%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU679^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:04 EDT 2024
% Result : Theorem 3.00s 0.98s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 287
% Syntax : Number of formulae : 412 ( 50 unt; 241 typ; 0 def)
% Number of atoms : 1540 ( 205 equ; 0 cnn)
% Maximal formula atoms : 385 ( 9 avg)
% Number of connectives : 4868 ( 211 ~; 270 |; 306 &;3438 @)
% ( 55 <=>; 588 =>; 0 <=; 0 <~>)
% Maximal formula depth : 372 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 241 ( 241 >; 0 *; 0 +; 0 <<)
% Number of symbols : 245 ( 241 usr; 202 con; 0-4 aty)
% Number of variables : 828 ( 182 ^ 595 !; 51 ?; 828 :)
% 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_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_255,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_256,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_257,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_258,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_259,type,
esk6_2: $i > ( $i > $o ) > $i ).
thf(decl_260,type,
esk7_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_261,type,
esk8_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_262,type,
esk9_2: $i > ( $i > $o ) > $i ).
thf(decl_263,type,
esk10_2: $i > ( $i > $o ) > $i ).
thf(decl_264,type,
esk11_2: $i > ( $i > $o ) > $i ).
thf(decl_265,type,
esk12_1: $i > $i ).
thf(decl_266,type,
esk13_1: $i > $i ).
thf(decl_267,type,
esk14_3: $i > $i > $i > $i ).
thf(decl_268,type,
esk15_4: $i > $i > $i > $i > $i ).
thf(decl_269,type,
esk16_3: $i > $i > $i > $i ).
thf(decl_270,type,
esk17_3: $i > $i > $i > $i ).
thf(decl_271,type,
esk18_4: $i > $i > $i > $i > $i ).
thf(decl_272,type,
esk19_3: $i > $i > $i > $i ).
thf(decl_273,type,
esk20_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_274,type,
esk21_4: $i > $i > ( $i > $i ) > $i > $i ).
thf(decl_275,type,
esk22_0: $i ).
thf(decl_276,type,
esk23_0: $i ).
thf(decl_277,type,
esk24_0: $i > $i ).
thf(decl_278,type,
esk25_0: $i ).
thf(decl_279,type,
epred1_0: $i > $o ).
thf(decl_280,type,
epred2_1: ( $i > $i ) > $i > $i > $o ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
& ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ex1 @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',singletonprop) ).
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/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X31 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(lamp,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
=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X33 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
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/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(lam,axiom,
( lam
= ( ^ [X4: $i,X5: $i,X32: $i > $i] :
( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X32 @ X2 )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam) ).
thf(c_0_42,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X162: $i] :
( ( in @ X162
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X162 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_43,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_44,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X169: $i] :
( ( in @ X169
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X169 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_45,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_46,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X162: $i] :
( ( in @ X162
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X162 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,plain,
( lamProp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X31 @ Z0 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamProp]) ).
thf(c_0_55,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X169: $i] :
( ( in @ X169
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X169 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
thf(c_0_56,plain,
( apProp
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
@ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[apProp]) ).
thf(c_0_57,plain,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_58,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_59,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_60,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_61,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_62,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_63,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_64,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X168: $i] :
( ( in @ X168
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X168 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_47,c_0_43]) ).
thf(c_0_65,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X167: $i] :
( ( in @ X167 @ X21 )
& ( X21
= ( setadjoin @ X167 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_43]) ).
thf(c_0_66,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X166: $i] :
( ( in @ X166
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X166 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_48,c_0_43]) ).
thf(c_0_67,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 ) )
=> ? [X161: $i] :
( ( in @ X161
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X161 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_49,c_0_43]) ).
thf(c_0_68,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_50,c_0_45]) ).
thf(c_0_69,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 ) )
=> ? [X165: $i] :
( ( in @ X165
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X165 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_51,c_0_46]) ).
thf(c_0_70,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X164: $i] :
( ( in @ X164
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X164 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_52,c_0_46]) ).
thf(c_0_71,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X163: $i] :
( ( in @ X163
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X163 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_53,c_0_46]) ).
thf(c_0_72,plain,
( lamProp
= ( ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( ( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X31 @ Z0 )
= Z1 ) )
@ ( cartprod @ X4 @ X5 ) )
& ! [X181: $i] :
( ( in @ X181 @ X4 )
=> ? [X182: $i] :
( ( in @ X182
@ ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X181 @ Z0 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z1: $i,Z2: $i] :
( ( X31 @ Z1 )
= Z2 ) ) ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X181 @ Z0 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z1: $i,Z2: $i] :
( ( X31 @ Z1 )
= Z2 ) ) ) )
= ( setadjoin @ X182 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_73,axiom,
( funcinfuncset
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X179: $i] :
( ( in @ X179 @ X4 )
=> ? [X180: $i] :
( ( in @ X180
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X179 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X179 @ Z0 ) @ X30 ) )
= ( setadjoin @ X180 @ emptyset ) ) ) ) )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcinfuncset,c_0_55]) ).
thf(c_0_74,axiom,
( infuncsetfunc
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X177: $i] :
( ( in @ X177 @ X4 )
=> ? [X178: $i] :
( ( in @ X178
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X177 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X177 @ Z0 ) @ X30 ) )
= ( setadjoin @ X178 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[infuncsetfunc,c_0_55]) ).
thf(c_0_75,axiom,
( app
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X175: $i] :
( ( in @ X175 @ X4 )
=> ? [X176: $i] :
( ( in @ X176
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X175 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X175 @ Z0 ) @ X30 ) )
= ( setadjoin @ X176 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[app,c_0_55]) ).
thf(c_0_76,plain,
( apProp
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X173: $i] :
( ( in @ X173 @ X4 )
=> ? [X174: $i] :
( ( in @ X174
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X173 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X173 @ Z0 ) @ X30 ) )
= ( setadjoin @ X174 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
@ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_56,c_0_55]) ).
thf(c_0_77,plain,
( funcImageSingleton
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X170: $i] :
( ( in @ X170 @ X4 )
=> ? [X171: $i] :
( ( in @ X171
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X170 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X170 @ Z0 ) @ X30 ) )
= ( setadjoin @ X171 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X172: $i] :
( ( in @ X172
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) )
= ( setadjoin @ X172 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_57,c_0_55]),c_0_43]) ).
thf(c_0_78,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
=> ( ! [X183: $i,X184: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X183 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X183 @ ( setadjoin @ X184 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X185: $i,X186: $i] : ( iskpair @ ( kpair @ X185 @ X186 ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( ! [X187: $i,X188: $i,X189: $i] :
( ( in @ X189 @ X187 )
=> ! [X190: $i] :
( ( in @ X190 @ X188 )
=> ( in @ ( kpair @ X189 @ X190 ) @ ( cartprod @ X187 @ X188 ) ) ) )
=> ( ! [X191: $i,X192: $i,X193: $i] :
( ( in @ X193 @ ( cartprod @ X191 @ X192 ) )
=> ? [X194: $i] :
( ( in @ X194 @ X191 )
& ? [X195: $i] :
( ( in @ X195 @ X192 )
& ( X193
= ( kpair @ X194 @ X195 ) ) ) ) )
=> ( ! [X196: $i,X197: $i,X198: $i] :
( ( in @ X198 @ ( cartprod @ X196 @ X197 ) )
=> ( iskpair @ X198 ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X199: $i,X200: $i > $o] :
( ! [X201: $i] :
( ( in @ X201 @ X199 )
=> ! [X202: $i] :
( ( in @ X202 @ X199 )
=> ( ( X200 @ X201 )
=> ( ( X200 @ X202 )
=> ( X201 = X202 ) ) ) ) )
=> ( ? [X203: $i] :
( ( in @ X203 @ X199 )
& ( X200 @ X203 ) )
=> ? [X204: $i] :
( ( in @ X204 @ ( dsetconstr @ X199 @ X200 ) )
& ( ( dsetconstr @ X199 @ X200 )
= ( setadjoin @ X204 @ emptyset ) ) ) ) )
=> ( ! [X205: $i,X206: $i > $o] :
( ? [X207: $i] :
( ( in @ X207 @ ( dsetconstr @ X205 @ X206 ) )
& ( ( dsetconstr @ X205 @ X206 )
= ( setadjoin @ X207 @ emptyset ) ) )
=> ? [X208: $i] :
( ( in @ X208 @ X205 )
& ( X206 @ X208 ) ) )
=> ( ! [X209: $i,X210: $i > $o,X211: $i] :
( ( in @ X211 @ X209 )
=> ( ( X210 @ X211 )
=> ( ! [X212: $i] :
( ( in @ X212 @ X209 )
=> ( ( X210 @ X212 )
=> ( X212 = X211 ) ) )
=> ? [X213: $i] :
( ( in @ X213 @ ( dsetconstr @ X209 @ X210 ) )
& ( ( dsetconstr @ X209 @ X210 )
= ( setadjoin @ X213 @ emptyset ) ) ) ) ) )
=> ( ! [X214: $i,X215: $i > $o] :
( ! [X216: $i] :
( ( in @ X216 @ X214 )
=> ! [X217: $i] :
( ( in @ X217 @ X214 )
=> ( ( X215 @ X216 )
=> ( ( X215 @ X217 )
=> ( X216 = X217 ) ) ) ) )
=> ( ? [X218: $i] :
( ( in @ X218 @ X214 )
& ( X215 @ X218 ) )
=> ? [X219: $i] :
( ( in @ X219 @ ( dsetconstr @ X214 @ X215 ) )
& ( ( dsetconstr @ X214 @ X215 )
= ( setadjoin @ X219 @ emptyset ) ) ) ) )
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X220: $i] :
( ( iskpair @ X220 )
=> ? [X221: $i] :
( ( in @ X221
@ ( dsetconstr @ ( setunion @ X220 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X220 ) ) )
& ( ( dsetconstr @ ( setunion @ X220 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X220 ) )
= ( setadjoin @ X221 @ emptyset ) ) ) )
=> ( ! [X222: $i] :
( ? [X223: $i] :
( ( in @ X223 @ X222 )
& ( X222
= ( setadjoin @ X223 @ emptyset ) ) )
=> ( in @ ( setunion @ X222 ) @ X222 ) )
=> ( ! [X224: $i,X225: $i] :
( ( kfst @ ( kpair @ X224 @ X225 ) )
= X224 )
=> ( ! [X226: $i,X227: $i,X228: $i] :
( ( in @ X228 @ ( cartprod @ X226 @ X227 ) )
=> ( in @ ( kfst @ X228 ) @ X226 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X229: $i] :
( ( iskpair @ X229 )
=> ? [X230: $i] :
( ( in @ X230
@ ( dsetconstr @ ( setunion @ X229 )
@ ^ [Z0: $i] :
( X229
= ( kpair @ ( kfst @ X229 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X229 )
@ ^ [Z0: $i] :
( X229
= ( kpair @ ( kfst @ X229 ) @ Z0 ) ) )
= ( setadjoin @ X230 @ emptyset ) ) ) )
=> ( ! [X231: $i,X232: $i] :
( ( ksnd @ ( kpair @ X231 @ X232 ) )
= X232 )
=> ( ! [X233: $i] :
( ( iskpair @ X233 )
=> ( ( kpair @ ( kfst @ X233 ) @ ( ksnd @ X233 ) )
= X233 ) )
=> ( ! [X234: $i,X235: $i,X236: $i] :
( ( in @ X236 @ ( cartprod @ X234 @ X235 ) )
=> ( in @ ( ksnd @ X236 ) @ X235 ) )
=> ( ! [X237: $i,X238: $i,X239: $i,X240: $i] :
( ( in @ ( kpair @ X239 @ X240 ) @ ( cartprod @ X237 @ X238 ) )
=> ( in @ X239 @ X237 ) )
=> ( ! [X241: $i,X242: $i,X243: $i,X244: $i] :
( ( in @ ( kpair @ X243 @ X244 ) @ ( cartprod @ X241 @ X242 ) )
=> ( in @ X244 @ X242 ) )
=> ( cartprodmempaircEq
=> ( ! [X245: $i,X246: $i,X247: $i] :
( ( in @ X247 @ X245 )
=> ! [X248: $i] :
( ( in @ X248 @ X246 )
=> ( ( kfst @ ( kpair @ X247 @ X248 ) )
= X247 ) ) )
=> ( ! [X249: $i,X250: $i,X251: $i] :
( ( in @ X251 @ X249 )
=> ! [X252: $i] :
( ( in @ X252 @ X250 )
=> ( ( ksnd @ ( kpair @ X251 @ X252 ) )
= X252 ) ) )
=> ( ! [X253: $i,X254: $i,X255: $i] :
( ( in @ X255 @ ( cartprod @ X253 @ X254 ) )
=> ( ( kpair @ ( kfst @ X255 ) @ ( ksnd @ X255 ) )
= X255 ) )
=> ( ! [X256: $i,X257: $i,X258: $i > $i > $o,X259: $i] :
( ( in @ X259 @ X256 )
=> ! [X260: $i] :
( ( in @ X260 @ X257 )
=> ( ( X258 @ X259 @ X260 )
=> ( in @ ( kpair @ X259 @ X260 ) @ ( dpsetconstr @ X256 @ X257 @ X258 ) ) ) ) )
=> ( ! [X261: $i,X262: $i,X263: $i > $i > $o] : ( subset @ ( dpsetconstr @ X261 @ X262 @ X263 ) @ ( cartprod @ X261 @ X262 ) )
=> ( ! [X264: $i,X265: $i,X266: $i > $i > $o] : ( subset @ ( dpsetconstr @ X264 @ X265 @ X266 ) @ ( cartprod @ X264 @ X265 ) )
=> ( ! [X267: $i,X268: $i,X269: $i > $i > $o,X270: $i] :
( ( in @ X270 @ X267 )
=> ! [X271: $i] :
( ( in @ X271 @ X268 )
=> ( ( in @ ( kpair @ X270 @ X271 ) @ ( dpsetconstr @ X267 @ X268 @ X269 ) )
=> ( X269 @ X270 @ X271 ) ) ) )
=> ( ! [X272: $i,X273: $i,X274: $i > $i > $o,X275: $i,X276: $i] :
( ( in @ ( kpair @ X275 @ X276 ) @ ( dpsetconstr @ X272 @ X273 @ X274 ) )
=> ( in @ X275 @ X272 ) )
=> ( ! [X277: $i,X278: $i,X279: $i > $i > $o,X280: $i,X281: $i] :
( ( in @ ( kpair @ X280 @ X281 ) @ ( dpsetconstr @ X277 @ X278 @ X279 ) )
=> ( in @ X281 @ X278 ) )
=> ( ! [X282: $i,X283: $i,X284: $i > $i > $o,X285: $i,X286: $i] :
( ( in @ ( kpair @ X285 @ X286 ) @ ( dpsetconstr @ X282 @ X283 @ X284 ) )
=> ( X284 @ X285 @ X286 ) )
=> ( ! [X287: $i,X288: $i,X289: $i] :
( ( ( subset @ X289 @ ( cartprod @ X287 @ X288 ) )
& ! [X290: $i] :
( ( in @ X290 @ X287 )
=> ? [X291: $i] :
( ( in @ X291
@ ( dsetconstr @ X288
@ ^ [Z0: $i] : ( in @ ( kpair @ X290 @ Z0 ) @ X289 ) ) )
& ( ( dsetconstr @ X288
@ ^ [Z0: $i] : ( in @ ( kpair @ X290 @ Z0 ) @ X289 ) )
= ( setadjoin @ X291 @ emptyset ) ) ) ) )
=> ! [X292: $i] :
( ( in @ X292 @ X287 )
=> ? [X293: $i] :
( ( in @ X293
@ ( dsetconstr @ X288
@ ^ [Z0: $i] : ( in @ ( kpair @ X292 @ Z0 ) @ X289 ) ) )
& ( ( dsetconstr @ X288
@ ^ [Z0: $i] : ( in @ ( kpair @ X292 @ Z0 ) @ X289 ) )
= ( setadjoin @ X293 @ emptyset ) ) ) ) )
=> ( ! [X294: $i,X295: $i,X296: $i] :
( ( ( subset @ X296 @ ( cartprod @ X294 @ X295 ) )
& ! [X297: $i] :
( ( in @ X297 @ X294 )
=> ? [X298: $i] :
( ( in @ X298
@ ( dsetconstr @ X295
@ ^ [Z0: $i] : ( in @ ( kpair @ X297 @ Z0 ) @ X296 ) ) )
& ( ( dsetconstr @ X295
@ ^ [Z0: $i] : ( in @ ( kpair @ X297 @ Z0 ) @ X296 ) )
= ( setadjoin @ X298 @ emptyset ) ) ) ) )
=> ! [X299: $i] :
( ( in @ X299 @ X294 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X295
@ ^ [Z0: $i] : ( in @ ( kpair @ X299 @ Z0 ) @ X296 ) ) )
@ X295 ) ) )
=> ( ! [X300: $i,X301: $i,X302: $i] :
( ( ( subset @ X302 @ ( cartprod @ X300 @ X301 ) )
& ! [X303: $i] :
( ( in @ X303 @ X300 )
=> ? [X304: $i] :
( ( in @ X304
@ ( dsetconstr @ X301
@ ^ [Z0: $i] : ( in @ ( kpair @ X303 @ Z0 ) @ X302 ) ) )
& ( ( dsetconstr @ X301
@ ^ [Z0: $i] : ( in @ ( kpair @ X303 @ Z0 ) @ X302 ) )
= ( setadjoin @ X304 @ emptyset ) ) ) ) )
=> ! [X305: $i] :
( ( in @ X305 @ X300 )
=> ( in @ ( ap @ X300 @ X301 @ X302 @ X305 ) @ X301 ) ) )
=> ( ! [X306: $i,X307: $i,X308: $i] :
( ( in @ X308 @ ( funcSet @ X306 @ X307 ) )
=> ( ( subset @ X308 @ ( cartprod @ X306 @ X307 ) )
& ! [X309: $i] :
( ( in @ X309 @ X306 )
=> ? [X310: $i] :
( ( in @ X310
@ ( dsetconstr @ X307
@ ^ [Z0: $i] : ( in @ ( kpair @ X309 @ Z0 ) @ X308 ) ) )
& ( ( dsetconstr @ X307
@ ^ [Z0: $i] : ( in @ ( kpair @ X309 @ Z0 ) @ X308 ) )
= ( setadjoin @ X310 @ emptyset ) ) ) ) ) )
=> ( ! [X311: $i,X312: $i,X313: $i] :
( ( in @ X313 @ ( funcSet @ X311 @ X312 ) )
=> ! [X314: $i] :
( ( in @ X314 @ X311 )
=> ( in @ ( ap @ X311 @ X312 @ X313 @ X314 ) @ X312 ) ) )
=> ( ! [X315: $i,X316: $i,X317: $i] :
( ( ( subset @ X317 @ ( cartprod @ X315 @ X316 ) )
& ! [X318: $i] :
( ( in @ X318 @ X315 )
=> ? [X319: $i] :
( ( in @ X319
@ ( dsetconstr @ X316
@ ^ [Z0: $i] : ( in @ ( kpair @ X318 @ Z0 ) @ X317 ) ) )
& ( ( dsetconstr @ X316
@ ^ [Z0: $i] : ( in @ ( kpair @ X318 @ Z0 ) @ X317 ) )
= ( setadjoin @ X319 @ emptyset ) ) ) ) )
=> ( in @ X317 @ ( funcSet @ X315 @ X316 ) ) )
=> ( ! [X320: $i,X321: $i,X322: $i > $i] :
( ! [X323: $i] :
( ( in @ X323 @ X320 )
=> ( in @ ( X322 @ X323 ) @ X321 ) )
=> ( ( subset
@ ( dpsetconstr @ X320 @ X321
@ ^ [Z0: $i] : ( $eq @ ( X322 @ Z0 ) ) )
@ ( cartprod @ X320 @ X321 ) )
& ! [X324: $i] :
( ( in @ X324 @ X320 )
=> ? [X325: $i] :
( ( in @ X325
@ ( dsetconstr @ X321
@ ^ [Z0: $i] :
( in @ ( kpair @ X324 @ Z0 )
@ ( dpsetconstr @ X320 @ X321
@ ^ [Z1: $i] : ( $eq @ ( X322 @ Z1 ) ) ) ) ) )
& ( ( dsetconstr @ X321
@ ^ [Z0: $i] :
( in @ ( kpair @ X324 @ Z0 )
@ ( dpsetconstr @ X320 @ X321
@ ^ [Z1: $i] : ( $eq @ ( X322 @ Z1 ) ) ) ) )
= ( setadjoin @ X325 @ emptyset ) ) ) ) ) )
=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( ( subset @ ( lam @ X4 @ X5 @ X33 ) @ ( cartprod @ X4 @ X5 ) )
& ! [X326: $i] :
( ( in @ X326 @ X4 )
=> ? [X327: $i] :
( ( in @ X327
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X326 @ Z0 ) @ ( lam @ X4 @ X5 @ X33 ) ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X326 @ Z0 ) @ ( lam @ X4 @ X5 @ X33 ) ) )
= ( setadjoin @ X327 @ 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)],[lamp])]),c_0_55]),cartprodsndpairEq]),ksndpairEq]),cartprodfstpairEq]),kfstpairEq]),kpairsurjEq]),kpairp]),kpairiskpair]),cartprodpairsurjEq]),cartprodpairmemER]),cartprodpairmemEL]),cartprodsndin]),cartprodfstin]),cartprodmempair]),cartprodmempair1]),cartprodpairin]),c_0_58]),c_0_59]),c_0_60]),c_0_61]),c_0_62]),c_0_63]),ap2p]),c_0_64]),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]),c_0_74]),c_0_75]),c_0_76]),c_0_77])]) ).
thf(c_0_79,plain,
! [X328: $i,X329: $i,X330: $i > $i] :
( ( lam @ X328 @ X329 @ X330 )
= ( dpsetconstr @ X328 @ X329
@ ^ [Z0: $i] : ( $eq @ ( X330 @ Z0 ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[lam])])]) ).
thf(c_0_80,negated_conjecture,
! [X335: $i,X336: $i,X337: $i,X338: $i,X339: $i,X340: $i,X341: $i,X342: $i,X343: $i,X344: $i,X345: $i,X348: $i,X349: $i,X350: $i,X351: $i,X352: $i > $o,X355: $i,X357: $i,X358: $i > $o,X359: $i,X361: $i,X362: $i > $o,X363: $i,X366: $i,X367: $i > $o,X370: $i,X372: $i,X374: $i,X375: $i,X376: $i,X377: $i,X378: $i,X379: $i,X380: $i,X381: $i,X383: $i,X384: $i,X385: $i,X386: $i,X387: $i,X388: $i,X389: $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 > $i > $o,X411: $i,X412: $i,X413: $i,X414: $i,X415: $i > $i > $o,X416: $i,X417: $i,X418: $i > $i > $o,X419: $i,X420: $i,X421: $i > $i > $o,X422: $i,X423: $i,X424: $i,X425: $i,X426: $i > $i > $o,X427: $i,X428: $i,X429: $i,X430: $i,X431: $i > $i > $o,X432: $i,X433: $i,X434: $i,X435: $i,X436: $i > $i > $o,X437: $i,X438: $i,X439: $i,X440: $i,X441: $i,X443: $i,X444: $i,X446: $i,X447: $i,X448: $i,X450: $i,X451: $i,X452: $i,X453: $i,X454: $i,X456: $i,X457: $i,X458: $i,X459: $i,X460: $i,X461: $i,X463: $i,X464: $i,X465: $i,X466: $i,X467: $i,X468: $i,X469: $i,X471: $i,X472: $i,X473: $i,X474: $i > $i,X476: $i,X481: $i,X483: $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 @ X335 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X335 @ ( setadjoin @ X336 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X337 @ X338 ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& ( ~ ( in @ X341 @ X339 )
| ~ ( in @ X342 @ X340 )
| ( in @ ( kpair @ X341 @ X342 ) @ ( cartprod @ X339 @ X340 ) ) )
& ( ( in @ ( esk1_3 @ X343 @ X344 @ X345 ) @ X343 )
| ~ ( in @ X345 @ ( cartprod @ X343 @ X344 ) ) )
& ( ( in @ ( esk2_3 @ X343 @ X344 @ X345 ) @ X344 )
| ~ ( in @ X345 @ ( cartprod @ X343 @ X344 ) ) )
& ( ( X345
= ( kpair @ ( esk1_3 @ X343 @ X344 @ X345 ) @ ( esk2_3 @ X343 @ X344 @ X345 ) ) )
| ~ ( in @ X345 @ ( cartprod @ X343 @ X344 ) ) )
& ( ~ ( in @ X350 @ ( cartprod @ X348 @ X349 ) )
| ( iskpair @ X350 ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk5_2 @ X351 @ X352 ) @ ( dsetconstr @ X351 @ X352 ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( in @ ( esk3_2 @ X351 @ X352 ) @ X351 ) )
& ( ( ( dsetconstr @ X351 @ X352 )
= ( setadjoin @ ( esk5_2 @ X351 @ X352 ) @ emptyset ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( in @ ( esk3_2 @ X351 @ X352 ) @ X351 ) )
& ( ( in @ ( esk5_2 @ X351 @ X352 ) @ ( dsetconstr @ X351 @ X352 ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( in @ ( esk4_2 @ X351 @ X352 ) @ X351 ) )
& ( ( ( dsetconstr @ X351 @ X352 )
= ( setadjoin @ ( esk5_2 @ X351 @ X352 ) @ emptyset ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( in @ ( esk4_2 @ X351 @ X352 ) @ X351 ) )
& ( ( in @ ( esk5_2 @ X351 @ X352 ) @ ( dsetconstr @ X351 @ X352 ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( X352 @ ( esk3_2 @ X351 @ X352 ) ) )
& ( ( ( dsetconstr @ X351 @ X352 )
= ( setadjoin @ ( esk5_2 @ X351 @ X352 ) @ emptyset ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( X352 @ ( esk3_2 @ X351 @ X352 ) ) )
& ( ( in @ ( esk5_2 @ X351 @ X352 ) @ ( dsetconstr @ X351 @ X352 ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( X352 @ ( esk4_2 @ X351 @ X352 ) ) )
& ( ( ( dsetconstr @ X351 @ X352 )
= ( setadjoin @ ( esk5_2 @ X351 @ X352 ) @ emptyset ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( X352 @ ( esk4_2 @ X351 @ X352 ) ) )
& ( ( in @ ( esk5_2 @ X351 @ X352 ) @ ( dsetconstr @ X351 @ X352 ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( ( esk3_2 @ X351 @ X352 )
!= ( esk4_2 @ X351 @ X352 ) ) )
& ( ( ( dsetconstr @ X351 @ X352 )
= ( setadjoin @ ( esk5_2 @ X351 @ X352 ) @ emptyset ) )
| ~ ( in @ X355 @ X351 )
| ~ ( X352 @ X355 )
| ( ( esk3_2 @ X351 @ X352 )
!= ( esk4_2 @ X351 @ X352 ) ) )
& ( ( in @ ( esk6_2 @ X357 @ X358 ) @ X357 )
| ~ ( in @ X359 @ ( dsetconstr @ X357 @ X358 ) )
| ( ( dsetconstr @ X357 @ X358 )
!= ( setadjoin @ X359 @ emptyset ) ) )
& ( ( X358 @ ( esk6_2 @ X357 @ X358 ) )
| ~ ( in @ X359 @ ( dsetconstr @ X357 @ X358 ) )
| ( ( dsetconstr @ X357 @ X358 )
!= ( setadjoin @ X359 @ emptyset ) ) )
& ( ( in @ ( esk8_3 @ X361 @ X362 @ X363 ) @ ( dsetconstr @ X361 @ X362 ) )
| ( in @ ( esk7_3 @ X361 @ X362 @ X363 ) @ X361 )
| ~ ( X362 @ X363 )
| ~ ( in @ X363 @ X361 ) )
& ( ( ( dsetconstr @ X361 @ X362 )
= ( setadjoin @ ( esk8_3 @ X361 @ X362 @ X363 ) @ emptyset ) )
| ( in @ ( esk7_3 @ X361 @ X362 @ X363 ) @ X361 )
| ~ ( X362 @ X363 )
| ~ ( in @ X363 @ X361 ) )
& ( ( in @ ( esk8_3 @ X361 @ X362 @ X363 ) @ ( dsetconstr @ X361 @ X362 ) )
| ( X362 @ ( esk7_3 @ X361 @ X362 @ X363 ) )
| ~ ( X362 @ X363 )
| ~ ( in @ X363 @ X361 ) )
& ( ( ( dsetconstr @ X361 @ X362 )
= ( setadjoin @ ( esk8_3 @ X361 @ X362 @ X363 ) @ emptyset ) )
| ( X362 @ ( esk7_3 @ X361 @ X362 @ X363 ) )
| ~ ( X362 @ X363 )
| ~ ( in @ X363 @ X361 ) )
& ( ( in @ ( esk8_3 @ X361 @ X362 @ X363 ) @ ( dsetconstr @ X361 @ X362 ) )
| ( ( esk7_3 @ X361 @ X362 @ X363 )
!= X363 )
| ~ ( X362 @ X363 )
| ~ ( in @ X363 @ X361 ) )
& ( ( ( dsetconstr @ X361 @ X362 )
= ( setadjoin @ ( esk8_3 @ X361 @ X362 @ X363 ) @ emptyset ) )
| ( ( esk7_3 @ X361 @ X362 @ X363 )
!= X363 )
| ~ ( X362 @ X363 )
| ~ ( in @ X363 @ X361 ) )
& ( ( in @ ( esk11_2 @ X366 @ X367 ) @ ( dsetconstr @ X366 @ X367 ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( in @ ( esk9_2 @ X366 @ X367 ) @ X366 ) )
& ( ( ( dsetconstr @ X366 @ X367 )
= ( setadjoin @ ( esk11_2 @ X366 @ X367 ) @ emptyset ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( in @ ( esk9_2 @ X366 @ X367 ) @ X366 ) )
& ( ( in @ ( esk11_2 @ X366 @ X367 ) @ ( dsetconstr @ X366 @ X367 ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( in @ ( esk10_2 @ X366 @ X367 ) @ X366 ) )
& ( ( ( dsetconstr @ X366 @ X367 )
= ( setadjoin @ ( esk11_2 @ X366 @ X367 ) @ emptyset ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( in @ ( esk10_2 @ X366 @ X367 ) @ X366 ) )
& ( ( in @ ( esk11_2 @ X366 @ X367 ) @ ( dsetconstr @ X366 @ X367 ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( X367 @ ( esk9_2 @ X366 @ X367 ) ) )
& ( ( ( dsetconstr @ X366 @ X367 )
= ( setadjoin @ ( esk11_2 @ X366 @ X367 ) @ emptyset ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( X367 @ ( esk9_2 @ X366 @ X367 ) ) )
& ( ( in @ ( esk11_2 @ X366 @ X367 ) @ ( dsetconstr @ X366 @ X367 ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( X367 @ ( esk10_2 @ X366 @ X367 ) ) )
& ( ( ( dsetconstr @ X366 @ X367 )
= ( setadjoin @ ( esk11_2 @ X366 @ X367 ) @ emptyset ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( X367 @ ( esk10_2 @ X366 @ X367 ) ) )
& ( ( in @ ( esk11_2 @ X366 @ X367 ) @ ( dsetconstr @ X366 @ X367 ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( ( esk9_2 @ X366 @ X367 )
!= ( esk10_2 @ X366 @ X367 ) ) )
& ( ( ( dsetconstr @ X366 @ X367 )
= ( setadjoin @ ( esk11_2 @ X366 @ X367 ) @ emptyset ) )
| ~ ( in @ X370 @ X366 )
| ~ ( X367 @ X370 )
| ( ( esk9_2 @ X366 @ X367 )
!= ( esk10_2 @ X366 @ X367 ) ) )
& singletonsuniq
& setukpairinjL1
& ( ( in @ ( esk12_1 @ X372 )
@ ( dsetconstr @ ( setunion @ X372 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X372 ) ) )
| ~ ( iskpair @ X372 ) )
& ( ( ( dsetconstr @ ( setunion @ X372 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X372 ) )
= ( setadjoin @ ( esk12_1 @ X372 ) @ emptyset ) )
| ~ ( iskpair @ X372 ) )
& ( ~ ( in @ X375 @ X374 )
| ( X374
!= ( setadjoin @ X375 @ emptyset ) )
| ( in @ ( setunion @ X374 ) @ X374 ) )
& ( ( kfst @ ( kpair @ X376 @ X377 ) )
= X376 )
& ( ~ ( in @ X380 @ ( cartprod @ X378 @ X379 ) )
| ( in @ ( kfst @ X380 ) @ X378 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ( in @ ( esk13_1 @ X381 )
@ ( dsetconstr @ ( setunion @ X381 )
@ ^ [Z0: $i] :
( X381
= ( kpair @ ( kfst @ X381 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X381 ) )
& ( ( ( dsetconstr @ ( setunion @ X381 )
@ ^ [Z0: $i] :
( X381
= ( kpair @ ( kfst @ X381 ) @ Z0 ) ) )
= ( setadjoin @ ( esk13_1 @ X381 ) @ emptyset ) )
| ~ ( iskpair @ X381 ) )
& ( ( ksnd @ ( kpair @ X383 @ X384 ) )
= X384 )
& ( ~ ( iskpair @ X385 )
| ( ( kpair @ ( kfst @ X385 ) @ ( ksnd @ X385 ) )
= X385 ) )
& ( ~ ( in @ X388 @ ( cartprod @ X386 @ X387 ) )
| ( in @ ( ksnd @ X388 ) @ X387 ) )
& ( ~ ( in @ ( kpair @ X391 @ X392 ) @ ( cartprod @ X389 @ X390 ) )
| ( in @ X391 @ X389 ) )
& ( ~ ( in @ ( kpair @ X395 @ X396 ) @ ( cartprod @ X393 @ X394 ) )
| ( in @ X396 @ X394 ) )
& cartprodmempaircEq
& ( ~ ( in @ X399 @ X397 )
| ~ ( in @ X400 @ X398 )
| ( ( kfst @ ( kpair @ X399 @ X400 ) )
= X399 ) )
& ( ~ ( in @ X403 @ X401 )
| ~ ( in @ X404 @ X402 )
| ( ( ksnd @ ( kpair @ X403 @ X404 ) )
= X404 ) )
& ( ~ ( in @ X407 @ ( cartprod @ X405 @ X406 ) )
| ( ( kpair @ ( kfst @ X407 ) @ ( ksnd @ X407 ) )
= X407 ) )
& ( ~ ( in @ X411 @ X408 )
| ~ ( in @ X412 @ X409 )
| ~ ( X410 @ X411 @ X412 )
| ( in @ ( kpair @ X411 @ X412 ) @ ( dpsetconstr @ X408 @ X409 @ X410 ) ) )
& ( subset @ ( dpsetconstr @ X413 @ X414 @ X415 ) @ ( cartprod @ X413 @ X414 ) )
& ( subset @ ( dpsetconstr @ X416 @ X417 @ X418 ) @ ( cartprod @ X416 @ X417 ) )
& ( ~ ( in @ X422 @ X419 )
| ~ ( in @ X423 @ X420 )
| ~ ( in @ ( kpair @ X422 @ X423 ) @ ( dpsetconstr @ X419 @ X420 @ X421 ) )
| ( X421 @ X422 @ X423 ) )
& ( ~ ( in @ ( kpair @ X427 @ X428 ) @ ( dpsetconstr @ X424 @ X425 @ X426 ) )
| ( in @ X427 @ X424 ) )
& ( ~ ( in @ ( kpair @ X432 @ X433 ) @ ( dpsetconstr @ X429 @ X430 @ X431 ) )
| ( in @ X433 @ X430 ) )
& ( ~ ( in @ ( kpair @ X437 @ X438 ) @ ( dpsetconstr @ X434 @ X435 @ X436 ) )
| ( X436 @ X437 @ X438 ) )
& ( ( in @ ( esk15_4 @ X439 @ X440 @ X441 @ X444 )
@ ( dsetconstr @ X440
@ ^ [Z0: $i] : ( in @ ( kpair @ X444 @ Z0 ) @ X441 ) ) )
| ~ ( in @ X444 @ X439 )
| ( in @ ( esk14_3 @ X439 @ X440 @ X441 ) @ X439 )
| ~ ( subset @ X441 @ ( cartprod @ X439 @ X440 ) ) )
& ( ( ( dsetconstr @ X440
@ ^ [Z0: $i] : ( in @ ( kpair @ X444 @ Z0 ) @ X441 ) )
= ( setadjoin @ ( esk15_4 @ X439 @ X440 @ X441 @ X444 ) @ emptyset ) )
| ~ ( in @ X444 @ X439 )
| ( in @ ( esk14_3 @ X439 @ X440 @ X441 ) @ X439 )
| ~ ( subset @ X441 @ ( cartprod @ X439 @ X440 ) ) )
& ( ( in @ ( esk15_4 @ X439 @ X440 @ X441 @ X444 )
@ ( dsetconstr @ X440
@ ^ [Z0: $i] : ( in @ ( kpair @ X444 @ Z0 ) @ X441 ) ) )
| ~ ( in @ X444 @ X439 )
| ~ ( in @ X443
@ ( dsetconstr @ X440
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X439 @ X440 @ X441 ) @ Z0 ) @ X441 ) ) )
| ( ( dsetconstr @ X440
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X439 @ X440 @ X441 ) @ Z0 ) @ X441 ) )
!= ( setadjoin @ X443 @ emptyset ) )
| ~ ( subset @ X441 @ ( cartprod @ X439 @ X440 ) ) )
& ( ( ( dsetconstr @ X440
@ ^ [Z0: $i] : ( in @ ( kpair @ X444 @ Z0 ) @ X441 ) )
= ( setadjoin @ ( esk15_4 @ X439 @ X440 @ X441 @ X444 ) @ emptyset ) )
| ~ ( in @ X444 @ X439 )
| ~ ( in @ X443
@ ( dsetconstr @ X440
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X439 @ X440 @ X441 ) @ Z0 ) @ X441 ) ) )
| ( ( dsetconstr @ X440
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk14_3 @ X439 @ X440 @ X441 ) @ Z0 ) @ X441 ) )
!= ( setadjoin @ X443 @ emptyset ) )
| ~ ( subset @ X441 @ ( cartprod @ X439 @ X440 ) ) )
& ( ( in @ ( esk16_3 @ X446 @ X447 @ X448 ) @ X446 )
| ~ ( subset @ X448 @ ( cartprod @ X446 @ X447 ) )
| ~ ( in @ X451 @ X446 )
| ( in
@ ( setunion
@ ( dsetconstr @ X447
@ ^ [Z0: $i] : ( in @ ( kpair @ X451 @ Z0 ) @ X448 ) ) )
@ X447 ) )
& ( ~ ( in @ X450
@ ( dsetconstr @ X447
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk16_3 @ X446 @ X447 @ X448 ) @ Z0 ) @ X448 ) ) )
| ( ( dsetconstr @ X447
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk16_3 @ X446 @ X447 @ X448 ) @ Z0 ) @ X448 ) )
!= ( setadjoin @ X450 @ emptyset ) )
| ~ ( subset @ X448 @ ( cartprod @ X446 @ X447 ) )
| ~ ( in @ X451 @ X446 )
| ( in
@ ( setunion
@ ( dsetconstr @ X447
@ ^ [Z0: $i] : ( in @ ( kpair @ X451 @ Z0 ) @ X448 ) ) )
@ X447 ) )
& ( ( in @ ( esk17_3 @ X452 @ X453 @ X454 ) @ X452 )
| ~ ( subset @ X454 @ ( cartprod @ X452 @ X453 ) )
| ~ ( in @ X457 @ X452 )
| ( in @ ( ap @ X452 @ X453 @ X454 @ X457 ) @ X453 ) )
& ( ~ ( in @ X456
@ ( dsetconstr @ X453
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk17_3 @ X452 @ X453 @ X454 ) @ Z0 ) @ X454 ) ) )
| ( ( dsetconstr @ X453
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk17_3 @ X452 @ X453 @ X454 ) @ Z0 ) @ X454 ) )
!= ( setadjoin @ X456 @ emptyset ) )
| ~ ( subset @ X454 @ ( cartprod @ X452 @ X453 ) )
| ~ ( in @ X457 @ X452 )
| ( in @ ( ap @ X452 @ X453 @ X454 @ X457 ) @ X453 ) )
& ( ( subset @ X460 @ ( cartprod @ X458 @ X459 ) )
| ~ ( in @ X460 @ ( funcSet @ X458 @ X459 ) ) )
& ( ( in @ ( esk18_4 @ X458 @ X459 @ X460 @ X461 )
@ ( dsetconstr @ X459
@ ^ [Z0: $i] : ( in @ ( kpair @ X461 @ Z0 ) @ X460 ) ) )
| ~ ( in @ X461 @ X458 )
| ~ ( in @ X460 @ ( funcSet @ X458 @ X459 ) ) )
& ( ( ( dsetconstr @ X459
@ ^ [Z0: $i] : ( in @ ( kpair @ X461 @ Z0 ) @ X460 ) )
= ( setadjoin @ ( esk18_4 @ X458 @ X459 @ X460 @ X461 ) @ emptyset ) )
| ~ ( in @ X461 @ X458 )
| ~ ( in @ X460 @ ( funcSet @ X458 @ X459 ) ) )
& ( ~ ( in @ X465 @ ( funcSet @ X463 @ X464 ) )
| ~ ( in @ X466 @ X463 )
| ( in @ ( ap @ X463 @ X464 @ X465 @ X466 ) @ X464 ) )
& ( ( in @ ( esk19_3 @ X467 @ X468 @ X469 ) @ X467 )
| ~ ( subset @ X469 @ ( cartprod @ X467 @ X468 ) )
| ( in @ X469 @ ( funcSet @ X467 @ X468 ) ) )
& ( ~ ( in @ X471
@ ( dsetconstr @ X468
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk19_3 @ X467 @ X468 @ X469 ) @ Z0 ) @ X469 ) ) )
| ( ( dsetconstr @ X468
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk19_3 @ X467 @ X468 @ X469 ) @ Z0 ) @ X469 ) )
!= ( setadjoin @ X471 @ emptyset ) )
| ~ ( subset @ X469 @ ( cartprod @ X467 @ X468 ) )
| ( in @ X469 @ ( funcSet @ X467 @ X468 ) ) )
& ( ( subset
@ ( dpsetconstr @ X472 @ X473
@ ^ [Z0: $i] : ( $eq @ ( X474 @ Z0 ) ) )
@ ( cartprod @ X472 @ X473 ) )
| ( in @ ( esk20_3 @ X472 @ X473 @ X474 ) @ X472 ) )
& ( ( in @ ( esk21_4 @ X472 @ X473 @ X474 @ X476 )
@ ( dsetconstr @ X473
@ ^ [Z0: $i] :
( in @ ( kpair @ X476 @ Z0 )
@ ( dpsetconstr @ X472 @ X473
@ ^ [Z1: $i] : ( $eq @ ( X474 @ Z1 ) ) ) ) ) )
| ~ ( in @ X476 @ X472 )
| ( in @ ( esk20_3 @ X472 @ X473 @ X474 ) @ X472 ) )
& ( ( ( dsetconstr @ X473
@ ^ [Z0: $i] :
( in @ ( kpair @ X476 @ Z0 )
@ ( dpsetconstr @ X472 @ X473
@ ^ [Z1: $i] : ( $eq @ ( X474 @ Z1 ) ) ) ) )
= ( setadjoin @ ( esk21_4 @ X472 @ X473 @ X474 @ X476 ) @ emptyset ) )
| ~ ( in @ X476 @ X472 )
| ( in @ ( esk20_3 @ X472 @ X473 @ X474 ) @ X472 ) )
& ( ( subset
@ ( dpsetconstr @ X472 @ X473
@ ^ [Z0: $i] : ( $eq @ ( X474 @ Z0 ) ) )
@ ( cartprod @ X472 @ X473 ) )
| ~ ( in @ ( X474 @ ( esk20_3 @ X472 @ X473 @ X474 ) ) @ X473 ) )
& ( ( in @ ( esk21_4 @ X472 @ X473 @ X474 @ X476 )
@ ( dsetconstr @ X473
@ ^ [Z0: $i] :
( in @ ( kpair @ X476 @ Z0 )
@ ( dpsetconstr @ X472 @ X473
@ ^ [Z1: $i] : ( $eq @ ( X474 @ Z1 ) ) ) ) ) )
| ~ ( in @ X476 @ X472 )
| ~ ( in @ ( X474 @ ( esk20_3 @ X472 @ X473 @ X474 ) ) @ X473 ) )
& ( ( ( dsetconstr @ X473
@ ^ [Z0: $i] :
( in @ ( kpair @ X476 @ Z0 )
@ ( dpsetconstr @ X472 @ X473
@ ^ [Z1: $i] : ( $eq @ ( X474 @ Z1 ) ) ) ) )
= ( setadjoin @ ( esk21_4 @ X472 @ X473 @ X474 @ X476 ) @ emptyset ) )
| ~ ( in @ X476 @ X472 )
| ~ ( in @ ( X474 @ ( esk20_3 @ X472 @ X473 @ X474 ) ) @ X473 ) )
& ( ~ ( in @ X481 @ esk22_0 )
| ( in @ ( esk24_0 @ X481 ) @ esk23_0 ) )
& ( ( in @ esk25_0 @ esk22_0 )
| ~ ( subset @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) @ ( cartprod @ esk22_0 @ esk23_0 ) ) )
& ( ~ ( in @ X483
@ ( dsetconstr @ esk23_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk25_0 @ Z0 ) @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) ) ) )
| ( ( dsetconstr @ esk23_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk25_0 @ Z0 ) @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) ) )
!= ( setadjoin @ X483 @ emptyset ) )
| ~ ( subset @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) @ ( cartprod @ esk22_0 @ esk23_0 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])])])])]) ).
thf(c_0_81,plain,
! [X484: $i,X485: $i,X486: $i > $i] :
( ( lam @ X484 @ X485 @ X486 )
= ( dpsetconstr @ X484 @ X485
@ ^ [Z0: $i] : ( $eq @ ( X486 @ Z0 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_79]) ).
thf(c_0_82,plain,
! [X493: $i,X31: $i > $i] :
( ( epred2_1 @ X31 @ X493 )
= ( $eq @ ( X31 @ X493 ) ) ),
introduced(definition) ).
thf(c_0_83,plain,
! [X543: $i,X544: $i > $i] :
( ( epred2_1 @ X544 @ X543 )
= ( $eq @ ( X544 @ X543 ) ) ),
inference(variable_rename,[status(thm)],]) ).
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_80]) ).
thf(c_0_85,negated_conjecture,
! [X2: $i] :
( ( in @ ( esk24_0 @ X2 ) @ esk23_0 )
| ~ ( in @ X2 @ esk22_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_86,negated_conjecture,
( ( in @ esk25_0 @ esk22_0 )
| ~ ( subset @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) @ ( cartprod @ esk22_0 @ esk23_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_87,plain,
! [X2: $i,X3: $i,X31: $i > $i] :
( ( lam @ X2 @ X3 @ X31 )
= ( dpsetconstr @ X2 @ X3 @ ( epred2_1 @ X31 ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_81]),c_0_82]) ).
thf(c_0_88,negated_conjecture,
! [X2: $i,X6: $i > $i > $o,X3: $i] : ( subset @ ( dpsetconstr @ X2 @ X3 @ X6 ) @ ( cartprod @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_89,plain,
! [X31: $i > $i,X2: $i] :
( ( epred2_1 @ X31 @ X2 )
= ( $eq @ ( X31 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
thf(c_0_90,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_80]) ).
thf(c_0_91,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_92,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_80]) ).
thf(c_0_93,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_80]) ).
thf(c_0_94,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( in @ ( esk5_2 @ esk23_0 @ X1 ) @ ( dsetconstr @ esk23_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk23_0 @ X1 ) )
| ~ ( in @ X2 @ esk22_0 )
| ~ ( X1 @ ( esk24_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
thf(c_0_95,negated_conjecture,
in @ esk25_0 @ esk22_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).
thf(c_0_96,plain,
! [X2: $i,X31: $i > $i,X546: $i] :
( ( epred2_1 @ X31 @ X2 @ X546 )
<=> ( ( X31 @ X2 )
= X546 ) ),
inference(arg_cong,[status(thm)],[c_0_89]) ).
thf(c_0_97,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( in @ ( esk5_2 @ esk23_0 @ X1 ) @ ( dsetconstr @ esk23_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk23_0 @ X1 ) )
| ~ ( in @ X2 @ esk22_0 )
| ~ ( X1 @ ( esk24_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_90,c_0_85]) ).
thf(c_0_98,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_80]) ).
thf(c_0_99,negated_conjecture,
! [X2: $i,X3: $i] :
( ( epred2_1 @ ksnd @ ( kpair @ X2 @ X3 ) )
= ( $eq @ X3 ) ),
inference(spm,[status(thm)],[c_0_89,c_0_91]) ).
thf(c_0_100,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk23_0 @ X1 ) )
| ~ ( in @ X2 @ esk22_0 )
| ~ ( X1 @ ( esk24_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_85]) ).
thf(c_0_101,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk23_0 @ X1 ) )
| ~ ( in @ X2 @ esk22_0 )
| ~ ( X1 @ ( esk24_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_93,c_0_85]) ).
thf(c_0_102,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_80]) ).
thf(c_0_103,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk23_0 @ X1 ) @ ( dsetconstr @ esk23_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk23_0 @ X1 ) )
| ~ ( X1 @ ( esk24_0 @ esk25_0 ) ) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
thf(c_0_104,plain,
! [X31: $i > $i,X2: $i] : ( epred2_1 @ X31 @ X2 @ ( X31 @ X2 ) ),
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_96])]) ).
thf(c_0_105,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk23_0 @ X1 ) @ ( dsetconstr @ esk23_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk23_0 @ X1 ) )
| ~ ( X1 @ ( esk24_0 @ esk25_0 ) ) ),
inference(spm,[status(thm)],[c_0_97,c_0_95]) ).
thf(c_0_106,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( in @ ( esk5_2 @ esk23_0 @ X1 ) @ ( dsetconstr @ esk23_0 @ X1 ) )
| ( ( esk4_2 @ esk23_0 @ X1 )
!= ( esk3_2 @ esk23_0 @ X1 ) )
| ~ ( in @ X2 @ esk22_0 )
| ~ ( X1 @ ( esk24_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_98,c_0_85]) ).
thf(c_0_107,negated_conjecture,
! [X2: $i,X3: $i,X547: $i] :
( ( epred2_1 @ ksnd @ ( kpair @ X2 @ X3 ) @ X547 )
<=> ( X3 = X547 ) ),
inference(arg_cong,[status(thm)],[c_0_99]) ).
thf(c_0_108,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ X1 ) )
| ( X1 @ ( esk3_2 @ esk23_0 @ X1 ) )
| ~ ( X1 @ ( esk24_0 @ esk25_0 ) ) ),
inference(spm,[status(thm)],[c_0_100,c_0_95]) ).
thf(c_0_109,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ X1 ) )
| ( X1 @ ( esk4_2 @ esk23_0 @ X1 ) )
| ~ ( X1 @ ( esk24_0 @ esk25_0 ) ) ),
inference(spm,[status(thm)],[c_0_101,c_0_95]) ).
thf(c_0_110,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ X1 ) )
| ( ( esk4_2 @ esk23_0 @ X1 )
!= ( esk3_2 @ esk23_0 @ X1 ) )
| ~ ( in @ X2 @ esk22_0 )
| ~ ( X1 @ ( esk24_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_102,c_0_85]) ).
thf(c_0_111,plain,
! [X2: $i,X31: $i > $i,X3: $i] :
( ( ( X31 @ X2 )
= X3 )
| ~ ( epred2_1 @ X31 @ X2 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_96]) ).
thf(c_0_112,plain,
( ( in @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( epred2_1 @ esk24_0 @ esk25_0 @ ( esk3_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
thf(c_0_113,plain,
( ( in @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( epred2_1 @ esk24_0 @ esk25_0 @ ( esk4_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_105,c_0_104]) ).
thf(c_0_114,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk5_2 @ esk23_0 @ X1 ) @ ( dsetconstr @ esk23_0 @ X1 ) )
| ( ( esk4_2 @ esk23_0 @ X1 )
!= ( esk3_2 @ esk23_0 @ X1 ) )
| ~ ( X1 @ ( esk24_0 @ esk25_0 ) ) ),
inference(spm,[status(thm)],[c_0_106,c_0_95]) ).
thf(c_0_115,negated_conjecture,
! [X2: $i,X3: $i] : ( epred2_1 @ ksnd @ ( kpair @ X2 @ X3 ) @ X3 ),
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_107])]) ).
thf(c_0_116,plain,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ emptyset )
= ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( epred2_1 @ esk24_0 @ esk25_0 @ ( esk3_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_108,c_0_104]) ).
thf(c_0_117,plain,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ emptyset )
= ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( epred2_1 @ esk24_0 @ esk25_0 @ ( esk4_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_109,c_0_104]) ).
thf(c_0_118,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ X1 ) )
| ( ( esk4_2 @ esk23_0 @ X1 )
!= ( esk3_2 @ esk23_0 @ X1 ) )
| ~ ( X1 @ ( esk24_0 @ esk25_0 ) ) ),
inference(spm,[status(thm)],[c_0_110,c_0_95]) ).
thf(c_0_119,plain,
( ( ( esk24_0 @ esk25_0 )
= ( esk3_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( in @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
thf(c_0_120,plain,
( ( ( esk24_0 @ esk25_0 )
= ( esk4_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( in @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_113]) ).
thf(c_0_121,negated_conjecture,
( ( in @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( ( esk4_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) )
!= ( esk3_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_99]),c_0_89]),c_0_99]),c_0_89]),c_0_99]),c_0_89]),c_0_99]),c_0_89]) ).
thf(c_0_122,plain,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ emptyset )
= ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( ( esk24_0 @ esk25_0 )
= ( esk3_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_116]) ).
thf(c_0_123,plain,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ emptyset )
= ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( ( esk24_0 @ esk25_0 )
= ( esk4_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_117]) ).
thf(c_0_124,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ emptyset )
= ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) )
| ( ( esk4_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) )
!= ( esk3_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_115]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_89]),c_0_89]),c_0_89]),c_0_89]) ).
thf(c_0_125,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( X1 @ ( esk6_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
| ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_126,plain,
in @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121]) ).
thf(c_0_127,plain,
( ( setadjoin @ ( esk5_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ emptyset )
= ( dsetconstr @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]) ).
thf(c_0_128,plain,
! [X545: $i] :
( ( ~ ( epred1_0 @ X545 )
| ( in @ ( kpair @ esk25_0 @ X545 ) @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) ) )
& ( ~ ( in @ ( kpair @ esk25_0 @ X545 ) @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) )
| ( epred1_0 @ X545 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_129,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk6_2 @ X2 @ X1 ) @ X2 )
| ~ ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
| ( ( dsetconstr @ X2 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_130,negated_conjecture,
epred2_1 @ esk24_0 @ esk25_0 @ ( esk6_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127])]) ).
thf(c_0_131,plain,
! [X2: $i] :
( ( epred1_0 @ X2 )
| ~ ( in @ ( kpair @ esk25_0 @ X2 ) @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_132,negated_conjecture,
! [X3: $i,X2: $i,X6: $i > $i > $o,X5: $i,X4: $i] :
( ( in @ ( kpair @ X2 @ X4 ) @ ( dpsetconstr @ X3 @ X5 @ X6 ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X5 )
| ~ ( X6 @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_133,negated_conjecture,
in @ ( esk6_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) ) @ esk23_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_126]),c_0_127])]) ).
thf(c_0_134,plain,
( ( esk6_2 @ esk23_0 @ ( epred2_1 @ esk24_0 @ esk25_0 ) )
= ( esk24_0 @ esk25_0 ) ),
inference(spm,[status(thm)],[c_0_111,c_0_130]) ).
thf(c_0_135,plain,
! [X2: $i] :
( ( epred1_0 @ X2 )
| ~ ( in @ ( kpair @ esk25_0 @ X2 ) @ ( dpsetconstr @ esk22_0 @ esk23_0 @ ( epred2_1 @ esk24_0 ) ) ) ),
inference(rw,[status(thm)],[c_0_131,c_0_87]) ).
thf(c_0_136,plain,
! [X2: $i,X31: $i > $i,X4: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ ( X31 @ X2 ) ) @ ( dpsetconstr @ X3 @ X4 @ ( epred2_1 @ X31 ) ) )
| ~ ( in @ ( X31 @ X2 ) @ X4 )
| ~ ( in @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_132,c_0_104]) ).
thf(c_0_137,negated_conjecture,
in @ ( esk24_0 @ esk25_0 ) @ esk23_0,
inference(rw,[status(thm)],[c_0_133,c_0_134]) ).
thf(c_0_138,plain,
! [X2: $i] :
( ( in @ ( kpair @ esk25_0 @ X2 ) @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_139,plain,
epred1_0 @ ( esk24_0 @ esk25_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_95])]) ).
thf(c_0_140,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i > $i > $o] :
( ( X6 @ X2 @ X3 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ X4 @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_141,negated_conjecture,
! [X2: $i] :
( ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 )
| ~ ( iskpair @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_142,plain,
! [X2: $i] :
( ( in @ ( kpair @ esk25_0 @ X2 ) @ ( dpsetconstr @ esk22_0 @ esk23_0 @ ( epred2_1 @ esk24_0 ) ) )
| ~ ( epred1_0 @ X2 ) ),
inference(rw,[status(thm)],[c_0_138,c_0_87]) ).
thf(c_0_143,negated_conjecture,
( ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk3_2 @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_103,c_0_139]) ).
thf(c_0_144,negated_conjecture,
( ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk4_2 @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_105,c_0_139]) ).
thf(c_0_145,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk3_2 @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_108,c_0_139]) ).
thf(c_0_146,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk4_2 @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_109,c_0_139]) ).
thf(c_0_147,plain,
! [X491: $i] :
( ( epred1_0 @ X491 )
<=> ( in @ ( kpair @ esk25_0 @ X491 ) @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) ) ),
introduced(definition) ).
thf(c_0_148,negated_conjecture,
! [X3: $i,X6: $i > $i > $o,X4: $i,X2: $i] :
( ( X6 @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
| ~ ( in @ X2 @ ( dpsetconstr @ X3 @ X4 @ X6 ) )
| ~ ( iskpair @ X2 ) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
thf(c_0_149,plain,
( ( in @ ( kpair @ esk25_0 @ ( esk3_2 @ esk23_0 @ epred1_0 ) ) @ ( dpsetconstr @ esk22_0 @ esk23_0 @ ( epred2_1 @ esk24_0 ) ) )
| ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
thf(c_0_150,negated_conjecture,
! [X3: $i,X2: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_151,negated_conjecture,
! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_152,plain,
( ( in @ ( kpair @ esk25_0 @ ( esk4_2 @ esk23_0 @ epred1_0 ) ) @ ( dpsetconstr @ esk22_0 @ esk23_0 @ ( epred2_1 @ esk24_0 ) ) )
| ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_142,c_0_144]) ).
thf(c_0_153,plain,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( in @ ( kpair @ esk25_0 @ ( esk3_2 @ esk23_0 @ epred1_0 ) ) @ ( dpsetconstr @ esk22_0 @ esk23_0 @ ( epred2_1 @ esk24_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_142,c_0_145]) ).
thf(c_0_154,plain,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( in @ ( kpair @ esk25_0 @ ( esk4_2 @ esk23_0 @ epred1_0 ) ) @ ( dpsetconstr @ esk22_0 @ esk23_0 @ ( epred2_1 @ esk24_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_142,c_0_146]) ).
thf(c_0_155,negated_conjecture,
! [X2: $i] :
( ( ( in @ X2 @ ( dsetconstr @ esk23_0 @ epred1_0 ) )
!= $true )
| ( ( dsetconstr @ esk23_0 @ epred1_0 )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( subset @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) @ ( cartprod @ esk22_0 @ esk23_0 ) ) ),
inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_80]),c_0_147]),c_0_147]) ).
thf(c_0_156,negated_conjecture,
( ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( epred2_1 @ esk24_0 @ esk25_0 @ ( esk3_2 @ esk23_0 @ epred1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_150]),c_0_91]),c_0_151])]) ).
thf(c_0_157,negated_conjecture,
( ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( epred2_1 @ esk24_0 @ esk25_0 @ ( esk4_2 @ esk23_0 @ epred1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_152]),c_0_150]),c_0_91]),c_0_151])]) ).
thf(c_0_158,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( epred2_1 @ esk24_0 @ esk25_0 @ ( esk3_2 @ esk23_0 @ epred1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_153]),c_0_150]),c_0_91]),c_0_151])]) ).
thf(c_0_159,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( epred2_1 @ esk24_0 @ esk25_0 @ ( esk4_2 @ esk23_0 @ epred1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_154]),c_0_150]),c_0_91]),c_0_151])]) ).
thf(c_0_160,negated_conjecture,
! [X2: $i] :
( ( ( dsetconstr @ esk23_0 @ epred1_0 )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( subset @ ( lam @ esk22_0 @ esk23_0 @ esk24_0 ) @ ( cartprod @ esk22_0 @ esk23_0 ) )
| ~ ( in @ X2 @ ( dsetconstr @ esk23_0 @ epred1_0 ) ) ),
inference(cn,[status(thm)],[c_0_155]) ).
thf(c_0_161,plain,
( ( ( esk24_0 @ esk25_0 )
= ( esk3_2 @ esk23_0 @ epred1_0 ) )
| ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_156]) ).
thf(c_0_162,plain,
( ( ( esk24_0 @ esk25_0 )
= ( esk4_2 @ esk23_0 @ epred1_0 ) )
| ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_157]) ).
thf(c_0_163,negated_conjecture,
( ( in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( ( esk4_2 @ esk23_0 @ epred1_0 )
!= ( esk3_2 @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_114,c_0_139]) ).
thf(c_0_164,plain,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( ( esk24_0 @ esk25_0 )
= ( esk3_2 @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_158]) ).
thf(c_0_165,plain,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( ( esk24_0 @ esk25_0 )
= ( esk4_2 @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_159]) ).
thf(c_0_166,negated_conjecture,
( ( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) )
| ( ( esk4_2 @ esk23_0 @ epred1_0 )
!= ( esk3_2 @ esk23_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_118,c_0_139]) ).
thf(c_0_167,negated_conjecture,
! [X2: $i] :
( ( ( dsetconstr @ esk23_0 @ epred1_0 )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ ( dsetconstr @ esk23_0 @ epred1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_87]),c_0_88])]) ).
thf(c_0_168,plain,
in @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ ( dsetconstr @ esk23_0 @ epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]) ).
thf(c_0_169,plain,
( ( setadjoin @ ( esk5_2 @ esk23_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk23_0 @ epred1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]) ).
thf(c_0_170,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_169])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU679^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:01:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 3.00/0.98 # Version: 3.1.0-ho
% 3.00/0.98 # Preprocessing class: HSLMSLSSLLLCHSA.
% 3.00/0.98 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.00/0.98 # Starting ho_unfolding_5 with 1200s (4) cores
% 3.00/0.98 # Starting pre_casc_3 with 300s (1) cores
% 3.00/0.98 # Starting new_ho_10_cnf2 with 300s (1) cores
% 3.00/0.98 # Starting full_lambda_10 with 300s (1) cores
% 3.00/0.98 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 3.00/0.98 # pre_casc_3 with pid 11490 completed with status 0
% 3.00/0.98 # Result found by pre_casc_3
% 3.00/0.98 # Preprocessing class: HSLMSLSSLLLCHSA.
% 3.00/0.98 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.00/0.98 # Starting ho_unfolding_5 with 1200s (4) cores
% 3.00/0.98 # Starting pre_casc_3 with 300s (1) cores
% 3.00/0.98 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 3.00/0.98 # Search class: HGHSM-FSLM32-MHSMMSBN
% 3.00/0.98 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 3.00/0.98 # Starting full_lambda_5 with 28s (1) cores
% 3.00/0.98 # full_lambda_5 with pid 11495 completed with status 0
% 3.00/0.98 # Result found by full_lambda_5
% 3.00/0.98 # Preprocessing class: HSLMSLSSLLLCHSA.
% 3.00/0.98 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 3.00/0.98 # Starting ho_unfolding_5 with 1200s (4) cores
% 3.00/0.98 # Starting pre_casc_3 with 300s (1) cores
% 3.00/0.98 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 3.00/0.98 # Search class: HGHSM-FSLM32-MHSMMSBN
% 3.00/0.98 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 3.00/0.98 # Starting full_lambda_5 with 28s (1) cores
% 3.00/0.98 # Preprocessing time : 0.004 s
% 3.00/0.98 # Presaturation interreduction done
% 3.00/0.98
% 3.00/0.98 # Proof found!
% 3.00/0.98 # SZS status Theorem
% 3.00/0.98 # SZS output start CNFRefutation
% See solution above
% 3.00/0.98 # Parsed axioms : 436
% 3.00/0.98 # Removed by relevancy pruning/SinE : 393
% 3.00/0.98 # Initial clauses : 254
% 3.00/0.98 # Removed in clause preprocessing : 0
% 3.00/0.98 # Initial clauses in saturation : 254
% 3.00/0.98 # Processed clauses : 2072
% 3.00/0.98 # ...of these trivial : 38
% 3.00/0.98 # ...subsumed : 594
% 3.00/0.98 # ...remaining for further processing : 1440
% 3.00/0.98 # Other redundant clauses eliminated : 197
% 3.00/0.98 # Clauses deleted for lack of memory : 0
% 3.00/0.98 # Backward-subsumed : 64
% 3.00/0.98 # Backward-rewritten : 160
% 3.00/0.98 # Generated clauses : 13764
% 3.00/0.98 # ...of the previous two non-redundant : 13074
% 3.00/0.98 # ...aggressively subsumed : 0
% 3.00/0.98 # Contextual simplify-reflections : 36
% 3.00/0.98 # Paramodulations : 13164
% 3.00/0.98 # Factorizations : 0
% 3.00/0.98 # NegExts : 101
% 3.00/0.98 # Equation resolutions : 197
% 3.00/0.98 # Disequality decompositions : 0
% 3.00/0.98 # Total rewrite steps : 2317
% 3.00/0.98 # ...of those cached : 2068
% 3.00/0.98 # Propositional unsat checks : 0
% 3.00/0.98 # Propositional check models : 0
% 3.00/0.98 # Propositional check unsatisfiable : 0
% 3.00/0.98 # Propositional clauses : 0
% 3.00/0.98 # Propositional clauses after purity: 0
% 3.00/0.98 # Propositional unsat core size : 0
% 3.00/0.98 # Propositional preprocessing time : 0.000
% 3.00/0.98 # Propositional encoding time : 0.000
% 3.00/0.98 # Propositional solver time : 0.000
% 3.00/0.98 # Success case prop preproc time : 0.000
% 3.00/0.98 # Success case prop encoding time : 0.000
% 3.00/0.98 # Success case prop solver time : 0.000
% 3.00/0.98 # Current number of processed clauses : 908
% 3.00/0.98 # Positive orientable unit clauses : 225
% 3.00/0.98 # Positive unorientable unit clauses: 1
% 3.00/0.98 # Negative unit clauses : 0
% 3.00/0.98 # Non-unit-clauses : 682
% 3.00/0.98 # Current number of unprocessed clauses: 11286
% 3.00/0.98 # ...number of literals in the above : 47538
% 3.00/0.98 # Current number of archived formulas : 0
% 3.00/0.98 # Current number of archived clauses : 531
% 3.00/0.98 # Clause-clause subsumption calls (NU) : 58095
% 3.00/0.98 # Rec. Clause-clause subsumption calls : 36056
% 3.00/0.98 # Non-unit clause-clause subsumptions : 687
% 3.00/0.98 # Unit Clause-clause subsumption calls : 3029
% 3.00/0.98 # Rewrite failures with RHS unbound : 0
% 3.00/0.98 # BW rewrite match attempts : 524
% 3.00/0.98 # BW rewrite match successes : 20
% 3.00/0.98 # Condensation attempts : 0
% 3.00/0.98 # Condensation successes : 0
% 3.00/0.98 # Termbank termtop insertions : 498564
% 3.00/0.98 # Search garbage collected termcells : 8940
% 3.00/0.98
% 3.00/0.98 # -------------------------------------------------
% 3.00/0.98 # User time : 0.448 s
% 3.00/0.98 # System time : 0.015 s
% 3.00/0.98 # Total time : 0.464 s
% 3.00/0.98 # Maximum resident set size: 4904 pages
% 3.00/0.98
% 3.00/0.98 # -------------------------------------------------
% 3.00/0.98 # User time : 0.459 s
% 3.00/0.98 # System time : 0.018 s
% 3.00/0.98 # Total time : 0.477 s
% 3.00/0.98 # Maximum resident set size: 2204 pages
% 3.00/0.98 % E---3.1 exiting
% 3.00/0.98 % E exiting
%------------------------------------------------------------------------------