%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU704^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 03:29:17 EDT 2024
% Result : Theorem 0.99s 0.75s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 308
% Syntax : Number of formulae : 424 ( 40 unt; 266 typ; 0 def)
% Number of atoms : 1621 ( 227 equ; 0 cnn)
% Maximal formula atoms : 460 ( 10 avg)
% Number of connectives : 4875 ( 259 ~; 376 |; 332 &;3155 @)
% ( 53 <=>; 700 =>; 0 <=; 0 <~>)
% Maximal formula depth : 407 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 248 ( 248 >; 0 *; 0 +; 0 <<)
% Number of symbols : 270 ( 266 usr; 228 con; 0-4 aty)
% Number of variables : 717 ( 105 ^ 573 !; 39 ?; 717 :)
% 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_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_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
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_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,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_280,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_281,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_282,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_283,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_284,type,
esk6_2: $i > ( $i > $o ) > $i ).
thf(decl_285,type,
esk7_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_286,type,
esk8_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_287,type,
esk9_2: $i > ( $i > $o ) > $i ).
thf(decl_288,type,
esk10_2: $i > ( $i > $o ) > $i ).
thf(decl_289,type,
esk11_2: $i > ( $i > $o ) > $i ).
thf(decl_290,type,
esk12_1: $i > $i ).
thf(decl_291,type,
esk13_1: $i > $i ).
thf(decl_292,type,
esk14_4: $i > $i > $i > $i > $i ).
thf(decl_293,type,
esk15_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_294,type,
esk16_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_295,type,
esk17_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_296,type,
esk18_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_297,type,
esk19_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_298,type,
esk20_4: $i > $i > $i > $i > $i ).
thf(decl_299,type,
esk21_4: $i > $i > $i > $i > $i ).
thf(decl_300,type,
esk22_4: $i > $i > $i > $i > $i ).
thf(decl_301,type,
esk23_4: $i > $i > $i > $i > $i ).
thf(decl_302,type,
esk24_4: $i > $i > $i > $i > $i ).
thf(decl_303,type,
esk25_4: $i > $i > $i > $i > $i ).
thf(decl_304,type,
esk26_0: $i ).
thf(decl_305,type,
epred1_0: $o ).
thf(decl_306,type,
esk27_0: $i ).
thf(decl_307,type,
esk28_0: $i ).
thf(decl_308,type,
epred2_0: $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(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/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(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/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(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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(ifSingleton,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
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.p',kpairiskpair) ).
thf(c_0_40,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X186: $i] :
( ( in @ X186
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X186 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_41,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_42,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_43,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_44,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_45,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X186: $i] :
( ( in @ X186
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X186 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_42]) ).
thf(c_0_60,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_42]) ).
thf(c_0_61,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_42]) ).
thf(c_0_62,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_42]) ).
thf(c_0_63,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_43,c_0_42]) ).
thf(c_0_64,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_65,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ? [X194: $i] :
( ( in @ X194
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X194 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_66,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 ) )
=> ? [X189: $i] :
( ( in @ X189
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X189 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_46,c_0_45]) ).
thf(c_0_67,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X188: $i] :
( ( in @ X188
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X188 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_47,c_0_45]) ).
thf(c_0_68,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X187: $i] :
( ( in @ X187
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X187 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_48,c_0_45]) ).
thf(c_0_69,plain,
( funcImageSingleton
= ( ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X193: $i] :
( ( in @ X193
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) )
= ( setadjoin @ X193 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_49,c_0_41]) ).
thf(c_0_70,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X192: $i] :
( ( in @ X192
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X192 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_50,c_0_41]) ).
thf(c_0_71,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X191: $i] :
( ( in @ X191 @ X21 )
& ( X21
= ( setadjoin @ X191 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_41]) ).
thf(c_0_72,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X190: $i] :
( ( in @ X190
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X190 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_51,c_0_41]) ).
thf(c_0_73,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 ) )
=> ? [X185: $i] :
( ( in @ X185
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X185 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_52,c_0_41]) ).
thf(c_0_74,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
=> ( ! [X195: $i,X196: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X195 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X195 @ ( setadjoin @ X196 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X197: $i,X198: $i] : ( iskpair @ ( kpair @ X197 @ X198 ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( ! [X199: $i,X200: $i,X201: $i] :
( ( in @ X201 @ X199 )
=> ! [X202: $i] :
( ( in @ X202 @ X200 )
=> ( in @ ( kpair @ X201 @ X202 ) @ ( cartprod @ X199 @ X200 ) ) ) )
=> ( ! [X203: $i,X204: $i,X205: $i] :
( ( in @ X205 @ ( cartprod @ X203 @ X204 ) )
=> ? [X206: $i] :
( ( in @ X206 @ X203 )
& ? [X207: $i] :
( ( in @ X207 @ X204 )
& ( X205
= ( kpair @ X206 @ X207 ) ) ) ) )
=> ( ! [X208: $i,X209: $i,X210: $i] :
( ( in @ X210 @ ( cartprod @ X208 @ X209 ) )
=> ( iskpair @ X210 ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X211: $i,X212: $i > $o] :
( ! [X213: $i] :
( ( in @ X213 @ X211 )
=> ! [X214: $i] :
( ( in @ X214 @ X211 )
=> ( ( X212 @ X213 )
=> ( ( X212 @ X214 )
=> ( X213 = X214 ) ) ) ) )
=> ( ? [X215: $i] :
( ( in @ X215 @ X211 )
& ( X212 @ X215 ) )
=> ? [X216: $i] :
( ( in @ X216 @ ( dsetconstr @ X211 @ X212 ) )
& ( ( dsetconstr @ X211 @ X212 )
= ( setadjoin @ X216 @ emptyset ) ) ) ) )
=> ( ! [X217: $i,X218: $i > $o] :
( ? [X219: $i] :
( ( in @ X219 @ ( dsetconstr @ X217 @ X218 ) )
& ( ( dsetconstr @ X217 @ X218 )
= ( setadjoin @ X219 @ emptyset ) ) )
=> ? [X220: $i] :
( ( in @ X220 @ X217 )
& ( X218 @ X220 ) ) )
=> ( ! [X221: $i,X222: $i > $o,X223: $i] :
( ( in @ X223 @ X221 )
=> ( ( X222 @ X223 )
=> ( ! [X224: $i] :
( ( in @ X224 @ X221 )
=> ( ( X222 @ X224 )
=> ( X224 = X223 ) ) )
=> ? [X225: $i] :
( ( in @ X225 @ ( dsetconstr @ X221 @ X222 ) )
& ( ( dsetconstr @ X221 @ X222 )
= ( setadjoin @ X225 @ emptyset ) ) ) ) ) )
=> ( ! [X226: $i,X227: $i > $o] :
( ! [X228: $i] :
( ( in @ X228 @ X226 )
=> ! [X229: $i] :
( ( in @ X229 @ X226 )
=> ( ( X227 @ X228 )
=> ( ( X227 @ X229 )
=> ( X228 = X229 ) ) ) ) )
=> ( ? [X230: $i] :
( ( in @ X230 @ X226 )
& ( X227 @ X230 ) )
=> ? [X231: $i] :
( ( in @ X231 @ ( dsetconstr @ X226 @ X227 ) )
& ( ( dsetconstr @ X226 @ X227 )
= ( setadjoin @ X231 @ emptyset ) ) ) ) )
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X232: $i] :
( ( iskpair @ X232 )
=> ? [X233: $i] :
( ( in @ X233
@ ( dsetconstr @ ( setunion @ X232 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X232 ) ) )
& ( ( dsetconstr @ ( setunion @ X232 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X232 ) )
= ( setadjoin @ X233 @ emptyset ) ) ) )
=> ( ! [X234: $i] :
( ? [X235: $i] :
( ( in @ X235 @ X234 )
& ( X234
= ( setadjoin @ X235 @ emptyset ) ) )
=> ( in @ ( setunion @ X234 ) @ X234 ) )
=> ( ! [X236: $i,X237: $i] :
( ( kfst @ ( kpair @ X236 @ X237 ) )
= X236 )
=> ( ! [X238: $i,X239: $i,X240: $i] :
( ( in @ X240 @ ( cartprod @ X238 @ X239 ) )
=> ( in @ ( kfst @ X240 ) @ X238 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X241: $i] :
( ( iskpair @ X241 )
=> ? [X242: $i] :
( ( in @ X242
@ ( dsetconstr @ ( setunion @ X241 )
@ ^ [Z0: $i] :
( X241
= ( kpair @ ( kfst @ X241 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X241 )
@ ^ [Z0: $i] :
( X241
= ( kpair @ ( kfst @ X241 ) @ Z0 ) ) )
= ( setadjoin @ X242 @ emptyset ) ) ) )
=> ( ! [X243: $i,X244: $i] :
( ( ksnd @ ( kpair @ X243 @ X244 ) )
= X244 )
=> ( ! [X245: $i] :
( ( iskpair @ X245 )
=> ( ( kpair @ ( kfst @ X245 ) @ ( ksnd @ X245 ) )
= X245 ) )
=> ( ! [X246: $i,X247: $i,X248: $i] :
( ( in @ X248 @ ( cartprod @ X246 @ X247 ) )
=> ( in @ ( ksnd @ X248 ) @ X247 ) )
=> ( ! [X249: $i,X250: $i,X251: $i,X252: $i] :
( ( in @ ( kpair @ X251 @ X252 ) @ ( cartprod @ X249 @ X250 ) )
=> ( in @ X251 @ X249 ) )
=> ( ! [X253: $i,X254: $i,X255: $i,X256: $i] :
( ( in @ ( kpair @ X255 @ X256 ) @ ( cartprod @ X253 @ X254 ) )
=> ( in @ X256 @ X254 ) )
=> ( cartprodmempaircEq
=> ( ! [X257: $i,X258: $i,X259: $i] :
( ( in @ X259 @ X257 )
=> ! [X260: $i] :
( ( in @ X260 @ X258 )
=> ( ( kfst @ ( kpair @ X259 @ X260 ) )
= X259 ) ) )
=> ( ! [X261: $i,X262: $i,X263: $i] :
( ( in @ X263 @ X261 )
=> ! [X264: $i] :
( ( in @ X264 @ X262 )
=> ( ( ksnd @ ( kpair @ X263 @ X264 ) )
= X264 ) ) )
=> ( ! [X265: $i,X266: $i,X267: $i] :
( ( in @ X267 @ ( cartprod @ X265 @ X266 ) )
=> ( ( kpair @ ( kfst @ X267 ) @ ( ksnd @ X267 ) )
= X267 ) )
=> ( ! [X268: $i,X269: $i,X270: $i > $i > $o,X271: $i] :
( ( in @ X271 @ X268 )
=> ! [X272: $i] :
( ( in @ X272 @ X269 )
=> ( ( X270 @ X271 @ X272 )
=> ( in @ ( kpair @ X271 @ X272 ) @ ( dpsetconstr @ X268 @ X269 @ X270 ) ) ) ) )
=> ( ! [X273: $i,X274: $i,X275: $i > $i > $o] : ( subset @ ( dpsetconstr @ X273 @ X274 @ X275 ) @ ( cartprod @ X273 @ X274 ) )
=> ( ! [X276: $i,X277: $i,X278: $i > $i > $o] : ( subset @ ( dpsetconstr @ X276 @ X277 @ X278 ) @ ( cartprod @ X276 @ X277 ) )
=> ( ! [X279: $i,X280: $i,X281: $i > $i > $o,X282: $i] :
( ( in @ X282 @ X279 )
=> ! [X283: $i] :
( ( in @ X283 @ X280 )
=> ( ( in @ ( kpair @ X282 @ X283 ) @ ( dpsetconstr @ X279 @ X280 @ X281 ) )
=> ( X281 @ X282 @ X283 ) ) ) )
=> ( ! [X284: $i,X285: $i,X286: $i > $i > $o,X287: $i,X288: $i] :
( ( in @ ( kpair @ X287 @ X288 ) @ ( dpsetconstr @ X284 @ X285 @ X286 ) )
=> ( in @ X287 @ X284 ) )
=> ( ! [X289: $i,X290: $i,X291: $i > $i > $o,X292: $i,X293: $i] :
( ( in @ ( kpair @ X292 @ X293 ) @ ( dpsetconstr @ X289 @ X290 @ X291 ) )
=> ( in @ X293 @ X290 ) )
=> ( ! [X294: $i,X295: $i,X296: $i > $i > $o,X297: $i,X298: $i] :
( ( in @ ( kpair @ X297 @ X298 ) @ ( dpsetconstr @ X294 @ X295 @ X296 ) )
=> ( X296 @ X297 @ X298 ) )
=> ( ! [X299: $i,X300: $i,X301: $i] :
( ( func @ X299 @ X300 @ X301 )
=> ! [X302: $i] :
( ( in @ X302 @ X299 )
=> ? [X303: $i] :
( ( in @ X303
@ ( dsetconstr @ X300
@ ^ [Z0: $i] : ( in @ ( kpair @ X302 @ Z0 ) @ X301 ) ) )
& ( ( dsetconstr @ X300
@ ^ [Z0: $i] : ( in @ ( kpair @ X302 @ Z0 ) @ X301 ) )
= ( setadjoin @ X303 @ emptyset ) ) ) ) )
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( ! [X304: $i,X305: $i,X306: $i > $i] :
( ! [X307: $i] :
( ( in @ X307 @ X304 )
=> ( in @ ( X306 @ X307 ) @ X305 ) )
=> ( func @ X304 @ X305
@ ( dpsetconstr @ X304 @ X305
@ ^ [Z0: $i] : ( $eq @ ( X306 @ Z0 ) ) ) ) )
=> ( lamp
=> ( lam2p
=> ( ! [X308: $i,X309: $i,X310: $i] :
( ( subset @ X310 @ ( cartprod @ X308 @ X309 ) )
=> ! [X311: $i > $o] :
( ! [X312: $i] :
( ( in @ X312 @ X308 )
=> ! [X313: $i] :
( ( in @ X313 @ X309 )
=> ( ( in @ ( kpair @ X312 @ X313 ) @ X310 )
=> ( X311 @ ( kpair @ X312 @ X313 ) ) ) ) )
=> ! [X314: $i] :
( ( in @ X314 @ X310 )
=> ( X311 @ X314 ) ) ) )
=> ( ! [X315: $i,X316: $i,X317: $i] :
( ( subset @ X317 @ ( cartprod @ X315 @ X316 ) )
=> ! [X318: $i > $o] :
( ! [X319: $i] :
( ( in @ X319 @ X315 )
=> ! [X320: $i] :
( ( in @ X320 @ X316 )
=> ( ( in @ ( kpair @ X319 @ X320 ) @ X317 )
=> ( X318 @ ( kpair @ X319 @ X320 ) ) ) ) )
=> ! [X321: $i] :
( ( in @ X321 @ X317 )
=> ( X318 @ X321 ) ) ) )
=> ( ! [X322: $i,X323: $i > $o] :
( ? [X324: $i] :
( ( in @ X324 @ ( dsetconstr @ X322 @ X323 ) )
& ( ( dsetconstr @ X322 @ X323 )
= ( setadjoin @ X324 @ emptyset ) ) )
=> ! [X325: $i] :
( ( in @ X325 @ X322 )
=> ! [X326: $i] :
( ( in @ X326 @ X322 )
=> ( ( X323 @ X325 )
=> ( ( X323 @ X326 )
=> ( X325 = X326 ) ) ) ) ) )
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( ! [X327: $i,X328: $i,X329: $i] :
( ( subset @ X329 @ ( cartprod @ X327 @ X328 ) )
=> ! [X330: $i] :
( ( subset @ X330 @ ( cartprod @ X327 @ X328 ) )
=> ( ! [X331: $i] :
( ( in @ X331 @ X327 )
=> ! [X332: $i] :
( ( in @ X332 @ X328 )
=> ( ( in @ ( kpair @ X331 @ X332 ) @ X329 )
=> ( in @ ( kpair @ X331 @ X332 ) @ X330 ) ) ) )
=> ( subset @ X329 @ X330 ) ) ) )
=> ( ! [X333: $i,X334: $i,X335: $i] :
( ( subset @ X335 @ ( cartprod @ X333 @ X334 ) )
=> ! [X336: $i] :
( ( subset @ X336 @ ( cartprod @ X333 @ X334 ) )
=> ( ! [X337: $i] :
( ( in @ X337 @ X333 )
=> ! [X338: $i] :
( ( in @ X338 @ X334 )
=> ( ( in @ ( kpair @ X337 @ X338 ) @ X335 )
=> ( in @ ( kpair @ X337 @ X338 ) @ X336 ) ) ) )
=> ( ! [X339: $i] :
( ( in @ X339 @ X333 )
=> ! [X340: $i] :
( ( in @ X340 @ X334 )
=> ( ( in @ ( kpair @ X339 @ X340 ) @ X336 )
=> ( in @ ( kpair @ X339 @ X340 ) @ X335 ) ) ) )
=> ( X335 = X336 ) ) ) ) )
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ? [X341: $i] :
( ( in @ X341
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X43
& ( Z0 = X2 ) )
| ( ~ X43
& ( Z0 = X3 ) ) ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X43
& ( Z0 = X2 ) )
| ( ~ X43
& ( Z0 = X3 ) ) ) )
= ( setadjoin @ X341 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[ifSingleton])]),c_0_41]),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]),c_0_62]),c_0_63]),cartprodsndpairEq]),ksndpairEq]),c_0_64]),cartprodpairmemER]),cartprodpairmemEL]),cartprodsndin]),cartprodmempair1]),cartprodpairin]),cartprodpairsurjEq]),cartprodfstpairEq]),cartprodfstin]),kfstpairEq]),kpairsurjEq]),cartprodmempair]),kpairp]),kpairiskpair]),c_0_65]),c_0_66]),c_0_67]),c_0_68]),c_0_69]),c_0_70]),c_0_71]),c_0_72]),c_0_73])]) ).
thf(c_0_75,plain,
! [X512: $i] :
( ( ~ epred1_0
| epred1_0
| ~ ( epred2_0 @ X512 ) )
& ( ( X512 = esk28_0 )
| epred1_0
| ~ ( epred2_0 @ X512 ) )
& ( ~ epred1_0
| ( X512 = esk27_0 )
| ~ ( epred2_0 @ X512 ) )
& ( ( X512 = esk28_0 )
| ( X512 = esk27_0 )
| ~ ( epred2_0 @ X512 ) )
& ( ~ epred1_0
| ( X512 != esk27_0 )
| ( epred2_0 @ X512 ) )
& ( epred1_0
| ( X512 != esk28_0 )
| ( epred2_0 @ X512 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])]) ).
thf(c_0_76,negated_conjecture,
! [X342: $i,X343: $i,X344: $i,X345: $i,X346: $i,X347: $i,X348: $i,X349: $i,X350: $i,X351: $i,X352: $i,X355: $i,X356: $i,X357: $i,X358: $i,X359: $i > $o,X362: $i,X364: $i,X365: $i > $o,X366: $i,X368: $i,X369: $i > $o,X370: $i,X373: $i,X374: $i > $o,X377: $i,X379: $i,X381: $i,X382: $i,X383: $i,X384: $i,X385: $i,X386: $i,X387: $i,X388: $i,X390: $i,X391: $i,X392: $i,X393: $i,X394: $i,X395: $i,X396: $i,X397: $i,X398: $i,X399: $i,X400: $i,X401: $i,X402: $i,X403: $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 > $i > $o,X418: $i,X419: $i,X420: $i,X421: $i,X422: $i > $i > $o,X423: $i,X424: $i,X425: $i > $i > $o,X426: $i,X427: $i,X428: $i > $i > $o,X429: $i,X430: $i,X431: $i,X432: $i,X433: $i > $i > $o,X434: $i,X435: $i,X436: $i,X437: $i,X438: $i > $i > $o,X439: $i,X440: $i,X441: $i,X442: $i,X443: $i > $i > $o,X444: $i,X445: $i,X446: $i,X447: $i,X448: $i,X449: $i,X451: $i,X452: $i,X453: $i > $i,X455: $i,X456: $i,X457: $i,X458: $i > $o,X461: $i,X462: $i,X463: $i,X464: $i,X465: $i > $o,X468: $i,X469: $i,X470: $i > $o,X471: $i,X472: $i,X473: $i,X474: $i,X475: $i,X476: $i,X477: $i,X480: $i,X481: $i,X482: $i,X483: $i,X492: $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 @ X342 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X342 @ ( setadjoin @ X343 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X344 @ X345 ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& ( ~ ( in @ X348 @ X346 )
| ~ ( in @ X349 @ X347 )
| ( in @ ( kpair @ X348 @ X349 ) @ ( cartprod @ X346 @ X347 ) ) )
& ( ( in @ ( esk1_3 @ X350 @ X351 @ X352 ) @ X350 )
| ~ ( in @ X352 @ ( cartprod @ X350 @ X351 ) ) )
& ( ( in @ ( esk2_3 @ X350 @ X351 @ X352 ) @ X351 )
| ~ ( in @ X352 @ ( cartprod @ X350 @ X351 ) ) )
& ( ( X352
= ( kpair @ ( esk1_3 @ X350 @ X351 @ X352 ) @ ( esk2_3 @ X350 @ X351 @ X352 ) ) )
| ~ ( in @ X352 @ ( cartprod @ X350 @ X351 ) ) )
& ( ~ ( in @ X357 @ ( cartprod @ X355 @ X356 ) )
| ( iskpair @ X357 ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk5_2 @ X358 @ X359 ) @ ( dsetconstr @ X358 @ X359 ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( in @ ( esk3_2 @ X358 @ X359 ) @ X358 ) )
& ( ( ( dsetconstr @ X358 @ X359 )
= ( setadjoin @ ( esk5_2 @ X358 @ X359 ) @ emptyset ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( in @ ( esk3_2 @ X358 @ X359 ) @ X358 ) )
& ( ( in @ ( esk5_2 @ X358 @ X359 ) @ ( dsetconstr @ X358 @ X359 ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( in @ ( esk4_2 @ X358 @ X359 ) @ X358 ) )
& ( ( ( dsetconstr @ X358 @ X359 )
= ( setadjoin @ ( esk5_2 @ X358 @ X359 ) @ emptyset ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( in @ ( esk4_2 @ X358 @ X359 ) @ X358 ) )
& ( ( in @ ( esk5_2 @ X358 @ X359 ) @ ( dsetconstr @ X358 @ X359 ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( X359 @ ( esk3_2 @ X358 @ X359 ) ) )
& ( ( ( dsetconstr @ X358 @ X359 )
= ( setadjoin @ ( esk5_2 @ X358 @ X359 ) @ emptyset ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( X359 @ ( esk3_2 @ X358 @ X359 ) ) )
& ( ( in @ ( esk5_2 @ X358 @ X359 ) @ ( dsetconstr @ X358 @ X359 ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( X359 @ ( esk4_2 @ X358 @ X359 ) ) )
& ( ( ( dsetconstr @ X358 @ X359 )
= ( setadjoin @ ( esk5_2 @ X358 @ X359 ) @ emptyset ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( X359 @ ( esk4_2 @ X358 @ X359 ) ) )
& ( ( in @ ( esk5_2 @ X358 @ X359 ) @ ( dsetconstr @ X358 @ X359 ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( ( esk3_2 @ X358 @ X359 )
!= ( esk4_2 @ X358 @ X359 ) ) )
& ( ( ( dsetconstr @ X358 @ X359 )
= ( setadjoin @ ( esk5_2 @ X358 @ X359 ) @ emptyset ) )
| ~ ( in @ X362 @ X358 )
| ~ ( X359 @ X362 )
| ( ( esk3_2 @ X358 @ X359 )
!= ( esk4_2 @ X358 @ X359 ) ) )
& ( ( in @ ( esk6_2 @ X364 @ X365 ) @ X364 )
| ~ ( in @ X366 @ ( dsetconstr @ X364 @ X365 ) )
| ( ( dsetconstr @ X364 @ X365 )
!= ( setadjoin @ X366 @ emptyset ) ) )
& ( ( X365 @ ( esk6_2 @ X364 @ X365 ) )
| ~ ( in @ X366 @ ( dsetconstr @ X364 @ X365 ) )
| ( ( dsetconstr @ X364 @ X365 )
!= ( setadjoin @ X366 @ emptyset ) ) )
& ( ( in @ ( esk8_3 @ X368 @ X369 @ X370 ) @ ( dsetconstr @ X368 @ X369 ) )
| ( in @ ( esk7_3 @ X368 @ X369 @ X370 ) @ X368 )
| ~ ( X369 @ X370 )
| ~ ( in @ X370 @ X368 ) )
& ( ( ( dsetconstr @ X368 @ X369 )
= ( setadjoin @ ( esk8_3 @ X368 @ X369 @ X370 ) @ emptyset ) )
| ( in @ ( esk7_3 @ X368 @ X369 @ X370 ) @ X368 )
| ~ ( X369 @ X370 )
| ~ ( in @ X370 @ X368 ) )
& ( ( in @ ( esk8_3 @ X368 @ X369 @ X370 ) @ ( dsetconstr @ X368 @ X369 ) )
| ( X369 @ ( esk7_3 @ X368 @ X369 @ X370 ) )
| ~ ( X369 @ X370 )
| ~ ( in @ X370 @ X368 ) )
& ( ( ( dsetconstr @ X368 @ X369 )
= ( setadjoin @ ( esk8_3 @ X368 @ X369 @ X370 ) @ emptyset ) )
| ( X369 @ ( esk7_3 @ X368 @ X369 @ X370 ) )
| ~ ( X369 @ X370 )
| ~ ( in @ X370 @ X368 ) )
& ( ( in @ ( esk8_3 @ X368 @ X369 @ X370 ) @ ( dsetconstr @ X368 @ X369 ) )
| ( ( esk7_3 @ X368 @ X369 @ X370 )
!= X370 )
| ~ ( X369 @ X370 )
| ~ ( in @ X370 @ X368 ) )
& ( ( ( dsetconstr @ X368 @ X369 )
= ( setadjoin @ ( esk8_3 @ X368 @ X369 @ X370 ) @ emptyset ) )
| ( ( esk7_3 @ X368 @ X369 @ X370 )
!= X370 )
| ~ ( X369 @ X370 )
| ~ ( in @ X370 @ X368 ) )
& ( ( in @ ( esk11_2 @ X373 @ X374 ) @ ( dsetconstr @ X373 @ X374 ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( in @ ( esk9_2 @ X373 @ X374 ) @ X373 ) )
& ( ( ( dsetconstr @ X373 @ X374 )
= ( setadjoin @ ( esk11_2 @ X373 @ X374 ) @ emptyset ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( in @ ( esk9_2 @ X373 @ X374 ) @ X373 ) )
& ( ( in @ ( esk11_2 @ X373 @ X374 ) @ ( dsetconstr @ X373 @ X374 ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( in @ ( esk10_2 @ X373 @ X374 ) @ X373 ) )
& ( ( ( dsetconstr @ X373 @ X374 )
= ( setadjoin @ ( esk11_2 @ X373 @ X374 ) @ emptyset ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( in @ ( esk10_2 @ X373 @ X374 ) @ X373 ) )
& ( ( in @ ( esk11_2 @ X373 @ X374 ) @ ( dsetconstr @ X373 @ X374 ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( X374 @ ( esk9_2 @ X373 @ X374 ) ) )
& ( ( ( dsetconstr @ X373 @ X374 )
= ( setadjoin @ ( esk11_2 @ X373 @ X374 ) @ emptyset ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( X374 @ ( esk9_2 @ X373 @ X374 ) ) )
& ( ( in @ ( esk11_2 @ X373 @ X374 ) @ ( dsetconstr @ X373 @ X374 ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( X374 @ ( esk10_2 @ X373 @ X374 ) ) )
& ( ( ( dsetconstr @ X373 @ X374 )
= ( setadjoin @ ( esk11_2 @ X373 @ X374 ) @ emptyset ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( X374 @ ( esk10_2 @ X373 @ X374 ) ) )
& ( ( in @ ( esk11_2 @ X373 @ X374 ) @ ( dsetconstr @ X373 @ X374 ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( ( esk9_2 @ X373 @ X374 )
!= ( esk10_2 @ X373 @ X374 ) ) )
& ( ( ( dsetconstr @ X373 @ X374 )
= ( setadjoin @ ( esk11_2 @ X373 @ X374 ) @ emptyset ) )
| ~ ( in @ X377 @ X373 )
| ~ ( X374 @ X377 )
| ( ( esk9_2 @ X373 @ X374 )
!= ( esk10_2 @ X373 @ X374 ) ) )
& singletonsuniq
& setukpairinjL1
& ( ( in @ ( esk12_1 @ X379 )
@ ( dsetconstr @ ( setunion @ X379 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X379 ) ) )
| ~ ( iskpair @ X379 ) )
& ( ( ( dsetconstr @ ( setunion @ X379 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X379 ) )
= ( setadjoin @ ( esk12_1 @ X379 ) @ emptyset ) )
| ~ ( iskpair @ X379 ) )
& ( ~ ( in @ X382 @ X381 )
| ( X381
!= ( setadjoin @ X382 @ emptyset ) )
| ( in @ ( setunion @ X381 ) @ X381 ) )
& ( ( kfst @ ( kpair @ X383 @ X384 ) )
= X383 )
& ( ~ ( in @ X387 @ ( cartprod @ X385 @ X386 ) )
| ( in @ ( kfst @ X387 ) @ X385 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ( in @ ( esk13_1 @ X388 )
@ ( dsetconstr @ ( setunion @ X388 )
@ ^ [Z0: $i] :
( X388
= ( kpair @ ( kfst @ X388 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X388 ) )
& ( ( ( dsetconstr @ ( setunion @ X388 )
@ ^ [Z0: $i] :
( X388
= ( kpair @ ( kfst @ X388 ) @ Z0 ) ) )
= ( setadjoin @ ( esk13_1 @ X388 ) @ emptyset ) )
| ~ ( iskpair @ X388 ) )
& ( ( ksnd @ ( kpair @ X390 @ X391 ) )
= X391 )
& ( ~ ( iskpair @ X392 )
| ( ( kpair @ ( kfst @ X392 ) @ ( ksnd @ X392 ) )
= X392 ) )
& ( ~ ( in @ X395 @ ( cartprod @ X393 @ X394 ) )
| ( in @ ( ksnd @ X395 ) @ X394 ) )
& ( ~ ( in @ ( kpair @ X398 @ X399 ) @ ( cartprod @ X396 @ X397 ) )
| ( in @ X398 @ X396 ) )
& ( ~ ( in @ ( kpair @ X402 @ X403 ) @ ( cartprod @ X400 @ X401 ) )
| ( in @ X403 @ X401 ) )
& cartprodmempaircEq
& ( ~ ( in @ X406 @ X404 )
| ~ ( in @ X407 @ X405 )
| ( ( kfst @ ( kpair @ X406 @ X407 ) )
= X406 ) )
& ( ~ ( in @ X410 @ X408 )
| ~ ( in @ X411 @ X409 )
| ( ( ksnd @ ( kpair @ X410 @ X411 ) )
= X411 ) )
& ( ~ ( in @ X414 @ ( cartprod @ X412 @ X413 ) )
| ( ( kpair @ ( kfst @ X414 ) @ ( ksnd @ X414 ) )
= X414 ) )
& ( ~ ( in @ X418 @ X415 )
| ~ ( in @ X419 @ X416 )
| ~ ( X417 @ X418 @ X419 )
| ( in @ ( kpair @ X418 @ X419 ) @ ( dpsetconstr @ X415 @ X416 @ X417 ) ) )
& ( subset @ ( dpsetconstr @ X420 @ X421 @ X422 ) @ ( cartprod @ X420 @ X421 ) )
& ( subset @ ( dpsetconstr @ X423 @ X424 @ X425 ) @ ( cartprod @ X423 @ X424 ) )
& ( ~ ( in @ X429 @ X426 )
| ~ ( in @ X430 @ X427 )
| ~ ( in @ ( kpair @ X429 @ X430 ) @ ( dpsetconstr @ X426 @ X427 @ X428 ) )
| ( X428 @ X429 @ X430 ) )
& ( ~ ( in @ ( kpair @ X434 @ X435 ) @ ( dpsetconstr @ X431 @ X432 @ X433 ) )
| ( in @ X434 @ X431 ) )
& ( ~ ( in @ ( kpair @ X439 @ X440 ) @ ( dpsetconstr @ X436 @ X437 @ X438 ) )
| ( in @ X440 @ X437 ) )
& ( ~ ( in @ ( kpair @ X444 @ X445 ) @ ( dpsetconstr @ X441 @ X442 @ X443 ) )
| ( X443 @ X444 @ X445 ) )
& ( ( in @ ( esk14_4 @ X446 @ X447 @ X448 @ X449 )
@ ( dsetconstr @ X447
@ ^ [Z0: $i] : ( in @ ( kpair @ X449 @ Z0 ) @ X448 ) ) )
| ~ ( in @ X449 @ X446 )
| ~ ( func @ X446 @ X447 @ X448 ) )
& ( ( ( dsetconstr @ X447
@ ^ [Z0: $i] : ( in @ ( kpair @ X449 @ Z0 ) @ X448 ) )
= ( setadjoin @ ( esk14_4 @ X446 @ X447 @ X448 @ X449 ) @ emptyset ) )
| ~ ( in @ X449 @ X446 )
| ~ ( func @ X446 @ X447 @ X448 ) )
& apProp
& app
& infuncsetfunc
& ap2p
& funcinfuncset
& ( ( in @ ( esk15_3 @ X451 @ X452 @ X453 ) @ X451 )
| ( func @ X451 @ X452
@ ( dpsetconstr @ X451 @ X452
@ ^ [Z0: $i] : ( $eq @ ( X453 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X453 @ ( esk15_3 @ X451 @ X452 @ X453 ) ) @ X452 )
| ( func @ X451 @ X452
@ ( dpsetconstr @ X451 @ X452
@ ^ [Z0: $i] : ( $eq @ ( X453 @ Z0 ) ) ) ) )
& lamp
& lam2p
& ( ( in @ ( esk16_4 @ X455 @ X456 @ X457 @ X458 ) @ X455 )
| ~ ( in @ X461 @ X457 )
| ( X458 @ X461 )
| ~ ( subset @ X457 @ ( cartprod @ X455 @ X456 ) ) )
& ( ( in @ ( esk17_4 @ X455 @ X456 @ X457 @ X458 ) @ X456 )
| ~ ( in @ X461 @ X457 )
| ( X458 @ X461 )
| ~ ( subset @ X457 @ ( cartprod @ X455 @ X456 ) ) )
& ( ( in @ ( kpair @ ( esk16_4 @ X455 @ X456 @ X457 @ X458 ) @ ( esk17_4 @ X455 @ X456 @ X457 @ X458 ) ) @ X457 )
| ~ ( in @ X461 @ X457 )
| ( X458 @ X461 )
| ~ ( subset @ X457 @ ( cartprod @ X455 @ X456 ) ) )
& ( ~ ( X458 @ ( kpair @ ( esk16_4 @ X455 @ X456 @ X457 @ X458 ) @ ( esk17_4 @ X455 @ X456 @ X457 @ X458 ) ) )
| ~ ( in @ X461 @ X457 )
| ( X458 @ X461 )
| ~ ( subset @ X457 @ ( cartprod @ X455 @ X456 ) ) )
& ( ( in @ ( esk18_4 @ X462 @ X463 @ X464 @ X465 ) @ X462 )
| ~ ( in @ X468 @ X464 )
| ( X465 @ X468 )
| ~ ( subset @ X464 @ ( cartprod @ X462 @ X463 ) ) )
& ( ( in @ ( esk19_4 @ X462 @ X463 @ X464 @ X465 ) @ X463 )
| ~ ( in @ X468 @ X464 )
| ( X465 @ X468 )
| ~ ( subset @ X464 @ ( cartprod @ X462 @ X463 ) ) )
& ( ( in @ ( kpair @ ( esk18_4 @ X462 @ X463 @ X464 @ X465 ) @ ( esk19_4 @ X462 @ X463 @ X464 @ X465 ) ) @ X464 )
| ~ ( in @ X468 @ X464 )
| ( X465 @ X468 )
| ~ ( subset @ X464 @ ( cartprod @ X462 @ X463 ) ) )
& ( ~ ( X465 @ ( kpair @ ( esk18_4 @ X462 @ X463 @ X464 @ X465 ) @ ( esk19_4 @ X462 @ X463 @ X464 @ X465 ) ) )
| ~ ( in @ X468 @ X464 )
| ( X465 @ X468 )
| ~ ( subset @ X464 @ ( cartprod @ X462 @ X463 ) ) )
& ( ~ ( in @ X471 @ ( dsetconstr @ X469 @ X470 ) )
| ( ( dsetconstr @ X469 @ X470 )
!= ( setadjoin @ X471 @ emptyset ) )
| ~ ( in @ X472 @ X469 )
| ~ ( in @ X473 @ X469 )
| ~ ( X470 @ X472 )
| ~ ( X470 @ X473 )
| ( X472 = X473 ) )
& funcGraphProp1
& funcGraphProp3
& funcGraphProp2
& funcextLem
& funcGraphProp4
& ( ( in @ ( esk20_4 @ X474 @ X475 @ X476 @ X477 ) @ X474 )
| ( subset @ X476 @ X477 )
| ~ ( subset @ X477 @ ( cartprod @ X474 @ X475 ) )
| ~ ( subset @ X476 @ ( cartprod @ X474 @ X475 ) ) )
& ( ( in @ ( esk21_4 @ X474 @ X475 @ X476 @ X477 ) @ X475 )
| ( subset @ X476 @ X477 )
| ~ ( subset @ X477 @ ( cartprod @ X474 @ X475 ) )
| ~ ( subset @ X476 @ ( cartprod @ X474 @ X475 ) ) )
& ( ( in @ ( kpair @ ( esk20_4 @ X474 @ X475 @ X476 @ X477 ) @ ( esk21_4 @ X474 @ X475 @ X476 @ X477 ) ) @ X476 )
| ( subset @ X476 @ X477 )
| ~ ( subset @ X477 @ ( cartprod @ X474 @ X475 ) )
| ~ ( subset @ X476 @ ( cartprod @ X474 @ X475 ) ) )
& ( ~ ( in @ ( kpair @ ( esk20_4 @ X474 @ X475 @ X476 @ X477 ) @ ( esk21_4 @ X474 @ X475 @ X476 @ X477 ) ) @ X477 )
| ( subset @ X476 @ X477 )
| ~ ( subset @ X477 @ ( cartprod @ X474 @ X475 ) )
| ~ ( subset @ X476 @ ( cartprod @ X474 @ X475 ) ) )
& ( ( in @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ X480 )
| ( X482 = X483 )
| ( in @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ X480 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) @ X481 )
| ( X482 = X483 )
| ( in @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ X480 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( kpair @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X483 )
| ( X482 = X483 )
| ( in @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ X480 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ~ ( in @ ( kpair @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X482 )
| ( X482 = X483 )
| ( in @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ X480 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ X480 )
| ( X482 = X483 )
| ( in @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) @ X481 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) @ X481 )
| ( X482 = X483 )
| ( in @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) @ X481 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( kpair @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X483 )
| ( X482 = X483 )
| ( in @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) @ X481 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ~ ( in @ ( kpair @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X482 )
| ( X482 = X483 )
| ( in @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) @ X481 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ X480 )
| ( X482 = X483 )
| ( in @ ( kpair @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X482 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) @ X481 )
| ( X482 = X483 )
| ( in @ ( kpair @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X482 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( kpair @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X483 )
| ( X482 = X483 )
| ( in @ ( kpair @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X482 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ~ ( in @ ( kpair @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X482 )
| ( X482 = X483 )
| ( in @ ( kpair @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X482 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ X480 )
| ( X482 = X483 )
| ~ ( in @ ( kpair @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X483 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) @ X481 )
| ( X482 = X483 )
| ~ ( in @ ( kpair @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X483 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ( in @ ( kpair @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X483 )
| ( X482 = X483 )
| ~ ( in @ ( kpair @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X483 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& ( ~ ( in @ ( kpair @ ( esk24_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk25_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X482 )
| ( X482 = X483 )
| ~ ( in @ ( kpair @ ( esk22_4 @ X480 @ X481 @ X482 @ X483 ) @ ( esk23_4 @ X480 @ X481 @ X482 @ X483 ) ) @ X483 )
| ~ ( subset @ X483 @ ( cartprod @ X480 @ X481 ) )
| ~ ( subset @ X482 @ ( cartprod @ X480 @ X481 ) ) )
& funcext
& funcext2
& ap2apEq1
& ap2apEq2
& beta1
& eta1
& lam2lamEq
& beta2
& eta2
& iffalseProp1
& iffalseProp2
& iftrueProp1
& iftrueProp2
& ( in @ esk27_0 @ esk26_0 )
& ( in @ esk28_0 @ esk26_0 )
& ( ~ ( in @ X492
@ ( dsetconstr @ esk26_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk27_0 ) )
| ( ~ epred1_0
& ( Z0 = esk28_0 ) ) ) ) )
| ( ( dsetconstr @ esk26_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk27_0 ) )
| ( ~ epred1_0
& ( Z0 = esk28_0 ) ) ) )
!= ( setadjoin @ X492 @ emptyset ) ) ) ),
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_74])])])])])]) ).
thf(c_0_77,plain,
! [X2: $i] :
( ( epred2_0 @ X2 )
| ~ epred1_0
| ( X2 != esk27_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_78,plain,
! [X2: $i] :
( epred1_0
| ( epred2_0 @ X2 )
| ( X2 != esk28_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_79,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk5_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( X1 @ ( esk4_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_80,negated_conjecture,
in @ esk28_0 @ esk26_0,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_81,plain,
( ( epred2_0 @ esk27_0 )
| ~ epred1_0 ),
inference(er,[status(thm)],[c_0_77]) ).
thf(c_0_82,plain,
( ( epred2_0 @ esk28_0 )
| epred1_0 ),
inference(er,[status(thm)],[c_0_78]) ).
thf(c_0_83,negated_conjecture,
in @ esk27_0 @ esk26_0,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_84,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk5_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( X1 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_85,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_86,plain,
( ( epred2_0 @ esk28_0 )
| ( epred2_0 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
thf(c_0_87,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_83]) ).
thf(c_0_88,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk5_2 @ X2 @ X1 ) @ emptyset ) )
| ( X1 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_89,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk5_2 @ X2 @ X1 ) @ emptyset ) )
| ( X1 @ ( esk4_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_90,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_84,c_0_80]) ).
thf(c_0_91,plain,
! [X2: $i] :
( ( X2 = esk28_0 )
| epred1_0
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_92,plain,
( ( in @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk4_2 @ esk26_0 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
thf(c_0_93,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( in @ ( esk5_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 )
| ( ( esk3_2 @ X2 @ X1 )
!= ( esk4_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_94,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_88,c_0_80]) ).
thf(c_0_95,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_89,c_0_80]) ).
thf(c_0_96,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk5_2 @ X2 @ X1 ) @ emptyset ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 )
| ( ( esk3_2 @ X2 @ X1 )
!= ( esk4_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_97,plain,
! [X493: $i] :
( ( epred2_0 @ X493 )
<=> ( ( epred1_0
& ( X493 = esk27_0 ) )
| ( ~ epred1_0
& ( X493 = esk28_0 ) ) ) ),
introduced(definition) ).
thf(c_0_98,plain,
( ( in @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk3_2 @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_90,c_0_86]) ).
thf(c_0_99,plain,
( ( esk28_0
= ( esk4_2 @ esk26_0 @ epred2_0 ) )
| ( in @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| epred1_0 ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
thf(c_0_100,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( ( esk4_2 @ esk26_0 @ X1 )
!= ( esk3_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_93,c_0_80]) ).
thf(c_0_101,plain,
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk3_2 @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_94,c_0_86]) ).
thf(c_0_102,plain,
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk4_2 @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_86]) ).
thf(c_0_103,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ X1 ) )
| ( ( esk4_2 @ esk26_0 @ X1 )
!= ( esk3_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_80]) ).
thf(c_0_104,negated_conjecture,
! [X2: $i] :
( ( ( in @ X2 @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
!= $true )
| ( ( dsetconstr @ esk26_0 @ epred2_0 )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_76]),c_0_97]),c_0_97]) ).
thf(c_0_105,plain,
( ( esk28_0
= ( esk3_2 @ esk26_0 @ epred2_0 ) )
| ( in @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_98]),c_0_81]) ).
thf(c_0_106,plain,
( ( esk28_0
= ( esk4_2 @ esk26_0 @ epred2_0 ) )
| ( in @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_99]) ).
thf(c_0_107,plain,
( ( in @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 )
| ( ( esk4_2 @ esk26_0 @ epred2_0 )
!= ( esk3_2 @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_100,c_0_86]) ).
thf(c_0_108,plain,
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( esk28_0
= ( esk3_2 @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_101]),c_0_81]) ).
thf(c_0_109,plain,
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( esk28_0
= ( esk4_2 @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_102]),c_0_81]) ).
thf(c_0_110,plain,
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 )
| ( ( esk4_2 @ esk26_0 @ epred2_0 )
!= ( esk3_2 @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_103,c_0_86]) ).
thf(c_0_111,negated_conjecture,
! [X2: $i] :
( ( ( dsetconstr @ esk26_0 @ epred2_0 )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ ( dsetconstr @ esk26_0 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[c_0_104]) ).
thf(c_0_112,plain,
( ( in @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
thf(c_0_113,plain,
( ( ( setadjoin @ ( esk5_2 @ esk26_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk27_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]) ).
thf(c_0_114,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk11_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( X1 @ ( esk10_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_115,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk11_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( X1 @ ( esk9_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_116,negated_conjecture,
epred2_0 @ esk27_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
thf(c_0_117,plain,
! [X2: $i] :
( ( X2 = esk27_0 )
| ~ epred1_0
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_118,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk11_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk10_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_114,c_0_80]) ).
thf(c_0_119,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk11_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk10_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_114,c_0_83]) ).
thf(c_0_120,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk11_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk9_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_115,c_0_80]) ).
thf(c_0_121,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk11_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk9_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_115,c_0_83]) ).
thf(c_0_122,plain,
( ( esk28_0 = esk27_0 )
| epred1_0 ),
inference(spm,[status(thm)],[c_0_91,c_0_116]) ).
thf(c_0_123,plain,
! [X2: $i] :
( ( X2 = esk27_0 )
| ( epred2_0 @ esk28_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_117,c_0_82]) ).
thf(c_0_124,plain,
( ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk10_2 @ esk26_0 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_86]),c_0_119]) ).
thf(c_0_125,plain,
( ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ ( esk9_2 @ esk26_0 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_86]),c_0_121]) ).
thf(c_0_126,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( in @ ( esk11_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 )
| ( ( esk9_2 @ X2 @ X1 )
!= ( esk10_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_127,plain,
! [X2: $i] :
( ( X2 = esk28_0 )
| ( X2 = esk27_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_128,plain,
! [X2: $i] :
( ( esk28_0 = esk27_0 )
| ( X2 = esk27_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_117,c_0_122]) ).
thf(c_0_129,plain,
( ( ( esk10_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
thf(c_0_130,plain,
( ( ( esk9_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( epred2_0 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_123,c_0_125]) ).
thf(c_0_131,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk11_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( ( esk10_2 @ esk26_0 @ X1 )
!= ( esk9_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk28_0 ) ),
inference(spm,[status(thm)],[c_0_126,c_0_80]) ).
thf(c_0_132,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk11_2 @ esk26_0 @ X1 ) @ ( dsetconstr @ esk26_0 @ X1 ) )
| ( ( esk10_2 @ esk26_0 @ X1 )
!= ( esk9_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_126,c_0_83]) ).
thf(c_0_133,plain,
( ( esk28_0
= ( esk10_2 @ esk26_0 @ epred2_0 ) )
| ( ( esk10_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_127,c_0_124]) ).
thf(c_0_134,plain,
( ( ( esk10_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( esk28_0 = esk27_0 )
| ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
thf(c_0_135,plain,
( ( esk28_0
= ( esk9_2 @ esk26_0 @ epred2_0 ) )
| ( ( esk9_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_127,c_0_125]) ).
thf(c_0_136,plain,
( ( ( esk9_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( esk28_0 = esk27_0 )
| ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_128,c_0_130]) ).
thf(c_0_137,plain,
( ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( ( esk10_2 @ esk26_0 @ epred2_0 )
!= ( esk9_2 @ esk26_0 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_86]),c_0_132]) ).
thf(c_0_138,plain,
( ( ( esk10_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
thf(c_0_139,plain,
( ( ( esk9_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
thf(c_0_140,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk11_2 @ X2 @ X1 ) @ emptyset ) )
| ( X1 @ ( esk9_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_141,plain,
in @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ ( dsetconstr @ esk26_0 @ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]) ).
thf(c_0_142,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk11_2 @ esk26_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk9_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_140,c_0_83]) ).
thf(c_0_143,negated_conjecture,
( ( setadjoin @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ emptyset )
!= ( dsetconstr @ esk26_0 @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_111,c_0_141]) ).
thf(c_0_144,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk11_2 @ X2 @ X1 ) @ emptyset ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 )
| ( ( esk9_2 @ X2 @ X1 )
!= ( esk10_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_145,negated_conjecture,
epred2_0 @ ( esk9_2 @ esk26_0 @ epred2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_116]),c_0_143]) ).
thf(c_0_146,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk11_2 @ X2 @ X1 ) @ emptyset ) )
| ( X1 @ ( esk10_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_147,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk11_2 @ esk26_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ X1 ) )
| ( ( esk10_2 @ esk26_0 @ X1 )
!= ( esk9_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_144,c_0_83]) ).
thf(c_0_148,plain,
( ( ( esk9_2 @ esk26_0 @ epred2_0 )
= esk27_0 )
| ( esk28_0 = esk27_0 ) ),
inference(spm,[status(thm)],[c_0_128,c_0_145]) ).
thf(c_0_149,plain,
( ( esk28_0
= ( esk9_2 @ esk26_0 @ epred2_0 ) )
| ( ( esk9_2 @ esk26_0 @ epred2_0 )
= esk27_0 ) ),
inference(spm,[status(thm)],[c_0_127,c_0_145]) ).
thf(c_0_150,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk11_2 @ esk26_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ X1 ) )
| ( X1 @ ( esk10_2 @ esk26_0 @ X1 ) )
| ~ ( X1 @ esk27_0 ) ),
inference(spm,[status(thm)],[c_0_146,c_0_83]) ).
thf(c_0_151,negated_conjecture,
( ( ( setadjoin @ ( esk11_2 @ esk26_0 @ epred2_0 ) @ emptyset )
= ( dsetconstr @ esk26_0 @ epred2_0 ) )
| ( ( esk10_2 @ esk26_0 @ epred2_0 )
!= ( esk9_2 @ esk26_0 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_147,c_0_116]) ).
thf(c_0_152,plain,
( ( esk9_2 @ esk26_0 @ epred2_0 )
= esk27_0 ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
thf(c_0_153,negated_conjecture,
epred2_0 @ ( esk10_2 @ esk26_0 @ epred2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_116]),c_0_143]) ).
thf(c_0_154,negated_conjecture,
( ( esk10_2 @ esk26_0 @ epred2_0 )
!= esk27_0 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_152]),c_0_143]) ).
thf(c_0_155,plain,
esk28_0 = esk27_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_153]),c_0_154]) ).
thf(c_0_156,plain,
! [X2: $i] :
( ( X2 = esk27_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_155])]) ).
thf(c_0_157,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_153]),c_0_154]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU704^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n014.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun May 19 16:54:08 EDT 2024
% 0.13/0.37 % CPUTime :
% 0.22/0.48 Running higher-order theorem proving
% 0.22/0.48 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
% 0.99/0.75 # Version: 3.1.0-ho
% 0.99/0.75 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.99/0.75 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.75 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.99/0.75 # Starting pre_casc_3 with 300s (1) cores
% 0.99/0.75 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.99/0.75 # Starting full_lambda_10 with 300s (1) cores
% 0.99/0.75 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.99/0.75 # pre_casc_3 with pid 321 completed with status 0
% 0.99/0.75 # Result found by pre_casc_3
% 0.99/0.75 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.99/0.75 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.75 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.99/0.75 # Starting pre_casc_3 with 300s (1) cores
% 0.99/0.75 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.99/0.75 # Search class: HGHSM-FSLM32-MHSMMSBN
% 0.99/0.75 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.99/0.75 # Starting full_lambda_5 with 28s (1) cores
% 0.99/0.75 # full_lambda_5 with pid 326 completed with status 0
% 0.99/0.75 # Result found by full_lambda_5
% 0.99/0.75 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.99/0.75 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.75 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.99/0.75 # Starting pre_casc_3 with 300s (1) cores
% 0.99/0.75 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.99/0.75 # Search class: HGHSM-FSLM32-MHSMMSBN
% 0.99/0.75 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.99/0.75 # Starting full_lambda_5 with 28s (1) cores
% 0.99/0.75 # Preprocessing time : 0.004 s
% 0.99/0.75 # Presaturation interreduction done
% 0.99/0.75
% 0.99/0.75 # Proof found!
% 0.99/0.75 # SZS status Theorem
% 0.99/0.75 # SZS output start CNFRefutation
% See solution above
% 0.99/0.75 # Parsed axioms : 483
% 0.99/0.75 # Removed by relevancy pruning/SinE : 443
% 0.99/0.75 # Initial clauses : 290
% 0.99/0.75 # Removed in clause preprocessing : 1
% 0.99/0.75 # Initial clauses in saturation : 289
% 0.99/0.75 # Processed clauses : 931
% 0.99/0.75 # ...of these trivial : 5
% 0.99/0.75 # ...subsumed : 88
% 0.99/0.75 # ...remaining for further processing : 838
% 0.99/0.75 # Other redundant clauses eliminated : 19
% 0.99/0.75 # Clauses deleted for lack of memory : 0
% 0.99/0.75 # Backward-subsumed : 42
% 0.99/0.75 # Backward-rewritten : 83
% 0.99/0.75 # Generated clauses : 4478
% 0.99/0.75 # ...of the previous two non-redundant : 4438
% 0.99/0.75 # ...aggressively subsumed : 0
% 0.99/0.75 # Contextual simplify-reflections : 21
% 0.99/0.75 # Paramodulations : 4363
% 0.99/0.75 # Factorizations : 0
% 0.99/0.75 # NegExts : 35
% 0.99/0.75 # Equation resolutions : 19
% 0.99/0.75 # Disequality decompositions : 0
% 0.99/0.75 # Total rewrite steps : 492
% 0.99/0.75 # ...of those cached : 444
% 0.99/0.75 # Propositional unsat checks : 0
% 0.99/0.75 # Propositional check models : 0
% 0.99/0.75 # Propositional check unsatisfiable : 0
% 0.99/0.75 # Propositional clauses : 0
% 0.99/0.75 # Propositional clauses after purity: 0
% 0.99/0.75 # Propositional unsat core size : 0
% 0.99/0.75 # Propositional preprocessing time : 0.000
% 0.99/0.75 # Propositional encoding time : 0.000
% 0.99/0.75 # Propositional solver time : 0.000
% 0.99/0.75 # Success case prop preproc time : 0.000
% 0.99/0.75 # Success case prop encoding time : 0.000
% 0.99/0.75 # Success case prop solver time : 0.000
% 0.99/0.75 # Current number of processed clauses : 405
% 0.99/0.75 # Positive orientable unit clauses : 199
% 0.99/0.75 # Positive unorientable unit clauses: 1
% 0.99/0.75 # Negative unit clauses : 2
% 0.99/0.75 # Non-unit-clauses : 203
% 0.99/0.75 # Current number of unprocessed clauses: 4052
% 0.99/0.75 # ...number of literals in the above : 19959
% 0.99/0.75 # Current number of archived formulas : 0
% 0.99/0.75 # Current number of archived clauses : 430
% 0.99/0.75 # Clause-clause subsumption calls (NU) : 9169
% 0.99/0.75 # Rec. Clause-clause subsumption calls : 4674
% 0.99/0.75 # Non-unit clause-clause subsumptions : 147
% 0.99/0.75 # Unit Clause-clause subsumption calls : 1081
% 0.99/0.75 # Rewrite failures with RHS unbound : 0
% 0.99/0.75 # BW rewrite match attempts : 5
% 0.99/0.75 # BW rewrite match successes : 4
% 0.99/0.75 # Condensation attempts : 0
% 0.99/0.75 # Condensation successes : 0
% 0.99/0.75 # Termbank termtop insertions : 157797
% 0.99/0.75 # Search garbage collected termcells : 9523
% 0.99/0.75
% 0.99/0.75 # -------------------------------------------------
% 0.99/0.75 # User time : 0.227 s
% 0.99/0.75 # System time : 0.013 s
% 0.99/0.75 # Total time : 0.240 s
% 0.99/0.75 # Maximum resident set size: 5032 pages
% 0.99/0.75
% 0.99/0.75 # -------------------------------------------------
% 0.99/0.75 # User time : 0.241 s
% 0.99/0.75 # System time : 0.015 s
% 0.99/0.75 # Total time : 0.256 s
% 0.99/0.75 # Maximum resident set size: 2248 pages
% 0.99/0.75 % E---3.1 exiting
% 0.99/0.75 % E exiting
%------------------------------------------------------------------------------