> ? [X787: $i] :
( ( in @ X787 @ X784 )
& ~ ( X785 @ X787 ) ) )
=> ( ! [X788: $i > $o] :
( ? [X789: $i] :
( ( X788 @ X789 )
& ! [X790: $i] :
( ( X788 @ X790 )
=> ( X789 = X790 ) ) )
=> ( exu @ X788 ) )
=> ( ! [X791: $i > $o] :
( ? [X792: $i] : ( X791 @ X792 )
=> ( ! [X793: $i,X794: $i] :
( ( X791 @ X793 )
=> ( ( X791 @ X794 )
=> ( X793 = X794 ) ) )
=> ( exu @ X791 ) ) )
=> ( ! [X795: $i > $o] :
( ? [X796: $i] :
! [X797: $i] :
( ( X795 @ X797 )
<=> ( X797 = X796 ) )
=> ( exu @ X795 ) )
=> ( ! [X798: $i,X799: $i] :
( ( X798 = X799 )
=> ! [X800: $i,X801: $i] :
( ( X800 = X801 )
=> ( ( in @ X800 @ X798 )
=> ( in @ X801 @ X799 ) ) ) )
=> ( ! [X802: $i,X803: $i] :
( ( X802 = X803 )
=> ! [X804: $i,X805: $i] :
( ( X804 = X805 )
=> ( ( in @ X804 @ X802 )
<=> ( in @ X805 @ X803 ) ) ) )
=> ( ! [X806: $i > $o] :
( ( exu @ X806 )
=> ! [X807: $i,X808: $i] :
( ( X806 @ X807 )
=> ( ( X806 @ X808 )
=> ( X807 = X808 ) ) ) )
=> ( ! [X809: $i > $o,X810: $i > $o] :
( ! [X811: $i,X812: $i] :
( ( X811 = X812 )
=> ( ( X809 @ X811 )
<=> ( X810 @ X812 ) ) )
=> ( ( exu @ X809 )
<=> ( exu @ X810 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X813: $i,X814: $i] :
( ( X813 = X814 )
=> ! [X815: $i,X816: $i] :
( ( X815 = X816 )
=> ( ( setadjoin @ X813 @ X815 )
= ( setadjoin @ X814 @ X816 ) ) ) )
=> ( ! [X817: $i,X818: $i] :
( ( X817 = X818 )
=> ( ( powerset @ X817 )
= ( powerset @ X818 ) ) )
=> ( ! [X819: $i,X820: $i] :
( ( X819 = X820 )
=> ( ( setunion @ X819 )
= ( setunion @ X820 ) ) )
=> ( ( omega = omega )
=> ( ! [X821: $i > $o] :
( ( exu @ X821 )
=> ! [X822: $i,X823: $i] :
( ( X821 @ X822 )
=> ( ( X821 @ X823 )
=> ( X822 = X823 ) ) ) )
=> ( ! [X824: $i > $o,X825: $i > $o] :
( ! [X826: $i,X827: $i] :
( ( X826 = X827 )
=> ( ( X824 @ X826 )
<=> ( X825 @ X827 ) ) )
=> ( ( exu @ X824 )
=> ( ( exu @ X825 )
=> ( ( descr @ X824 )
= ( descr @ X825 ) ) ) ) )
=> ( ! [X828: $i,X829: $i] :
( ( X828 = X829 )
=> ! [X830: $i > $o,X831: $i > $o] :
( ! [X832: $i] :
( ( in @ X832 @ X828 )
=> ! [X833: $i] :
( ( in @ X833 @ X829 )
=> ( ( X832 = X833 )
=> ( ( X830 @ X832 )
<=> ( X831 @ X833 ) ) ) ) )
=> ( ( dsetconstr @ X828 @ X830 )
= ( dsetconstr @ X829 @ X831 ) ) ) )
=> ( ! [X834: $i,X835: $i] :
( ! [X836: $i] :
( ( in @ X836 @ X834 )
=> ( in @ X836 @ X835 ) )
=> ( subset @ X834 @ X835 ) )
=> ( ! [X837: $i,X838: $i] :
( ( X837 = X838 )
=> ( subset @ X838 @ X837 ) )
=> ( ! [X839: $i,X840: $i] :
( ( X839 = X840 )
=> ( subset @ X839 @ X840 ) )
=> ( ! [X841: $i,X842: $i] :
( ! [X843: $i] :
( ( in @ X843 @ X841 )
=> ( in @ X843 @ X842 ) )
=> ( subset @ X841 @ X842 ) )
=> ( ! [X844: $i] : ( subset @ emptyset @ X844 )
=> ( ! [X845: $i,X846: $i,X847: $i] :
( ( subset @ X845 @ X846 )
=> ( ( in @ X847 @ X845 )
=> ( in @ X847 @ X846 ) ) )
=> ( ! [X848: $i,X849: $i,X850: $i] :
( ( subset @ X848 @ X849 )
=> ( ~ ( in @ X850 @ X849 )
=> ~ ( in @ X850 @ X848 ) ) )
=> ( ! [X851: $i,X852: $i,X853: $i] :
( ( in @ X853 @ X851 )
=> ( ~ ( in @ X853 @ X852 )
=> ~ ( subset @ X851 @ X852 ) ) )
=> ( ! [X854: $i,X855: $i] :
( ~ ( subset @ X854 @ X855 )
=> ( X854 != X855 ) )
=> ( ! [X856: $i,X857: $i,X858: $i] :
( ( in @ X858 @ X856 )
=> ( ~ ( in @ X858 @ X857 )
=> ( X856 != X857 ) ) )
=> ( ! [X859: $i] : ( subset @ X859 @ X859 )
=> ( ! [X860: $i,X861: $i,X862: $i] :
( ( subset @ X860 @ X861 )
=> ( ( subset @ X861 @ X862 )
=> ( subset @ X860 @ X862 ) ) )
=> ( ! [X863: $i,X864: $i] : ( subset @ X864 @ ( setadjoin @ X863 @ X864 ) )
=> ( ! [X865: $i,X866: $i,X867: $i] :
( ( subset @ X865 @ X867 )
=> ( subset @ X865 @ ( setadjoin @ X866 @ X867 ) ) )
=> ( ! [X868: $i,X869: $i] :
( ( subset @ X868 @ X869 )
=> ( in @ X868 @ ( powerset @ X869 ) ) )
=> ( ! [X870: $i,X871: $i] :
( ( subset @ X870 @ X871 )
=> ( ( subset @ X871 @ X870 )
=> ( X870 = X871 ) ) )
=> ( ! [X872: $i] :
( ( subset @ X872 @ emptyset )
=> ( X872 = emptyset ) )
=> ( ! [X873: $i,X874: $i] :
( ( subset @ X874 @ X873 )
=> ( in @ X874 @ ( powerset @ X873 ) ) )
=> ( ! [X875: $i,X876: $i] :
( ( in @ X876 @ ( powerset @ X875 ) )
=> ( subset @ X876 @ X875 ) )
=> ( ! [X877: $i] : ( in @ X877 @ ( powerset @ X877 ) )
=> ( ! [X878: $i,X879: $i] :
( ( subset @ X878 @ X879 )
=> ( subset @ ( powerset @ X878 ) @ ( powerset @ X879 ) ) )
=> ( ! [X880: $i,X881: $i > $o] : ( in @ ( dsetconstr @ X880 @ X881 ) @ ( powerset @ X880 ) )
=> ( ! [X882: $i,X883: $i > $o] : ( subset @ ( dsetconstr @ X882 @ X883 ) @ X882 )
=> ( ! [X884: $i,X885: $i,X886: $i] :
( ( in @ X886 @ X884 )
=> ( in @ X886 @ ( binunion @ X884 @ X885 ) ) )
=> ( ! [X887: $i,X888: $i] : ( in @ X888 @ ( setadjoin @ X887 @ ( setadjoin @ X888 @ emptyset ) ) )
=> ( ! [X889: $i,X890: $i,X891: $i] :
( ( in @ X891 @ X890 )
=> ( in @ X891 @ ( binunion @ X889 @ X890 ) ) )
=> ( ! [X892: $i,X893: $i,X894: $i,X895: $o] :
( ( in @ X894 @ ( binunion @ X892 @ X893 ) )
=> ( ( ( in @ X894 @ X892 )
=> X895 )
=> ( ( ( in @ X894 @ X893 )
=> X895 )
=> X895 ) ) )
=> ( ! [X896: $i,X897: $i,X898: $i] :
( ( in @ X898 @ ( binunion @ X896 @ X897 ) )
=> ( ( in @ X898 @ X896 )
| ( in @ X898 @ X897 ) ) )
=> ( ! [X899: $i,X900: $i] : ( subset @ X899 @ ( binunion @ X899 @ X900 ) )
=> ( ! [X901: $i,X902: $i] : ( subset @ X902 @ ( binunion @ X901 @ X902 ) )
=> ( ! [X903: $i,X904: $i,X905: $i] :
( ( in @ X905 @ X903 )
=> ( ( in @ X905 @ X904 )
=> ( in @ X905 @ ( binintersect @ X903 @ X904 ) ) ) )
=> ( ! [X906: $i,X907: $i,X908: $i] :
( ( subset @ X908 @ X906 )
=> ( ( subset @ X908 @ X907 )
=> ( subset @ X908 @ ( binintersect @ X906 @ X907 ) ) ) )
=> ( ! [X909: $i,X910: $i,X911: $i] :
( ( in @ X911 @ ( binintersect @ X909 @ X910 ) )
=> ( in @ X911 @ X909 ) )
=> ( ! [X912: $i,X913: $i] : ( subset @ ( binintersect @ X912 @ X913 ) @ X912 )
=> ( ! [X914: $i,X915: $i] :
( ( subset @ X914 @ X915 )
=> ( ( binintersect @ X914 @ X915 )
= X914 ) )
=> ( ! [X916: $i,X917: $i] :
( ( ( binintersect @ X916 @ X917 )
= X917 )
=> ( subset @ X917 @ X916 ) )
=> ( ! [X918: $i,X919: $i,X920: $i] :
( ( in @ X920 @ ( binintersect @ X918 @ X919 ) )
=> ( in @ X920 @ X919 ) )
=> ( ! [X921: $i,X922: $i] :
( ~ ? [X923: $i] :
( ( in @ X923 @ X921 )
& ( in @ X923 @ X922 ) )
=> ( ( binintersect @ X921 @ X922 )
= emptyset ) )
=> ( ! [X924: $i,X925: $i] : ( subset @ ( binintersect @ X924 @ X925 ) @ X925 )
=> ( ! [X926: $i,X927: $i] :
( ( subset @ X927 @ X926 )
=> ( ( binintersect @ X926 @ X927 )
= X927 ) )
=> ( ! [X928: $i,X929: $i] :
( ( ( binintersect @ X928 @ X929 )
= X928 )
=> ( subset @ X928 @ X929 ) )
=> ( ! [X930: $i,X931: $i,X932: $i] :
( ( binintersect @ X930 @ ( binunion @ X931 @ X932 ) )
= ( binunion @ ( binintersect @ X930 @ X931 ) @ ( binintersect @ X930 @ X932 ) ) )
=> ( ! [X933: $i,X934: $i,X935: $i] :
( ( in @ X935 @ X933 )
=> ( ~ ( in @ X935 @ X934 )
=> ( in @ X935 @ ( setminus @ X933 @ X934 ) ) ) )
=> ( ! [X936: $i,X937: $i,X938: $i] :
( ( in @ X938 @ ( setminus @ X936 @ X937 ) )
=> ( in @ X938 @ X936 ) )
=> ( ! [X939: $i,X940: $i,X941: $i] :
( ( in @ X941 @ ( setminus @ X939 @ X940 ) )
=> ~ ( in @ X941 @ X940 ) )
=> ( ! [X942: $i,X943: $i] :
( ( subset @ X942 @ X943 )
=> ( ( setminus @ X942 @ X943 )
= emptyset ) )
=> ( ! [X944: $i,X945: $i,X946: $i] :
( ~ ( in @ X946 @ ( setminus @ X944 @ X945 ) )
=> ( ( in @ X946 @ X944 )
=> ( in @ X946 @ X945 ) ) )
=> ( ! [X947: $i,X948: $i,X949: $i] :
( ~ ( in @ X949 @ ( setminus @ X947 @ X948 ) )
=> ( ~ ( in @ X949 @ X948 )
=> ~ ( in @ X949 @ X947 ) ) )
=> ( ! [X950: $i,X951: $i,X952: $i] :
( ~ ( in @ X952 @ X950 )
=> ~ ( in @ X952 @ ( setminus @ X950 @ X951 ) ) )
=> ( ! [X953: $i,X954: $i,X955: $i] :
( ( in @ X955 @ X954 )
=> ~ ( in @ X955 @ ( setminus @ X953 @ X954 ) ) )
=> ( ! [X956: $i,X957: $i] : ( subset @ ( setminus @ X956 @ X957 ) @ X956 )
=> ( ! [X958: $i,X959: $i] :
( ( ( setminus @ X958 @ X959 )
= emptyset )
=> ( subset @ X958 @ X959 ) )
=> ( ! [X960: $i,X961: $i,X962: $i] :
( ( in @ X962 @ ( symdiff @ X960 @ X961 ) )
=> ! [X963: $o] :
( ( ( in @ X962 @ X960 )
=> ( ~ ( in @ X962 @ X961 )
=> X963 ) )
=> ( ( ~ ( in @ X962 @ X960 )
=> ( ( in @ X962 @ X961 )
=> X963 ) )
=> X963 ) ) )
=> ( ! [X964: $i,X965: $i,X966: $i] :
( ( in @ X966 @ X964 )
=> ( ~ ( in @ X966 @ X965 )
=> ( in @ X966 @ ( symdiff @ X964 @ X965 ) ) ) )
=> ( ! [X967: $i,X968: $i,X969: $i] :
( ~ ( in @ X969 @ X967 )
=> ( ( in @ X969 @ X968 )
=> ( in @ X969 @ ( symdiff @ X967 @ X968 ) ) ) )
=> ( ! [X970: $i,X971: $i,X972: $i] :
( ( in @ X972 @ X970 )
=> ( ( in @ X972 @ X971 )
=> ~ ( in @ X972 @ ( symdiff @ X970 @ X971 ) ) ) )
=> ( ! [X973: $i,X974: $i,X975: $i] :
( ~ ( in @ X975 @ X973 )
=> ( ~ ( in @ X975 @ X974 )
=> ~ ( in @ X975 @ ( symdiff @ X973 @ X974 ) ) ) )
=> ( ! [X976: $i,X977: $i] : ( in @ X977 @ ( setadjoin @ X976 @ ( setadjoin @ X977 @ emptyset ) ) )
=> ( ! [X978: $i,X979: $i] : ( in @ X978 @ ( setunion @ ( setadjoin @ ( setadjoin @ X978 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X978 @ ( setadjoin @ X979 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X980: $i,X981: $i] : ( in @ X981 @ ( setunion @ ( setadjoin @ ( setadjoin @ X980 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X980 @ ( setadjoin @ X981 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X982: $i,X983: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X982 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X982 @ ( setadjoin @ X983 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X984: $i,X985: $i] : ( iskpair @ ( kpair @ X984 @ X985 ) )
=> ( ! [X986: $i,X987: $i] :
( ( in @ X987 @ X986 )
=> ( subset @ ( setadjoin @ X987 @ emptyset ) @ X986 ) )
=> ( ! [X988: $i,X989: $i] :
( ( in @ X989 @ X988 )
=> ( in @ ( setadjoin @ X989 @ emptyset ) @ ( powerset @ X988 ) ) )
=> ( ! [X990: $i,X991: $i,X992: $i] :
( ( in @ X992 @ X990 )
=> ( in @ ( setadjoin @ X992 @ emptyset ) @ ( powerset @ ( binunion @ X990 @ X991 ) ) ) )
=> ( ! [X993: $i,X994: $i,X995: $i] :
( ( in @ X995 @ ( setadjoin @ X993 @ ( setadjoin @ X994 @ emptyset ) ) )
=> ( ( X995 = X993 )
| ( X995 = X994 ) ) )
=> ( ! [X996: $i,X997: $i,X998: $i] :
( ( in @ X998 @ X996 )
=> ! [X999: $i] :
( ( in @ X999 @ X997 )
=> ( subset @ ( setadjoin @ X998 @ ( setadjoin @ X999 @ emptyset ) ) @ ( binunion @ X996 @ X997 ) ) ) )
=> ( ! [X1000: $i,X1001: $i,X1002: $i] :
( ( in @ X1002 @ X1000 )
=> ! [X1003: $i] :
( ( in @ X1003 @ X1001 )
=> ( in @ ( setadjoin @ X1002 @ ( setadjoin @ X1003 @ emptyset ) ) @ ( powerset @ ( binunion @ X1000 @ X1001 ) ) ) ) )
=> ( ! [X1004: $i,X1005: $i,X1006: $i] :
( ( in @ X1006 @ X1004 )
=> ! [X1007: $i] :
( ( in @ X1007 @ X1005 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1006 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1006 @ ( setadjoin @ X1007 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1004 @ X1005 ) ) ) ) )
=> ( ! [X1008: $i,X1009: $i,X1010: $i] :
( ( in @ X1010 @ X1008 )
=> ! [X1011: $i] :
( ( in @ X1011 @ X1009 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1010 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1010 @ ( setadjoin @ X1011 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1008 @ X1009 ) ) ) ) ) )
=> ( ! [X1012: $i,X1013: $i,X1014: $i] :
( ( in @ X1014 @ X1012 )
=> ! [X1015: $i] :
( ( in @ X1015 @ X1013 )
=> ( in @ ( kpair @ X1014 @ X1015 ) @ ( powerset @ ( powerset @ ( binunion @ X1012 @ X1013 ) ) ) ) ) )
=> ( ! [X1016: $i,X1017: $i,X1018: $i] :
( ( in @ X1018 @ X1016 )
=> ! [X1019: $i] :
( ( in @ X1019 @ X1017 )
=> ( in @ ( kpair @ X1018 @ X1019 ) @ ( cartprod @ X1016 @ X1017 ) ) ) )
=> ( ! [X1020: $i,X1021: $i,X1022: $i] :
( ( in @ X1022 @ ( cartprod @ X1020 @ X1021 ) )
=> ? [X1023: $i] :
( ( in @ X1023 @ X1020 )
& ? [X1024: $i] :
( ( in @ X1024 @ X1021 )
& ( X1022
= ( kpair @ X1023 @ X1024 ) ) ) ) )
=> ( ! [X1025: $i,X1026: $i,X1027: $i] :
( ( in @ X1027 @ ( cartprod @ X1025 @ X1026 ) )
=> ( iskpair @ X1027 ) )
=> ( ! [X1028: $i,X1029: $i] :
( ( in @ X1029 @ ( setunion @ X1028 ) )
=> ? [X1030: $i] :
( ( in @ X1030 @ X1028 )
& ( in @ X1029 @ X1030 ) ) )
=> ( ! [X1031: $i] : ( subset @ ( setunion @ ( setadjoin @ X1031 @ emptyset ) ) @ X1031 )
=> ( ! [X1032: $i] : ( subset @ X1032 @ ( setunion @ ( setadjoin @ X1032 @ emptyset ) ) )
=> ( ! [X1033: $i] :
( ( setunion @ ( setadjoin @ X1033 @ emptyset ) )
= X1033 )
=> ( ! [X1034: $i,X1035: $i > $o] :
( ! [X1036: $i] :
( ( in @ X1036 @ X1034 )
=> ! [X1037: $i] :
( ( in @ X1037 @ X1034 )
=> ( ( X1035 @ X1036 )
=> ( ( X1035 @ X1037 )
=> ( X1036 = X1037 ) ) ) ) )
=> ( ? [X1038: $i] :
( ( in @ X1038 @ X1034 )
& ( X1035 @ X1038 ) )
=> ( singleton @ ( dsetconstr @ X1034 @ X1035 ) ) ) )
=> ( ! [X1039: $i,X1040: $i > $o] :
( ( ex1 @ X1039 @ X1040 )
=> ? [X1041: $i] :
( ( in @ X1041 @ X1039 )
& ( X1040 @ X1041 ) ) )
=> ( ! [X1042: $i,X1043: $i > $o,X1044: $i] :
( ( in @ X1044 @ X1042 )
=> ( ( X1043 @ X1044 )
=> ( ! [X1045: $i] :
( ( in @ X1045 @ X1042 )
=> ( ( X1043 @ X1045 )
=> ( X1045 = X1044 ) ) )
=> ( ex1 @ X1042 @ X1043 ) ) ) )
=> ( ! [X1046: $i,X1047: $i > $o] :
( ! [X1048: $i] :
( ( in @ X1048 @ X1046 )
=> ! [X1049: $i] :
( ( in @ X1049 @ X1046 )
=> ( ( X1047 @ X1048 )
=> ( ( X1047 @ X1049 )
=> ( X1048 = X1049 ) ) ) ) )
=> ( ? [X1050: $i] :
( ( in @ X1050 @ X1046 )
& ( X1047 @ X1050 ) )
=> ( ex1 @ X1046 @ X1047 ) ) )
=> ( ! [X1051: $i,X1052: $i] :
( ( ( setadjoin @ X1051 @ emptyset )
= ( setadjoin @ X1052 @ emptyset ) )
=> ( X1051 = X1052 ) )
=> ( ! [X1053: $i,X1054: $i,X1055: $i] :
( ( in @ ( setadjoin @ X1055 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1053 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1053 @ ( setadjoin @ X1054 @ emptyset ) ) @ emptyset ) ) )
=> ( X1053 = X1055 ) )
=> ( ! [X1056: $i] :
( ( iskpair @ X1056 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1056 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1056 ) ) ) )
=> ( ! [X1057: $i] :
( ( singleton @ X1057 )
=> ( in @ ( setunion @ X1057 ) @ X1057 ) )
=> ( ! [X1058: $i,X1059: $i] :
( ( kfst @ ( kpair @ X1058 @ X1059 ) )
= X1058 )
=> ( ! [X1060: $i,X1061: $i,X1062: $i] :
( ( in @ X1062 @ ( cartprod @ X1060 @ X1061 ) )
=> ( in @ ( kfst @ X1062 ) @ X1060 ) )
=> ( ! [X1063: $i,X1064: $i,X1065: $i,X1066: $i] :
( ( ( setadjoin @ ( setadjoin @ X1063 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1063 @ ( setadjoin @ X1064 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1065 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1065 @ ( setadjoin @ X1066 @ emptyset ) ) @ emptyset ) ) )
=> ( X1063 = X1065 ) )
=> ( ! [X1067: $i,X1068: $i,X1069: $i,X1070: $i] :
( ( ( kpair @ X1067 @ X1068 )
= ( kpair @ X1069 @ X1070 ) )
=> ( X1067 = X1069 ) )
=> ( ! [X1071: $i,X1072: $i] :
( ( X1071 = X1072 )
=> ( ( setadjoin @ X1071 @ ( setadjoin @ X1072 @ emptyset ) )
= ( setadjoin @ X1071 @ emptyset ) ) )
=> ( ! [X1073: $i,X1074: $i] :
( ( X1073 = X1074 )
=> ( ( setadjoin @ ( setadjoin @ X1073 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1073 @ ( setadjoin @ X1074 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1073 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1075: $i,X1076: $i,X1077: $i,X1078: $i] :
( ( ( setadjoin @ ( setadjoin @ X1075 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1075 @ ( setadjoin @ X1076 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1077 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1077 @ ( setadjoin @ X1078 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1077 = X1078 )
=> ( X1076 = X1078 ) ) )
=> ( ! [X1079: $i,X1080: $i,X1081: $i] :
( ( ( setadjoin @ X1079 @ ( setadjoin @ X1080 @ emptyset ) )
= ( setadjoin @ X1081 @ emptyset ) )
=> ( X1079 = X1080 ) )
=> ( ! [X1082: $i,X1083: $i,X1084: $i,X1085: $i] :
( ( ( setadjoin @ ( setadjoin @ X1082 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1082 @ ( setadjoin @ X1083 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1084 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1084 @ ( setadjoin @ X1085 @ emptyset ) ) @ emptyset ) ) )
=> ( X1083 = X1085 ) )
=> ( ! [X1086: $i,X1087: $i,X1088: $i,X1089: $i] :
( ( ( kpair @ X1086 @ X1087 )
= ( kpair @ X1088 @ X1089 ) )
=> ( X1087 = X1089 ) )
=> ( ! [X1090: $i] :
( ( iskpair @ X1090 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1090 )
@ ^ [Z0: $i] :
( X1090
= ( kpair @ ( kfst @ X1090 ) @ Z0 ) ) ) ) )
=> ( ! [X1091: $i,X1092: $i] :
( ( ksnd @ ( kpair @ X1091 @ X1092 ) )
= X1092 )
=> ( ! [X1093: $i] :
( ( iskpair @ X1093 )
=> ( ( kpair @ ( kfst @ X1093 ) @ ( ksnd @ X1093 ) )
= X1093 ) )
=> ( ! [X1094: $i,X1095: $i,X1096: $i] :
( ( in @ X1096 @ ( cartprod @ X1094 @ X1095 ) )
=> ( in @ ( ksnd @ X1096 ) @ X1095 ) )
=> ( ! [X1097: $i,X1098: $i,X1099: $i,X1100: $i] :
( ( in @ ( kpair @ X1099 @ X1100 ) @ ( cartprod @ X1097 @ X1098 ) )
=> ( in @ X1099 @ X1097 ) )
=> ( ! [X1101: $i,X1102: $i,X1103: $i,X1104: $i] :
( ( in @ ( kpair @ X1103 @ X1104 ) @ ( cartprod @ X1101 @ X1102 ) )
=> ( in @ X1104 @ X1102 ) )
=> ( ! [X1105: $i,X1106: $i,X1107: $i] :
( ( in @ X1107 @ X1105 )
=> ! [X1108: $i] :
( ( in @ X1108 @ X1106 )
=> ( ( kpair @ X1107 @ X1108 )
= ( kpair @ X1107 @ X1108 ) ) ) )
=> ( ! [X1109: $i,X1110: $i,X1111: $i] :
( ( in @ X1111 @ X1109 )
=> ! [X1112: $i] :
( ( in @ X1112 @ X1110 )
=> ( ( kfst @ ( kpair @ X1111 @ X1112 ) )
= X1111 ) ) )
=> ( ! [X1113: $i,X1114: $i,X1115: $i] :
( ( in @ X1115 @ X1113 )
=> ! [X1116: $i] :
( ( in @ X1116 @ X1114 )
=> ( ( ksnd @ ( kpair @ X1115 @ X1116 ) )
= X1116 ) ) )
=> ( ! [X1117: $i,X1118: $i,X1119: $i] :
( ( in @ X1119 @ ( cartprod @ X1117 @ X1118 ) )
=> ( ( kpair @ ( kfst @ X1119 ) @ ( ksnd @ X1119 ) )
= X1119 ) )
=> ( ! [X1120: $i,X1121: $i,X1122: $i > $i > $o,X1123: $i] :
( ( in @ X1123 @ X1120 )
=> ! [X1124: $i] :
( ( in @ X1124 @ X1121 )
=> ( ( X1122 @ X1123 @ X1124 )
=> ( in @ ( kpair @ X1123 @ X1124 ) @ ( dpsetconstr @ X1120 @ X1121 @ X1122 ) ) ) ) )
=> ( ! [X1125: $i,X1126: $i,X1127: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1125 @ X1126 @ X1127 ) @ ( cartprod @ X1125 @ X1126 ) )
=> ( ! [X1128: $i,X1129: $i,X1130: $i > $i > $o] : ( breln @ X1128 @ X1129 @ ( dpsetconstr @ X1128 @ X1129 @ X1130 ) )
=> ( ! [X1131: $i,X1132: $i,X1133: $i > $i > $o,X1134: $i] :
( ( in @ X1134 @ X1131 )
=> ! [X1135: $i] :
( ( in @ X1135 @ X1132 )
=> ( ( in @ ( kpair @ X1134 @ X1135 ) @ ( dpsetconstr @ X1131 @ X1132 @ X1133 ) )
=> ( X1133 @ X1134 @ X1135 ) ) ) )
=> ( ! [X1136: $i,X1137: $i,X1138: $i > $i > $o,X1139: $i,X1140: $i] :
( ( in @ ( kpair @ X1139 @ X1140 ) @ ( dpsetconstr @ X1136 @ X1137 @ X1138 ) )
=> ( in @ X1139 @ X1136 ) )
=> ( ! [X1141: $i,X1142: $i,X1143: $i > $i > $o,X1144: $i,X1145: $i] :
( ( in @ ( kpair @ X1144 @ X1145 ) @ ( dpsetconstr @ X1141 @ X1142 @ X1143 ) )
=> ( in @ X1145 @ X1142 ) )
=> ( ! [X1146: $i,X1147: $i,X1148: $i > $i > $o,X1149: $i,X1150: $i] :
( ( in @ ( kpair @ X1149 @ X1150 ) @ ( dpsetconstr @ X1146 @ X1147 @ X1148 ) )
=> ( X1148 @ X1149 @ X1150 ) )
=> ( ! [X1151: $i,X1152: $i,X1153: $i] :
( ( func @ X1151 @ X1152 @ X1153 )
=> ! [X1154: $i] :
( ( in @ X1154 @ X1151 )
=> ( singleton
@ ( dsetconstr @ X1152
@ ^ [Z0: $i] : ( in @ ( kpair @ X1154 @ Z0 ) @ X1153 ) ) ) ) )
=> ( ! [X1155: $i,X1156: $i,X1157: $i] :
( ( func @ X1155 @ X1156 @ X1157 )
=> ! [X1158: $i] :
( ( in @ X1158 @ X1155 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1156
@ ^ [Z0: $i] : ( in @ ( kpair @ X1158 @ Z0 ) @ X1157 ) ) )
@ X1156 ) ) )
=> ( ! [X1159: $i,X1160: $i,X1161: $i] :
( ( func @ X1159 @ X1160 @ X1161 )
=> ! [X1162: $i] :
( ( in @ X1162 @ X1159 )
=> ( in @ ( ap @ X1159 @ X1160 @ X1161 @ X1162 ) @ X1160 ) ) )
=> ( ! [X1163: $i,X1164: $i,X1165: $i] :
( ( in @ X1165 @ ( funcSet @ X1163 @ X1164 ) )
=> ( func @ X1163 @ X1164 @ X1165 ) )
=> ( ! [X1166: $i,X1167: $i,X1168: $i] :
( ( in @ X1168 @ ( funcSet @ X1166 @ X1167 ) )
=> ! [X1169: $i] :
( ( in @ X1169 @ X1166 )
=> ( in @ ( ap @ X1166 @ X1167 @ X1168 @ X1169 ) @ X1167 ) ) )
=> ( ! [X1170: $i,X1171: $i,X1172: $i] :
( ( func @ X1170 @ X1171 @ X1172 )
=> ( in @ X1172 @ ( funcSet @ X1170 @ X1171 ) ) )
=> ( ! [X1173: $i,X1174: $i,X1175: $i > $i] :
( ! [X1176: $i] :
( ( in @ X1176 @ X1173 )
=> ( in @ ( X1175 @ X1176 ) @ X1174 ) )
=> ( func @ X1173 @ X1174
@ ( dpsetconstr @ X1173 @ X1174
@ ^ [Z0: $i] : ( $eq @ ( X1175 @ Z0 ) ) ) ) )
=> ( ! [X1177: $i,X1178: $i,X1179: $i > $i] :
( ! [X1180: $i] :
( ( in @ X1180 @ X1177 )
=> ( in @ ( X1179 @ X1180 ) @ X1178 ) )
=> ( func @ X1177 @ X1178 @ ( lam @ X1177 @ X1178 @ X1179 ) ) )
=> ( ! [X1181: $i,X1182: $i,X1183: $i > $i] :
( ! [X1184: $i] :
( ( in @ X1184 @ X1181 )
=> ( in @ ( X1183 @ X1184 ) @ X1182 ) )
=> ( in @ ( lam @ X1181 @ X1182 @ X1183 ) @ ( funcSet @ X1181 @ X1182 ) ) )
=> ( ! [X1185: $i,X1186: $i,X1187: $i] :
( ( breln @ X1185 @ X1186 @ X1187 )
=> ! [X1188: $i > $o] :
( ! [X1189: $i] :
( ( in @ X1189 @ X1185 )
=> ! [X1190: $i] :
( ( in @ X1190 @ X1186 )
=> ( ( in @ ( kpair @ X1189 @ X1190 ) @ X1187 )
=> ( X1188 @ ( kpair @ X1189 @ X1190 ) ) ) ) )
=> ! [X1191: $i] :
( ( in @ X1191 @ X1187 )
=> ( X1188 @ X1191 ) ) ) )
=> ( ! [X1192: $i,X1193: $i,X1194: $i] :
( ( breln @ X1192 @ X1193 @ X1194 )
=> ! [X1195: $i > $o] :
( ! [X1196: $i] :
( ( in @ X1196 @ X1192 )
=> ! [X1197: $i] :
( ( in @ X1197 @ X1193 )
=> ( ( in @ ( kpair @ X1196 @ X1197 ) @ X1194 )
=> ( X1195 @ ( kpair @ X1196 @ X1197 ) ) ) ) )
=> ! [X1198: $i] :
( ( in @ X1198 @ X1194 )
=> ( X1195 @ X1198 ) ) ) )
=> ( ! [X1199: $i,X1200: $i > $o] :
( ( ex1 @ X1199 @ X1200 )
=> ! [X1201: $i] :
( ( in @ X1201 @ X1199 )
=> ! [X1202: $i] :
( ( in @ X1202 @ X1199 )
=> ( ( X1200 @ X1201 )
=> ( ( X1200 @ X1202 )
=> ( X1201 = X1202 ) ) ) ) ) )
=> ( ! [X1203: $i,X1204: $i,X1205: $i] :
( ( func @ X1203 @ X1204 @ X1205 )
=> ! [X1206: $i] :
( ( in @ X1206 @ X1203 )
=> ( in @ ( kpair @ X1206 @ ( ap @ X1203 @ X1204 @ X1205 @ X1206 ) ) @ X1205 ) ) )
=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X30 @ X2 ) ) @ X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[funcGraphProp3]),cartprodpairmemEL]),funcGraphProp1]),c_0_201]),quantDeMorgan4]),c_0_202]),c_0_203]),singletonsuniq]),prop2setI]),setukpairinjL1]),c_0_204]),notdexE]),theprop]),kfstpairEq]),notdallE]),cartprodfstin]),setukpairinjL2]),c_0_205]),setukpairinjL]),setukpairinjR11]),c_0_206]),setukpairinjR12]),setukpairinjR1]),c_0_207]),upairequniteq]),inCongP]),setukpairinjR2]),setukpairinjR]),c_0_208]),in__Cong]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),c_0_209]),notequalI2]),cartprodpairmemER]),cartprodmempaircEq]),c_0_210]),cartprodfstpairEq]),cartprodsndpairEq]),emptyset__Cong]),cartprodpairsurjEq]),c_0_211]),setadjoin__Cong]),c_0_212]),c_0_213]),c_0_214]),c_0_215]),powerset__Cong]),c_0_216]),c_0_217]),setunion__Cong]),c_0_218]),c_0_219]),omega__Cong]),app]),infuncsetfunc]),c_0_220]),ap2p]),funcinfuncset]),c_0_221]),c_0_222]),c_0_223]),c_0_224]),c_0_225]),brelnall1]),subsetI1]),brelnall2]),c_0_226]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),setminusSubset2]),setminusERneg]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_227]),c_0_228]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),quantDeMorgan1]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),quantDeMorgan2]),binintersectSubset4]),quantDeMorgan3]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_229]),vacuousDall]),c_0_230]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_231]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_232]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_233]),nonemptyE1]),c_0_234]),noeltsimpempty]),emptyI]),setext]),c_0_235]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_236]),c_0_237]),c_0_238]),c_0_239]),c_0_240]),wellorderingAx]),foundationAx]),c_0_241]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_242]) ).
thf(c_0_244,negated_conjecture,
! [X1207: $i,X1208: $i,X1210: $i,X1211: $i,X1212: $i,X1213: $i,X1214: $i,X1215: $i,X1216: $i,X1217: $i,X1218: $i,X1220: $i,X1221: $i,X1223: $i,X1224: $i,X1225: $i,X1226: $i,X1227: $i,X1229: $i,X1230: $i > $i > $o,X1231: $i,X1234: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i,X1241: $i,X1242: $i > $o,X1243: $i,X1244: $i > $o,X1245: $i,X1246: $i,X1247: $i > $o,X1248: $i,X1249: $i,X1250: $i > $o,X1251: $i,X1252: $i > $o,X1254: $i,X1255: $o,X1256: $i,X1257: $i,X1258: $o,X1259: $i,X1260: $i,X1261: $i > $o,X1263: $i,X1264: $i,X1267: $i,X1269: $i,X1271: $i,X1272: $i > $o,X1273: $i,X1274: $i,X1276: $i,X1277: $i > $o,X1278: $i,X1279: $i,X1280: $i,X1281: $i,X1282: $i,X1283: $i,X1284: $i,X1285: $i,X1286: $i,X1287: $i,X1288: $i,X1289: $o,X1290: $i,X1291: $i,X1292: $i,X1293: $i,X1294: $i,X1295: $i,X1297: $i,X1298: $i,X1299: $i,X1300: $i,X1301: $i,X1302: $i,X1303: $i,X1304: $i,X1305: $i,X1306: $i,X1307: $o,X1309: $i,X1310: $i,X1311: $i > $o,X1313: $i,X1314: $i,X1315: $i,X1317: $i,X1318: $i,X1319: $i,X1320: $i,X1321: $i,X1322: $i,X1323: $i,X1324: $i,X1325: $i,X1326: $i,X1327: $i,X1328: $i,X1329: $i,X1330: $i,X1331: $i,X1332: $i,X1333: $i > $o,X1334: $i,X1335: $i > $o,X1336: $i,X1337: $i,X1338: $i > $o,X1339: $i,X1341: $i,X1342: $i > $o,X1344: $i,X1345: $i,X1346: $i > $o,X1348: $i,X1349: $i,X1350: $i > $o,X1351: $i,X1353: $o,X1354: $i,X1355: $i > $o,X1357: $i,X1358: $i,X1359: $i > $o,X1360: $i,X1362: $i > $o,X1363: $i,X1365: $i > $o,X1366: $i,X1369: $i > $o,X1370: $i,X1372: $i,X1373: $i,X1374: $i,X1375: $i,X1376: $i,X1377: $i,X1378: $i,X1379: $i,X1380: $i > $o,X1381: $i,X1382: $i,X1383: $i > $o,X1384: $i > $o,X1387: $i,X1388: $i,X1389: $i,X1390: $i,X1391: $i,X1392: $i,X1393: $i,X1394: $i,X1395: $i > $o,X1396: $i,X1397: $i,X1398: $i > $o,X1399: $i > $o,X1402: $i,X1403: $i,X1404: $i > $o,X1405: $i > $o,X1408: $i,X1409: $i,X1411: $i,X1412: $i,X1413: $i,X1414: $i,X1415: $i,X1416: $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: $i,X1447: $i,X1448: $i,X1449: $i,X1450: $i,X1451: $i,X1452: $i,X1453: $i,X1454: $i,X1455: $i > $o,X1456: $i,X1457: $i > $o,X1458: $i,X1459: $i,X1460: $i,X1461: $i,X1462: $i,X1463: $i,X1464: $i,X1465: $i,X1466: $i,X1467: $i,X1468: $i,X1469: $o,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,X1498: $i,X1499: $i,X1500: $i,X1501: $i,X1502: $i,X1503: $i,X1504: $i,X1505: $i,X1506: $i,X1507: $i,X1508: $i,X1509: $i,X1510: $i,X1511: $i,X1512: $i,X1513: $i,X1514: $i,X1515: $i,X1516: $i,X1517: $i,X1518: $i,X1519: $i,X1520: $i,X1521: $i,X1522: $i,X1523: $i,X1524: $i,X1525: $i,X1526: $i,X1527: $i,X1528: $i,X1529: $i,X1530: $i,X1531: $i,X1532: $i,X1533: $i,X1534: $i,X1535: $i,X1536: $i,X1537: $o,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,X1599: $i,X1600: $i,X1601: $i,X1602: $i,X1603: $i,X1605: $i,X1606: $i,X1607: $i,X1608: $i,X1609: $i > $o,X1612: $i,X1613: $i,X1614: $i > $o,X1616: $i,X1617: $i > $o,X1618: $i,X1620: $i,X1621: $i > $o,X1624: $i,X1625: $i,X1626: $i,X1627: $i,X1628: $i,X1629: $i,X1630: $i,X1631: $i,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,X1646: $i,X1647: $i,X1648: $i,X1649: $i,X1650: $i,X1651: $i,X1652: $i,X1653: $i,X1654: $i,X1655: $i,X1656: $i,X1657: $i,X1658: $i,X1659: $i,X1660: $i,X1661: $i,X1662: $i,X1663: $i,X1664: $i,X1665: $i,X1666: $i,X1667: $i,X1668: $i,X1669: $i,X1670: $i,X1671: $i,X1672: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i,X1678: $i,X1679: $i,X1680: $i,X1681: $i,X1682: $i,X1683: $i,X1684: $i,X1685: $i,X1686: $i,X1687: $i,X1688: $i,X1689: $i,X1690: $i,X1691: $i,X1692: $i,X1693: $i,X1694: $i,X1695: $i,X1696: $i > $i > $o,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i > $i > $o,X1702: $i,X1703: $i,X1704: $i > $i > $o,X1705: $i,X1706: $i,X1707: $i > $i > $o,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i > $i > $o,X1713: $i,X1714: $i,X1715: $i,X1716: $i,X1717: $i > $i > $o,X1718: $i,X1719: $i,X1720: $i,X1721: $i,X1722: $i > $i > $o,X1723: $i,X1724: $i,X1725: $i,X1726: $i,X1727: $i,X1728: $i,X1729: $i,X1730: $i,X1731: $i,X1732: $i,X1733: $i,X1734: $i,X1735: $i,X1736: $i,X1737: $i,X1738: $i,X1739: $i,X1740: $i,X1741: $i,X1742: $i,X1743: $i,X1744: $i,X1745: $i,X1746: $i,X1747: $i,X1748: $i,X1749: $i > $i,X1751: $i,X1752: $i,X1753: $i > $i,X1755: $i,X1756: $i,X1757: $i > $i,X1759: $i,X1760: $i,X1761: $i,X1762: $i > $o,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1769: $i > $o,X1772: $i,X1773: $i,X1774: $i > $o,X1775: $i,X1776: $i,X1777: $i,X1778: $i,X1779: $i,X1780: $i] :
( ( ~ ( in @ ( esk1_2 @ X1207 @ X1208 ) @ X1207 )
| ~ ( in @ ( esk1_2 @ X1207 @ X1208 ) @ X1208 )
| ( X1207 = X1208 ) )
& ( ( in @ ( esk1_2 @ X1207 @ X1208 ) @ X1207 )
| ( in @ ( esk1_2 @ X1207 @ X1208 ) @ X1208 )
| ( X1207 = X1208 ) )
& ~ ( in @ X1210 @ emptyset )
& ( ~ ( in @ X1213 @ ( setadjoin @ X1211 @ X1212 ) )
| ( X1213 = X1211 )
| ( in @ X1213 @ X1212 ) )
& ( ( X1213 != X1211 )
| ( in @ X1213 @ ( setadjoin @ X1211 @ X1212 ) ) )
& ( ~ ( in @ X1213 @ X1212 )
| ( in @ X1213 @ ( setadjoin @ X1211 @ X1212 ) ) )
& ( ~ ( in @ X1215 @ ( powerset @ X1214 ) )
| ~ ( in @ X1216 @ X1215 )
| ( in @ X1216 @ X1214 ) )
& ( ( in @ ( esk2_2 @ X1217 @ X1218 ) @ X1218 )
| ( in @ X1218 @ ( powerset @ X1217 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1217 @ X1218 ) @ X1217 )
| ( in @ X1218 @ ( powerset @ X1217 ) ) )
& ( ( in @ X1221 @ ( esk3_2 @ X1220 @ X1221 ) )
| ~ ( in @ X1221 @ ( setunion @ X1220 ) ) )
& ( ( in @ ( esk3_2 @ X1220 @ X1221 ) @ X1220 )
| ~ ( in @ X1221 @ ( setunion @ X1220 ) ) )
& ( ~ ( in @ X1224 @ X1225 )
| ~ ( in @ X1225 @ X1223 )
| ( in @ X1224 @ ( setunion @ X1223 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1226 @ omega )
| ( in @ ( setadjoin @ X1226 @ X1226 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1227 ) @ omega )
| ~ ( in @ emptyset @ X1227 )
| ~ ( in @ X1229 @ omega )
| ( in @ X1229 @ X1227 ) )
& ( ( in @ ( esk4_1 @ X1227 ) @ X1227 )
| ~ ( in @ emptyset @ X1227 )
| ~ ( in @ X1229 @ omega )
| ( in @ X1229 @ X1227 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1227 ) @ ( esk4_1 @ X1227 ) ) @ X1227 )
| ~ ( in @ emptyset @ X1227 )
| ~ ( in @ X1229 @ omega )
| ( in @ X1229 @ X1227 ) )
& ( ( in @ ( esk7_3 @ X1230 @ X1231 @ X1234 ) @ X1231 )
| ~ ( in @ X1234 @ ( esk6_2 @ X1230 @ X1231 ) )
| ( in @ ( esk5_2 @ X1230 @ X1231 ) @ X1231 ) )
& ( ( X1230 @ ( esk7_3 @ X1230 @ X1231 @ X1234 ) @ X1234 )
| ~ ( in @ X1234 @ ( esk6_2 @ X1230 @ X1231 ) )
| ( in @ ( esk5_2 @ X1230 @ X1231 ) @ X1231 ) )
& ( ~ ( in @ X1237 @ X1231 )
| ~ ( X1230 @ X1237 @ X1236 )
| ( in @ X1236 @ ( esk6_2 @ X1230 @ X1231 ) )
| ( in @ ( esk5_2 @ X1230 @ X1231 ) @ X1231 ) )
& ( ( in @ ( esk7_3 @ X1230 @ X1231 @ X1234 ) @ X1231 )
| ~ ( in @ X1234 @ ( esk6_2 @ X1230 @ X1231 ) )
| ~ ( exu @ ( X1230 @ ( esk5_2 @ X1230 @ X1231 ) ) ) )
& ( ( X1230 @ ( esk7_3 @ X1230 @ X1231 @ X1234 ) @ X1234 )
| ~ ( in @ X1234 @ ( esk6_2 @ X1230 @ X1231 ) )
| ~ ( exu @ ( X1230 @ ( esk5_2 @ X1230 @ X1231 ) ) ) )
& ( ~ ( in @ X1237 @ X1231 )
| ~ ( X1230 @ X1237 @ X1236 )
| ( in @ X1236 @ ( esk6_2 @ X1230 @ X1231 ) )
| ~ ( exu @ ( X1230 @ ( esk5_2 @ X1230 @ X1231 ) ) ) )
& ( ( in @ ( esk8_1 @ X1238 ) @ X1238 )
| ~ ( in @ X1239 @ X1238 ) )
& ( ~ ( in @ X1241 @ ( esk8_1 @ X1238 ) )
| ~ ( in @ X1241 @ X1238 )
| ~ ( in @ X1239 @ X1238 ) )
& epred1_0
& ( ~ ( exu @ X1242 )
| ( X1242 @ ( descr @ X1242 ) ) )
& ( ~ ( in @ X1245 @ X1243 )
| ~ ( X1244 @ X1245 )
| ( in @ X1245 @ ( dsetconstr @ X1243 @ X1244 ) ) )
& ( ~ ( in @ X1248 @ ( dsetconstr @ X1246 @ X1247 ) )
| ( in @ X1248 @ X1246 ) )
& ( ~ ( in @ X1251 @ ( dsetconstr @ X1249 @ X1250 ) )
| ( X1250 @ X1251 ) )
& ( ( X1252 @ ( esk9_1 @ X1252 ) )
| ~ ( exu @ X1252 ) )
& ( ~ ( X1252 @ X1254 )
| ( ( esk9_1 @ X1252 )
= X1254 )
| ~ ( exu @ X1252 ) )
& ( ~ ( in @ X1256 @ ( prop2set @ X1255 ) )
| X1255 )
& ( ~ ( in @ X1257 @ emptyset )
| X1258 )
& ( ~ ( in @ X1259 @ emptyset )
| ~ $true )
& ~ ( in @ X1260 @ emptyset )
& ( ~ ( exu @ X1261 )
| ( X1261 @ ( esk10_1 @ X1261 ) ) )
& ( ( in @ ( esk12_2 @ X1263 @ X1264 ) @ X1264 )
| ( X1263 = X1264 )
| ( in @ ( esk11_2 @ X1263 @ X1264 ) @ X1263 ) )
& ( ~ ( in @ ( esk12_2 @ X1263 @ X1264 ) @ X1263 )
| ( X1263 = X1264 )
| ( in @ ( esk11_2 @ X1263 @ X1264 ) @ X1263 ) )
& ( ( in @ ( esk12_2 @ X1263 @ X1264 ) @ X1264 )
| ( X1263 = X1264 )
| ~ ( in @ ( esk11_2 @ X1263 @ X1264 ) @ X1264 ) )
& ( ~ ( in @ ( esk12_2 @ X1263 @ X1264 ) @ X1263 )
| ( X1263 = X1264 )
| ~ ( in @ ( esk11_2 @ X1263 @ X1264 ) @ X1264 ) )
& ( ( in @ ( esk13_1 @ X1267 ) @ X1267 )
| ( X1267 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1269 ) @ X1269 )
| ( X1269 = emptyset ) )
& ( ~ ( in @ X1273 @ ( dsetconstr @ X1271 @ X1272 ) )
| ( X1272 @ X1273 )
| ~ ( in @ X1273 @ X1271 ) )
& ( ~ ( X1272 @ X1273 )
| ( in @ X1273 @ ( dsetconstr @ X1271 @ X1272 ) )
| ~ ( in @ X1273 @ X1271 ) )
& ( ~ ( nonempty @ X1274 )
| ( in @ ( esk15_1 @ X1274 ) @ X1274 ) )
& ( ~ ( in @ X1278 @ X1276 )
| ~ ( X1277 @ X1278 )
| ( nonempty @ ( dsetconstr @ X1276 @ X1277 ) ) )
& ( ~ ( in @ X1280 @ X1279 )
| ( nonempty @ X1279 ) )
& ( in @ X1281 @ ( setadjoin @ X1281 @ X1282 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1285 @ X1284 )
| ( in @ X1285 @ ( setadjoin @ X1283 @ X1284 ) ) )
& ( ( in @ X1288 @ X1287 )
| X1289
| ( X1288 = X1286 )
| ~ ( in @ X1288 @ ( setadjoin @ X1286 @ X1287 ) ) )
& ( ~ X1289
| X1289
| ( X1288 = X1286 )
| ~ ( in @ X1288 @ ( setadjoin @ X1286 @ X1287 ) ) )
& ( ( in @ X1288 @ X1287 )
| X1289
| ~ X1289
| ~ ( in @ X1288 @ ( setadjoin @ X1286 @ X1287 ) ) )
& ( ~ X1289
| X1289
| ~ X1289
| ~ ( in @ X1288 @ ( setadjoin @ X1286 @ X1287 ) ) )
& ( ~ ( in @ X1292 @ ( setadjoin @ X1290 @ X1291 ) )
| ( X1292 = X1290 )
| ( in @ X1292 @ X1291 ) )
& ( ( dsetconstr @ X1293
@ ^ [Z0: $i] : $true )
= X1293 )
& ( ( in @ ( esk16_2 @ X1294 @ X1295 ) @ X1295 )
| ( in @ X1295 @ ( powerset @ X1294 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1294 @ X1295 ) @ X1294 )
| ( in @ X1295 @ ( powerset @ X1294 ) ) )
& ( in @ emptyset @ ( powerset @ X1297 ) )
& ( in @ emptyset @ ( powerset @ X1298 ) )
& ( ~ ( in @ X1300 @ ( powerset @ X1299 ) )
| ~ ( in @ X1301 @ X1300 )
| ( in @ X1301 @ X1299 ) )
& ( ~ ( in @ X1303 @ X1304 )
| ~ ( in @ X1304 @ X1302 )
| ( in @ X1303 @ ( setunion @ X1302 ) ) )
& ( ( in @ X1306 @ ( esk17_3 @ X1305 @ X1306 @ X1307 ) )
| X1307
| ~ ( in @ X1306 @ ( setunion @ X1305 ) ) )
& ( ( in @ ( esk17_3 @ X1305 @ X1306 @ X1307 ) @ X1305 )
| X1307
| ~ ( in @ X1306 @ ( setunion @ X1305 ) ) )
& ( ~ X1307
| X1307
| ~ ( in @ X1306 @ ( setunion @ X1305 ) ) )
& ( ~ ( in @ X1310 @ X1309 )
| ( in @ X1310 @ ( powerset @ ( setunion @ X1309 ) ) ) )
& ( ~ ( X1311 @ X1313 )
| ( X1313
= ( esk18_1 @ X1311 ) )
| ~ ( exu @ X1311 ) )
& ( ( X1314
!= ( esk18_1 @ X1311 ) )
| ( X1311 @ X1314 )
| ~ ( exu @ X1311 ) )
& ( ( in @ ( esk19_1 @ X1315 ) @ X1315 )
| ~ ( nonempty @ X1315 ) )
& ( $true
| ~ ( nonempty @ X1315 ) )
& ( ~ ( in @ X1317 @ ( setadjoin @ X1318 @ emptyset ) )
| ( X1317 = X1318 ) )
& ( ( X1319 = X1320 )
| ~ ( in @ X1320 @ ( setadjoin @ X1319 @ emptyset ) ) )
& ( ( X1321 != X1322 )
| ( in @ X1321 @ ( setadjoin @ X1322 @ emptyset ) ) )
& ( ~ ( in @ X1323 @ ( setadjoin @ X1324 @ emptyset ) )
| ( in @ X1324 @ ( setadjoin @ X1323 @ emptyset ) ) )
& ( ~ ( in @ X1327 @ ( setadjoin @ X1325 @ ( setadjoin @ X1326 @ emptyset ) ) )
| ( X1327 = X1325 )
| ( X1327 = X1326 ) )
& ( in @ X1328 @ ( setadjoin @ X1328 @ ( setadjoin @ X1329 @ emptyset ) ) )
& ( in @ X1331 @ ( setadjoin @ X1330 @ ( setadjoin @ X1331 @ emptyset ) ) )
& ( ~ ( in @ X1334 @ X1332 )
| ~ ( X1333 @ X1334 )
| ( ( dsetconstr @ X1332 @ X1333 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1336 @ emptyset )
| ( X1335 @ X1336 ) )
& ( ( in @ ( esk20_2 @ X1337 @ X1338 ) @ X1337 )
| ~ ( in @ X1339 @ X1337 )
| ( X1338 @ X1339 ) )
& ( ~ ( X1338 @ ( esk20_2 @ X1337 @ X1338 ) )
| ~ ( in @ X1339 @ X1337 )
| ( X1338 @ X1339 ) )
& ( ( in @ ( esk21_2 @ X1341 @ X1342 ) @ X1341 )
| ~ ( in @ X1344 @ X1341 )
| ~ ( X1342 @ X1344 ) )
& ( ( X1342 @ ( esk21_2 @ X1341 @ X1342 ) )
| ~ ( in @ X1344 @ X1341 )
| ~ ( X1342 @ X1344 ) )
& ( ( in @ ( esk22_2 @ X1345 @ X1346 ) @ X1345 )
| ~ ( in @ X1348 @ X1345 )
| ~ ( X1346 @ X1348 ) )
& ( ( X1346 @ ( esk22_2 @ X1345 @ X1346 ) )
| ~ ( in @ X1348 @ X1345 )
| ~ ( X1346 @ X1348 ) )
& ( ( in @ ( esk23_2 @ X1349 @ X1350 ) @ X1349 )
| ~ ( in @ X1351 @ X1349 )
| ( X1350 @ X1351 ) )
& ( ~ ( X1350 @ ( esk23_2 @ X1349 @ X1350 ) )
| ~ ( in @ X1351 @ X1349 )
| ( X1350 @ X1351 ) )
& ( ~ X1353
| ( in @ emptyset @ ( prop2set @ X1353 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1354 @ X1355 ) @ X1354 )
| ~ ( in @ X1357 @ X1354 )
| ~ ( X1355 @ X1357 ) )
& ( ( X1355 @ ( esk24_2 @ X1354 @ X1355 ) )
| ~ ( in @ X1357 @ X1354 )
| ~ ( X1355 @ X1357 ) )
& ( ( in @ ( esk25_2 @ X1358 @ X1359 ) @ X1358 )
| ~ ( in @ X1360 @ X1358 )
| ( X1359 @ X1360 ) )
& ( ~ ( X1359 @ ( esk25_2 @ X1358 @ X1359 ) )
| ~ ( in @ X1360 @ X1358 )
| ( X1359 @ X1360 ) )
& ( ( X1362 @ ( esk26_2 @ X1362 @ X1363 ) )
| ~ ( X1362 @ X1363 )
| ( exu @ X1362 ) )
& ( ( X1363
!= ( esk26_2 @ X1362 @ X1363 ) )
| ~ ( X1362 @ X1363 )
| ( exu @ X1362 ) )
& ( ( X1365 @ ( esk27_1 @ X1365 ) )
| ( exu @ X1365 )
| ~ ( X1365 @ X1366 ) )
& ( ( X1365 @ ( esk28_1 @ X1365 ) )
| ( exu @ X1365 )
| ~ ( X1365 @ X1366 ) )
& ( ( ( esk27_1 @ X1365 )
!= ( esk28_1 @ X1365 ) )
| ( exu @ X1365 )
| ~ ( X1365 @ X1366 ) )
& ( ~ ( X1369 @ ( esk29_2 @ X1369 @ X1370 ) )
| ( ( esk29_2 @ X1369 @ X1370 )
!= X1370 )
| ( exu @ X1369 ) )
& ( ( X1369 @ ( esk29_2 @ X1369 @ X1370 ) )
| ( ( esk29_2 @ X1369 @ X1370 )
= X1370 )
| ( exu @ X1369 ) )
& ( ( X1372 != X1373 )
| ( X1374 != X1375 )
| ~ ( in @ X1374 @ X1372 )
| ( in @ X1375 @ X1373 ) )
& ( ~ ( in @ X1378 @ X1376 )
| ( in @ X1379 @ X1377 )
| ( X1378 != X1379 )
| ( X1376 != X1377 ) )
& ( ~ ( in @ X1379 @ X1377 )
| ( in @ X1378 @ X1376 )
| ( X1378 != X1379 )
| ( X1376 != X1377 ) )
& ( ~ ( exu @ X1380 )
| ~ ( X1380 @ X1381 )
| ~ ( X1380 @ X1382 )
| ( X1381 = X1382 ) )
& ( ~ ( exu @ X1383 )
| ( exu @ X1384 )
| ( ( esk30_2 @ X1383 @ X1384 )
= ( esk31_2 @ X1383 @ X1384 ) ) )
& ( ~ ( exu @ X1384 )
| ( exu @ X1383 )
| ( ( esk30_2 @ X1383 @ X1384 )
= ( esk31_2 @ X1383 @ X1384 ) ) )
& ( ~ ( exu @ X1383 )
| ( exu @ X1384 )
| ~ ( X1383 @ ( esk30_2 @ X1383 @ X1384 ) )
| ~ ( X1384 @ ( esk31_2 @ X1383 @ X1384 ) ) )
& ( ~ ( exu @ X1384 )
| ( exu @ X1383 )
| ~ ( X1383 @ ( esk30_2 @ X1383 @ X1384 ) )
| ~ ( X1384 @ ( esk31_2 @ X1383 @ X1384 ) ) )
& ( ~ ( exu @ X1383 )
| ( exu @ X1384 )
| ( X1383 @ ( esk30_2 @ X1383 @ X1384 ) )
| ( X1384 @ ( esk31_2 @ X1383 @ X1384 ) ) )
& ( ~ ( exu @ X1384 )
| ( exu @ X1383 )
| ( X1383 @ ( esk30_2 @ X1383 @ X1384 ) )
| ( X1384 @ ( esk31_2 @ X1383 @ X1384 ) ) )
& ( emptyset = emptyset )
& ( ( X1387 != X1388 )
| ( X1389 != X1390 )
| ( ( setadjoin @ X1387 @ X1389 )
= ( setadjoin @ X1388 @ X1390 ) ) )
& ( ( X1391 != X1392 )
| ( ( powerset @ X1391 )
= ( powerset @ X1392 ) ) )
& ( ( X1393 != X1394 )
| ( ( setunion @ X1393 )
= ( setunion @ X1394 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1395 )
| ~ ( X1395 @ X1396 )
| ~ ( X1395 @ X1397 )
| ( X1396 = X1397 ) )
& ( ( ( esk32_2 @ X1398 @ X1399 )
= ( esk33_2 @ X1398 @ X1399 ) )
| ~ ( exu @ X1398 )
| ~ ( exu @ X1399 )
| ( ( descr @ X1398 )
= ( descr @ X1399 ) ) )
& ( ~ ( X1398 @ ( esk32_2 @ X1398 @ X1399 ) )
| ~ ( X1399 @ ( esk33_2 @ X1398 @ X1399 ) )
| ~ ( exu @ X1398 )
| ~ ( exu @ X1399 )
| ( ( descr @ X1398 )
= ( descr @ X1399 ) ) )
& ( ( X1398 @ ( esk32_2 @ X1398 @ X1399 ) )
| ( X1399 @ ( esk33_2 @ X1398 @ X1399 ) )
| ~ ( exu @ X1398 )
| ~ ( exu @ X1399 )
| ( ( descr @ X1398 )
= ( descr @ X1399 ) ) )
& ( ( in @ ( esk34_4 @ X1402 @ X1403 @ X1404 @ X1405 ) @ X1402 )
| ( ( dsetconstr @ X1402 @ X1404 )
= ( dsetconstr @ X1403 @ X1405 ) )
| ( X1402 != X1403 ) )
& ( ( in @ ( esk35_4 @ X1402 @ X1403 @ X1404 @ X1405 ) @ X1403 )
| ( ( dsetconstr @ X1402 @ X1404 )
= ( dsetconstr @ X1403 @ X1405 ) )
| ( X1402 != X1403 ) )
& ( ( ( esk34_4 @ X1402 @ X1403 @ X1404 @ X1405 )
= ( esk35_4 @ X1402 @ X1403 @ X1404 @ X1405 ) )
| ( ( dsetconstr @ X1402 @ X1404 )
= ( dsetconstr @ X1403 @ X1405 ) )
| ( X1402 != X1403 ) )
& ( ~ ( X1404 @ ( esk34_4 @ X1402 @ X1403 @ X1404 @ X1405 ) )
| ~ ( X1405 @ ( esk35_4 @ X1402 @ X1403 @ X1404 @ X1405 ) )
| ( ( dsetconstr @ X1402 @ X1404 )
= ( dsetconstr @ X1403 @ X1405 ) )
| ( X1402 != X1403 ) )
& ( ( X1404 @ ( esk34_4 @ X1402 @ X1403 @ X1404 @ X1405 ) )
| ( X1405 @ ( esk35_4 @ X1402 @ X1403 @ X1404 @ X1405 ) )
| ( ( dsetconstr @ X1402 @ X1404 )
= ( dsetconstr @ X1403 @ X1405 ) )
| ( X1402 != X1403 ) )
& ( ( in @ ( esk36_2 @ X1408 @ X1409 ) @ X1408 )
| ( subset @ X1408 @ X1409 ) )
& ( ~ ( in @ ( esk36_2 @ X1408 @ X1409 ) @ X1409 )
| ( subset @ X1408 @ X1409 ) )
& ( ( X1411 != X1412 )
| ( subset @ X1412 @ X1411 ) )
& ( ( X1413 != X1414 )
| ( subset @ X1413 @ X1414 ) )
& ( ( in @ ( esk37_2 @ X1415 @ X1416 ) @ X1415 )
| ( subset @ X1415 @ X1416 ) )
& ( ~ ( in @ ( esk37_2 @ X1415 @ X1416 ) @ X1416 )
| ( subset @ X1415 @ X1416 ) )
& ( subset @ emptyset @ X1418 )
& ( ~ ( subset @ X1419 @ X1420 )
| ~ ( in @ X1421 @ X1419 )
| ( in @ X1421 @ X1420 ) )
& ( ~ ( subset @ X1422 @ X1423 )
| ( in @ X1424 @ X1423 )
| ~ ( in @ X1424 @ X1422 ) )
& ( ~ ( in @ X1427 @ X1425 )
| ( in @ X1427 @ X1426 )
| ~ ( subset @ X1425 @ X1426 ) )
& ( ( subset @ X1428 @ X1429 )
| ( X1428 != X1429 ) )
& ( ~ ( in @ X1432 @ X1430 )
| ( in @ X1432 @ X1431 )
| ( X1430 != X1431 ) )
& ( subset @ X1433 @ X1433 )
& ( ~ ( subset @ X1434 @ X1435 )
| ~ ( subset @ X1435 @ X1436 )
| ( subset @ X1434 @ X1436 ) )
& ( subset @ X1438 @ ( setadjoin @ X1437 @ X1438 ) )
& ( ~ ( subset @ X1439 @ X1441 )
| ( subset @ X1439 @ ( setadjoin @ X1440 @ X1441 ) ) )
& ( ~ ( subset @ X1442 @ X1443 )
| ( in @ X1442 @ ( powerset @ X1443 ) ) )
& ( ~ ( subset @ X1444 @ X1445 )
| ~ ( subset @ X1445 @ X1444 )
| ( X1444 = X1445 ) )
& ( ~ ( subset @ X1446 @ emptyset )
| ( X1446 = emptyset ) )
& ( ~ ( subset @ X1448 @ X1447 )
| ( in @ X1448 @ ( powerset @ X1447 ) ) )
& ( ~ ( in @ X1450 @ ( powerset @ X1449 ) )
| ( subset @ X1450 @ X1449 ) )
& ( in @ X1451 @ ( powerset @ X1451 ) )
& ( ~ ( subset @ X1452 @ X1453 )
| ( subset @ ( powerset @ X1452 ) @ ( powerset @ X1453 ) ) )
& ( in @ ( dsetconstr @ X1454 @ X1455 ) @ ( powerset @ X1454 ) )
& ( subset @ ( dsetconstr @ X1456 @ X1457 ) @ X1456 )
& ( ~ ( in @ X1460 @ X1458 )
| ( in @ X1460 @ ( binunion @ X1458 @ X1459 ) ) )
& ( in @ X1462 @ ( setadjoin @ X1461 @ ( setadjoin @ X1462 @ emptyset ) ) )
& ( ~ ( in @ X1465 @ X1464 )
| ( in @ X1465 @ ( binunion @ X1463 @ X1464 ) ) )
& ( ( in @ X1468 @ X1467 )
| X1469
| ( in @ X1468 @ X1466 )
| ~ ( in @ X1468 @ ( binunion @ X1466 @ X1467 ) ) )
& ( ~ X1469
| X1469
| ( in @ X1468 @ X1466 )
| ~ ( in @ X1468 @ ( binunion @ X1466 @ X1467 ) ) )
& ( ( in @ X1468 @ X1467 )
| X1469
| ~ X1469
| ~ ( in @ X1468 @ ( binunion @ X1466 @ X1467 ) ) )
& ( ~ X1469
| X1469
| ~ X1469
| ~ ( in @ X1468 @ ( binunion @ X1466 @ X1467 ) ) )
& ( ~ ( in @ X1472 @ ( binunion @ X1470 @ X1471 ) )
| ( in @ X1472 @ X1470 )
| ( in @ X1472 @ X1471 ) )
& ( subset @ X1473 @ ( binunion @ X1473 @ X1474 ) )
& ( subset @ X1476 @ ( binunion @ X1475 @ X1476 ) )
& ( ~ ( in @ X1479 @ X1477 )
| ~ ( in @ X1479 @ X1478 )
| ( in @ X1479 @ ( binintersect @ X1477 @ X1478 ) ) )
& ( ~ ( subset @ X1482 @ X1480 )
| ~ ( subset @ X1482 @ X1481 )
| ( subset @ X1482 @ ( binintersect @ X1480 @ X1481 ) ) )
& ( ~ ( in @ X1485 @ ( binintersect @ X1483 @ X1484 ) )
| ( in @ X1485 @ X1483 ) )
& ( subset @ ( binintersect @ X1486 @ X1487 ) @ X1486 )
& ( ~ ( subset @ X1488 @ X1489 )
| ( ( binintersect @ X1488 @ X1489 )
= X1488 ) )
& ( ( ( binintersect @ X1490 @ X1491 )
!= X1491 )
| ( subset @ X1491 @ X1490 ) )
& ( ~ ( in @ X1494 @ ( binintersect @ X1492 @ X1493 ) )
| ( in @ X1494 @ X1493 ) )
& ( ( in @ ( esk38_2 @ X1495 @ X1496 ) @ X1495 )
| ( ( binintersect @ X1495 @ X1496 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1495 @ X1496 ) @ X1496 )
| ( ( binintersect @ X1495 @ X1496 )
= emptyset ) )
& ( subset @ ( binintersect @ X1498 @ X1499 ) @ X1499 )
& ( ~ ( subset @ X1501 @ X1500 )
| ( ( binintersect @ X1500 @ X1501 )
= X1501 ) )
& ( ( ( binintersect @ X1502 @ X1503 )
!= X1502 )
| ( subset @ X1502 @ X1503 ) )
& ( ( binintersect @ X1504 @ ( binunion @ X1505 @ X1506 ) )
= ( binunion @ ( binintersect @ X1504 @ X1505 ) @ ( binintersect @ X1504 @ X1506 ) ) )
& ( ~ ( in @ X1509 @ X1507 )
| ( in @ X1509 @ X1508 )
| ( in @ X1509 @ ( setminus @ X1507 @ X1508 ) ) )
& ( ~ ( in @ X1512 @ ( setminus @ X1510 @ X1511 ) )
| ( in @ X1512 @ X1510 ) )
& ( ~ ( in @ X1515 @ ( setminus @ X1513 @ X1514 ) )
| ~ ( in @ X1515 @ X1514 ) )
& ( ~ ( subset @ X1516 @ X1517 )
| ( ( setminus @ X1516 @ X1517 )
= emptyset ) )
& ( ( in @ X1520 @ ( setminus @ X1518 @ X1519 ) )
| ~ ( in @ X1520 @ X1518 )
| ( in @ X1520 @ X1519 ) )
& ( ( in @ X1523 @ ( setminus @ X1521 @ X1522 ) )
| ( in @ X1523 @ X1522 )
| ~ ( in @ X1523 @ X1521 ) )
& ( ( in @ X1526 @ X1524 )
| ~ ( in @ X1526 @ ( setminus @ X1524 @ X1525 ) ) )
& ( ~ ( in @ X1529 @ X1528 )
| ~ ( in @ X1529 @ ( setminus @ X1527 @ X1528 ) ) )
& ( subset @ ( setminus @ X1530 @ X1531 ) @ X1530 )
& ( ( ( setminus @ X1532 @ X1533 )
!= emptyset )
| ( subset @ X1532 @ X1533 ) )
& ( ~ ( in @ X1536 @ X1534 )
| X1537
| ( in @ X1536 @ X1534 )
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ( in @ X1536 @ X1535 )
| X1537
| ( in @ X1536 @ X1534 )
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ~ X1537
| X1537
| ( in @ X1536 @ X1534 )
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ~ ( in @ X1536 @ X1534 )
| X1537
| ~ ( in @ X1536 @ X1535 )
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ( in @ X1536 @ X1535 )
| X1537
| ~ ( in @ X1536 @ X1535 )
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ~ X1537
| X1537
| ~ ( in @ X1536 @ X1535 )
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ~ ( in @ X1536 @ X1534 )
| X1537
| ~ X1537
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ( in @ X1536 @ X1535 )
| X1537
| ~ X1537
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ~ X1537
| X1537
| ~ X1537
| ~ ( in @ X1536 @ ( symdiff @ X1534 @ X1535 ) ) )
& ( ~ ( in @ X1540 @ X1538 )
| ( in @ X1540 @ X1539 )
| ( in @ X1540 @ ( symdiff @ X1538 @ X1539 ) ) )
& ( ( in @ X1543 @ X1541 )
| ~ ( in @ X1543 @ X1542 )
| ( in @ X1543 @ ( symdiff @ X1541 @ X1542 ) ) )
& ( ~ ( in @ X1546 @ X1544 )
| ~ ( in @ X1546 @ X1545 )
| ~ ( in @ X1546 @ ( symdiff @ X1544 @ X1545 ) ) )
& ( ( in @ X1549 @ X1547 )
| ( in @ X1549 @ X1548 )
| ~ ( in @ X1549 @ ( symdiff @ X1547 @ X1548 ) ) )
& ( in @ X1551 @ ( setadjoin @ X1550 @ ( setadjoin @ X1551 @ emptyset ) ) )
& ( in @ X1552 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1552 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1552 @ ( setadjoin @ X1553 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1555 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1554 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1554 @ ( setadjoin @ X1555 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1556 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1556 @ ( setadjoin @ X1557 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1558 @ X1559 ) )
& ( ~ ( in @ X1561 @ X1560 )
| ( subset @ ( setadjoin @ X1561 @ emptyset ) @ X1560 ) )
& ( ~ ( in @ X1563 @ X1562 )
| ( in @ ( setadjoin @ X1563 @ emptyset ) @ ( powerset @ X1562 ) ) )
& ( ~ ( in @ X1566 @ X1564 )
| ( in @ ( setadjoin @ X1566 @ emptyset ) @ ( powerset @ ( binunion @ X1564 @ X1565 ) ) ) )
& ( ~ ( in @ X1569 @ ( setadjoin @ X1567 @ ( setadjoin @ X1568 @ emptyset ) ) )
| ( X1569 = X1567 )
| ( X1569 = X1568 ) )
& ( ~ ( in @ X1572 @ X1570 )
| ~ ( in @ X1573 @ X1571 )
| ( subset @ ( setadjoin @ X1572 @ ( setadjoin @ X1573 @ emptyset ) ) @ ( binunion @ X1570 @ X1571 ) ) )
& ( ~ ( in @ X1576 @ X1574 )
| ~ ( in @ X1577 @ X1575 )
| ( in @ ( setadjoin @ X1576 @ ( setadjoin @ X1577 @ emptyset ) ) @ ( powerset @ ( binunion @ X1574 @ X1575 ) ) ) )
& ( ~ ( in @ X1580 @ X1578 )
| ~ ( in @ X1581 @ X1579 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1580 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1580 @ ( setadjoin @ X1581 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1578 @ X1579 ) ) ) )
& ( ~ ( in @ X1584 @ X1582 )
| ~ ( in @ X1585 @ X1583 )
| ( in @ ( setadjoin @ ( setadjoin @ X1584 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1584 @ ( setadjoin @ X1585 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1582 @ X1583 ) ) ) ) )
& ( ~ ( in @ X1588 @ X1586 )
| ~ ( in @ X1589 @ X1587 )
| ( in @ ( kpair @ X1588 @ X1589 ) @ ( powerset @ ( powerset @ ( binunion @ X1586 @ X1587 ) ) ) ) )
& ( ~ ( in @ X1592 @ X1590 )
| ~ ( in @ X1593 @ X1591 )
| ( in @ ( kpair @ X1592 @ X1593 ) @ ( cartprod @ X1590 @ X1591 ) ) )
& ( ( in @ ( esk39_3 @ X1594 @ X1595 @ X1596 ) @ X1594 )
| ~ ( in @ X1596 @ ( cartprod @ X1594 @ X1595 ) ) )
& ( ( in @ ( esk40_3 @ X1594 @ X1595 @ X1596 ) @ X1595 )
| ~ ( in @ X1596 @ ( cartprod @ X1594 @ X1595 ) ) )
& ( ( X1596
= ( kpair @ ( esk39_3 @ X1594 @ X1595 @ X1596 ) @ ( esk40_3 @ X1594 @ X1595 @ X1596 ) ) )
| ~ ( in @ X1596 @ ( cartprod @ X1594 @ X1595 ) ) )
& ( ~ ( in @ X1601 @ ( cartprod @ X1599 @ X1600 ) )
| ( iskpair @ X1601 ) )
& ( ( in @ ( esk41_2 @ X1602 @ X1603 ) @ X1602 )
| ~ ( in @ X1603 @ ( setunion @ X1602 ) ) )
& ( ( in @ X1603 @ ( esk41_2 @ X1602 @ X1603 ) )
| ~ ( in @ X1603 @ ( setunion @ X1602 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1605 @ emptyset ) ) @ X1605 )
& ( subset @ X1606 @ ( setunion @ ( setadjoin @ X1606 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1607 @ emptyset ) )
= X1607 )
& ( ( in @ ( esk42_2 @ X1608 @ X1609 ) @ X1608 )
| ~ ( in @ X1612 @ X1608 )
| ~ ( X1609 @ X1612 )
| ( singleton @ ( dsetconstr @ X1608 @ X1609 ) ) )
& ( ( in @ ( esk43_2 @ X1608 @ X1609 ) @ X1608 )
| ~ ( in @ X1612 @ X1608 )
| ~ ( X1609 @ X1612 )
| ( singleton @ ( dsetconstr @ X1608 @ X1609 ) ) )
& ( ( X1609 @ ( esk42_2 @ X1608 @ X1609 ) )
| ~ ( in @ X1612 @ X1608 )
| ~ ( X1609 @ X1612 )
| ( singleton @ ( dsetconstr @ X1608 @ X1609 ) ) )
& ( ( X1609 @ ( esk43_2 @ X1608 @ X1609 ) )
| ~ ( in @ X1612 @ X1608 )
| ~ ( X1609 @ X1612 )
| ( singleton @ ( dsetconstr @ X1608 @ X1609 ) ) )
& ( ( ( esk42_2 @ X1608 @ X1609 )
!= ( esk43_2 @ X1608 @ X1609 ) )
| ~ ( in @ X1612 @ X1608 )
| ~ ( X1609 @ X1612 )
| ( singleton @ ( dsetconstr @ X1608 @ X1609 ) ) )
& ( ( in @ ( esk44_2 @ X1613 @ X1614 ) @ X1613 )
| ~ ( ex1 @ X1613 @ X1614 ) )
& ( ( X1614 @ ( esk44_2 @ X1613 @ X1614 ) )
| ~ ( ex1 @ X1613 @ X1614 ) )
& ( ( in @ ( esk45_3 @ X1616 @ X1617 @ X1618 ) @ X1616 )
| ( ex1 @ X1616 @ X1617 )
| ~ ( X1617 @ X1618 )
| ~ ( in @ X1618 @ X1616 ) )
& ( ( X1617 @ ( esk45_3 @ X1616 @ X1617 @ X1618 ) )
| ( ex1 @ X1616 @ X1617 )
| ~ ( X1617 @ X1618 )
| ~ ( in @ X1618 @ X1616 ) )
& ( ( ( esk45_3 @ X1616 @ X1617 @ X1618 )
!= X1618 )
| ( ex1 @ X1616 @ X1617 )
| ~ ( X1617 @ X1618 )
| ~ ( in @ X1618 @ X1616 ) )
& ( ( in @ ( esk46_2 @ X1620 @ X1621 ) @ X1620 )
| ~ ( in @ X1624 @ X1620 )
| ~ ( X1621 @ X1624 )
| ( ex1 @ X1620 @ X1621 ) )
& ( ( in @ ( esk47_2 @ X1620 @ X1621 ) @ X1620 )
| ~ ( in @ X1624 @ X1620 )
| ~ ( X1621 @ X1624 )
| ( ex1 @ X1620 @ X1621 ) )
& ( ( X1621 @ ( esk46_2 @ X1620 @ X1621 ) )
| ~ ( in @ X1624 @ X1620 )
| ~ ( X1621 @ X1624 )
| ( ex1 @ X1620 @ X1621 ) )
& ( ( X1621 @ ( esk47_2 @ X1620 @ X1621 ) )
| ~ ( in @ X1624 @ X1620 )
| ~ ( X1621 @ X1624 )
| ( ex1 @ X1620 @ X1621 ) )
& ( ( ( esk46_2 @ X1620 @ X1621 )
!= ( esk47_2 @ X1620 @ X1621 ) )
| ~ ( in @ X1624 @ X1620 )
| ~ ( X1621 @ X1624 )
| ( ex1 @ X1620 @ X1621 ) )
& ( ( ( setadjoin @ X1625 @ emptyset )
!= ( setadjoin @ X1626 @ emptyset ) )
| ( X1625 = X1626 ) )
& ( ~ ( in @ ( setadjoin @ X1629 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1627 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1627 @ ( setadjoin @ X1628 @ emptyset ) ) @ emptyset ) ) )
| ( X1627 = X1629 ) )
& ( ~ ( iskpair @ X1630 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1630 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1630 ) ) ) )
& ( ~ ( singleton @ X1631 )
| ( in @ ( setunion @ X1631 ) @ X1631 ) )
& ( ( kfst @ ( kpair @ X1632 @ X1633 ) )
= X1632 )
& ( ~ ( in @ X1636 @ ( cartprod @ X1634 @ X1635 ) )
| ( in @ ( kfst @ X1636 ) @ X1634 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1637 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1637 @ ( setadjoin @ X1638 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1639 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1639 @ ( setadjoin @ X1640 @ emptyset ) ) @ emptyset ) ) )
| ( X1637 = X1639 ) )
& ( ( ( kpair @ X1641 @ X1642 )
!= ( kpair @ X1643 @ X1644 ) )
| ( X1641 = X1643 ) )
& ( ( X1645 != X1646 )
| ( ( setadjoin @ X1645 @ ( setadjoin @ X1646 @ emptyset ) )
= ( setadjoin @ X1645 @ emptyset ) ) )
& ( ( X1647 != X1648 )
| ( ( setadjoin @ ( setadjoin @ X1647 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1647 @ ( setadjoin @ X1648 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1647 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1649 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1649 @ ( setadjoin @ X1650 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1651 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1651 @ ( setadjoin @ X1652 @ emptyset ) ) @ emptyset ) ) )
| ( X1651 != X1652 )
| ( X1650 = X1652 ) )
& ( ( ( setadjoin @ X1653 @ ( setadjoin @ X1654 @ emptyset ) )
!= ( setadjoin @ X1655 @ emptyset ) )
| ( X1653 = X1654 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1656 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1656 @ ( setadjoin @ X1657 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1658 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1658 @ ( setadjoin @ X1659 @ emptyset ) ) @ emptyset ) ) )
| ( X1657 = X1659 ) )
& ( ( ( kpair @ X1660 @ X1661 )
!= ( kpair @ X1662 @ X1663 ) )
| ( X1661 = X1663 ) )
& ( ~ ( iskpair @ X1664 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1664 )
@ ^ [Z0: $i] :
( X1664
= ( kpair @ ( kfst @ X1664 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X1665 @ X1666 ) )
= X1666 )
& ( ~ ( iskpair @ X1667 )
| ( ( kpair @ ( kfst @ X1667 ) @ ( ksnd @ X1667 ) )
= X1667 ) )
& ( ~ ( in @ X1670 @ ( cartprod @ X1668 @ X1669 ) )
| ( in @ ( ksnd @ X1670 ) @ X1669 ) )
& ( ~ ( in @ ( kpair @ X1673 @ X1674 ) @ ( cartprod @ X1671 @ X1672 ) )
| ( in @ X1673 @ X1671 ) )
& ( ~ ( in @ ( kpair @ X1677 @ X1678 ) @ ( cartprod @ X1675 @ X1676 ) )
| ( in @ X1678 @ X1676 ) )
& ( ~ ( in @ X1681 @ X1679 )
| ~ ( in @ X1682 @ X1680 )
| ( ( kpair @ X1681 @ X1682 )
= ( kpair @ X1681 @ X1682 ) ) )
& ( ~ ( in @ X1685 @ X1683 )
| ~ ( in @ X1686 @ X1684 )
| ( ( kfst @ ( kpair @ X1685 @ X1686 ) )
= X1685 ) )
& ( ~ ( in @ X1689 @ X1687 )
| ~ ( in @ X1690 @ X1688 )
| ( ( ksnd @ ( kpair @ X1689 @ X1690 ) )
= X1690 ) )
& ( ~ ( in @ X1693 @ ( cartprod @ X1691 @ X1692 ) )
| ( ( kpair @ ( kfst @ X1693 ) @ ( ksnd @ X1693 ) )
= X1693 ) )
& ( ~ ( in @ X1697 @ X1694 )
| ~ ( in @ X1698 @ X1695 )
| ~ ( X1696 @ X1697 @ X1698 )
| ( in @ ( kpair @ X1697 @ X1698 ) @ ( dpsetconstr @ X1694 @ X1695 @ X1696 ) ) )
& ( subset @ ( dpsetconstr @ X1699 @ X1700 @ X1701 ) @ ( cartprod @ X1699 @ X1700 ) )
& ( breln @ X1702 @ X1703 @ ( dpsetconstr @ X1702 @ X1703 @ X1704 ) )
& ( ~ ( in @ X1708 @ X1705 )
| ~ ( in @ X1709 @ X1706 )
| ~ ( in @ ( kpair @ X1708 @ X1709 ) @ ( dpsetconstr @ X1705 @ X1706 @ X1707 ) )
| ( X1707 @ X1708 @ X1709 ) )
& ( ~ ( in @ ( kpair @ X1713 @ X1714 ) @ ( dpsetconstr @ X1710 @ X1711 @ X1712 ) )
| ( in @ X1713 @ X1710 ) )
& ( ~ ( in @ ( kpair @ X1718 @ X1719 ) @ ( dpsetconstr @ X1715 @ X1716 @ X1717 ) )
| ( in @ X1719 @ X1716 ) )
& ( ~ ( in @ ( kpair @ X1723 @ X1724 ) @ ( dpsetconstr @ X1720 @ X1721 @ X1722 ) )
| ( X1722 @ X1723 @ X1724 ) )
& ( ~ ( func @ X1725 @ X1726 @ X1727 )
| ~ ( in @ X1728 @ X1725 )
| ( singleton
@ ( dsetconstr @ X1726
@ ^ [Z0: $i] : ( in @ ( kpair @ X1728 @ Z0 ) @ X1727 ) ) ) )
& ( ~ ( func @ X1729 @ X1730 @ X1731 )
| ~ ( in @ X1732 @ X1729 )
| ( in
@ ( setunion
@ ( dsetconstr @ X1730
@ ^ [Z0: $i] : ( in @ ( kpair @ X1732 @ Z0 ) @ X1731 ) ) )
@ X1730 ) )
& ( ~ ( func @ X1733 @ X1734 @ X1735 )
| ~ ( in @ X1736 @ X1733 )
| ( in @ ( ap @ X1733 @ X1734 @ X1735 @ X1736 ) @ X1734 ) )
& ( ~ ( in @ X1739 @ ( funcSet @ X1737 @ X1738 ) )
| ( func @ X1737 @ X1738 @ X1739 ) )
& ( ~ ( in @ X1742 @ ( funcSet @ X1740 @ X1741 ) )
| ~ ( in @ X1743 @ X1740 )
| ( in @ ( ap @ X1740 @ X1741 @ X1742 @ X1743 ) @ X1741 ) )
& ( ~ ( func @ X1744 @ X1745 @ X1746 )
| ( in @ X1746 @ ( funcSet @ X1744 @ X1745 ) ) )
& ( ( in @ ( esk48_3 @ X1747 @ X1748 @ X1749 ) @ X1747 )
| ( func @ X1747 @ X1748
@ ( dpsetconstr @ X1747 @ X1748
@ ^ [Z0: $i] : ( $eq @ ( X1749 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X1749 @ ( esk48_3 @ X1747 @ X1748 @ X1749 ) ) @ X1748 )
| ( func @ X1747 @ X1748
@ ( dpsetconstr @ X1747 @ X1748
@ ^ [Z0: $i] : ( $eq @ ( X1749 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X1751 @ X1752 @ X1753 ) @ X1751 )
| ( func @ X1751 @ X1752 @ ( lam @ X1751 @ X1752 @ X1753 ) ) )
& ( ~ ( in @ ( X1753 @ ( esk49_3 @ X1751 @ X1752 @ X1753 ) ) @ X1752 )
| ( func @ X1751 @ X1752 @ ( lam @ X1751 @ X1752 @ X1753 ) ) )
& ( ( in @ ( esk50_3 @ X1755 @ X1756 @ X1757 ) @ X1755 )
| ( in @ ( lam @ X1755 @ X1756 @ X1757 ) @ ( funcSet @ X1755 @ X1756 ) ) )
& ( ~ ( in @ ( X1757 @ ( esk50_3 @ X1755 @ X1756 @ X1757 ) ) @ X1756 )
| ( in @ ( lam @ X1755 @ X1756 @ X1757 ) @ ( funcSet @ X1755 @ X1756 ) ) )
& ( ( in @ ( esk51_4 @ X1759 @ X1760 @ X1761 @ X1762 ) @ X1759 )
| ~ ( in @ X1765 @ X1761 )
| ( X1762 @ X1765 )
| ~ ( breln @ X1759 @ X1760 @ X1761 ) )
& ( ( in @ ( esk52_4 @ X1759 @ X1760 @ X1761 @ X1762 ) @ X1760 )
| ~ ( in @ X1765 @ X1761 )
| ( X1762 @ X1765 )
| ~ ( breln @ X1759 @ X1760 @ X1761 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X1759 @ X1760 @ X1761 @ X1762 ) @ ( esk52_4 @ X1759 @ X1760 @ X1761 @ X1762 ) ) @ X1761 )
| ~ ( in @ X1765 @ X1761 )
| ( X1762 @ X1765 )
| ~ ( breln @ X1759 @ X1760 @ X1761 ) )
& ( ~ ( X1762 @ ( kpair @ ( esk51_4 @ X1759 @ X1760 @ X1761 @ X1762 ) @ ( esk52_4 @ X1759 @ X1760 @ X1761 @ X1762 ) ) )
| ~ ( in @ X1765 @ X1761 )
| ( X1762 @ X1765 )
| ~ ( breln @ X1759 @ X1760 @ X1761 ) )
& ( ( in @ ( esk53_4 @ X1766 @ X1767 @ X1768 @ X1769 ) @ X1766 )
| ~ ( in @ X1772 @ X1768 )
| ( X1769 @ X1772 )
| ~ ( breln @ X1766 @ X1767 @ X1768 ) )
& ( ( in @ ( esk54_4 @ X1766 @ X1767 @ X1768 @ X1769 ) @ X1767 )
| ~ ( in @ X1772 @ X1768 )
| ( X1769 @ X1772 )
| ~ ( breln @ X1766 @ X1767 @ X1768 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X1766 @ X1767 @ X1768 @ X1769 ) @ ( esk54_4 @ X1766 @ X1767 @ X1768 @ X1769 ) ) @ X1768 )
| ~ ( in @ X1772 @ X1768 )
| ( X1769 @ X1772 )
| ~ ( breln @ X1766 @ X1767 @ X1768 ) )
& ( ~ ( X1769 @ ( kpair @ ( esk53_4 @ X1766 @ X1767 @ X1768 @ X1769 ) @ ( esk54_4 @ X1766 @ X1767 @ X1768 @ X1769 ) ) )
| ~ ( in @ X1772 @ X1768 )
| ( X1769 @ X1772 )
| ~ ( breln @ X1766 @ X1767 @ X1768 ) )
& ( ~ ( ex1 @ X1773 @ X1774 )
| ~ ( in @ X1775 @ X1773 )
| ~ ( in @ X1776 @ X1773 )
| ~ ( X1774 @ X1775 )
| ~ ( X1774 @ X1776 )
| ( X1775 = X1776 ) )
& ( ~ ( func @ X1777 @ X1778 @ X1779 )
| ~ ( in @ X1780 @ X1777 )
| ( in @ ( kpair @ X1780 @ ( ap @ X1777 @ X1778 @ X1779 @ X1780 ) ) @ X1779 ) )
& ( in @ esk57_0 @ ( funcSet @ esk55_0 @ esk56_0 ) )
& ( in @ esk58_0 @ esk55_0 )
& ~ ( in @ ( kpair @ esk58_0 @ ( ap @ esk55_0 @ esk56_0 @ esk57_0 @ esk58_0 ) ) @ esk57_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_243])])])])])])]) ).
thf(c_0_245,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( func @ X3 @ X4 @ X2 )
| ~ ( in @ X2 @ ( funcSet @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
thf(c_0_246,negated_conjecture,
in @ esk57_0 @ ( funcSet @ esk55_0 @ esk56_0 ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
thf(c_0_247,negated_conjecture,
~ ( in @ ( kpair @ esk58_0 @ ( ap @ esk55_0 @ esk56_0 @ esk57_0 @ esk58_0 ) ) @ esk57_0 ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
thf(c_0_248,negated_conjecture,
! [X3: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( kpair @ X5 @ ( ap @ X2 @ X3 @ X4 @ X5 ) ) @ X4 )
| ~ ( func @ X2 @ X3 @ X4 )
| ~ ( in @ X5 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
thf(c_0_249,negated_conjecture,
in @ esk58_0 @ esk55_0,
inference(split_conjunct,[status(thm)],[c_0_244]) ).
thf(c_0_250,negated_conjecture,
func @ esk55_0 @ esk56_0 @ esk57_0,
inference(spm,[status(thm)],[c_0_245,c_0_246]) ).
thf(c_0_251,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_248]),c_0_249])]),c_0_250])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU685^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n020.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 17:04:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 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
% 1.90/0.77 # Version: 3.1.0-ho
% 1.90/0.77 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.90/0.77 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.90/0.77 # Starting ehoh_best5 with 300s (1) cores
% 1.90/0.77 # Starting almost_fo_3_lam with 300s (1) cores
% 1.90/0.77 # Starting new_bool_5 with 300s (1) cores
% 1.90/0.77 # Starting pre_casc_3 with 300s (1) cores
% 1.90/0.77 # Starting ho_unfolding_8 with 300s (1) cores
% 1.90/0.77 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.90/0.77 # Starting new_bool_3 with 300s (1) cores
% 1.90/0.77 # Starting new_ho_5 with 300s (1) cores
% 1.90/0.77 # new_bool_5 with pid 14974 completed with status 0
% 1.90/0.77 # Result found by new_bool_5
% 1.90/0.77 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.90/0.77 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.90/0.77 # Starting ehoh_best5 with 300s (1) cores
% 1.90/0.77 # Starting almost_fo_3_lam with 300s (1) cores
% 1.90/0.77 # Starting new_bool_5 with 300s (1) cores
% 1.90/0.77 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.90/0.77 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.90/0.77 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.90/0.77 # Starting ho_unfolding_8 with 55s (1) cores
% 1.90/0.77 # ho_unfolding_8 with pid 14986 completed with status 0
% 1.90/0.77 # Result found by ho_unfolding_8
% 1.90/0.77 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.90/0.77 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.90/0.77 # Starting ehoh_best5 with 300s (1) cores
% 1.90/0.77 # Starting almost_fo_3_lam with 300s (1) cores
% 1.90/0.77 # Starting new_bool_5 with 300s (1) cores
% 1.90/0.77 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.90/0.77 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.90/0.77 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.90/0.77 # Starting ho_unfolding_8 with 55s (1) cores
% 1.90/0.77 # Preprocessing time : 0.051 s
% 1.90/0.77 # Presaturation interreduction done
% 1.90/0.77
% 1.90/0.77 # Proof found!
% 1.90/0.77 # SZS status Theorem
% 1.90/0.77 # SZS output start CNFRefutation
% See solution above
% 1.90/0.77 # Parsed axioms : 447
% 1.90/0.77 # Removed by relevancy pruning/SinE : 246
% 1.90/0.77 # Initial clauses : 313
% 1.90/0.77 # Removed in clause preprocessing : 26
% 1.90/0.77 # Initial clauses in saturation : 287
% 1.90/0.77 # Processed clauses : 548
% 1.90/0.77 # ...of these trivial : 9
% 1.90/0.77 # ...subsumed : 27
% 1.90/0.77 # ...remaining for further processing : 511
% 1.90/0.77 # Other redundant clauses eliminated : 33
% 1.90/0.77 # Clauses deleted for lack of memory : 0
% 1.90/0.77 # Backward-subsumed : 0
% 1.90/0.77 # Backward-rewritten : 2
% 1.90/0.77 # Generated clauses : 4427
% 1.90/0.77 # ...of the previous two non-redundant : 4277
% 1.90/0.77 # ...aggressively subsumed : 0
% 1.90/0.77 # Contextual simplify-reflections : 0
% 1.90/0.77 # Paramodulations : 4379
% 1.90/0.77 # Factorizations : 2
% 1.90/0.77 # NegExts : 0
% 1.90/0.77 # Equation resolutions : 38
% 1.90/0.77 # Disequality decompositions : 0
% 1.90/0.77 # Total rewrite steps : 124
% 1.90/0.77 # ...of those cached : 83
% 1.90/0.77 # Propositional unsat checks : 0
% 1.90/0.77 # Propositional check models : 0
% 1.90/0.77 # Propositional check unsatisfiable : 0
% 1.90/0.77 # Propositional clauses : 0
% 1.90/0.77 # Propositional clauses after purity: 0
% 1.90/0.77 # Propositional unsat core size : 0
% 1.90/0.77 # Propositional preprocessing time : 0.000
% 1.90/0.77 # Propositional encoding time : 0.000
% 1.90/0.77 # Propositional solver time : 0.000
% 1.90/0.77 # Success case prop preproc time : 0.000
% 1.90/0.77 # Success case prop encoding time : 0.000
% 1.90/0.77 # Success case prop solver time : 0.000
% 1.90/0.77 # Current number of processed clauses : 249
% 1.90/0.77 # Positive orientable unit clauses : 37
% 1.90/0.77 # Positive unorientable unit clauses: 0
% 1.90/0.77 # Negative unit clauses : 3
% 1.90/0.77 # Non-unit-clauses : 209
% 1.90/0.77 # Current number of unprocessed clauses: 4260
% 1.90/0.77 # ...number of literals in the above : 14959
% 1.90/0.77 # Current number of archived formulas : 0
% 1.90/0.77 # Current number of archived clauses : 249
% 1.90/0.77 # Clause-clause subsumption calls (NU) : 15718
% 1.90/0.77 # Rec. Clause-clause subsumption calls : 9486
% 1.90/0.77 # Non-unit clause-clause subsumptions : 22
% 1.90/0.77 # Unit Clause-clause subsumption calls : 73
% 1.90/0.77 # Rewrite failures with RHS unbound : 0
% 1.90/0.77 # BW rewrite match attempts : 24
% 1.90/0.77 # BW rewrite match successes : 2
% 1.90/0.77 # Condensation attempts : 0
% 1.90/0.77 # Condensation successes : 0
% 1.90/0.77 # Termbank termtop insertions : 109285
% 1.90/0.77 # Search garbage collected termcells : 18311
% 1.90/0.77
% 1.90/0.77 # -------------------------------------------------
% 1.90/0.77 # User time : 0.234 s
% 1.90/0.77 # System time : 0.021 s
% 1.90/0.77 # Total time : 0.255 s
% 1.90/0.77 # Maximum resident set size: 6392 pages
% 1.90/0.77
% 1.90/0.77 # -------------------------------------------------
% 1.90/0.77 # User time : 0.245 s
% 1.90/0.77 # System time : 0.024 s
% 1.90/0.77 # Total time : 0.269 s
% 1.90/0.77 # Maximum resident set size: 2288 pages
% 1.90/0.77 % E---3.1 exiting
% 1.90/0.77 % E exiting
%------------------------------------------------------------------------------