%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU695^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 15:10:10 EDT 2024
% Result : Theorem 0.37s 0.92s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 47
% Syntax : Number of formulae : 97 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 1302 ( 120 equ; 0 cnn)
% Maximal formula atoms : 424 ( 13 avg)
% Number of connectives : 4051 ( 161 ~; 203 |; 275 &;2696 @)
% ( 56 <=>; 660 =>; 0 <=; 0 <~>)
% Maximal formula depth : 402 ( 17 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 259 ( 256 usr; 217 con; 0-4 aty)
% Number of variables : 708 ( 85 ^ 603 !; 20 ?; 708 :)
% 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_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_271,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_272,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_273,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_274,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_275,type,
esk6_1: $i > $i ).
thf(decl_276,type,
esk7_1: $i > $i ).
thf(decl_277,type,
esk8_4: $i > $i > $i > $i > $i ).
thf(decl_278,type,
esk9_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_279,type,
esk10_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_280,type,
esk11_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_281,type,
esk12_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_282,type,
esk13_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_283,type,
esk14_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_284,type,
esk15_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_285,type,
esk16_4: $i > $i > $i > $i > $i ).
thf(decl_286,type,
esk17_4: $i > $i > $i > $i > $i ).
thf(decl_287,type,
esk18_4: $i > $i > $i > $i > $i ).
thf(decl_288,type,
esk19_4: $i > $i > $i > $i > $i ).
thf(decl_289,type,
esk20_4: $i > $i > $i > $i > $i ).
thf(decl_290,type,
esk21_4: $i > $i > $i > $i > $i ).
thf(decl_291,type,
esk22_4: $i > $i > $i > $i > $i ).
thf(decl_292,type,
esk23_0: $i ).
thf(decl_293,type,
esk24_0: $i ).
thf(decl_294,type,
esk25_0: $i > $i ).
thf(decl_295,type,
esk26_0: $i ).
thf(decl_296,type,
epred1_1: ( $i > $i ) > $i > $i > $o ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',funcImageSingleton) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',singleton) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',singletonprop) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',kfstsingleton) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',breln) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',setOfPairsIsBReln) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',lamp) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',theprop) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X34: $i] :
( ( breln @ X4 @ X5 @ X34 )
=> ! [X36: $i] :
( ( breln @ X4 @ X5 @ X36 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X36 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X36 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X34 ) ) ) )
=> ( X34 = X36 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',eqbreln) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X34: $i] :
( ( breln @ X4 @ X5 @ X34 )
=> ! [X36: $i] :
( ( breln @ X4 @ X5 @ X36 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X36 ) ) ) )
=> ( subset @ X34 @ X36 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',subbreln) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X34: $i] :
( ( breln @ X4 @ X5 @ X34 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X34 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',brelnall2) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X34: $i] :
( ( breln @ X4 @ X5 @ X34 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X34 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',brelnall1) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',lamProp) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',dpsetconstrER) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',dpsetconstrEL2) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',dpsetconstrEL1) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',dpsetconstrERa) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',dpsetconstrSub) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',dpsetconstrI) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X33 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',lam2p) ).
thf(beta1,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
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X37 @ X3 ) )
@ X2 )
= ( X37 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',beta1) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodsndpairEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',ksndpairEq) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodfstpairEq) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',kfstpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',kpairsurjEq) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',kpairp) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',kpairiskpair) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodpairsurjEq) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodpairmemER) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodpairmemEL) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodsndin) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodfstin) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodmempair) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodmempair1) ).
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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',cartprodpairin) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',ap2apEq1) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( in @ X35 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ( X29 = X35 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',funcext2) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',funcGraphProp4) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',funcGraphProp3) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',funcinfuncset) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',ap2p) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',infuncsetfunc) ).
thf(lam,axiom,
( lam
= ( ^ [X4: $i,X5: $i,X31: $i > $i] :
( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X31 @ X2 )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p',lam) ).
thf(c_0_45,plain,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_46,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_47,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_48,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_49,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_50,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_51,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_52,plain,
( lamp
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X32 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_53,plain,
( funcImageSingleton
= ( ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X205: $i] :
( ( in @ X205
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) )
= ( setadjoin @ X205 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_54,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X203: $i] :
( ( in @ X203 @ X21 )
& ( X21
= ( setadjoin @ X203 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_46]) ).
thf(c_0_55,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 ) )
=> ? [X200: $i] :
( ( in @ X200
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X200 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_47,c_0_46]) ).
thf(c_0_56,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X204: $i] :
( ( in @ X204
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X204 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_48,c_0_46]) ).
thf(c_0_57,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X202: $i] :
( ( in @ X202
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X202 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_49,c_0_46]) ).
thf(c_0_58,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X34: $i] :
( ( subset @ X34 @ ( cartprod @ X4 @ X5 ) )
=> ! [X36: $i] :
( ( subset @ X36 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X36 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X36 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X34 ) ) ) )
=> ( X34 = X36 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_50]) ).
thf(c_0_59,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X34: $i] :
( ( subset @ X34 @ ( cartprod @ X4 @ X5 ) )
=> ! [X36: $i] :
( ( subset @ X36 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X36 ) ) ) )
=> ( subset @ X34 @ X36 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_50]) ).
thf(c_0_60,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X34: $i] :
( ( subset @ X34 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X34 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_50]) ).
thf(c_0_61,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X34: $i] :
( ( subset @ X34 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X34 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_50]) ).
thf(c_0_62,plain,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X30 @ Z0 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamProp]) ).
thf(c_0_63,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_64,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_65,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_66,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_67,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_51,c_0_50]) ).
thf(c_0_68,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_69,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_70,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_71,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
=> ( ! [X206: $i,X207: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X206 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X206 @ ( setadjoin @ X207 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X208: $i,X209: $i] : ( iskpair @ ( kpair @ X208 @ X209 ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( ! [X210: $i,X211: $i,X212: $i] :
( ( in @ X212 @ X210 )
=> ! [X213: $i] :
( ( in @ X213 @ X211 )
=> ( in @ ( kpair @ X212 @ X213 ) @ ( cartprod @ X210 @ X211 ) ) ) )
=> ( ! [X214: $i,X215: $i,X216: $i] :
( ( in @ X216 @ ( cartprod @ X214 @ X215 ) )
=> ? [X217: $i] :
( ( in @ X217 @ X214 )
& ? [X218: $i] :
( ( in @ X218 @ X215 )
& ( X216
= ( kpair @ X217 @ X218 ) ) ) ) )
=> ( ! [X219: $i,X220: $i,X221: $i] :
( ( in @ X221 @ ( cartprod @ X219 @ X220 ) )
=> ( iskpair @ X221 ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X222: $i,X223: $i > $o] :
( ! [X224: $i] :
( ( in @ X224 @ X222 )
=> ! [X225: $i] :
( ( in @ X225 @ X222 )
=> ( ( X223 @ X224 )
=> ( ( X223 @ X225 )
=> ( X224 = X225 ) ) ) ) )
=> ( ? [X226: $i] :
( ( in @ X226 @ X222 )
& ( X223 @ X226 ) )
=> ? [X227: $i] :
( ( in @ X227 @ ( dsetconstr @ X222 @ X223 ) )
& ( ( dsetconstr @ X222 @ X223 )
= ( setadjoin @ X227 @ emptyset ) ) ) ) )
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X228: $i] :
( ( iskpair @ X228 )
=> ? [X229: $i] :
( ( in @ X229
@ ( dsetconstr @ ( setunion @ X228 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X228 ) ) )
& ( ( dsetconstr @ ( setunion @ X228 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X228 ) )
= ( setadjoin @ X229 @ emptyset ) ) ) )
=> ( ! [X230: $i] :
( ? [X231: $i] :
( ( in @ X231 @ X230 )
& ( X230
= ( setadjoin @ X231 @ emptyset ) ) )
=> ( in @ ( setunion @ X230 ) @ X230 ) )
=> ( ! [X232: $i,X233: $i] :
( ( kfst @ ( kpair @ X232 @ X233 ) )
= X232 )
=> ( ! [X234: $i,X235: $i,X236: $i] :
( ( in @ X236 @ ( cartprod @ X234 @ X235 ) )
=> ( in @ ( kfst @ X236 ) @ X234 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X237: $i] :
( ( iskpair @ X237 )
=> ? [X238: $i] :
( ( in @ X238
@ ( dsetconstr @ ( setunion @ X237 )
@ ^ [Z0: $i] :
( X237
= ( kpair @ ( kfst @ X237 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X237 )
@ ^ [Z0: $i] :
( X237
= ( kpair @ ( kfst @ X237 ) @ Z0 ) ) )
= ( setadjoin @ X238 @ emptyset ) ) ) )
=> ( ! [X239: $i,X240: $i] :
( ( ksnd @ ( kpair @ X239 @ X240 ) )
= X240 )
=> ( ! [X241: $i] :
( ( iskpair @ X241 )
=> ( ( kpair @ ( kfst @ X241 ) @ ( ksnd @ X241 ) )
= X241 ) )
=> ( ! [X242: $i,X243: $i,X244: $i] :
( ( in @ X244 @ ( cartprod @ X242 @ X243 ) )
=> ( in @ ( ksnd @ X244 ) @ X243 ) )
=> ( ! [X245: $i,X246: $i,X247: $i,X248: $i] :
( ( in @ ( kpair @ X247 @ X248 ) @ ( cartprod @ X245 @ X246 ) )
=> ( in @ X247 @ X245 ) )
=> ( ! [X249: $i,X250: $i,X251: $i,X252: $i] :
( ( in @ ( kpair @ X251 @ X252 ) @ ( cartprod @ X249 @ X250 ) )
=> ( in @ X252 @ X250 ) )
=> ( cartprodmempaircEq
=> ( ! [X253: $i,X254: $i,X255: $i] :
( ( in @ X255 @ X253 )
=> ! [X256: $i] :
( ( in @ X256 @ X254 )
=> ( ( kfst @ ( kpair @ X255 @ X256 ) )
= X255 ) ) )
=> ( ! [X257: $i,X258: $i,X259: $i] :
( ( in @ X259 @ X257 )
=> ! [X260: $i] :
( ( in @ X260 @ X258 )
=> ( ( ksnd @ ( kpair @ X259 @ X260 ) )
= X260 ) ) )
=> ( ! [X261: $i,X262: $i,X263: $i] :
( ( in @ X263 @ ( cartprod @ X261 @ X262 ) )
=> ( ( kpair @ ( kfst @ X263 ) @ ( ksnd @ X263 ) )
= X263 ) )
=> ( ! [X264: $i,X265: $i,X266: $i > $i > $o,X267: $i] :
( ( in @ X267 @ X264 )
=> ! [X268: $i] :
( ( in @ X268 @ X265 )
=> ( ( X266 @ X267 @ X268 )
=> ( in @ ( kpair @ X267 @ X268 ) @ ( dpsetconstr @ X264 @ X265 @ X266 ) ) ) ) )
=> ( ! [X269: $i,X270: $i,X271: $i > $i > $o] : ( subset @ ( dpsetconstr @ X269 @ X270 @ X271 ) @ ( cartprod @ X269 @ X270 ) )
=> ( ! [X272: $i,X273: $i,X274: $i > $i > $o] : ( subset @ ( dpsetconstr @ X272 @ X273 @ X274 ) @ ( cartprod @ X272 @ X273 ) )
=> ( ! [X275: $i,X276: $i,X277: $i > $i > $o,X278: $i] :
( ( in @ X278 @ X275 )
=> ! [X279: $i] :
( ( in @ X279 @ X276 )
=> ( ( in @ ( kpair @ X278 @ X279 ) @ ( dpsetconstr @ X275 @ X276 @ X277 ) )
=> ( X277 @ X278 @ X279 ) ) ) )
=> ( ! [X280: $i,X281: $i,X282: $i > $i > $o,X283: $i,X284: $i] :
( ( in @ ( kpair @ X283 @ X284 ) @ ( dpsetconstr @ X280 @ X281 @ X282 ) )
=> ( in @ X283 @ X280 ) )
=> ( ! [X285: $i,X286: $i,X287: $i > $i > $o,X288: $i,X289: $i] :
( ( in @ ( kpair @ X288 @ X289 ) @ ( dpsetconstr @ X285 @ X286 @ X287 ) )
=> ( in @ X289 @ X286 ) )
=> ( ! [X290: $i,X291: $i,X292: $i > $i > $o,X293: $i,X294: $i] :
( ( in @ ( kpair @ X293 @ X294 ) @ ( dpsetconstr @ X290 @ X291 @ X292 ) )
=> ( X292 @ X293 @ X294 ) )
=> ( ! [X295: $i,X296: $i,X297: $i] :
( ( func @ X295 @ X296 @ X297 )
=> ! [X298: $i] :
( ( in @ X298 @ X295 )
=> ? [X299: $i] :
( ( in @ X299
@ ( dsetconstr @ X296
@ ^ [Z0: $i] : ( in @ ( kpair @ X298 @ Z0 ) @ X297 ) ) )
& ( ( dsetconstr @ X296
@ ^ [Z0: $i] : ( in @ ( kpair @ X298 @ Z0 ) @ X297 ) )
= ( setadjoin @ X299 @ emptyset ) ) ) ) )
=> ( apProp
=> ( app
=> ( ! [X300: $i,X301: $i,X302: $i] :
( ( in @ X302 @ ( funcSet @ X300 @ X301 ) )
=> ( func @ X300 @ X301 @ X302 ) )
=> ( ! [X303: $i,X304: $i,X305: $i] :
( ( in @ X305 @ ( funcSet @ X303 @ X304 ) )
=> ! [X306: $i] :
( ( in @ X306 @ X303 )
=> ( in @ ( ap @ X303 @ X304 @ X305 @ X306 ) @ X304 ) ) )
=> ( ! [X307: $i,X308: $i,X309: $i] :
( ( func @ X307 @ X308 @ X309 )
=> ( in @ X309 @ ( funcSet @ X307 @ X308 ) ) )
=> ( ! [X310: $i,X311: $i,X312: $i > $i] :
( ! [X313: $i] :
( ( in @ X313 @ X310 )
=> ( in @ ( X312 @ X313 ) @ X311 ) )
=> ( func @ X310 @ X311
@ ( dpsetconstr @ X310 @ X311
@ ^ [Z0: $i] : ( $eq @ ( X312 @ Z0 ) ) ) ) )
=> ( ! [X314: $i,X315: $i,X316: $i > $i] :
( ! [X317: $i] :
( ( in @ X317 @ X314 )
=> ( in @ ( X316 @ X317 ) @ X315 ) )
=> ( func @ X314 @ X315 @ ( lam @ X314 @ X315 @ X316 ) ) )
=> ( ! [X318: $i,X319: $i,X320: $i > $i] :
( ! [X321: $i] :
( ( in @ X321 @ X318 )
=> ( in @ ( X320 @ X321 ) @ X319 ) )
=> ( in @ ( lam @ X318 @ X319 @ X320 ) @ ( funcSet @ X318 @ X319 ) ) )
=> ( ! [X322: $i,X323: $i,X324: $i] :
( ( subset @ X324 @ ( cartprod @ X322 @ X323 ) )
=> ! [X325: $i > $o] :
( ! [X326: $i] :
( ( in @ X326 @ X322 )
=> ! [X327: $i] :
( ( in @ X327 @ X323 )
=> ( ( in @ ( kpair @ X326 @ X327 ) @ X324 )
=> ( X325 @ ( kpair @ X326 @ X327 ) ) ) ) )
=> ! [X328: $i] :
( ( in @ X328 @ X324 )
=> ( X325 @ X328 ) ) ) )
=> ( ! [X329: $i,X330: $i,X331: $i] :
( ( subset @ X331 @ ( cartprod @ X329 @ X330 ) )
=> ! [X332: $i > $o] :
( ! [X333: $i] :
( ( in @ X333 @ X329 )
=> ! [X334: $i] :
( ( in @ X334 @ X330 )
=> ( ( in @ ( kpair @ X333 @ X334 ) @ X331 )
=> ( X332 @ ( kpair @ X333 @ X334 ) ) ) ) )
=> ! [X335: $i] :
( ( in @ X335 @ X331 )
=> ( X332 @ X335 ) ) ) )
=> ( ex1E2
=> ( funcGraphProp1
=> ( ! [X336: $i,X337: $i,X338: $i] :
( ( in @ X338 @ ( funcSet @ X336 @ X337 ) )
=> ! [X339: $i] :
( ( in @ X339 @ X336 )
=> ( in @ ( kpair @ X339 @ ( ap @ X336 @ X337 @ X338 @ X339 ) ) @ X338 ) ) )
=> ( funcGraphProp2
=> ( funcextLem
=> ( ! [X340: $i,X341: $i,X342: $i] :
( ( in @ X342 @ ( funcSet @ X340 @ X341 ) )
=> ! [X343: $i] :
( ( in @ X343 @ X340 )
=> ! [X344: $i] :
( ( in @ X344 @ X341 )
=> ( ( in @ ( kpair @ X343 @ X344 ) @ X342 )
=> ( ( ap @ X340 @ X341 @ X342 @ X343 )
= X344 ) ) ) ) )
=> ( ! [X345: $i,X346: $i,X347: $i] :
( ( subset @ X347 @ ( cartprod @ X345 @ X346 ) )
=> ! [X348: $i] :
( ( subset @ X348 @ ( cartprod @ X345 @ X346 ) )
=> ( ! [X349: $i] :
( ( in @ X349 @ X345 )
=> ! [X350: $i] :
( ( in @ X350 @ X346 )
=> ( ( in @ ( kpair @ X349 @ X350 ) @ X347 )
=> ( in @ ( kpair @ X349 @ X350 ) @ X348 ) ) ) )
=> ( subset @ X347 @ X348 ) ) ) )
=> ( ! [X351: $i,X352: $i,X353: $i] :
( ( subset @ X353 @ ( cartprod @ X351 @ X352 ) )
=> ! [X354: $i] :
( ( subset @ X354 @ ( cartprod @ X351 @ X352 ) )
=> ( ! [X355: $i] :
( ( in @ X355 @ X351 )
=> ! [X356: $i] :
( ( in @ X356 @ X352 )
=> ( ( in @ ( kpair @ X355 @ X356 ) @ X353 )
=> ( in @ ( kpair @ X355 @ X356 ) @ X354 ) ) ) )
=> ( ! [X357: $i] :
( ( in @ X357 @ X351 )
=> ! [X358: $i] :
( ( in @ X358 @ X352 )
=> ( ( in @ ( kpair @ X357 @ X358 ) @ X354 )
=> ( in @ ( kpair @ X357 @ X358 ) @ X353 ) ) ) )
=> ( X353 = X354 ) ) ) ) )
=> ( funcext
=> ( ! [X359: $i,X360: $i,X361: $i] :
( ( in @ X361 @ ( funcSet @ X359 @ X360 ) )
=> ! [X362: $i] :
( ( in @ X362 @ ( funcSet @ X359 @ X360 ) )
=> ( ! [X363: $i] :
( ( in @ X363 @ X359 )
=> ( ( ap @ X359 @ X360 @ X361 @ X363 )
= ( ap @ X359 @ X360 @ X362 @ X363 ) ) )
=> ( X361 = X362 ) ) ) )
=> ( ! [X364: $i,X365: $i,X366: $i] :
( ( in @ X366 @ ( funcSet @ X364 @ X365 ) )
=> ! [X367: $i] :
( ( in @ X367 @ X364 )
=> ( ( ap @ X364 @ X365 @ X366 @ X367 )
= ( ap @ X364 @ X365 @ X366 @ X367 ) ) ) )
=> ( ap2apEq2
=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ ( lam @ X4 @ X5 @ X37 ) @ X2 )
= ( X37 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[beta1])]),c_0_52]),c_0_53]),c_0_54]),c_0_55]),cartprodsndpairEq]),ksndpairEq]),cartprodfstpairEq]),kfstpairEq]),kpairsurjEq]),c_0_56]),c_0_57]),kpairp]),kpairiskpair]),c_0_58]),c_0_59]),c_0_60]),c_0_61]),cartprodpairsurjEq]),cartprodpairmemER]),cartprodpairmemEL]),cartprodsndin]),cartprodfstin]),cartprodmempair]),cartprodmempair1]),cartprodpairin]),ap2apEq1]),funcext2]),funcGraphProp4]),funcGraphProp3]),funcinfuncset]),ap2p]),infuncsetfunc]),c_0_62]),c_0_63]),c_0_64]),c_0_65]),c_0_66]),c_0_67]),c_0_68]),c_0_69]),c_0_70])]) ).
thf(c_0_72,plain,
! [X368: $i,X369: $i,X370: $i > $i] :
( ( lam @ X368 @ X369 @ X370 )
= ( dpsetconstr @ X368 @ X369
@ ^ [Z0: $i] : ( $eq @ ( X370 @ Z0 ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[lam])])]) ).
thf(c_0_73,negated_conjecture,
! [X371: $i,X372: $i,X373: $i,X374: $i,X375: $i,X376: $i,X377: $i,X378: $i,X379: $i,X380: $i,X381: $i,X384: $i,X385: $i,X386: $i,X387: $i,X388: $i > $o,X391: $i,X393: $i,X395: $i,X396: $i,X397: $i,X398: $i,X399: $i,X400: $i,X401: $i,X402: $i,X404: $i,X405: $i,X406: $i,X407: $i,X408: $i,X409: $i,X410: $i,X411: $i,X412: $i,X413: $i,X414: $i,X415: $i,X416: $i,X417: $i,X418: $i,X419: $i,X420: $i,X421: $i,X422: $i,X423: $i,X424: $i,X425: $i,X426: $i,X427: $i,X428: $i,X429: $i,X430: $i,X431: $i > $i > $o,X432: $i,X433: $i,X434: $i,X435: $i,X436: $i > $i > $o,X437: $i,X438: $i,X439: $i > $i > $o,X440: $i,X441: $i,X442: $i > $i > $o,X443: $i,X444: $i,X445: $i,X446: $i,X447: $i > $i > $o,X448: $i,X449: $i,X450: $i,X451: $i,X452: $i > $i > $o,X453: $i,X454: $i,X455: $i,X456: $i,X457: $i > $i > $o,X458: $i,X459: $i,X460: $i,X461: $i,X462: $i,X463: $i,X465: $i,X466: $i,X467: $i,X468: $i,X469: $i,X470: $i,X471: $i,X472: $i,X473: $i,X474: $i,X475: $i,X476: $i,X477: $i > $i,X479: $i,X480: $i,X481: $i > $i,X483: $i,X484: $i,X485: $i > $i,X487: $i,X488: $i,X489: $i,X490: $i > $o,X493: $i,X494: $i,X495: $i,X496: $i,X497: $i > $o,X500: $i,X501: $i,X502: $i,X503: $i,X504: $i,X505: $i,X506: $i,X507: $i,X508: $i,X509: $i,X510: $i,X511: $i,X512: $i,X513: $i,X516: $i,X517: $i,X518: $i,X519: $i,X524: $i,X525: $i,X526: $i,X527: $i,X529: $i,X530: $i,X531: $i,X532: $i,X536: $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
& ( iskpair @ ( setadjoin @ ( setadjoin @ X371 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X371 @ ( setadjoin @ X372 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X373 @ X374 ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& ( ~ ( in @ X377 @ X375 )
| ~ ( in @ X378 @ X376 )
| ( in @ ( kpair @ X377 @ X378 ) @ ( cartprod @ X375 @ X376 ) ) )
& ( ( in @ ( esk1_3 @ X379 @ X380 @ X381 ) @ X379 )
| ~ ( in @ X381 @ ( cartprod @ X379 @ X380 ) ) )
& ( ( in @ ( esk2_3 @ X379 @ X380 @ X381 ) @ X380 )
| ~ ( in @ X381 @ ( cartprod @ X379 @ X380 ) ) )
& ( ( X381
= ( kpair @ ( esk1_3 @ X379 @ X380 @ X381 ) @ ( esk2_3 @ X379 @ X380 @ X381 ) ) )
| ~ ( in @ X381 @ ( cartprod @ X379 @ X380 ) ) )
& ( ~ ( in @ X386 @ ( cartprod @ X384 @ X385 ) )
| ( iskpair @ X386 ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk5_2 @ X387 @ X388 ) @ ( dsetconstr @ X387 @ X388 ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( in @ ( esk3_2 @ X387 @ X388 ) @ X387 ) )
& ( ( ( dsetconstr @ X387 @ X388 )
= ( setadjoin @ ( esk5_2 @ X387 @ X388 ) @ emptyset ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( in @ ( esk3_2 @ X387 @ X388 ) @ X387 ) )
& ( ( in @ ( esk5_2 @ X387 @ X388 ) @ ( dsetconstr @ X387 @ X388 ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( in @ ( esk4_2 @ X387 @ X388 ) @ X387 ) )
& ( ( ( dsetconstr @ X387 @ X388 )
= ( setadjoin @ ( esk5_2 @ X387 @ X388 ) @ emptyset ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( in @ ( esk4_2 @ X387 @ X388 ) @ X387 ) )
& ( ( in @ ( esk5_2 @ X387 @ X388 ) @ ( dsetconstr @ X387 @ X388 ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( X388 @ ( esk3_2 @ X387 @ X388 ) ) )
& ( ( ( dsetconstr @ X387 @ X388 )
= ( setadjoin @ ( esk5_2 @ X387 @ X388 ) @ emptyset ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( X388 @ ( esk3_2 @ X387 @ X388 ) ) )
& ( ( in @ ( esk5_2 @ X387 @ X388 ) @ ( dsetconstr @ X387 @ X388 ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( X388 @ ( esk4_2 @ X387 @ X388 ) ) )
& ( ( ( dsetconstr @ X387 @ X388 )
= ( setadjoin @ ( esk5_2 @ X387 @ X388 ) @ emptyset ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( X388 @ ( esk4_2 @ X387 @ X388 ) ) )
& ( ( in @ ( esk5_2 @ X387 @ X388 ) @ ( dsetconstr @ X387 @ X388 ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( ( esk3_2 @ X387 @ X388 )
!= ( esk4_2 @ X387 @ X388 ) ) )
& ( ( ( dsetconstr @ X387 @ X388 )
= ( setadjoin @ ( esk5_2 @ X387 @ X388 ) @ emptyset ) )
| ~ ( in @ X391 @ X387 )
| ~ ( X388 @ X391 )
| ( ( esk3_2 @ X387 @ X388 )
!= ( esk4_2 @ X387 @ X388 ) ) )
& ex1E1
& ex1I
& ex1I2
& singletonsuniq
& setukpairinjL1
& ( ( in @ ( esk6_1 @ X393 )
@ ( dsetconstr @ ( setunion @ X393 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X393 ) ) )
| ~ ( iskpair @ X393 ) )
& ( ( ( dsetconstr @ ( setunion @ X393 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X393 ) )
= ( setadjoin @ ( esk6_1 @ X393 ) @ emptyset ) )
| ~ ( iskpair @ X393 ) )
& ( ~ ( in @ X396 @ X395 )
| ( X395
!= ( setadjoin @ X396 @ emptyset ) )
| ( in @ ( setunion @ X395 ) @ X395 ) )
& ( ( kfst @ ( kpair @ X397 @ X398 ) )
= X397 )
& ( ~ ( in @ X401 @ ( cartprod @ X399 @ X400 ) )
| ( in @ ( kfst @ X401 ) @ X399 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ( in @ ( esk7_1 @ X402 )
@ ( dsetconstr @ ( setunion @ X402 )
@ ^ [Z0: $i] :
( X402
= ( kpair @ ( kfst @ X402 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X402 ) )
& ( ( ( dsetconstr @ ( setunion @ X402 )
@ ^ [Z0: $i] :
( X402
= ( kpair @ ( kfst @ X402 ) @ Z0 ) ) )
= ( setadjoin @ ( esk7_1 @ X402 ) @ emptyset ) )
| ~ ( iskpair @ X402 ) )
& ( ( ksnd @ ( kpair @ X404 @ X405 ) )
= X405 )
& ( ~ ( iskpair @ X406 )
| ( ( kpair @ ( kfst @ X406 ) @ ( ksnd @ X406 ) )
= X406 ) )
& ( ~ ( in @ X409 @ ( cartprod @ X407 @ X408 ) )
| ( in @ ( ksnd @ X409 ) @ X408 ) )
& ( ~ ( in @ ( kpair @ X412 @ X413 ) @ ( cartprod @ X410 @ X411 ) )
| ( in @ X412 @ X410 ) )
& ( ~ ( in @ ( kpair @ X416 @ X417 ) @ ( cartprod @ X414 @ X415 ) )
| ( in @ X417 @ X415 ) )
& cartprodmempaircEq
& ( ~ ( in @ X420 @ X418 )
| ~ ( in @ X421 @ X419 )
| ( ( kfst @ ( kpair @ X420 @ X421 ) )
= X420 ) )
& ( ~ ( in @ X424 @ X422 )
| ~ ( in @ X425 @ X423 )
| ( ( ksnd @ ( kpair @ X424 @ X425 ) )
= X425 ) )
& ( ~ ( in @ X428 @ ( cartprod @ X426 @ X427 ) )
| ( ( kpair @ ( kfst @ X428 ) @ ( ksnd @ X428 ) )
= X428 ) )
& ( ~ ( in @ X432 @ X429 )
| ~ ( in @ X433 @ X430 )
| ~ ( X431 @ X432 @ X433 )
| ( in @ ( kpair @ X432 @ X433 ) @ ( dpsetconstr @ X429 @ X430 @ X431 ) ) )
& ( subset @ ( dpsetconstr @ X434 @ X435 @ X436 ) @ ( cartprod @ X434 @ X435 ) )
& ( subset @ ( dpsetconstr @ X437 @ X438 @ X439 ) @ ( cartprod @ X437 @ X438 ) )
& ( ~ ( in @ X443 @ X440 )
| ~ ( in @ X444 @ X441 )
| ~ ( in @ ( kpair @ X443 @ X444 ) @ ( dpsetconstr @ X440 @ X441 @ X442 ) )
| ( X442 @ X443 @ X444 ) )
& ( ~ ( in @ ( kpair @ X448 @ X449 ) @ ( dpsetconstr @ X445 @ X446 @ X447 ) )
| ( in @ X448 @ X445 ) )
& ( ~ ( in @ ( kpair @ X453 @ X454 ) @ ( dpsetconstr @ X450 @ X451 @ X452 ) )
| ( in @ X454 @ X451 ) )
& ( ~ ( in @ ( kpair @ X458 @ X459 ) @ ( dpsetconstr @ X455 @ X456 @ X457 ) )
| ( X457 @ X458 @ X459 ) )
& ( ( in @ ( esk8_4 @ X460 @ X461 @ X462 @ X463 )
@ ( dsetconstr @ X461
@ ^ [Z0: $i] : ( in @ ( kpair @ X463 @ Z0 ) @ X462 ) ) )
| ~ ( in @ X463 @ X460 )
| ~ ( func @ X460 @ X461 @ X462 ) )
& ( ( ( dsetconstr @ X461
@ ^ [Z0: $i] : ( in @ ( kpair @ X463 @ Z0 ) @ X462 ) )
= ( setadjoin @ ( esk8_4 @ X460 @ X461 @ X462 @ X463 ) @ emptyset ) )
| ~ ( in @ X463 @ X460 )
| ~ ( func @ X460 @ X461 @ X462 ) )
& apProp
& app
& ( ~ ( in @ X467 @ ( funcSet @ X465 @ X466 ) )
| ( func @ X465 @ X466 @ X467 ) )
& ( ~ ( in @ X470 @ ( funcSet @ X468 @ X469 ) )
| ~ ( in @ X471 @ X468 )
| ( in @ ( ap @ X468 @ X469 @ X470 @ X471 ) @ X469 ) )
& ( ~ ( func @ X472 @ X473 @ X474 )
| ( in @ X474 @ ( funcSet @ X472 @ X473 ) ) )
& ( ( in @ ( esk9_3 @ X475 @ X476 @ X477 ) @ X475 )
| ( func @ X475 @ X476
@ ( dpsetconstr @ X475 @ X476
@ ^ [Z0: $i] : ( $eq @ ( X477 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X477 @ ( esk9_3 @ X475 @ X476 @ X477 ) ) @ X476 )
| ( func @ X475 @ X476
@ ( dpsetconstr @ X475 @ X476
@ ^ [Z0: $i] : ( $eq @ ( X477 @ Z0 ) ) ) ) )
& ( ( in @ ( esk10_3 @ X479 @ X480 @ X481 ) @ X479 )
| ( func @ X479 @ X480 @ ( lam @ X479 @ X480 @ X481 ) ) )
& ( ~ ( in @ ( X481 @ ( esk10_3 @ X479 @ X480 @ X481 ) ) @ X480 )
| ( func @ X479 @ X480 @ ( lam @ X479 @ X480 @ X481 ) ) )
& ( ( in @ ( esk11_3 @ X483 @ X484 @ X485 ) @ X483 )
| ( in @ ( lam @ X483 @ X484 @ X485 ) @ ( funcSet @ X483 @ X484 ) ) )
& ( ~ ( in @ ( X485 @ ( esk11_3 @ X483 @ X484 @ X485 ) ) @ X484 )
| ( in @ ( lam @ X483 @ X484 @ X485 ) @ ( funcSet @ X483 @ X484 ) ) )
& ( ( in @ ( esk12_4 @ X487 @ X488 @ X489 @ X490 ) @ X487 )
| ~ ( in @ X493 @ X489 )
| ( X490 @ X493 )
| ~ ( subset @ X489 @ ( cartprod @ X487 @ X488 ) ) )
& ( ( in @ ( esk13_4 @ X487 @ X488 @ X489 @ X490 ) @ X488 )
| ~ ( in @ X493 @ X489 )
| ( X490 @ X493 )
| ~ ( subset @ X489 @ ( cartprod @ X487 @ X488 ) ) )
& ( ( in @ ( kpair @ ( esk12_4 @ X487 @ X488 @ X489 @ X490 ) @ ( esk13_4 @ X487 @ X488 @ X489 @ X490 ) ) @ X489 )
| ~ ( in @ X493 @ X489 )
| ( X490 @ X493 )
| ~ ( subset @ X489 @ ( cartprod @ X487 @ X488 ) ) )
& ( ~ ( X490 @ ( kpair @ ( esk12_4 @ X487 @ X488 @ X489 @ X490 ) @ ( esk13_4 @ X487 @ X488 @ X489 @ X490 ) ) )
| ~ ( in @ X493 @ X489 )
| ( X490 @ X493 )
| ~ ( subset @ X489 @ ( cartprod @ X487 @ X488 ) ) )
& ( ( in @ ( esk14_4 @ X494 @ X495 @ X496 @ X497 ) @ X494 )
| ~ ( in @ X500 @ X496 )
| ( X497 @ X500 )
| ~ ( subset @ X496 @ ( cartprod @ X494 @ X495 ) ) )
& ( ( in @ ( esk15_4 @ X494 @ X495 @ X496 @ X497 ) @ X495 )
| ~ ( in @ X500 @ X496 )
| ( X497 @ X500 )
| ~ ( subset @ X496 @ ( cartprod @ X494 @ X495 ) ) )
& ( ( in @ ( kpair @ ( esk14_4 @ X494 @ X495 @ X496 @ X497 ) @ ( esk15_4 @ X494 @ X495 @ X496 @ X497 ) ) @ X496 )
| ~ ( in @ X500 @ X496 )
| ( X497 @ X500 )
| ~ ( subset @ X496 @ ( cartprod @ X494 @ X495 ) ) )
& ( ~ ( X497 @ ( kpair @ ( esk14_4 @ X494 @ X495 @ X496 @ X497 ) @ ( esk15_4 @ X494 @ X495 @ X496 @ X497 ) ) )
| ~ ( in @ X500 @ X496 )
| ( X497 @ X500 )
| ~ ( subset @ X496 @ ( cartprod @ X494 @ X495 ) ) )
& ex1E2
& funcGraphProp1
& ( ~ ( in @ X503 @ ( funcSet @ X501 @ X502 ) )
| ~ ( in @ X504 @ X501 )
| ( in @ ( kpair @ X504 @ ( ap @ X501 @ X502 @ X503 @ X504 ) ) @ X503 ) )
& funcGraphProp2
& funcextLem
& ( ~ ( in @ X507 @ ( funcSet @ X505 @ X506 ) )
| ~ ( in @ X508 @ X505 )
| ~ ( in @ X509 @ X506 )
| ~ ( in @ ( kpair @ X508 @ X509 ) @ X507 )
| ( ( ap @ X505 @ X506 @ X507 @ X508 )
= X509 ) )
& ( ( in @ ( esk16_4 @ X510 @ X511 @ X512 @ X513 ) @ X510 )
| ( subset @ X512 @ X513 )
| ~ ( subset @ X513 @ ( cartprod @ X510 @ X511 ) )
| ~ ( subset @ X512 @ ( cartprod @ X510 @ X511 ) ) )
& ( ( in @ ( esk17_4 @ X510 @ X511 @ X512 @ X513 ) @ X511 )
| ( subset @ X512 @ X513 )
| ~ ( subset @ X513 @ ( cartprod @ X510 @ X511 ) )
| ~ ( subset @ X512 @ ( cartprod @ X510 @ X511 ) ) )
& ( ( in @ ( kpair @ ( esk16_4 @ X510 @ X511 @ X512 @ X513 ) @ ( esk17_4 @ X510 @ X511 @ X512 @ X513 ) ) @ X512 )
| ( subset @ X512 @ X513 )
| ~ ( subset @ X513 @ ( cartprod @ X510 @ X511 ) )
| ~ ( subset @ X512 @ ( cartprod @ X510 @ X511 ) ) )
& ( ~ ( in @ ( kpair @ ( esk16_4 @ X510 @ X511 @ X512 @ X513 ) @ ( esk17_4 @ X510 @ X511 @ X512 @ X513 ) ) @ X513 )
| ( subset @ X512 @ X513 )
| ~ ( subset @ X513 @ ( cartprod @ X510 @ X511 ) )
| ~ ( subset @ X512 @ ( cartprod @ X510 @ X511 ) ) )
& ( ( in @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ X516 )
| ( X518 = X519 )
| ( in @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ X516 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) @ X517 )
| ( X518 = X519 )
| ( in @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ X516 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( kpair @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X519 )
| ( X518 = X519 )
| ( in @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ X516 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ~ ( in @ ( kpair @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X518 )
| ( X518 = X519 )
| ( in @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ X516 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ X516 )
| ( X518 = X519 )
| ( in @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) @ X517 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) @ X517 )
| ( X518 = X519 )
| ( in @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) @ X517 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( kpair @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X519 )
| ( X518 = X519 )
| ( in @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) @ X517 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ~ ( in @ ( kpair @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X518 )
| ( X518 = X519 )
| ( in @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) @ X517 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ X516 )
| ( X518 = X519 )
| ( in @ ( kpair @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X518 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) @ X517 )
| ( X518 = X519 )
| ( in @ ( kpair @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X518 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( kpair @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X519 )
| ( X518 = X519 )
| ( in @ ( kpair @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X518 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ~ ( in @ ( kpair @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X518 )
| ( X518 = X519 )
| ( in @ ( kpair @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X518 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ X516 )
| ( X518 = X519 )
| ~ ( in @ ( kpair @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X519 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) @ X517 )
| ( X518 = X519 )
| ~ ( in @ ( kpair @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X519 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ( in @ ( kpair @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X519 )
| ( X518 = X519 )
| ~ ( in @ ( kpair @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X519 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& ( ~ ( in @ ( kpair @ ( esk20_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk21_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X518 )
| ( X518 = X519 )
| ~ ( in @ ( kpair @ ( esk18_4 @ X516 @ X517 @ X518 @ X519 ) @ ( esk19_4 @ X516 @ X517 @ X518 @ X519 ) ) @ X519 )
| ~ ( subset @ X519 @ ( cartprod @ X516 @ X517 ) )
| ~ ( subset @ X518 @ ( cartprod @ X516 @ X517 ) ) )
& funcext
& ( ( in @ ( esk22_4 @ X524 @ X525 @ X526 @ X527 ) @ X524 )
| ( X526 = X527 )
| ~ ( in @ X527 @ ( funcSet @ X524 @ X525 ) )
| ~ ( in @ X526 @ ( funcSet @ X524 @ X525 ) ) )
& ( ( ( ap @ X524 @ X525 @ X526 @ ( esk22_4 @ X524 @ X525 @ X526 @ X527 ) )
!= ( ap @ X524 @ X525 @ X527 @ ( esk22_4 @ X524 @ X525 @ X526 @ X527 ) ) )
| ( X526 = X527 )
| ~ ( in @ X527 @ ( funcSet @ X524 @ X525 ) )
| ~ ( in @ X526 @ ( funcSet @ X524 @ X525 ) ) )
& ( ~ ( in @ X531 @ ( funcSet @ X529 @ X530 ) )
| ~ ( in @ X532 @ X529 )
| ( ( ap @ X529 @ X530 @ X531 @ X532 )
= ( ap @ X529 @ X530 @ X531 @ X532 ) ) )
& ap2apEq2
& ( ~ ( in @ X536 @ esk23_0 )
| ( in @ ( esk25_0 @ X536 ) @ esk24_0 ) )
& ( in @ esk26_0 @ esk23_0 )
& ( ( ap @ esk23_0 @ esk24_0 @ ( lam @ esk23_0 @ esk24_0 @ esk25_0 ) @ esk26_0 )
!= ( esk25_0 @ esk26_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_71])])])])])]) ).
thf(c_0_74,plain,
! [X538: $i,X539: $i,X540: $i > $i] :
( ( lam @ X538 @ X539 @ X540 )
= ( dpsetconstr @ X538 @ X539
@ ^ [Z0: $i] : ( $eq @ ( X540 @ Z0 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_72]) ).
thf(c_0_75,plain,
! [X541: $i,X30: $i > $i] :
( ( epred1_1 @ X30 @ X541 )
= ( $eq @ ( X30 @ X541 ) ) ),
introduced(definition) ).
thf(c_0_76,negated_conjecture,
! [X2: $i,X30: $i > $i,X3: $i] :
( ( func @ X2 @ X3 @ ( lam @ X2 @ X3 @ X30 ) )
| ~ ( in @ ( X30 @ ( esk10_3 @ X2 @ X3 @ X30 ) ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_77,negated_conjecture,
! [X2: $i] :
( ( in @ ( esk25_0 @ X2 ) @ esk24_0 )
| ~ ( in @ X2 @ esk23_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_78,plain,
! [X2: $i,X3: $i,X30: $i > $i] :
( ( lam @ X2 @ X3 @ X30 )
= ( dpsetconstr @ X2 @ X3 @ ( epred1_1 @ X30 ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_74]),c_0_75]) ).
thf(c_0_79,plain,
! [X557: $i,X558: $i > $i] :
( ( epred1_1 @ X558 @ X557 )
= ( $eq @ ( X558 @ X557 ) ) ),
inference(variable_rename,[status(thm)],]) ).
thf(c_0_80,negated_conjecture,
! [X2: $i] :
( ( func @ X2 @ esk24_0 @ ( dpsetconstr @ X2 @ esk24_0 @ ( epred1_1 @ esk25_0 ) ) )
| ~ ( in @ ( esk10_3 @ X2 @ esk24_0 @ esk25_0 ) @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
thf(c_0_81,negated_conjecture,
! [X2: $i,X3: $i,X30: $i > $i] :
( ( in @ ( esk10_3 @ X2 @ X3 @ X30 ) @ X2 )
| ( func @ X2 @ X3 @ ( lam @ X2 @ X3 @ X30 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_82,plain,
! [X30: $i > $i,X2: $i] :
( ( epred1_1 @ X30 @ X2 )
= ( $eq @ ( X30 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_83,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i > $i > $o] :
( ( X6 @ X2 @ X3 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ X4 @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_84,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_73]) ).
thf(c_0_85,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X4 @ ( funcSet @ X2 @ X3 ) )
| ~ ( func @ X2 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_86,negated_conjecture,
func @ esk23_0 @ esk24_0 @ ( dpsetconstr @ esk23_0 @ esk24_0 @ ( epred1_1 @ esk25_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_78])]) ).
thf(c_0_87,plain,
! [X2: $i,X30: $i > $i,X559: $i] :
( ( epred1_1 @ X30 @ X2 @ X559 )
<=> ( ( X30 @ X2 )
= X559 ) ),
inference(arg_cong,[status(thm)],[c_0_82]) ).
thf(c_0_88,negated_conjecture,
! [X2: $i,X7: $i,X6: $i > $i > $o,X5: $i,X4: $i,X3: $i] :
( ( X6 @ X2 @ ( ap @ X3 @ X4 @ ( dpsetconstr @ X5 @ X7 @ X6 ) @ X2 ) )
| ~ ( in @ ( dpsetconstr @ X5 @ X7 @ X6 ) @ ( funcSet @ X3 @ X4 ) )
| ~ ( in @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
thf(c_0_89,negated_conjecture,
in @ ( dpsetconstr @ esk23_0 @ esk24_0 @ ( epred1_1 @ esk25_0 ) ) @ ( funcSet @ esk23_0 @ esk24_0 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_90,negated_conjecture,
( ( ap @ esk23_0 @ esk24_0 @ ( lam @ esk23_0 @ esk24_0 @ esk25_0 ) @ esk26_0 )
!= ( esk25_0 @ esk26_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_91,plain,
! [X2: $i,X30: $i > $i,X3: $i] :
( ( ( X30 @ X2 )
= X3 )
| ~ ( epred1_1 @ X30 @ X2 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_87]) ).
thf(c_0_92,negated_conjecture,
! [X2: $i] :
( ( epred1_1 @ esk25_0 @ X2 @ ( ap @ esk23_0 @ esk24_0 @ ( dpsetconstr @ esk23_0 @ esk24_0 @ ( epred1_1 @ esk25_0 ) ) @ X2 ) )
| ~ ( in @ X2 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
thf(c_0_93,negated_conjecture,
( ( ap @ esk23_0 @ esk24_0 @ ( dpsetconstr @ esk23_0 @ esk24_0 @ ( epred1_1 @ esk25_0 ) ) @ esk26_0 )
!= ( esk25_0 @ esk26_0 ) ),
inference(rw,[status(thm)],[c_0_90,c_0_78]) ).
thf(c_0_94,plain,
! [X2: $i] :
( ( ( esk25_0 @ X2 )
= ( ap @ esk23_0 @ esk24_0 @ ( dpsetconstr @ esk23_0 @ esk24_0 @ ( epred1_1 @ esk25_0 ) ) @ X2 ) )
| ~ ( in @ X2 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
thf(c_0_95,negated_conjecture,
in @ esk26_0 @ esk23_0,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU695^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 21 13:43:38 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.18/0.51 Running higher-order theorem proving
% 0.18/0.51 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/tmp/tmp.JTt8LZtdP7/E---3.1_16535.p
% 0.37/0.92 # Version: 3.2.0-ho
% 0.37/0.92 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.37/0.92 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.92 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.37/0.92 # Starting pre_casc_3 with 300s (1) cores
% 0.37/0.92 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.37/0.92 # Starting full_lambda_10 with 300s (1) cores
% 0.37/0.92 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.37/0.92 # pre_casc_3 with pid 16614 completed with status 0
% 0.37/0.92 # Result found by pre_casc_3
% 0.37/0.92 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.37/0.92 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.92 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.37/0.92 # Starting pre_casc_3 with 300s (1) cores
% 0.37/0.92 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.37/0.92 # Search class: HGUSM-FSLM32-MHSMMFBN
% 0.37/0.92 # partial match(2): HGHSM-FSLM32-MHSMMSBN
% 0.37/0.92 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.92 # Starting full_lambda_5 with 28s (1) cores
% 0.37/0.92 # full_lambda_5 with pid 16620 completed with status 0
% 0.37/0.92 # Result found by full_lambda_5
% 0.37/0.92 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.37/0.92 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.92 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.37/0.92 # Starting pre_casc_3 with 300s (1) cores
% 0.37/0.92 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.37/0.92 # Search class: HGUSM-FSLM32-MHSMMFBN
% 0.37/0.92 # partial match(2): HGHSM-FSLM32-MHSMMSBN
% 0.37/0.92 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.92 # Starting full_lambda_5 with 28s (1) cores
% 0.37/0.92 # Preprocessing time : 0.004 s
% 0.37/0.92 # Presaturation interreduction done
% 0.37/0.92
% 0.37/0.92 # Proof found!
% 0.37/0.92 # SZS status Theorem
% 0.37/0.92 # SZS output start CNFRefutation
% See solution above
% 0.37/0.92 # Parsed axioms : 466
% 0.37/0.92 # Removed by relevancy pruning/SinE : 420
% 0.37/0.92 # Initial clauses : 264
% 0.37/0.92 # Removed in clause preprocessing : 1
% 0.37/0.92 # Initial clauses in saturation : 263
% 0.37/0.92 # Processed clauses : 1454
% 0.37/0.92 # ...of these trivial : 30
% 0.37/0.92 # ...subsumed : 329
% 0.37/0.92 # ...remaining for further processing : 1095
% 0.37/0.92 # Other redundant clauses eliminated : 13
% 0.37/0.92 # Clauses deleted for lack of memory : 0
% 0.37/0.92 # Backward-subsumed : 53
% 0.37/0.92 # Backward-rewritten : 56
% 0.37/0.92 # Generated clauses : 10674
% 0.37/0.92 # ...of the previous two non-redundant : 10434
% 0.37/0.92 # ...aggressively subsumed : 0
% 0.37/0.92 # Contextual simplify-reflections : 19
% 0.37/0.92 # Paramodulations : 10598
% 0.37/0.92 # Factorizations : 0
% 0.37/0.92 # NegExts : 24
% 0.37/0.92 # Equation resolutions : 14
% 0.37/0.92 # Disequality decompositions : 0
% 0.37/0.92 # Total rewrite steps : 1304
% 0.37/0.92 # ...of those cached : 1121
% 0.37/0.92 # Propositional unsat checks : 0
% 0.37/0.92 # Propositional check models : 0
% 0.37/0.92 # Propositional check unsatisfiable : 0
% 0.37/0.92 # Propositional clauses : 0
% 0.37/0.92 # Propositional clauses after purity: 0
% 0.37/0.92 # Propositional unsat core size : 0
% 0.37/0.92 # Propositional preprocessing time : 0.000
% 0.37/0.92 # Propositional encoding time : 0.000
% 0.37/0.92 # Propositional solver time : 0.000
% 0.37/0.92 # Success case prop preproc time : 0.000
% 0.37/0.92 # Success case prop encoding time : 0.000
% 0.37/0.92 # Success case prop solver time : 0.000
% 0.37/0.92 # Current number of processed clauses : 714
% 0.37/0.92 # Positive orientable unit clauses : 217
% 0.37/0.92 # Positive unorientable unit clauses: 2
% 0.37/0.92 # Negative unit clauses : 1
% 0.37/0.92 # Non-unit-clauses : 494
% 0.37/0.92 # Current number of unprocessed clauses: 9341
% 0.37/0.92 # ...number of literals in the above : 42572
% 0.37/0.92 # Current number of archived formulas : 0
% 0.37/0.92 # Current number of archived clauses : 380
% 0.37/0.92 # Clause-clause subsumption calls (NU) : 24040
% 0.37/0.92 # Rec. Clause-clause subsumption calls : 16984
% 0.37/0.92 # Non-unit clause-clause subsumptions : 394
% 0.37/0.92 # Unit Clause-clause subsumption calls : 2360
% 0.37/0.92 # Rewrite failures with RHS unbound : 0
% 0.37/0.92 # BW rewrite match attempts : 233
% 0.37/0.92 # BW rewrite match successes : 9
% 0.37/0.92 # Condensation attempts : 0
% 0.37/0.92 # Condensation successes : 0
% 0.37/0.92 # Termbank termtop insertions : 434676
% 0.37/0.92 # Search garbage collected termcells : 9056
% 0.37/0.92
% 0.37/0.92 # -------------------------------------------------
% 0.37/0.92 # User time : 0.344 s
% 0.37/0.92 # System time : 0.022 s
% 0.37/0.92 # Total time : 0.366 s
% 0.37/0.92 # Maximum resident set size: 5052 pages
% 0.37/0.92
% 0.37/0.92 # -------------------------------------------------
% 0.37/0.92 # User time : 0.356 s
% 0.37/0.92 # System time : 0.024 s
% 0.37/0.92 # Total time : 0.380 s
% 0.37/0.92 # Maximum resident set size: 2236 pages
% 0.37/0.92 % E---3.1 exiting
% 0.37/0.92 % E exiting
%------------------------------------------------------------------------------