%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU688^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 03:29:09 EDT 2024
% Result : Theorem 40.35s 5.56s
% Output : CNFRefutation 40.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 285
% Syntax : Number of formulae : 344 ( 36 unt; 256 typ; 0 def)
% Number of atoms : 1472 ( 166 equ; 0 cnn)
% Maximal formula atoms : 490 ( 16 avg)
% Number of connectives : 4831 ( 254 ~; 298 |; 338 &;3250 @)
% ( 34 <=>; 657 =>; 0 <=; 0 <~>)
% Maximal formula depth : 365 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 198 ( 198 >; 0 *; 0 +; 0 <<)
% Number of symbols : 259 ( 256 usr; 212 con; 0-4 aty)
% Number of variables : 659 ( 162 ^ 443 !; 54 ?; 659 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $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_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
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_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_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_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_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_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_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_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_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_264,type,
esk2_2: $i > ( $i > $o ) > $i ).
thf(decl_265,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_266,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_267,type,
esk5_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_268,type,
esk6_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_269,type,
esk7_2: $i > ( $i > $o ) > $i ).
thf(decl_270,type,
esk8_2: $i > ( $i > $o ) > $i ).
thf(decl_271,type,
esk9_2: $i > ( $i > $o ) > $i ).
thf(decl_272,type,
esk10_1: $i > $i ).
thf(decl_273,type,
esk11_1: $i > $i ).
thf(decl_274,type,
esk12_3: $i > $i > $i > $i ).
thf(decl_275,type,
esk13_4: $i > $i > $i > $i > $i ).
thf(decl_276,type,
esk14_3: $i > $i > $i > $i ).
thf(decl_277,type,
esk15_4: $i > $i > $i > $i > $i ).
thf(decl_278,type,
esk16_3: $i > $i > $i > $i ).
thf(decl_279,type,
esk17_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_280,type,
esk18_4: $i > $i > ( $i > $i ) > $i > $i ).
thf(decl_281,type,
esk19_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_282,type,
esk20_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_283,type,
esk21_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_284,type,
esk22_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_285,type,
esk23_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_286,type,
esk24_3: $i > $i > $i > $i ).
thf(decl_287,type,
esk25_3: $i > $i > $i > $i ).
thf(decl_288,type,
esk26_3: $i > $i > $i > $i ).
thf(decl_289,type,
esk27_4: $i > $i > $i > $i > $i ).
thf(decl_290,type,
esk28_4: $i > $i > $i > $i > $i ).
thf(decl_291,type,
esk29_0: $i ).
thf(decl_292,type,
esk30_0: $i ).
thf(decl_293,type,
esk31_0: $i ).
thf(decl_294,type,
esk32_0: $i ).
thf(decl_295,type,
esk33_0: $i ).
thf(decl_302,type,
epred7_2: $i > $i > $i > $o ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
& ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ex1 @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
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(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(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(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(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(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(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(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(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(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(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(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
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(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(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(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(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(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X35: $i] :
( ( func @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X30 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
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(funcGraphProp4,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X30 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X30 @ X2 ) ) @ X30 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp3) ).
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(c_0_27,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X129: $i] :
( ( in @ X129
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X129 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_28,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_29,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X136: $i] :
( ( in @ X136
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X136 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_30,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_31,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X129: $i] :
( ( in @ X129
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X129 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X136: $i] :
( ( in @ X136
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X136 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
thf(c_0_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,axiom,
( app
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X140: $i] :
( ( in @ X140 @ X4 )
=> ? [X141: $i] :
( ( in @ X141
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X140 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X140 @ Z0 ) @ X30 ) )
= ( setadjoin @ X141 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[app,c_0_32]) ).
thf(c_0_44,plain,
( funcImageSingleton
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X137: $i] :
( ( in @ X137 @ X4 )
=> ? [X138: $i] :
( ( in @ X138
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X137 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X137 @ Z0 ) @ X30 ) )
= ( setadjoin @ X138 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X139: $i] :
( ( in @ X139
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) )
= ( setadjoin @ X139 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_28]),c_0_32]) ).
thf(c_0_45,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X135: $i] :
( ( in @ X135
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X135 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_34,c_0_28]) ).
thf(c_0_46,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X134: $i] :
( ( in @ X134 @ X21 )
& ( X21
= ( setadjoin @ X134 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_28]) ).
thf(c_0_47,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X133: $i] :
( ( in @ X133
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X133 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_35,c_0_28]) ).
thf(c_0_48,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 ) )
=> ? [X128: $i] :
( ( in @ X128
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X128 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_36,c_0_28]) ).
thf(c_0_49,plain,
( lamp
= ( ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( ( subset
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) )
@ ( cartprod @ X4 @ X5 ) )
& ! [X146: $i] :
( ( in @ X146 @ X4 )
=> ? [X147: $i] :
( ( in @ X147
@ ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X146 @ Z0 )
@ ( lam @ X4 @ X5
@ ^ [Z1: $i] : ( X33 @ Z1 ) ) ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X146 @ Z0 )
@ ( lam @ X4 @ X5
@ ^ [Z1: $i] : ( X33 @ Z1 ) ) ) )
= ( setadjoin @ X147 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_37,c_0_32]) ).
thf(c_0_50,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X29: $i] :
( ( subset @ X29 @ ( cartprod @ X4 @ X5 ) )
=> ! [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 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_30]) ).
thf(c_0_51,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X29: $i] :
( ( subset @ X29 @ ( cartprod @ X4 @ X5 ) )
=> ! [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 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_30]) ).
thf(c_0_52,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_38,c_0_30]) ).
thf(c_0_53,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ? [X148: $i] :
( ( in @ X148
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X148 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_39,c_0_31]) ).
thf(c_0_54,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 ) )
=> ? [X132: $i] :
( ( in @ X132
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X132 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_40,c_0_31]) ).
thf(c_0_55,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X131: $i] :
( ( in @ X131
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X131 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_41,c_0_31]) ).
thf(c_0_56,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X130: $i] :
( ( in @ X130
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X130 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_42,c_0_31]) ).
thf(c_0_57,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_58,axiom,
( funcinfuncset
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X144: $i] :
( ( in @ X144 @ X4 )
=> ? [X145: $i] :
( ( in @ X145
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X144 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X144 @ Z0 ) @ X30 ) )
= ( setadjoin @ X145 @ emptyset ) ) ) ) )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcinfuncset,c_0_32]) ).
thf(c_0_59,axiom,
( infuncsetfunc
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X142: $i] :
( ( in @ X142 @ X4 )
=> ? [X143: $i] :
( ( in @ X143
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X142 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X142 @ Z0 ) @ X30 ) )
= ( setadjoin @ X143 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[infuncsetfunc,c_0_32]) ).
thf(c_0_60,axiom,
( funcextLem
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X153: $i] :
( ( in @ X153 @ X4 )
=> ? [X154: $i] :
( ( in @ X154
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X153 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X153 @ Z0 ) @ X30 ) )
= ( setadjoin @ X154 @ emptyset ) ) ) ) )
=> ! [X35: $i] :
( ( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
& ! [X155: $i] :
( ( in @ X155 @ X4 )
=> ? [X156: $i] :
( ( in @ X156
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X155 @ Z0 ) @ X35 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X155 @ Z0 ) @ X35 ) )
= ( setadjoin @ X156 @ emptyset ) ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[funcextLem,c_0_32]) ).
thf(c_0_61,axiom,
( funcGraphProp2
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X151: $i] :
( ( in @ X151 @ X4 )
=> ? [X152: $i] :
( ( in @ X152
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X151 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X151 @ Z0 ) @ X30 ) )
= ( setadjoin @ X152 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X30 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= X3 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[funcGraphProp2,c_0_32]) ).
thf(c_0_62,axiom,
( funcGraphProp1
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X149: $i] :
( ( in @ X149 @ X4 )
=> ? [X150: $i] :
( ( in @ X150
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X149 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X149 @ Z0 ) @ X30 ) )
= ( setadjoin @ X150 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X30 @ X2 ) ) @ X30 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcGraphProp1,c_0_32]) ).
thf(c_0_63,negated_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
=> ( ! [X157: $i,X158: $i > $o] :
( ! [X159: $i] :
( ( in @ X159 @ X157 )
=> ! [X160: $i] :
( ( in @ X160 @ X157 )
=> ( ( X158 @ X159 )
=> ( ( X158 @ X160 )
=> ( X159 = X160 ) ) ) ) )
=> ( ? [X161: $i] :
( ( in @ X161 @ X157 )
& ( X158 @ X161 ) )
=> ? [X162: $i] :
( ( in @ X162 @ ( dsetconstr @ X157 @ X158 ) )
& ( ( dsetconstr @ X157 @ X158 )
= ( setadjoin @ X162 @ emptyset ) ) ) ) )
=> ( ! [X163: $i,X164: $i > $o] :
( ? [X165: $i] :
( ( in @ X165 @ ( dsetconstr @ X163 @ X164 ) )
& ( ( dsetconstr @ X163 @ X164 )
= ( setadjoin @ X165 @ emptyset ) ) )
=> ? [X166: $i] :
( ( in @ X166 @ X163 )
& ( X164 @ X166 ) ) )
=> ( ! [X167: $i,X168: $i > $o,X169: $i] :
( ( in @ X169 @ X167 )
=> ( ( X168 @ X169 )
=> ( ! [X170: $i] :
( ( in @ X170 @ X167 )
=> ( ( X168 @ X170 )
=> ( X170 = X169 ) ) )
=> ? [X171: $i] :
( ( in @ X171 @ ( dsetconstr @ X167 @ X168 ) )
& ( ( dsetconstr @ X167 @ X168 )
= ( setadjoin @ X171 @ emptyset ) ) ) ) ) )
=> ( ! [X172: $i,X173: $i > $o] :
( ! [X174: $i] :
( ( in @ X174 @ X172 )
=> ! [X175: $i] :
( ( in @ X175 @ X172 )
=> ( ( X173 @ X174 )
=> ( ( X173 @ X175 )
=> ( X174 = X175 ) ) ) ) )
=> ( ? [X176: $i] :
( ( in @ X176 @ X172 )
& ( X173 @ X176 ) )
=> ? [X177: $i] :
( ( in @ X177 @ ( dsetconstr @ X172 @ X173 ) )
& ( ( dsetconstr @ X172 @ X173 )
= ( setadjoin @ X177 @ emptyset ) ) ) ) )
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X178: $i] :
( ( iskpair @ X178 )
=> ? [X179: $i] :
( ( in @ X179
@ ( dsetconstr @ ( setunion @ X178 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X178 ) ) )
& ( ( dsetconstr @ ( setunion @ X178 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X178 ) )
= ( setadjoin @ X179 @ emptyset ) ) ) )
=> ( ! [X180: $i] :
( ? [X181: $i] :
( ( in @ X181 @ X180 )
& ( X180
= ( setadjoin @ X181 @ emptyset ) ) )
=> ( in @ ( setunion @ X180 ) @ X180 ) )
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X182: $i] :
( ( iskpair @ X182 )
=> ? [X183: $i] :
( ( in @ X183
@ ( dsetconstr @ ( setunion @ X182 )
@ ^ [Z0: $i] :
( X182
= ( kpair @ ( kfst @ X182 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X182 )
@ ^ [Z0: $i] :
( X182
= ( kpair @ ( kfst @ X182 ) @ Z0 ) ) )
= ( setadjoin @ X183 @ emptyset ) ) ) )
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( ! [X184: $i,X185: $i,X186: $i > $i > $o] : ( subset @ ( dpsetconstr @ X184 @ X185 @ X186 ) @ ( cartprod @ X184 @ X185 ) )
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( ! [X187: $i,X188: $i,X189: $i] :
( ( ( subset @ X189 @ ( cartprod @ X187 @ X188 ) )
& ! [X190: $i] :
( ( in @ X190 @ X187 )
=> ? [X191: $i] :
( ( in @ X191
@ ( dsetconstr @ X188
@ ^ [Z0: $i] : ( in @ ( kpair @ X190 @ Z0 ) @ X189 ) ) )
& ( ( dsetconstr @ X188
@ ^ [Z0: $i] : ( in @ ( kpair @ X190 @ Z0 ) @ X189 ) )
= ( setadjoin @ X191 @ emptyset ) ) ) ) )
=> ! [X192: $i] :
( ( in @ X192 @ X187 )
=> ? [X193: $i] :
( ( in @ X193
@ ( dsetconstr @ X188
@ ^ [Z0: $i] : ( in @ ( kpair @ X192 @ Z0 ) @ X189 ) ) )
& ( ( dsetconstr @ X188
@ ^ [Z0: $i] : ( in @ ( kpair @ X192 @ Z0 ) @ X189 ) )
= ( setadjoin @ X193 @ emptyset ) ) ) ) )
=> ( apProp
=> ( ! [X194: $i,X195: $i,X196: $i] :
( ( ( subset @ X196 @ ( cartprod @ X194 @ X195 ) )
& ! [X197: $i] :
( ( in @ X197 @ X194 )
=> ? [X198: $i] :
( ( in @ X198
@ ( dsetconstr @ X195
@ ^ [Z0: $i] : ( in @ ( kpair @ X197 @ Z0 ) @ X196 ) ) )
& ( ( dsetconstr @ X195
@ ^ [Z0: $i] : ( in @ ( kpair @ X197 @ Z0 ) @ X196 ) )
= ( setadjoin @ X198 @ emptyset ) ) ) ) )
=> ! [X199: $i] :
( ( in @ X199 @ X194 )
=> ( in @ ( ap @ X194 @ X195 @ X196 @ X199 ) @ X195 ) ) )
=> ( ! [X200: $i,X201: $i,X202: $i] :
( ( in @ X202 @ ( funcSet @ X200 @ X201 ) )
=> ( ( subset @ X202 @ ( cartprod @ X200 @ X201 ) )
& ! [X203: $i] :
( ( in @ X203 @ X200 )
=> ? [X204: $i] :
( ( in @ X204
@ ( dsetconstr @ X201
@ ^ [Z0: $i] : ( in @ ( kpair @ X203 @ Z0 ) @ X202 ) ) )
& ( ( dsetconstr @ X201
@ ^ [Z0: $i] : ( in @ ( kpair @ X203 @ Z0 ) @ X202 ) )
= ( setadjoin @ X204 @ emptyset ) ) ) ) ) )
=> ( ! [X205: $i,X206: $i,X207: $i] :
( ( in @ X207 @ ( funcSet @ X205 @ X206 ) )
=> ! [X208: $i] :
( ( in @ X208 @ X205 )
=> ( in @ ( ap @ X205 @ X206 @ X207 @ X208 ) @ X206 ) ) )
=> ( ! [X209: $i,X210: $i,X211: $i] :
( ( ( subset @ X211 @ ( cartprod @ X209 @ X210 ) )
& ! [X212: $i] :
( ( in @ X212 @ X209 )
=> ? [X213: $i] :
( ( in @ X213
@ ( dsetconstr @ X210
@ ^ [Z0: $i] : ( in @ ( kpair @ X212 @ Z0 ) @ X211 ) ) )
& ( ( dsetconstr @ X210
@ ^ [Z0: $i] : ( in @ ( kpair @ X212 @ Z0 ) @ X211 ) )
= ( setadjoin @ X213 @ emptyset ) ) ) ) )
=> ( in @ X211 @ ( funcSet @ X209 @ X210 ) ) )
=> ( lamProp
=> ( ! [X214: $i,X215: $i,X216: $i > $i] :
( ! [X217: $i] :
( ( in @ X217 @ X214 )
=> ( in @ ( X216 @ X217 ) @ X215 ) )
=> ( ( subset @ ( lam @ X214 @ X215 @ X216 ) @ ( cartprod @ X214 @ X215 ) )
& ! [X218: $i] :
( ( in @ X218 @ X214 )
=> ? [X219: $i] :
( ( in @ X219
@ ( dsetconstr @ X215
@ ^ [Z0: $i] : ( in @ ( kpair @ X218 @ Z0 ) @ ( lam @ X214 @ X215 @ X216 ) ) ) )
& ( ( dsetconstr @ X215
@ ^ [Z0: $i] : ( in @ ( kpair @ X218 @ Z0 ) @ ( lam @ X214 @ X215 @ X216 ) ) )
= ( setadjoin @ X219 @ emptyset ) ) ) ) ) )
=> ( ! [X220: $i,X221: $i,X222: $i > $i] :
( ! [X223: $i] :
( ( in @ X223 @ X220 )
=> ( in @ ( X222 @ X223 ) @ X221 ) )
=> ( in @ ( lam @ X220 @ X221 @ X222 ) @ ( funcSet @ X220 @ X221 ) ) )
=> ( ! [X224: $i,X225: $i,X226: $i] :
( ( subset @ X226 @ ( cartprod @ X224 @ X225 ) )
=> ! [X227: $i > $o] :
( ! [X228: $i] :
( ( in @ X228 @ X224 )
=> ! [X229: $i] :
( ( in @ X229 @ X225 )
=> ( ( in @ ( kpair @ X228 @ X229 ) @ X226 )
=> ( X227 @ ( kpair @ X228 @ X229 ) ) ) ) )
=> ! [X230: $i] :
( ( in @ X230 @ X226 )
=> ( X227 @ X230 ) ) ) )
=> ( ! [X231: $i,X232: $i,X233: $i] :
( ( subset @ X233 @ ( cartprod @ X231 @ X232 ) )
=> ! [X234: $i > $o] :
( ! [X235: $i] :
( ( in @ X235 @ X231 )
=> ! [X236: $i] :
( ( in @ X236 @ X232 )
=> ( ( in @ ( kpair @ X235 @ X236 ) @ X233 )
=> ( X234 @ ( kpair @ X235 @ X236 ) ) ) ) )
=> ! [X237: $i] :
( ( in @ X237 @ X233 )
=> ( X234 @ X237 ) ) ) )
=> ( ! [X238: $i,X239: $i > $o] :
( ? [X240: $i] :
( ( in @ X240 @ ( dsetconstr @ X238 @ X239 ) )
& ( ( dsetconstr @ X238 @ X239 )
= ( setadjoin @ X240 @ emptyset ) ) )
=> ! [X241: $i] :
( ( in @ X241 @ X238 )
=> ! [X242: $i] :
( ( in @ X242 @ X238 )
=> ( ( X239 @ X241 )
=> ( ( X239 @ X242 )
=> ( X241 = X242 ) ) ) ) ) )
=> ( ! [X243: $i,X244: $i,X245: $i] :
( ( ( subset @ X245 @ ( cartprod @ X243 @ X244 ) )
& ! [X246: $i] :
( ( in @ X246 @ X243 )
=> ? [X247: $i] :
( ( in @ X247
@ ( dsetconstr @ X244
@ ^ [Z0: $i] : ( in @ ( kpair @ X246 @ Z0 ) @ X245 ) ) )
& ( ( dsetconstr @ X244
@ ^ [Z0: $i] : ( in @ ( kpair @ X246 @ Z0 ) @ X245 ) )
= ( setadjoin @ X247 @ emptyset ) ) ) ) )
=> ! [X248: $i] :
( ( in @ X248 @ X243 )
=> ( in @ ( kpair @ X248 @ ( ap @ X243 @ X244 @ X245 @ X248 ) ) @ X245 ) ) )
=> ( ! [X249: $i,X250: $i,X251: $i] :
( ( in @ X251 @ ( funcSet @ X249 @ X250 ) )
=> ! [X252: $i] :
( ( in @ X252 @ X249 )
=> ( in @ ( kpair @ X252 @ ( ap @ X249 @ X250 @ X251 @ X252 ) ) @ X251 ) ) )
=> ( ! [X253: $i,X254: $i,X255: $i] :
( ( ( subset @ X255 @ ( cartprod @ X253 @ X254 ) )
& ! [X256: $i] :
( ( in @ X256 @ X253 )
=> ? [X257: $i] :
( ( in @ X257
@ ( dsetconstr @ X254
@ ^ [Z0: $i] : ( in @ ( kpair @ X256 @ Z0 ) @ X255 ) ) )
& ( ( dsetconstr @ X254
@ ^ [Z0: $i] : ( in @ ( kpair @ X256 @ Z0 ) @ X255 ) )
= ( setadjoin @ X257 @ emptyset ) ) ) ) )
=> ! [X258: $i] :
( ( in @ X258 @ X253 )
=> ! [X259: $i] :
( ( in @ X259 @ X254 )
=> ( ( in @ ( kpair @ X258 @ X259 ) @ X255 )
=> ( ( ap @ X253 @ X254 @ X255 @ X258 )
= X259 ) ) ) ) )
=> ( ! [X260: $i,X261: $i,X262: $i] :
( ( ( subset @ X262 @ ( cartprod @ X260 @ X261 ) )
& ! [X263: $i] :
( ( in @ X263 @ X260 )
=> ? [X264: $i] :
( ( in @ X264
@ ( dsetconstr @ X261
@ ^ [Z0: $i] : ( in @ ( kpair @ X263 @ Z0 ) @ X262 ) ) )
& ( ( dsetconstr @ X261
@ ^ [Z0: $i] : ( in @ ( kpair @ X263 @ Z0 ) @ X262 ) )
= ( setadjoin @ X264 @ emptyset ) ) ) ) )
=> ! [X265: $i] :
( ( ( subset @ X265 @ ( cartprod @ X260 @ X261 ) )
& ! [X266: $i] :
( ( in @ X266 @ X260 )
=> ? [X267: $i] :
( ( in @ X267
@ ( dsetconstr @ X261
@ ^ [Z0: $i] : ( in @ ( kpair @ X266 @ Z0 ) @ X265 ) ) )
& ( ( dsetconstr @ X261
@ ^ [Z0: $i] : ( in @ ( kpair @ X266 @ Z0 ) @ X265 ) )
= ( setadjoin @ X267 @ emptyset ) ) ) ) )
=> ( ! [X268: $i] :
( ( in @ X268 @ X260 )
=> ( ( ap @ X260 @ X261 @ X262 @ X268 )
= ( ap @ X260 @ X261 @ X265 @ X268 ) ) )
=> ! [X269: $i] :
( ( in @ X269 @ X260 )
=> ! [X270: $i] :
( ( in @ X270 @ X261 )
=> ( ( in @ ( kpair @ X269 @ X270 ) @ X265 )
=> ( in @ ( kpair @ X269 @ X270 ) @ X262 ) ) ) ) ) ) )
=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X30 )
=> ( ( ap @ X4 @ X5 @ X30 @ X2 )
= X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[funcGraphProp4]),c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),c_0_52]),c_0_53]),c_0_54]),c_0_55]),c_0_56]),c_0_57]),c_0_58]),c_0_59]),c_0_60]),c_0_61]),funcGraphProp3]),c_0_62]),ap2p])]) ).
thf(c_0_64,negated_conjecture,
! [X274: $i,X275: $i > $o,X278: $i,X280: $i,X281: $i > $o,X282: $i,X284: $i,X285: $i > $o,X286: $i,X289: $i,X290: $i > $o,X293: $i,X295: $i,X297: $i,X298: $i,X299: $i,X301: $i,X302: $i,X303: $i > $i > $o,X304: $i,X305: $i,X306: $i,X308: $i,X309: $i,X311: $i,X312: $i,X313: $i,X315: $i,X316: $i,X317: $i,X318: $i,X319: $i,X320: $i,X322: $i,X323: $i,X324: $i,X325: $i,X326: $i,X327: $i,X328: $i,X330: $i,X331: $i,X332: $i,X333: $i > $i,X335: $i,X337: $i,X338: $i,X339: $i > $i,X341: $i,X342: $i,X343: $i,X344: $i > $o,X347: $i,X348: $i,X349: $i,X350: $i,X351: $i > $o,X354: $i,X355: $i,X356: $i > $o,X357: $i,X358: $i,X359: $i,X360: $i,X361: $i,X362: $i,X364: $i,X365: $i,X366: $i,X367: $i,X368: $i,X369: $i,X370: $i,X371: $i,X372: $i,X374: $i,X375: $i,X376: $i,X377: $i,X378: $i,X379: $i,X381: $i,X382: $i,X384: $i,X386: $i,X387: $i] :
( 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
& ( ( in @ ( esk3_2 @ X274 @ X275 ) @ ( dsetconstr @ X274 @ X275 ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( in @ ( esk1_2 @ X274 @ X275 ) @ X274 ) )
& ( ( ( dsetconstr @ X274 @ X275 )
= ( setadjoin @ ( esk3_2 @ X274 @ X275 ) @ emptyset ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( in @ ( esk1_2 @ X274 @ X275 ) @ X274 ) )
& ( ( in @ ( esk3_2 @ X274 @ X275 ) @ ( dsetconstr @ X274 @ X275 ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( in @ ( esk2_2 @ X274 @ X275 ) @ X274 ) )
& ( ( ( dsetconstr @ X274 @ X275 )
= ( setadjoin @ ( esk3_2 @ X274 @ X275 ) @ emptyset ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( in @ ( esk2_2 @ X274 @ X275 ) @ X274 ) )
& ( ( in @ ( esk3_2 @ X274 @ X275 ) @ ( dsetconstr @ X274 @ X275 ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( X275 @ ( esk1_2 @ X274 @ X275 ) ) )
& ( ( ( dsetconstr @ X274 @ X275 )
= ( setadjoin @ ( esk3_2 @ X274 @ X275 ) @ emptyset ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( X275 @ ( esk1_2 @ X274 @ X275 ) ) )
& ( ( in @ ( esk3_2 @ X274 @ X275 ) @ ( dsetconstr @ X274 @ X275 ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( X275 @ ( esk2_2 @ X274 @ X275 ) ) )
& ( ( ( dsetconstr @ X274 @ X275 )
= ( setadjoin @ ( esk3_2 @ X274 @ X275 ) @ emptyset ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( X275 @ ( esk2_2 @ X274 @ X275 ) ) )
& ( ( in @ ( esk3_2 @ X274 @ X275 ) @ ( dsetconstr @ X274 @ X275 ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( ( esk1_2 @ X274 @ X275 )
!= ( esk2_2 @ X274 @ X275 ) ) )
& ( ( ( dsetconstr @ X274 @ X275 )
= ( setadjoin @ ( esk3_2 @ X274 @ X275 ) @ emptyset ) )
| ~ ( in @ X278 @ X274 )
| ~ ( X275 @ X278 )
| ( ( esk1_2 @ X274 @ X275 )
!= ( esk2_2 @ X274 @ X275 ) ) )
& ( ( in @ ( esk4_2 @ X280 @ X281 ) @ X280 )
| ~ ( in @ X282 @ ( dsetconstr @ X280 @ X281 ) )
| ( ( dsetconstr @ X280 @ X281 )
!= ( setadjoin @ X282 @ emptyset ) ) )
& ( ( X281 @ ( esk4_2 @ X280 @ X281 ) )
| ~ ( in @ X282 @ ( dsetconstr @ X280 @ X281 ) )
| ( ( dsetconstr @ X280 @ X281 )
!= ( setadjoin @ X282 @ emptyset ) ) )
& ( ( in @ ( esk6_3 @ X284 @ X285 @ X286 ) @ ( dsetconstr @ X284 @ X285 ) )
| ( in @ ( esk5_3 @ X284 @ X285 @ X286 ) @ X284 )
| ~ ( X285 @ X286 )
| ~ ( in @ X286 @ X284 ) )
& ( ( ( dsetconstr @ X284 @ X285 )
= ( setadjoin @ ( esk6_3 @ X284 @ X285 @ X286 ) @ emptyset ) )
| ( in @ ( esk5_3 @ X284 @ X285 @ X286 ) @ X284 )
| ~ ( X285 @ X286 )
| ~ ( in @ X286 @ X284 ) )
& ( ( in @ ( esk6_3 @ X284 @ X285 @ X286 ) @ ( dsetconstr @ X284 @ X285 ) )
| ( X285 @ ( esk5_3 @ X284 @ X285 @ X286 ) )
| ~ ( X285 @ X286 )
| ~ ( in @ X286 @ X284 ) )
& ( ( ( dsetconstr @ X284 @ X285 )
= ( setadjoin @ ( esk6_3 @ X284 @ X285 @ X286 ) @ emptyset ) )
| ( X285 @ ( esk5_3 @ X284 @ X285 @ X286 ) )
| ~ ( X285 @ X286 )
| ~ ( in @ X286 @ X284 ) )
& ( ( in @ ( esk6_3 @ X284 @ X285 @ X286 ) @ ( dsetconstr @ X284 @ X285 ) )
| ( ( esk5_3 @ X284 @ X285 @ X286 )
!= X286 )
| ~ ( X285 @ X286 )
| ~ ( in @ X286 @ X284 ) )
& ( ( ( dsetconstr @ X284 @ X285 )
= ( setadjoin @ ( esk6_3 @ X284 @ X285 @ X286 ) @ emptyset ) )
| ( ( esk5_3 @ X284 @ X285 @ X286 )
!= X286 )
| ~ ( X285 @ X286 )
| ~ ( in @ X286 @ X284 ) )
& ( ( in @ ( esk9_2 @ X289 @ X290 ) @ ( dsetconstr @ X289 @ X290 ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( in @ ( esk7_2 @ X289 @ X290 ) @ X289 ) )
& ( ( ( dsetconstr @ X289 @ X290 )
= ( setadjoin @ ( esk9_2 @ X289 @ X290 ) @ emptyset ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( in @ ( esk7_2 @ X289 @ X290 ) @ X289 ) )
& ( ( in @ ( esk9_2 @ X289 @ X290 ) @ ( dsetconstr @ X289 @ X290 ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( in @ ( esk8_2 @ X289 @ X290 ) @ X289 ) )
& ( ( ( dsetconstr @ X289 @ X290 )
= ( setadjoin @ ( esk9_2 @ X289 @ X290 ) @ emptyset ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( in @ ( esk8_2 @ X289 @ X290 ) @ X289 ) )
& ( ( in @ ( esk9_2 @ X289 @ X290 ) @ ( dsetconstr @ X289 @ X290 ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( X290 @ ( esk7_2 @ X289 @ X290 ) ) )
& ( ( ( dsetconstr @ X289 @ X290 )
= ( setadjoin @ ( esk9_2 @ X289 @ X290 ) @ emptyset ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( X290 @ ( esk7_2 @ X289 @ X290 ) ) )
& ( ( in @ ( esk9_2 @ X289 @ X290 ) @ ( dsetconstr @ X289 @ X290 ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( X290 @ ( esk8_2 @ X289 @ X290 ) ) )
& ( ( ( dsetconstr @ X289 @ X290 )
= ( setadjoin @ ( esk9_2 @ X289 @ X290 ) @ emptyset ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( X290 @ ( esk8_2 @ X289 @ X290 ) ) )
& ( ( in @ ( esk9_2 @ X289 @ X290 ) @ ( dsetconstr @ X289 @ X290 ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( ( esk7_2 @ X289 @ X290 )
!= ( esk8_2 @ X289 @ X290 ) ) )
& ( ( ( dsetconstr @ X289 @ X290 )
= ( setadjoin @ ( esk9_2 @ X289 @ X290 ) @ emptyset ) )
| ~ ( in @ X293 @ X289 )
| ~ ( X290 @ X293 )
| ( ( esk7_2 @ X289 @ X290 )
!= ( esk8_2 @ X289 @ X290 ) ) )
& singletonsuniq
& setukpairinjL1
& ( ( in @ ( esk10_1 @ X295 )
@ ( dsetconstr @ ( setunion @ X295 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X295 ) ) )
| ~ ( iskpair @ X295 ) )
& ( ( ( dsetconstr @ ( setunion @ X295 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X295 ) )
= ( setadjoin @ ( esk10_1 @ X295 ) @ emptyset ) )
| ~ ( iskpair @ X295 ) )
& ( ~ ( in @ X298 @ X297 )
| ( X297
!= ( setadjoin @ X298 @ emptyset ) )
| ( in @ ( setunion @ X297 ) @ X297 ) )
& kfstpairEq
& cartprodfstin
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ( in @ ( esk11_1 @ X299 )
@ ( dsetconstr @ ( setunion @ X299 )
@ ^ [Z0: $i] :
( X299
= ( kpair @ ( kfst @ X299 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X299 ) )
& ( ( ( dsetconstr @ ( setunion @ X299 )
@ ^ [Z0: $i] :
( X299
= ( kpair @ ( kfst @ X299 ) @ Z0 ) ) )
= ( setadjoin @ ( esk11_1 @ X299 ) @ emptyset ) )
| ~ ( iskpair @ X299 ) )
& ksndpairEq
& kpairsurjEq
& cartprodsndin
& cartprodpairmemEL
& cartprodpairmemER
& cartprodmempaircEq
& cartprodfstpairEq
& cartprodsndpairEq
& cartprodpairsurjEq
& dpsetconstrI
& dpsetconstrSub
& ( subset @ ( dpsetconstr @ X301 @ X302 @ X303 ) @ ( cartprod @ X301 @ X302 ) )
& dpsetconstrERa
& dpsetconstrEL1
& dpsetconstrEL2
& dpsetconstrER
& ( ( in @ ( esk13_4 @ X304 @ X305 @ X306 @ X309 )
@ ( dsetconstr @ X305
@ ^ [Z0: $i] : ( in @ ( kpair @ X309 @ Z0 ) @ X306 ) ) )
| ~ ( in @ X309 @ X304 )
| ( in @ ( esk12_3 @ X304 @ X305 @ X306 ) @ X304 )
| ~ ( subset @ X306 @ ( cartprod @ X304 @ X305 ) ) )
& ( ( ( dsetconstr @ X305
@ ^ [Z0: $i] : ( in @ ( kpair @ X309 @ Z0 ) @ X306 ) )
= ( setadjoin @ ( esk13_4 @ X304 @ X305 @ X306 @ X309 ) @ emptyset ) )
| ~ ( in @ X309 @ X304 )
| ( in @ ( esk12_3 @ X304 @ X305 @ X306 ) @ X304 )
| ~ ( subset @ X306 @ ( cartprod @ X304 @ X305 ) ) )
& ( ( in @ ( esk13_4 @ X304 @ X305 @ X306 @ X309 )
@ ( dsetconstr @ X305
@ ^ [Z0: $i] : ( in @ ( kpair @ X309 @ Z0 ) @ X306 ) ) )
| ~ ( in @ X309 @ X304 )
| ~ ( in @ X308
@ ( dsetconstr @ X305
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk12_3 @ X304 @ X305 @ X306 ) @ Z0 ) @ X306 ) ) )
| ( ( dsetconstr @ X305
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk12_3 @ X304 @ X305 @ X306 ) @ Z0 ) @ X306 ) )
!= ( setadjoin @ X308 @ emptyset ) )
| ~ ( subset @ X306 @ ( cartprod @ X304 @ X305 ) ) )
& ( ( ( dsetconstr @ X305
@ ^ [Z0: $i] : ( in @ ( kpair @ X309 @ Z0 ) @ X306 ) )
= ( setadjoin @ ( esk13_4 @ X304 @ X305 @ X306 @ X309 ) @ emptyset ) )
| ~ ( in @ X309 @ X304 )
| ~ ( in @ X308
@ ( dsetconstr @ X305
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk12_3 @ X304 @ X305 @ X306 ) @ Z0 ) @ X306 ) ) )
| ( ( dsetconstr @ X305
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk12_3 @ X304 @ X305 @ X306 ) @ Z0 ) @ X306 ) )
!= ( setadjoin @ X308 @ emptyset ) )
| ~ ( subset @ X306 @ ( cartprod @ X304 @ X305 ) ) )
& apProp
& ( ( in @ ( esk14_3 @ X311 @ X312 @ X313 ) @ X311 )
| ~ ( subset @ X313 @ ( cartprod @ X311 @ X312 ) )
| ~ ( in @ X316 @ X311 )
| ( in @ ( ap @ X311 @ X312 @ X313 @ X316 ) @ X312 ) )
& ( ~ ( in @ X315
@ ( dsetconstr @ X312
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X311 @ X312 @ X313 ) @ Z0 ) @ X313 ) ) )
| ( ( dsetconstr @ X312
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X311 @ X312 @ X313 ) @ Z0 ) @ X313 ) )
!= ( setadjoin @ X315 @ emptyset ) )
| ~ ( subset @ X313 @ ( cartprod @ X311 @ X312 ) )
| ~ ( in @ X316 @ X311 )
| ( in @ ( ap @ X311 @ X312 @ X313 @ X316 ) @ X312 ) )
& ( ( subset @ X319 @ ( cartprod @ X317 @ X318 ) )
| ~ ( in @ X319 @ ( funcSet @ X317 @ X318 ) ) )
& ( ( in @ ( esk15_4 @ X317 @ X318 @ X319 @ X320 )
@ ( dsetconstr @ X318
@ ^ [Z0: $i] : ( in @ ( kpair @ X320 @ Z0 ) @ X319 ) ) )
| ~ ( in @ X320 @ X317 )
| ~ ( in @ X319 @ ( funcSet @ X317 @ X318 ) ) )
& ( ( ( dsetconstr @ X318
@ ^ [Z0: $i] : ( in @ ( kpair @ X320 @ Z0 ) @ X319 ) )
= ( setadjoin @ ( esk15_4 @ X317 @ X318 @ X319 @ X320 ) @ emptyset ) )
| ~ ( in @ X320 @ X317 )
| ~ ( in @ X319 @ ( funcSet @ X317 @ X318 ) ) )
& ( ~ ( in @ X324 @ ( funcSet @ X322 @ X323 ) )
| ~ ( in @ X325 @ X322 )
| ( in @ ( ap @ X322 @ X323 @ X324 @ X325 ) @ X323 ) )
& ( ( in @ ( esk16_3 @ X326 @ X327 @ X328 ) @ X326 )
| ~ ( subset @ X328 @ ( cartprod @ X326 @ X327 ) )
| ( in @ X328 @ ( funcSet @ X326 @ X327 ) ) )
& ( ~ ( in @ X330
@ ( dsetconstr @ X327
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk16_3 @ X326 @ X327 @ X328 ) @ Z0 ) @ X328 ) ) )
| ( ( dsetconstr @ X327
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk16_3 @ X326 @ X327 @ X328 ) @ Z0 ) @ X328 ) )
!= ( setadjoin @ X330 @ emptyset ) )
| ~ ( subset @ X328 @ ( cartprod @ X326 @ X327 ) )
| ( in @ X328 @ ( funcSet @ X326 @ X327 ) ) )
& lamProp
& ( ( subset @ ( lam @ X331 @ X332 @ X333 ) @ ( cartprod @ X331 @ X332 ) )
| ( in @ ( esk17_3 @ X331 @ X332 @ X333 ) @ X331 ) )
& ( ( in @ ( esk18_4 @ X331 @ X332 @ X333 @ X335 )
@ ( dsetconstr @ X332
@ ^ [Z0: $i] : ( in @ ( kpair @ X335 @ Z0 ) @ ( lam @ X331 @ X332 @ X333 ) ) ) )
| ~ ( in @ X335 @ X331 )
| ( in @ ( esk17_3 @ X331 @ X332 @ X333 ) @ X331 ) )
& ( ( ( dsetconstr @ X332
@ ^ [Z0: $i] : ( in @ ( kpair @ X335 @ Z0 ) @ ( lam @ X331 @ X332 @ X333 ) ) )
= ( setadjoin @ ( esk18_4 @ X331 @ X332 @ X333 @ X335 ) @ emptyset ) )
| ~ ( in @ X335 @ X331 )
| ( in @ ( esk17_3 @ X331 @ X332 @ X333 ) @ X331 ) )
& ( ( subset @ ( lam @ X331 @ X332 @ X333 ) @ ( cartprod @ X331 @ X332 ) )
| ~ ( in @ ( X333 @ ( esk17_3 @ X331 @ X332 @ X333 ) ) @ X332 ) )
& ( ( in @ ( esk18_4 @ X331 @ X332 @ X333 @ X335 )
@ ( dsetconstr @ X332
@ ^ [Z0: $i] : ( in @ ( kpair @ X335 @ Z0 ) @ ( lam @ X331 @ X332 @ X333 ) ) ) )
| ~ ( in @ X335 @ X331 )
| ~ ( in @ ( X333 @ ( esk17_3 @ X331 @ X332 @ X333 ) ) @ X332 ) )
& ( ( ( dsetconstr @ X332
@ ^ [Z0: $i] : ( in @ ( kpair @ X335 @ Z0 ) @ ( lam @ X331 @ X332 @ X333 ) ) )
= ( setadjoin @ ( esk18_4 @ X331 @ X332 @ X333 @ X335 ) @ emptyset ) )
| ~ ( in @ X335 @ X331 )
| ~ ( in @ ( X333 @ ( esk17_3 @ X331 @ X332 @ X333 ) ) @ X332 ) )
& ( ( in @ ( esk19_3 @ X337 @ X338 @ X339 ) @ X337 )
| ( in @ ( lam @ X337 @ X338 @ X339 ) @ ( funcSet @ X337 @ X338 ) ) )
& ( ~ ( in @ ( X339 @ ( esk19_3 @ X337 @ X338 @ X339 ) ) @ X338 )
| ( in @ ( lam @ X337 @ X338 @ X339 ) @ ( funcSet @ X337 @ X338 ) ) )
& ( ( in @ ( esk20_4 @ X341 @ X342 @ X343 @ X344 ) @ X341 )
| ~ ( in @ X347 @ X343 )
| ( X344 @ X347 )
| ~ ( subset @ X343 @ ( cartprod @ X341 @ X342 ) ) )
& ( ( in @ ( esk21_4 @ X341 @ X342 @ X343 @ X344 ) @ X342 )
| ~ ( in @ X347 @ X343 )
| ( X344 @ X347 )
| ~ ( subset @ X343 @ ( cartprod @ X341 @ X342 ) ) )
& ( ( in @ ( kpair @ ( esk20_4 @ X341 @ X342 @ X343 @ X344 ) @ ( esk21_4 @ X341 @ X342 @ X343 @ X344 ) ) @ X343 )
| ~ ( in @ X347 @ X343 )
| ( X344 @ X347 )
| ~ ( subset @ X343 @ ( cartprod @ X341 @ X342 ) ) )
& ( ~ ( X344 @ ( kpair @ ( esk20_4 @ X341 @ X342 @ X343 @ X344 ) @ ( esk21_4 @ X341 @ X342 @ X343 @ X344 ) ) )
| ~ ( in @ X347 @ X343 )
| ( X344 @ X347 )
| ~ ( subset @ X343 @ ( cartprod @ X341 @ X342 ) ) )
& ( ( in @ ( esk22_4 @ X348 @ X349 @ X350 @ X351 ) @ X348 )
| ~ ( in @ X354 @ X350 )
| ( X351 @ X354 )
| ~ ( subset @ X350 @ ( cartprod @ X348 @ X349 ) ) )
& ( ( in @ ( esk23_4 @ X348 @ X349 @ X350 @ X351 ) @ X349 )
| ~ ( in @ X354 @ X350 )
| ( X351 @ X354 )
| ~ ( subset @ X350 @ ( cartprod @ X348 @ X349 ) ) )
& ( ( in @ ( kpair @ ( esk22_4 @ X348 @ X349 @ X350 @ X351 ) @ ( esk23_4 @ X348 @ X349 @ X350 @ X351 ) ) @ X350 )
| ~ ( in @ X354 @ X350 )
| ( X351 @ X354 )
| ~ ( subset @ X350 @ ( cartprod @ X348 @ X349 ) ) )
& ( ~ ( X351 @ ( kpair @ ( esk22_4 @ X348 @ X349 @ X350 @ X351 ) @ ( esk23_4 @ X348 @ X349 @ X350 @ X351 ) ) )
| ~ ( in @ X354 @ X350 )
| ( X351 @ X354 )
| ~ ( subset @ X350 @ ( cartprod @ X348 @ X349 ) ) )
& ( ~ ( in @ X357 @ ( dsetconstr @ X355 @ X356 ) )
| ( ( dsetconstr @ X355 @ X356 )
!= ( setadjoin @ X357 @ emptyset ) )
| ~ ( in @ X358 @ X355 )
| ~ ( in @ X359 @ X355 )
| ~ ( X356 @ X358 )
| ~ ( X356 @ X359 )
| ( X358 = X359 ) )
& ( ( in @ ( esk24_3 @ X360 @ X361 @ X362 ) @ X360 )
| ~ ( subset @ X362 @ ( cartprod @ X360 @ X361 ) )
| ~ ( in @ X365 @ X360 )
| ( in @ ( kpair @ X365 @ ( ap @ X360 @ X361 @ X362 @ X365 ) ) @ X362 ) )
& ( ~ ( in @ X364
@ ( dsetconstr @ X361
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk24_3 @ X360 @ X361 @ X362 ) @ Z0 ) @ X362 ) ) )
| ( ( dsetconstr @ X361
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk24_3 @ X360 @ X361 @ X362 ) @ Z0 ) @ X362 ) )
!= ( setadjoin @ X364 @ emptyset ) )
| ~ ( subset @ X362 @ ( cartprod @ X360 @ X361 ) )
| ~ ( in @ X365 @ X360 )
| ( in @ ( kpair @ X365 @ ( ap @ X360 @ X361 @ X362 @ X365 ) ) @ X362 ) )
& ( ~ ( in @ X368 @ ( funcSet @ X366 @ X367 ) )
| ~ ( in @ X369 @ X366 )
| ( in @ ( kpair @ X369 @ ( ap @ X366 @ X367 @ X368 @ X369 ) ) @ X368 ) )
& ( ( in @ ( esk25_3 @ X370 @ X371 @ X372 ) @ X370 )
| ~ ( subset @ X372 @ ( cartprod @ X370 @ X371 ) )
| ~ ( in @ X375 @ X370 )
| ~ ( in @ X376 @ X371 )
| ~ ( in @ ( kpair @ X375 @ X376 ) @ X372 )
| ( ( ap @ X370 @ X371 @ X372 @ X375 )
= X376 ) )
& ( ~ ( in @ X374
@ ( dsetconstr @ X371
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk25_3 @ X370 @ X371 @ X372 ) @ Z0 ) @ X372 ) ) )
| ( ( dsetconstr @ X371
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk25_3 @ X370 @ X371 @ X372 ) @ Z0 ) @ X372 ) )
!= ( setadjoin @ X374 @ emptyset ) )
| ~ ( subset @ X372 @ ( cartprod @ X370 @ X371 ) )
| ~ ( in @ X375 @ X370 )
| ~ ( in @ X376 @ X371 )
| ~ ( in @ ( kpair @ X375 @ X376 ) @ X372 )
| ( ( ap @ X370 @ X371 @ X372 @ X375 )
= X376 ) )
& ( ( in @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) @ X377 )
| ~ ( in @ X386 @ X377 )
| ~ ( in @ X387 @ X378 )
| ~ ( in @ ( kpair @ X386 @ X387 ) @ X382 )
| ( in @ ( kpair @ X386 @ X387 ) @ X379 )
| ( in @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ X377 )
| ~ ( subset @ X382 @ ( cartprod @ X377 @ X378 ) )
| ( in @ ( esk26_3 @ X377 @ X378 @ X379 ) @ X377 )
| ~ ( subset @ X379 @ ( cartprod @ X377 @ X378 ) ) )
& ( ( ( ap @ X377 @ X378 @ X379 @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) )
!= ( ap @ X377 @ X378 @ X382 @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) ) )
| ~ ( in @ X386 @ X377 )
| ~ ( in @ X387 @ X378 )
| ~ ( in @ ( kpair @ X386 @ X387 ) @ X382 )
| ( in @ ( kpair @ X386 @ X387 ) @ X379 )
| ( in @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ X377 )
| ~ ( subset @ X382 @ ( cartprod @ X377 @ X378 ) )
| ( in @ ( esk26_3 @ X377 @ X378 @ X379 ) @ X377 )
| ~ ( subset @ X379 @ ( cartprod @ X377 @ X378 ) ) )
& ( ( in @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) @ X377 )
| ~ ( in @ X386 @ X377 )
| ~ ( in @ X387 @ X378 )
| ~ ( in @ ( kpair @ X386 @ X387 ) @ X382 )
| ( in @ ( kpair @ X386 @ X387 ) @ X379 )
| ~ ( in @ X384
@ ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ Z0 ) @ X382 ) ) )
| ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ Z0 ) @ X382 ) )
!= ( setadjoin @ X384 @ emptyset ) )
| ~ ( subset @ X382 @ ( cartprod @ X377 @ X378 ) )
| ( in @ ( esk26_3 @ X377 @ X378 @ X379 ) @ X377 )
| ~ ( subset @ X379 @ ( cartprod @ X377 @ X378 ) ) )
& ( ( ( ap @ X377 @ X378 @ X379 @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) )
!= ( ap @ X377 @ X378 @ X382 @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) ) )
| ~ ( in @ X386 @ X377 )
| ~ ( in @ X387 @ X378 )
| ~ ( in @ ( kpair @ X386 @ X387 ) @ X382 )
| ( in @ ( kpair @ X386 @ X387 ) @ X379 )
| ~ ( in @ X384
@ ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ Z0 ) @ X382 ) ) )
| ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ Z0 ) @ X382 ) )
!= ( setadjoin @ X384 @ emptyset ) )
| ~ ( subset @ X382 @ ( cartprod @ X377 @ X378 ) )
| ( in @ ( esk26_3 @ X377 @ X378 @ X379 ) @ X377 )
| ~ ( subset @ X379 @ ( cartprod @ X377 @ X378 ) ) )
& ( ( in @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) @ X377 )
| ~ ( in @ X386 @ X377 )
| ~ ( in @ X387 @ X378 )
| ~ ( in @ ( kpair @ X386 @ X387 ) @ X382 )
| ( in @ ( kpair @ X386 @ X387 ) @ X379 )
| ( in @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ X377 )
| ~ ( subset @ X382 @ ( cartprod @ X377 @ X378 ) )
| ~ ( in @ X381
@ ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk26_3 @ X377 @ X378 @ X379 ) @ Z0 ) @ X379 ) ) )
| ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk26_3 @ X377 @ X378 @ X379 ) @ Z0 ) @ X379 ) )
!= ( setadjoin @ X381 @ emptyset ) )
| ~ ( subset @ X379 @ ( cartprod @ X377 @ X378 ) ) )
& ( ( ( ap @ X377 @ X378 @ X379 @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) )
!= ( ap @ X377 @ X378 @ X382 @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) ) )
| ~ ( in @ X386 @ X377 )
| ~ ( in @ X387 @ X378 )
| ~ ( in @ ( kpair @ X386 @ X387 ) @ X382 )
| ( in @ ( kpair @ X386 @ X387 ) @ X379 )
| ( in @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ X377 )
| ~ ( subset @ X382 @ ( cartprod @ X377 @ X378 ) )
| ~ ( in @ X381
@ ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk26_3 @ X377 @ X378 @ X379 ) @ Z0 ) @ X379 ) ) )
| ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk26_3 @ X377 @ X378 @ X379 ) @ Z0 ) @ X379 ) )
!= ( setadjoin @ X381 @ emptyset ) )
| ~ ( subset @ X379 @ ( cartprod @ X377 @ X378 ) ) )
& ( ( in @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) @ X377 )
| ~ ( in @ X386 @ X377 )
| ~ ( in @ X387 @ X378 )
| ~ ( in @ ( kpair @ X386 @ X387 ) @ X382 )
| ( in @ ( kpair @ X386 @ X387 ) @ X379 )
| ~ ( in @ X384
@ ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ Z0 ) @ X382 ) ) )
| ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ Z0 ) @ X382 ) )
!= ( setadjoin @ X384 @ emptyset ) )
| ~ ( subset @ X382 @ ( cartprod @ X377 @ X378 ) )
| ~ ( in @ X381
@ ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk26_3 @ X377 @ X378 @ X379 ) @ Z0 ) @ X379 ) ) )
| ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk26_3 @ X377 @ X378 @ X379 ) @ Z0 ) @ X379 ) )
!= ( setadjoin @ X381 @ emptyset ) )
| ~ ( subset @ X379 @ ( cartprod @ X377 @ X378 ) ) )
& ( ( ( ap @ X377 @ X378 @ X379 @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) )
!= ( ap @ X377 @ X378 @ X382 @ ( esk28_4 @ X377 @ X378 @ X379 @ X382 ) ) )
| ~ ( in @ X386 @ X377 )
| ~ ( in @ X387 @ X378 )
| ~ ( in @ ( kpair @ X386 @ X387 ) @ X382 )
| ( in @ ( kpair @ X386 @ X387 ) @ X379 )
| ~ ( in @ X384
@ ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ Z0 ) @ X382 ) ) )
| ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk27_4 @ X377 @ X378 @ X379 @ X382 ) @ Z0 ) @ X382 ) )
!= ( setadjoin @ X384 @ emptyset ) )
| ~ ( subset @ X382 @ ( cartprod @ X377 @ X378 ) )
| ~ ( in @ X381
@ ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk26_3 @ X377 @ X378 @ X379 ) @ Z0 ) @ X379 ) ) )
| ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk26_3 @ X377 @ X378 @ X379 ) @ Z0 ) @ X379 ) )
!= ( setadjoin @ X381 @ emptyset ) )
| ~ ( subset @ X379 @ ( cartprod @ X377 @ X378 ) ) )
& ( in @ esk31_0 @ ( funcSet @ esk29_0 @ esk30_0 ) )
& ( in @ esk32_0 @ esk29_0 )
& ( in @ esk33_0 @ esk30_0 )
& ( in @ ( kpair @ esk32_0 @ esk33_0 ) @ esk31_0 )
& ( ( ap @ esk29_0 @ esk30_0 @ esk31_0 @ esk32_0 )
!= esk33_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(fof_nnf,[status(thm)],[c_0_63])])])])])]) ).
thf(c_0_65,plain,
! [X422: $i,X3: $i,X4: $i] :
( ( epred7_2 @ X4 @ X3 @ X422 )
<=> ( in @ ( kpair @ X3 @ X422 ) @ X4 ) ),
introduced(definition) ).
thf(c_0_66,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X3: $i] :
( ( ( in @ ( esk15_4 @ X2 @ X3 @ X4 @ X5 ) @ ( dsetconstr @ X3 @ ( epred7_2 @ X4 @ X5 ) ) )
= $true )
| ~ ( in @ X5 @ X2 )
| ~ ( in @ X4 @ ( funcSet @ X2 @ X3 ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_64]),c_0_65]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i > $o,X3: $i,X4: $i,X2: $i,X5: $i] :
( ( X4 = X5 )
| ~ ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
| ( ( dsetconstr @ X3 @ X1 )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X4 @ X3 )
| ~ ( in @ X5 @ X3 )
| ~ ( X1 @ X4 )
| ~ ( X1 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_68,negated_conjecture,
! [X3: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk15_4 @ X2 @ X3 @ X4 @ X5 ) @ ( dsetconstr @ X3 @ ( epred7_2 @ X4 @ X5 ) ) )
| ~ ( in @ X4 @ ( funcSet @ X2 @ X3 ) )
| ~ ( in @ X5 @ X2 ) ),
inference(cn,[status(thm)],[c_0_66]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i,X5: $i,X4: $i,X2: $i] :
( ( ( dsetconstr @ X2 @ ( epred7_2 @ X4 @ X3 ) )
= ( setadjoin @ ( esk15_4 @ X5 @ X2 @ X4 @ X3 ) @ emptyset ) )
| ~ ( in @ X3 @ X5 )
| ~ ( in @ X4 @ ( funcSet @ X5 @ X2 ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_64]),c_0_65]) ).
thf(c_0_70,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X8: $i,X7: $i,X5: $i] :
( ( X2 = X3 )
| ~ ( in @ X4 @ ( funcSet @ X5 @ X7 ) )
| ~ ( epred7_2 @ X4 @ X8 @ X3 )
| ~ ( epred7_2 @ X4 @ X8 @ X2 )
| ~ ( in @ X3 @ X7 )
| ~ ( in @ X2 @ X7 )
| ~ ( in @ X8 @ X5 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
thf(c_0_71,negated_conjecture,
in @ esk31_0 @ ( funcSet @ esk29_0 @ esk30_0 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_72,plain,
! [X445: $i,X446: $i,X447: $i] :
( ( ~ ( epred7_2 @ X447 @ X446 @ X445 )
| ( in @ ( kpair @ X446 @ X445 ) @ X447 ) )
& ( ~ ( in @ ( kpair @ X446 @ X445 ) @ X447 )
| ( epred7_2 @ X447 @ X446 @ X445 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_73,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( X2 = X3 )
| ~ ( epred7_2 @ esk31_0 @ X4 @ X3 )
| ~ ( epred7_2 @ esk31_0 @ X4 @ X2 )
| ~ ( in @ X3 @ esk30_0 )
| ~ ( in @ X2 @ esk30_0 )
| ~ ( in @ X4 @ esk29_0 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_74,plain,
! [X2: $i,X3: $i,X4: $i] :
( ( epred7_2 @ X4 @ X2 @ X3 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
thf(c_0_75,plain,
! [X2: $i,X3: $i,X4: $i] :
( ( X2 = X3 )
| ~ ( in @ ( kpair @ X4 @ X3 ) @ esk31_0 )
| ~ ( epred7_2 @ esk31_0 @ X4 @ X2 )
| ~ ( in @ X3 @ esk30_0 )
| ~ ( in @ X2 @ esk30_0 )
| ~ ( in @ X4 @ esk29_0 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_76,negated_conjecture,
in @ ( kpair @ esk32_0 @ esk33_0 ) @ esk31_0,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_77,negated_conjecture,
in @ esk33_0 @ esk30_0,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_78,negated_conjecture,
in @ esk32_0 @ esk29_0,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_79,negated_conjecture,
! [X2: $i] :
( ( X2 = esk33_0 )
| ~ ( epred7_2 @ esk31_0 @ esk32_0 @ X2 )
| ~ ( in @ X2 @ esk30_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78])]) ).
thf(c_0_80,plain,
! [X2: $i] :
( ( X2 = esk33_0 )
| ~ ( in @ ( kpair @ esk32_0 @ X2 ) @ esk31_0 )
| ~ ( in @ X2 @ esk30_0 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_74]) ).
thf(c_0_81,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X3: $i] :
( ( in @ ( kpair @ X5 @ ( ap @ X3 @ X4 @ X2 @ X5 ) ) @ X2 )
| ~ ( in @ X2 @ ( funcSet @ X3 @ X4 ) )
| ~ ( in @ X5 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_82,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( ap @ X2 @ X3 @ esk31_0 @ esk32_0 )
= esk33_0 )
| ~ ( in @ ( ap @ X2 @ X3 @ esk31_0 @ esk32_0 ) @ esk30_0 )
| ~ ( in @ esk31_0 @ ( funcSet @ X2 @ X3 ) )
| ~ ( in @ esk32_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
thf(c_0_83,negated_conjecture,
( ( ap @ esk29_0 @ esk30_0 @ esk31_0 @ esk32_0 )
!= esk33_0 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_84,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X3: $i] :
( ( in @ ( ap @ X3 @ X4 @ X2 @ X5 ) @ X4 )
| ~ ( in @ X2 @ ( funcSet @ X3 @ X4 ) )
| ~ ( in @ X5 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_85,negated_conjecture,
~ ( in @ ( ap @ esk29_0 @ esk30_0 @ esk31_0 @ esk32_0 ) @ esk30_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_71]),c_0_78])]),c_0_83]) ).
thf(c_0_86,negated_conjecture,
! [X2: $i] :
( ( in @ ( ap @ esk29_0 @ esk30_0 @ esk31_0 @ X2 ) @ esk30_0 )
| ~ ( in @ X2 @ esk29_0 ) ),
inference(spm,[status(thm)],[c_0_84,c_0_71]) ).
thf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU688^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 17:45:23 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running higher-order theorem proving
% 0.17/0.43 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
% 40.35/5.56 # Version: 3.1.0-ho
% 40.35/5.56 # Preprocessing class: HSLMSLSSLLLCHFA.
% 40.35/5.56 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 40.35/5.56 # Starting ehoh_best5 with 300s (1) cores
% 40.35/5.56 # Starting almost_fo_3_lam with 300s (1) cores
% 40.35/5.56 # Starting new_bool_5 with 300s (1) cores
% 40.35/5.56 # Starting pre_casc_3 with 300s (1) cores
% 40.35/5.56 # Starting ho_unfolding_8 with 300s (1) cores
% 40.35/5.56 # Starting new_ho_10_cnf2 with 300s (1) cores
% 40.35/5.56 # Starting new_bool_3 with 300s (1) cores
% 40.35/5.56 # Starting new_ho_5 with 300s (1) cores
% 40.35/5.56 # new_ho_5 with pid 13745 completed with status 0
% 40.35/5.56 # Result found by new_ho_5
% 40.35/5.56 # Preprocessing class: HSLMSLSSLLLCHFA.
% 40.35/5.56 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 40.35/5.56 # Starting ehoh_best5 with 300s (1) cores
% 40.35/5.56 # Starting almost_fo_3_lam with 300s (1) cores
% 40.35/5.56 # Starting new_bool_5 with 300s (1) cores
% 40.35/5.56 # Starting pre_casc_3 with 300s (1) cores
% 40.35/5.56 # Starting ho_unfolding_8 with 300s (1) cores
% 40.35/5.56 # Starting new_ho_10_cnf2 with 300s (1) cores
% 40.35/5.56 # Starting new_bool_3 with 300s (1) cores
% 40.35/5.56 # Starting new_ho_5 with 300s (1) cores
% 40.35/5.56 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 40.35/5.56 # Search class: HGUSS-FSLM32-MHFMMSBN
% 40.35/5.56 # partial match(2): HGHSM-FSLM32-MHFMMSBN
% 40.35/5.56 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 40.35/5.56 # Starting ho_unfolding_8 with 61s (1) cores
% 40.35/5.56 # ho_unfolding_8 with pid 13746 completed with status 0
% 40.35/5.56 # Result found by ho_unfolding_8
% 40.35/5.56 # Preprocessing class: HSLMSLSSLLLCHFA.
% 40.35/5.56 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 40.35/5.56 # Starting ehoh_best5 with 300s (1) cores
% 40.35/5.56 # Starting almost_fo_3_lam with 300s (1) cores
% 40.35/5.56 # Starting new_bool_5 with 300s (1) cores
% 40.35/5.56 # Starting pre_casc_3 with 300s (1) cores
% 40.35/5.56 # Starting ho_unfolding_8 with 300s (1) cores
% 40.35/5.56 # Starting new_ho_10_cnf2 with 300s (1) cores
% 40.35/5.56 # Starting new_bool_3 with 300s (1) cores
% 40.35/5.56 # Starting new_ho_5 with 300s (1) cores
% 40.35/5.56 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 40.35/5.56 # Search class: HGUSS-FSLM32-MHFMMSBN
% 40.35/5.56 # partial match(2): HGHSM-FSLM32-MHFMMSBN
% 40.35/5.56 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 40.35/5.56 # Starting ho_unfolding_8 with 61s (1) cores
% 40.35/5.56 # Preprocessing time : 0.022 s
% 40.35/5.56 # Presaturation interreduction done
% 40.35/5.56
% 40.35/5.56 # Proof found!
% 40.35/5.56 # SZS status Theorem
% 40.35/5.56 # SZS output start CNFRefutation
% See solution above
% 40.35/5.56 # Parsed axioms : 453
% 40.35/5.56 # Removed by relevancy pruning/SinE : 425
% 40.35/5.56 # Initial clauses : 283
% 40.35/5.56 # Removed in clause preprocessing : 0
% 40.35/5.56 # Initial clauses in saturation : 283
% 40.35/5.56 # Processed clauses : 2563
% 40.35/5.56 # ...of these trivial : 10
% 40.35/5.56 # ...subsumed : 469
% 40.35/5.56 # ...remaining for further processing : 2084
% 40.35/5.56 # Other redundant clauses eliminated : 419
% 40.35/5.56 # Clauses deleted for lack of memory : 0
% 40.35/5.56 # Backward-subsumed : 91
% 40.35/5.56 # Backward-rewritten : 2
% 40.35/5.56 # Generated clauses : 83964
% 40.35/5.56 # ...of the previous two non-redundant : 82838
% 40.35/5.56 # ...aggressively subsumed : 0
% 40.35/5.56 # Contextual simplify-reflections : 71
% 40.35/5.56 # Paramodulations : 83166
% 40.35/5.56 # Factorizations : 0
% 40.35/5.56 # NegExts : 57
% 40.35/5.56 # Equation resolutions : 420
% 40.35/5.56 # Disequality decompositions : 0
% 40.35/5.56 # Total rewrite steps : 2797
% 40.35/5.56 # ...of those cached : 2734
% 40.35/5.56 # Propositional unsat checks : 0
% 40.35/5.56 # Propositional check models : 0
% 40.35/5.56 # Propositional check unsatisfiable : 0
% 40.35/5.56 # Propositional clauses : 0
% 40.35/5.56 # Propositional clauses after purity: 0
% 40.35/5.56 # Propositional unsat core size : 0
% 40.35/5.56 # Propositional preprocessing time : 0.000
% 40.35/5.56 # Propositional encoding time : 0.000
% 40.35/5.56 # Propositional solver time : 0.000
% 40.35/5.56 # Success case prop preproc time : 0.000
% 40.35/5.56 # Success case prop encoding time : 0.000
% 40.35/5.56 # Success case prop solver time : 0.000
% 40.35/5.56 # Current number of processed clauses : 1706
% 40.35/5.56 # Positive orientable unit clauses : 194
% 40.35/5.56 # Positive unorientable unit clauses: 0
% 40.35/5.56 # Negative unit clauses : 2
% 40.35/5.56 # Non-unit-clauses : 1510
% 40.35/5.56 # Current number of unprocessed clauses: 80792
% 40.35/5.56 # ...number of literals in the above : 530103
% 40.35/5.56 # Current number of archived formulas : 0
% 40.35/5.56 # Current number of archived clauses : 377
% 40.35/5.56 # Clause-clause subsumption calls (NU) : 204536
% 40.35/5.56 # Rec. Clause-clause subsumption calls : 31837
% 40.35/5.56 # Non-unit clause-clause subsumptions : 630
% 40.35/5.56 # Unit Clause-clause subsumption calls : 2551
% 40.35/5.56 # Rewrite failures with RHS unbound : 0
% 40.35/5.56 # BW rewrite match attempts : 7
% 40.35/5.56 # BW rewrite match successes : 2
% 40.35/5.56 # Condensation attempts : 0
% 40.35/5.56 # Condensation successes : 0
% 40.35/5.56 # Termbank termtop insertions : 3791333
% 40.35/5.56 # Search garbage collected termcells : 9156
% 40.35/5.56
% 40.35/5.56 # -------------------------------------------------
% 40.35/5.56 # User time : 4.882 s
% 40.35/5.56 # System time : 0.111 s
% 40.35/5.56 # Total time : 4.993 s
% 40.35/5.56 # Maximum resident set size: 4828 pages
% 40.35/5.56
% 40.35/5.56 # -------------------------------------------------
% 40.35/5.56 # User time : 4.893 s
% 40.35/5.56 # System time : 0.114 s
% 40.35/5.56 # Total time : 5.007 s
% 40.35/5.56 # Maximum resident set size: 2208 pages
% 40.35/5.56 % E---3.1 exiting
% 40.35/5.56 % E exiting
%------------------------------------------------------------------------------