%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU699^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:15 AM UTC 2026
% Result : Theorem 0.32s 0.43s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 1024 ( 38 equ; 0 cnn)
% Maximal formula atoms : 256 ( 35 avg)
% Number of connectives : 1759 ( 34 ~; 35 |; 222 &; 730 @)
% ( 19 <=>; 719 =>; 0 <=; 0 <~>)
% Maximal formula depth : 270 ( 41 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 232 ( 230 usr; 219 con; 0-4 aty)
% Number of variables : 209 ( 16 ^; 193 !; 0 ?; 209 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_25,type,
setextAx: $o ).
thf(decl_27,type,
emptysetAx: $o ).
thf(decl_29,type,
setadjoinAx: $o ).
thf(decl_31,type,
powersetAx: $o ).
thf(decl_33,type,
setunionAx: $o ).
thf(decl_35,type,
omega0Ax: $o ).
thf(decl_36,type,
omegaSAx: $o ).
thf(decl_37,type,
omegaIndAx: $o ).
thf(decl_38,type,
replAx: $o ).
thf(decl_39,type,
foundationAx: $o ).
thf(decl_40,type,
wellorderingAx: $o ).
thf(decl_42,type,
descrp: $o ).
thf(decl_44,type,
dsetconstrI: $o ).
thf(decl_45,type,
dsetconstrEL: $o ).
thf(decl_46,type,
dsetconstrER: $o ).
thf(decl_47,type,
exuE1: $o ).
thf(decl_49,type,
prop2setE: $o ).
thf(decl_50,type,
emptysetE: $o ).
thf(decl_51,type,
emptysetimpfalse: $o ).
thf(decl_52,type,
notinemptyset: $o ).
thf(decl_53,type,
exuE3e: $o ).
thf(decl_54,type,
setext: $o ).
thf(decl_55,type,
emptyI: $o ).
thf(decl_56,type,
noeltsimpempty: $o ).
thf(decl_57,type,
setbeta: $o ).
thf(decl_59,type,
nonemptyE1: $o ).
thf(decl_60,type,
nonemptyI: $o ).
thf(decl_61,type,
nonemptyI1: $o ).
thf(decl_62,type,
setadjoinIL: $o ).
thf(decl_63,type,
emptyinunitempty: $o ).
thf(decl_64,type,
setadjoinIR: $o ).
thf(decl_65,type,
setadjoinE: $o ).
thf(decl_66,type,
setadjoinOr: $o ).
thf(decl_67,type,
setoftrueEq: $o ).
thf(decl_68,type,
powersetI: $o ).
thf(decl_69,type,
emptyinPowerset: $o ).
thf(decl_70,type,
emptyInPowerset: $o ).
thf(decl_71,type,
powersetE: $o ).
thf(decl_72,type,
setunionI: $o ).
thf(decl_73,type,
setunionE: $o ).
thf(decl_74,type,
subPowSU: $o ).
thf(decl_75,type,
exuE2: $o ).
thf(decl_76,type,
nonemptyImpWitness: $o ).
thf(decl_77,type,
uniqinunit: $o ).
thf(decl_78,type,
notinsingleton: $o ).
thf(decl_79,type,
eqinunit: $o ).
thf(decl_80,type,
singletonsswitch: $o ).
thf(decl_81,type,
upairsetE: $o ).
thf(decl_82,type,
upairsetIL: $o ).
thf(decl_83,type,
upairsetIR: $o ).
thf(decl_84,type,
emptyE1: $o ).
thf(decl_85,type,
vacuousDall: $o ).
thf(decl_86,type,
quantDeMorgan1: $o ).
thf(decl_87,type,
quantDeMorgan2: $o ).
thf(decl_88,type,
quantDeMorgan3: $o ).
thf(decl_89,type,
quantDeMorgan4: $o ).
thf(decl_90,type,
prop2setI: $o ).
thf(decl_92,type,
prop2set2propI: $o ).
thf(decl_93,type,
notdexE: $o ).
thf(decl_94,type,
notdallE: $o ).
thf(decl_95,type,
exuI1: $o ).
thf(decl_96,type,
exuI3: $o ).
thf(decl_97,type,
exuI2: $o ).
thf(decl_98,type,
inCongP: $o ).
thf(decl_99,type,
in__Cong: $o ).
thf(decl_100,type,
exuE3u: $o ).
thf(decl_101,type,
exu__Cong: $o ).
thf(decl_102,type,
emptyset__Cong: $o ).
thf(decl_103,type,
setadjoin__Cong: $o ).
thf(decl_104,type,
powerset__Cong: $o ).
thf(decl_105,type,
setunion__Cong: $o ).
thf(decl_106,type,
omega__Cong: $o ).
thf(decl_107,type,
exuEu: $o ).
thf(decl_108,type,
descr__Cong: $o ).
thf(decl_109,type,
dsetconstr__Cong: $o ).
thf(decl_113,type,
subsetI1: $o ).
thf(decl_114,type,
eqimpsubset2: $o ).
thf(decl_115,type,
eqimpsubset1: $o ).
thf(decl_116,type,
subsetI2: $o ).
thf(decl_117,type,
emptysetsubset: $o ).
thf(decl_118,type,
subsetE: $o ).
thf(decl_119,type,
subsetE2: $o ).
thf(decl_120,type,
notsubsetI: $o ).
thf(decl_121,type,
notequalI1: $o ).
thf(decl_122,type,
notequalI2: $o ).
thf(decl_123,type,
subsetRefl: $o ).
thf(decl_124,type,
subsetTrans: $o ).
thf(decl_125,type,
setadjoinSub: $o ).
thf(decl_126,type,
setadjoinSub2: $o ).
thf(decl_127,type,
subset2powerset: $o ).
thf(decl_128,type,
setextsub: $o ).
thf(decl_129,type,
subsetemptysetimpeq: $o ).
thf(decl_130,type,
powersetI1: $o ).
thf(decl_131,type,
powersetE1: $o ).
thf(decl_132,type,
inPowerset: $o ).
thf(decl_133,type,
powersetsubset: $o ).
thf(decl_134,type,
sepInPowerset: $o ).
thf(decl_135,type,
sepSubset: $o ).
thf(decl_137,type,
binunionIL: $o ).
thf(decl_138,type,
upairset2IR: $o ).
thf(decl_139,type,
binunionIR: $o ).
thf(decl_140,type,
binunionEcases: $o ).
thf(decl_141,type,
binunionE: $o ).
thf(decl_142,type,
binunionLsub: $o ).
thf(decl_143,type,
binunionRsub: $o ).
thf(decl_145,type,
binintersectI: $o ).
thf(decl_146,type,
binintersectSubset5: $o ).
thf(decl_147,type,
binintersectEL: $o ).
thf(decl_148,type,
binintersectLsub: $o ).
thf(decl_149,type,
binintersectSubset2: $o ).
thf(decl_150,type,
binintersectSubset3: $o ).
thf(decl_151,type,
binintersectER: $o ).
thf(decl_152,type,
disjointsetsI1: $o ).
thf(decl_153,type,
binintersectRsub: $o ).
thf(decl_154,type,
binintersectSubset4: $o ).
thf(decl_155,type,
binintersectSubset1: $o ).
thf(decl_156,type,
bs114d: $o ).
thf(decl_159,type,
setminusI: $o ).
thf(decl_160,type,
setminusEL: $o ).
thf(decl_161,type,
setminusER: $o ).
thf(decl_162,type,
setminusSubset2: $o ).
thf(decl_163,type,
setminusERneg: $o ).
thf(decl_164,type,
setminusELneg: $o ).
thf(decl_165,type,
setminusILneg: $o ).
thf(decl_166,type,
setminusIRneg: $o ).
thf(decl_167,type,
setminusLsub: $o ).
thf(decl_168,type,
setminusSubset1: $o ).
thf(decl_170,type,
symdiffE: $o ).
thf(decl_171,type,
symdiffI1: $o ).
thf(decl_172,type,
symdiffI2: $o ).
thf(decl_173,type,
symdiffIneg1: $o ).
thf(decl_174,type,
symdiffIneg2: $o ).
thf(decl_176,type,
secondinupair: $o ).
thf(decl_177,type,
setukpairIL: $o ).
thf(decl_178,type,
setukpairIR: $o ).
thf(decl_179,type,
kpairiskpair: $o ).
thf(decl_180,type,
kpair: $i > $i > $i ).
thf(decl_181,type,
kpairp: $o ).
thf(decl_183,type,
singletonsubset: $o ).
thf(decl_184,type,
singletoninpowerset: $o ).
thf(decl_185,type,
singletoninpowunion: $o ).
thf(decl_186,type,
upairset2E: $o ).
thf(decl_187,type,
upairsubunion: $o ).
thf(decl_188,type,
upairinpowunion: $o ).
thf(decl_189,type,
ubforcartprodlem1: $o ).
thf(decl_190,type,
ubforcartprodlem2: $o ).
thf(decl_191,type,
ubforcartprodlem3: $o ).
thf(decl_192,type,
cartprodpairin: $o ).
thf(decl_193,type,
cartprodmempair1: $o ).
thf(decl_194,type,
cartprodmempair: $o ).
thf(decl_195,type,
setunionE2: $o ).
thf(decl_196,type,
setunionsingleton1: $o ).
thf(decl_197,type,
setunionsingleton2: $o ).
thf(decl_198,type,
setunionsingleton: $o ).
thf(decl_200,type,
singletonprop: $o ).
thf(decl_202,type,
ex1E1: $o ).
thf(decl_203,type,
ex1I: $o ).
thf(decl_204,type,
ex1I2: $o ).
thf(decl_205,type,
singletonsuniq: $o ).
thf(decl_210,type,
setukpairinjL1: $o ).
thf(decl_211,type,
kfstsingleton: $o ).
thf(decl_212,type,
theprop: $o ).
thf(decl_214,type,
kfstpairEq: $o ).
thf(decl_215,type,
cartprodfstin: $o ).
thf(decl_216,type,
setukpairinjL2: $o ).
thf(decl_217,type,
setukpairinjL: $o ).
thf(decl_218,type,
setukpairinjR11: $o ).
thf(decl_219,type,
setukpairinjR12: $o ).
thf(decl_220,type,
setukpairinjR1: $o ).
thf(decl_221,type,
upairequniteq: $o ).
thf(decl_222,type,
setukpairinjR2: $o ).
thf(decl_223,type,
setukpairinjR: $o ).
thf(decl_224,type,
ksndsingleton: $o ).
thf(decl_226,type,
ksndpairEq: $o ).
thf(decl_227,type,
kpairsurjEq: $o ).
thf(decl_228,type,
cartprodsndin: $o ).
thf(decl_229,type,
cartprodpairmemEL: $o ).
thf(decl_230,type,
cartprodpairmemER: $o ).
thf(decl_231,type,
cartprodmempaircEq: $o ).
thf(decl_232,type,
cartprodfstpairEq: $o ).
thf(decl_233,type,
cartprodsndpairEq: $o ).
thf(decl_234,type,
cartprodpairsurjEq: $o ).
thf(decl_237,type,
dpsetconstrI: $o ).
thf(decl_238,type,
dpsetconstrSub: $o ).
thf(decl_239,type,
setOfPairsIsBReln: $o ).
thf(decl_240,type,
dpsetconstrERa: $o ).
thf(decl_241,type,
dpsetconstrEL1: $o ).
thf(decl_242,type,
dpsetconstrEL2: $o ).
thf(decl_243,type,
dpsetconstrER: $o ).
thf(decl_244,type,
func: $i > $i > $i > $o ).
thf(decl_245,type,
funcSet: $i > $i > $i ).
thf(decl_246,type,
funcImageSingleton: $o ).
thf(decl_247,type,
apProp: $o ).
thf(decl_248,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_249,type,
app: $o ).
thf(decl_250,type,
infuncsetfunc: $o ).
thf(decl_251,type,
ap2p: $o ).
thf(decl_252,type,
funcinfuncset: $o ).
thf(decl_253,type,
lamProp: $o ).
thf(decl_254,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_255,type,
lamp: $o ).
thf(decl_256,type,
lam2p: $o ).
thf(decl_257,type,
brelnall1: $o ).
thf(decl_258,type,
brelnall2: $o ).
thf(decl_259,type,
ex1E2: $o ).
thf(decl_260,type,
funcGraphProp1: $o ).
thf(decl_261,type,
funcGraphProp3: $o ).
thf(decl_262,type,
funcGraphProp2: $o ).
thf(decl_263,type,
funcextLem: $o ).
thf(decl_264,type,
funcGraphProp4: $o ).
thf(decl_265,type,
subbreln: $o ).
thf(decl_266,type,
eqbreln: $o ).
thf(decl_267,type,
funcext: $o ).
thf(decl_268,type,
funcext2: $o ).
thf(decl_269,type,
ap2apEq1: $o ).
thf(decl_270,type,
ap2apEq2: $o ).
thf(decl_271,type,
beta1: $o ).
thf(decl_272,type,
eta1: $o ).
thf(decl_273,type,
lam2lamEq: $o ).
thf(decl_274,type,
beta2: $o ).
thf(decl_275,type,
esk1_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_276,type,
esk2_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_277,type,
esk3_4: $i > $i > $i > $i > $i ).
thf(decl_278,type,
esk4_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_279,type,
esk5_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_280,type,
esk6_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_281,type,
esk7_0: $i ).
thf(decl_282,type,
esk8_0: $i ).
thf(decl_283,type,
esk9_0: $i ).
thf(eta2,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',eta2) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',beta2) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',lam2lamEq) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',eta1) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',beta1) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',lam2p) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',lamp) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',ap2apEq1) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',funcext2) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',funcGraphProp4) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',funcGraphProp3) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',funcinfuncset) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',ap2p) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p',infuncsetfunc) ).
thf(c_0_14,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[eta2]) ).
thf(c_0_15,plain,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X38 @ Z0 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[beta2]) ).
thf(c_0_16,plain,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X37 @ Z0 ) )
= ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X37 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2lamEq]) ).
thf(c_0_17,plain,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
= X29 ) ) ),
inference(fof_simplification,[status(thm)],[eta1]) ).
thf(c_0_18,plain,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X36 @ Z0 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[beta1]) ).
thf(c_0_19,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X32 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_20,plain,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X31 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_21,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( 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
=> ( ! [X95: $i,X96: $i,X97: $i] :
( ( in @ X97 @ ( funcSet @ X95 @ X96 ) )
=> ( func @ X95 @ X96 @ X97 ) )
=> ( ! [X98: $i,X99: $i,X100: $i] :
( ( in @ X100 @ ( funcSet @ X98 @ X99 ) )
=> ! [X101: $i] :
( ( in @ X101 @ X98 )
=> ( in @ ( ap @ X98 @ X99 @ X100 @ X101 ) @ X99 ) ) )
=> ( ! [X102: $i,X103: $i,X104: $i] :
( ( func @ X102 @ X103 @ X104 )
=> ( in @ X104 @ ( funcSet @ X102 @ X103 ) ) )
=> ( lamProp
=> ( ! [X105: $i,X106: $i,X107: $i > $i] :
( ! [X108: $i] :
( ( in @ X108 @ X105 )
=> ( in @ ( X107 @ X108 ) @ X106 ) )
=> ( func @ X105 @ X106 @ ( lam @ X105 @ X106 @ X107 ) ) )
=> ( ! [X109: $i,X110: $i,X111: $i > $i] :
( ! [X112: $i] :
( ( in @ X112 @ X109 )
=> ( in @ ( X111 @ X112 ) @ X110 ) )
=> ( in @ ( lam @ X109 @ X110 @ X111 ) @ ( funcSet @ X109 @ X110 ) ) )
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( ! [X113: $i,X114: $i,X115: $i] :
( ( in @ X115 @ ( funcSet @ X113 @ X114 ) )
=> ! [X116: $i] :
( ( in @ X116 @ X113 )
=> ( in @ ( kpair @ X116 @ ( ap @ X113 @ X114 @ X115 @ X116 ) ) @ X115 ) ) )
=> ( funcGraphProp2
=> ( funcextLem
=> ( ! [X117: $i,X118: $i,X119: $i] :
( ( in @ X119 @ ( funcSet @ X117 @ X118 ) )
=> ! [X120: $i] :
( ( in @ X120 @ X117 )
=> ! [X121: $i] :
( ( in @ X121 @ X118 )
=> ( ( in @ ( kpair @ X120 @ X121 ) @ X119 )
=> ( ( ap @ X117 @ X118 @ X119 @ X120 )
= X121 ) ) ) ) )
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( ! [X122: $i,X123: $i,X124: $i] :
( ( in @ X124 @ ( funcSet @ X122 @ X123 ) )
=> ! [X125: $i] :
( ( in @ X125 @ ( funcSet @ X122 @ X123 ) )
=> ( ! [X126: $i] :
( ( in @ X126 @ X122 )
=> ( ( ap @ X122 @ X123 @ X124 @ X126 )
= ( ap @ X122 @ X123 @ X125 @ X126 ) ) )
=> ( X124 = X125 ) ) ) )
=> ( ! [X127: $i,X128: $i,X129: $i] :
( ( in @ X129 @ ( funcSet @ X127 @ X128 ) )
=> ! [X130: $i] :
( ( in @ X130 @ X127 )
=> ( ( ap @ X127 @ X128 @ X129 @ X130 )
= ( ap @ X127 @ X128 @ X129 @ X130 ) ) ) )
=> ( ap2apEq2
=> ( ! [X131: $i,X132: $i,X133: $i > $i] :
( ! [X134: $i] :
( ( in @ X134 @ X131 )
=> ( in @ ( X133 @ X134 ) @ X132 ) )
=> ! [X135: $i] :
( ( in @ X135 @ X131 )
=> ( ( ap @ X131 @ X132 @ ( lam @ X131 @ X132 @ X133 ) @ X135 )
= ( X133 @ X135 ) ) ) )
=> ( ! [X136: $i,X137: $i,X138: $i] :
( ( func @ X136 @ X137 @ X138 )
=> ( ( lam @ X136 @ X137 @ ( ap @ X136 @ X137 @ X138 ) )
= X138 ) )
=> ( ! [X139: $i,X140: $i,X141: $i > $i] :
( ! [X142: $i] :
( ( in @ X142 @ X139 )
=> ( in @ ( X141 @ X142 ) @ X140 ) )
=> ( ( lam @ X139 @ X140 @ X141 )
= ( lam @ X139 @ X140 @ X141 ) ) )
=> ( ! [X143: $i,X144: $i,X145: $i > $i] :
( ! [X146: $i] :
( ( in @ X146 @ X143 )
=> ( in @ ( X145 @ X146 ) @ X144 ) )
=> ! [X147: $i] :
( ( in @ X147 @ X143 )
=> ( ( ap @ X143 @ X144 @ ( lam @ X143 @ X144 @ X145 ) @ X147 )
= ( X145 @ X147 ) ) ) )
=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5 @ ( ap @ X4 @ X5 @ X29 ) )
= X29 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[c_0_14]),ap2apEq1]),funcext2]),funcGraphProp4]),funcGraphProp3]),funcinfuncset]),ap2p]),infuncsetfunc]),c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20])]) ).
thf(c_0_22,negated_conjecture,
! [X148: $i,X149: $i,X150: $i,X151: $i,X152: $i,X153: $i,X154: $i,X155: $i,X156: $i,X157: $i,X158: $i,X159: $i,X160: $i > $i,X162: $i,X163: $i,X164: $i > $i,X166: $i,X167: $i,X168: $i,X169: $i,X170: $i,X171: $i,X172: $i,X173: $i,X174: $i,X175: $i,X176: $i,X177: $i,X178: $i,X180: $i,X181: $i,X182: $i,X183: $i,X184: $i,X185: $i,X186: $i > $i,X188: $i,X189: $i,X190: $i,X191: $i,X192: $i,X193: $i,X194: $i > $i,X196: $i,X197: $i,X198: $i > $i,X200: $i] :
( setextAx
& emptysetAx
& setadjoinAx
& powersetAx
& setunionAx
& omega0Ax
& omegaSAx
& omegaIndAx
& replAx
& foundationAx
& wellorderingAx
& descrp
& dsetconstrI
& dsetconstrEL
& dsetconstrER
& exuE1
& prop2setE
& emptysetE
& emptysetimpfalse
& notinemptyset
& exuE3e
& setext
& emptyI
& noeltsimpempty
& setbeta
& nonemptyE1
& nonemptyI
& nonemptyI1
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& setoftrueEq
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& setunionI
& setunionE
& subPowSU
& exuE2
& nonemptyImpWitness
& uniqinunit
& notinsingleton
& eqinunit
& singletonsswitch
& upairsetE
& upairsetIL
& upairsetIR
& emptyE1
& vacuousDall
& quantDeMorgan1
& quantDeMorgan2
& quantDeMorgan3
& quantDeMorgan4
& prop2setI
& prop2set2propI
& notdexE
& notdallE
& exuI1
& exuI3
& exuI2
& inCongP
& in__Cong
& exuE3u
& exu__Cong
& emptyset__Cong
& setadjoin__Cong
& powerset__Cong
& setunion__Cong
& omega__Cong
& exuEu
& descr__Cong
& dsetconstr__Cong
& subsetI1
& eqimpsubset2
& eqimpsubset1
& subsetI2
& emptysetsubset
& subsetE
& subsetE2
& notsubsetI
& notequalI1
& notequalI2
& subsetRefl
& subsetTrans
& setadjoinSub
& setadjoinSub2
& subset2powerset
& setextsub
& subsetemptysetimpeq
& powersetI1
& powersetE1
& inPowerset
& powersetsubset
& sepInPowerset
& sepSubset
& binunionIL
& upairset2IR
& binunionIR
& binunionEcases
& binunionE
& binunionLsub
& binunionRsub
& binintersectI
& binintersectSubset5
& binintersectEL
& binintersectLsub
& binintersectSubset2
& binintersectSubset3
& binintersectER
& disjointsetsI1
& binintersectRsub
& binintersectSubset4
& binintersectSubset1
& bs114d
& setminusI
& setminusEL
& setminusER
& setminusSubset2
& setminusERneg
& setminusELneg
& setminusILneg
& setminusIRneg
& setminusLsub
& setminusSubset1
& symdiffE
& symdiffI1
& symdiffI2
& symdiffIneg1
& symdiffIneg2
& secondinupair
& setukpairIL
& setukpairIR
& kpairiskpair
& kpairp
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& cartprodpairin
& cartprodmempair1
& cartprodmempair
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& 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
& ( ~ ( in @ X150 @ ( funcSet @ X148 @ X149 ) )
| ( func @ X148 @ X149 @ X150 ) )
& ( ~ ( in @ X153 @ ( funcSet @ X151 @ X152 ) )
| ~ ( in @ X154 @ X151 )
| ( in @ ( ap @ X151 @ X152 @ X153 @ X154 ) @ X152 ) )
& ( ~ ( func @ X155 @ X156 @ X157 )
| ( in @ X157 @ ( funcSet @ X155 @ X156 ) ) )
& lamProp
& ( ( in @ ( esk1_3 @ X158 @ X159 @ X160 ) @ X158 )
| ( func @ X158 @ X159 @ ( lam @ X158 @ X159 @ X160 ) ) )
& ( ~ ( in @ ( X160 @ ( esk1_3 @ X158 @ X159 @ X160 ) ) @ X159 )
| ( func @ X158 @ X159 @ ( lam @ X158 @ X159 @ X160 ) ) )
& ( ( in @ ( esk2_3 @ X162 @ X163 @ X164 ) @ X162 )
| ( in @ ( lam @ X162 @ X163 @ X164 ) @ ( funcSet @ X162 @ X163 ) ) )
& ( ~ ( in @ ( X164 @ ( esk2_3 @ X162 @ X163 @ X164 ) ) @ X163 )
| ( in @ ( lam @ X162 @ X163 @ X164 ) @ ( funcSet @ X162 @ X163 ) ) )
& brelnall1
& brelnall2
& ex1E2
& funcGraphProp1
& ( ~ ( in @ X168 @ ( funcSet @ X166 @ X167 ) )
| ~ ( in @ X169 @ X166 )
| ( in @ ( kpair @ X169 @ ( ap @ X166 @ X167 @ X168 @ X169 ) ) @ X168 ) )
& funcGraphProp2
& funcextLem
& ( ~ ( in @ X172 @ ( funcSet @ X170 @ X171 ) )
| ~ ( in @ X173 @ X170 )
| ~ ( in @ X174 @ X171 )
| ~ ( in @ ( kpair @ X173 @ X174 ) @ X172 )
| ( ( ap @ X170 @ X171 @ X172 @ X173 )
= X174 ) )
& subbreln
& eqbreln
& funcext
& ( ( in @ ( esk3_4 @ X175 @ X176 @ X177 @ X178 ) @ X175 )
| ( X177 = X178 )
| ~ ( in @ X178 @ ( funcSet @ X175 @ X176 ) )
| ~ ( in @ X177 @ ( funcSet @ X175 @ X176 ) ) )
& ( ( ( ap @ X175 @ X176 @ X177 @ ( esk3_4 @ X175 @ X176 @ X177 @ X178 ) )
!= ( ap @ X175 @ X176 @ X178 @ ( esk3_4 @ X175 @ X176 @ X177 @ X178 ) ) )
| ( X177 = X178 )
| ~ ( in @ X178 @ ( funcSet @ X175 @ X176 ) )
| ~ ( in @ X177 @ ( funcSet @ X175 @ X176 ) ) )
& ( ~ ( in @ X182 @ ( funcSet @ X180 @ X181 ) )
| ~ ( in @ X183 @ X180 )
| ( ( ap @ X180 @ X181 @ X182 @ X183 )
= ( ap @ X180 @ X181 @ X182 @ X183 ) ) )
& ap2apEq2
& ( ( in @ ( esk4_3 @ X184 @ X185 @ X186 ) @ X184 )
| ~ ( in @ X188 @ X184 )
| ( ( ap @ X184 @ X185 @ ( lam @ X184 @ X185 @ X186 ) @ X188 )
= ( X186 @ X188 ) ) )
& ( ~ ( in @ ( X186 @ ( esk4_3 @ X184 @ X185 @ X186 ) ) @ X185 )
| ~ ( in @ X188 @ X184 )
| ( ( ap @ X184 @ X185 @ ( lam @ X184 @ X185 @ X186 ) @ X188 )
= ( X186 @ X188 ) ) )
& ( ~ ( func @ X189 @ X190 @ X191 )
| ( ( lam @ X189 @ X190 @ ( ap @ X189 @ X190 @ X191 ) )
= X191 ) )
& ( ( in @ ( esk5_3 @ X192 @ X193 @ X194 ) @ X192 )
| ( ( lam @ X192 @ X193 @ X194 )
= ( lam @ X192 @ X193 @ X194 ) ) )
& ( ~ ( in @ ( X194 @ ( esk5_3 @ X192 @ X193 @ X194 ) ) @ X193 )
| ( ( lam @ X192 @ X193 @ X194 )
= ( lam @ X192 @ X193 @ X194 ) ) )
& ( ( in @ ( esk6_3 @ X196 @ X197 @ X198 ) @ X196 )
| ~ ( in @ X200 @ X196 )
| ( ( ap @ X196 @ X197 @ ( lam @ X196 @ X197 @ X198 ) @ X200 )
= ( X198 @ X200 ) ) )
& ( ~ ( in @ ( X198 @ ( esk6_3 @ X196 @ X197 @ X198 ) ) @ X197 )
| ~ ( in @ X200 @ X196 )
| ( ( ap @ X196 @ X197 @ ( lam @ X196 @ X197 @ X198 ) @ X200 )
= ( X198 @ X200 ) ) )
& ( in @ esk9_0 @ ( funcSet @ esk7_0 @ esk8_0 ) )
& ( ( lam @ esk7_0 @ esk8_0 @ ( ap @ esk7_0 @ esk8_0 @ esk9_0 ) )
!= esk9_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_21])])])])])]) ).
thf(c_0_23,negated_conjecture,
( ( lam @ esk7_0 @ esk8_0 @ ( ap @ esk7_0 @ esk8_0 @ esk9_0 ) )
!= esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( ( lam @ X2 @ X3 @ ( ap @ X2 @ X3 @ X4 ) )
= X4 )
| ~ ( func @ X2 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,negated_conjecture,
~ ( func @ esk7_0 @ esk8_0 @ esk9_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( func @ X3 @ X4 @ X2 )
| ~ ( in @ X2 @ ( funcSet @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_27,negated_conjecture,
in @ esk9_0 @ ( funcSet @ esk7_0 @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU699^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n020.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 14:12:49 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.29 Running higher-order theorem proving
% 0.23/0.35 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/tmp/tmp.tdcTtcYe7v/E---3.1_1113978.p
% 0.32/0.42 % Version: 3.5.1-ho
% 0.32/0.42 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.32/0.42 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.42 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.32/0.42 % Starting pre_casc_3 with 300s (1) cores
% 0.32/0.42 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.32/0.42 % Starting full_lambda_10 with 300s (1) cores
% 0.32/0.42 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.32/0.42 % pre_casc_3 with pid 1113994 completed with status 0
% 0.32/0.42 % Result found by pre_casc_3
% 0.32/0.42 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.32/0.42 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.42 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.32/0.42 % Starting pre_casc_3 with 300s (1) cores
% 0.32/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.32/0.42 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.32/0.42 % Search class: HGUSF-FFMM33-SHSMMFNN
% 0.32/0.42 % partial match(5): HGUNM-FFMF32-SHSSMFNN
% 0.32/0.42 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.32/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.32/0.42 % SubtermCWHack with pid 1113999 completed with status 0
% 0.32/0.43 % Result found by SubtermCWHack
% 0.32/0.43 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.32/0.43 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.43 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.32/0.43 % Starting pre_casc_3 with 300s (1) cores
% 0.32/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.32/0.43 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.32/0.43 % Search class: HGUSF-FFMM33-SHSMMFNN
% 0.32/0.43 % partial match(5): HGUNM-FFMF32-SHSSMFNN
% 0.32/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.32/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.32/0.43 % Preprocessing time : 0.003 s
% 0.32/0.43
% 0.32/0.43 % Proof found!
% 0.32/0.43 % SZS status Theorem
% 0.32/0.43 % SZS output start CNFRefutation
% See solution above
% 0.32/0.43 % Parsed axioms : 473
% 0.32/0.43 % Removed by relevancy pruning/SinE : 459
% 0.32/0.43 % Initial clauses : 223
% 0.32/0.43 % Removed in clause preprocessing : 3
% 0.32/0.43 % Initial clauses in saturation : 220
% 0.32/0.43 % Processed clauses : 208
% 0.32/0.43 % ...of these trivial : 0
% 0.32/0.43 % ...subsumed : 0
% 0.32/0.43 % ...remaining for further processing : 208
% 0.32/0.43 % Other redundant clauses eliminated : 0
% 0.32/0.43 % Clauses deleted for lack of memory : 0
% 0.32/0.43 % Backward-subsumed : 0
% 0.32/0.43 % Backward-rewritten : 0
% 0.32/0.43 % Generated clauses : 3
% 0.32/0.43 % ...of the previous two non-redundant : 1
% 0.32/0.43 % ...aggressively subsumed : 0
% 0.32/0.43 % Contextual simplify-reflections : 0
% 0.32/0.43 % Paramodulations : 3
% 0.32/0.43 % Factorizations : 0
% 0.32/0.43 % NegExts : 0
% 0.32/0.43 % Equation resolutions : 0
% 0.32/0.43 % Disequality decompositions : 0
% 0.32/0.43 % Total rewrite steps : 1
% 0.32/0.43 % ...of those cached : 0
% 0.32/0.43 % Propositional unsat checks : 0
% 0.32/0.43 % Propositional check models : 0
% 0.32/0.43 % Propositional check unsatisfiable : 0
% 0.32/0.43 % Propositional clauses : 0
% 0.32/0.43 % Propositional clauses after purity: 0
% 0.32/0.43 % Propositional unsat core size : 0
% 0.32/0.43 % Propositional preprocessing time : 0.000
% 0.32/0.43 % Propositional encoding time : 0.000
% 0.32/0.43 % Propositional solver time : 0.000
% 0.32/0.43 % Success case prop preproc time : 0.000
% 0.32/0.43 % Success case prop encoding time : 0.000
% 0.32/0.43 % Success case prop solver time : 0.000
% 0.32/0.43 % Current number of processed clauses : 208
% 0.32/0.43 % Positive orientable unit clauses : 203
% 0.32/0.43 % Positive unorientable unit clauses: 0
% 0.32/0.43 % Negative unit clauses : 2
% 0.32/0.43 % Non-unit-clauses : 3
% 0.32/0.43 % Current number of unprocessed clauses: 13
% 0.32/0.43 % ...number of literals in the above : 39
% 0.32/0.43 % Current number of archived formulas : 0
% 0.32/0.43 % Current number of archived clauses : 0
% 0.32/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.32/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.32/0.43 % Non-unit clause-clause subsumptions : 0
% 0.32/0.43 % Unit Clause-clause subsumption calls : 0
% 0.32/0.43 % Rewrite failures with RHS unbound : 0
% 0.32/0.43 % BW rewrite match attempts : 0
% 0.32/0.43 % BW rewrite match successes : 0
% 0.32/0.43 % Condensation attempts : 0
% 0.32/0.43 % Condensation successes : 0
% 0.32/0.43 % Termbank termtop insertions : 15116
% 0.32/0.43 % Search garbage collected termcells : 6233
% 0.32/0.43
% 0.32/0.43 % -------------------------------------------------
% 0.32/0.43 % User time : 0.026 s
% 0.32/0.43 % System time : 0.009 s
% 0.32/0.43 % Total time : 0.035 s
% 0.32/0.43 % Maximum resident set size: 5928 pages
% 0.32/0.43
% 0.32/0.43 % -------------------------------------------------
% 0.32/0.43 % User time : 0.045 s
% 0.32/0.43 % System time : 0.019 s
% 0.32/0.43 % Total time : 0.064 s
% 0.32/0.43 % Maximum resident set size: 5376 pages
% 0.32/0.43 % E exiting
%------------------------------------------------------------------------------