%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU680^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:25:00 AM UTC 2026
% Result : Theorem 66.43s 10.12s
% Output : CNFRefutation 66.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 1145 ( 73 equ; 0 cnn)
% Maximal formula atoms : 286 ( 19 avg)
% Number of connectives : 2576 ( 88 ~; 106 |; 260 &;1431 @)
% ( 14 <=>; 677 =>; 0 <=; 0 <~>)
% Maximal formula depth : 256 ( 22 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 228 ( 225 usr; 201 con; 0-4 aty)
% Number of variables : 346 ( 104 ^; 214 !; 28 ?; 346 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_25,type,
setextAx: $o ).
thf(decl_26,type,
emptyset: $i ).
thf(decl_27,type,
emptysetAx: $o ).
thf(decl_28,type,
setadjoin: $i > $i > $i ).
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_43,type,
dsetconstr: $i > ( $i > $o ) > $i ).
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_110,type,
subset: $i > $i > $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_182,type,
cartprod: $i > $i > $i ).
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_199,type,
singleton: $i > $o ).
thf(decl_200,type,
singletonprop: $o ).
thf(decl_201,type,
ex1: $i > ( $i > $o ) > $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_235,type,
breln: $i > $i > $i > $o ).
thf(decl_236,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
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,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_257,type,
esk2_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_258,type,
esk3_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_259,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_260,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_261,type,
esk6_2: $i > ( $i > $o ) > $i ).
thf(decl_262,type,
esk7_3: $i > $i > $i > $i ).
thf(decl_263,type,
esk8_4: $i > $i > $i > $i > $i ).
thf(decl_264,type,
esk9_3: $i > $i > $i > $i ).
thf(decl_265,type,
esk10_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_266,type,
esk11_4: $i > $i > ( $i > $i ) > $i > $i ).
thf(decl_267,type,
esk12_0: $i ).
thf(decl_268,type,
esk13_0: $i ).
thf(decl_269,type,
esk14_0: $i > $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
& ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ex1 @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',breln) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.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/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',ex1I2) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',ex1I) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',ex1E1) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X33 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',lamp) ).
thf(lam2p,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
=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X34 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',lam2p) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',app) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',funcinfuncset) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X30 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.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/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p',lam) ).
thf(c_0_15,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X72: $i] :
( ( in @ X72
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X72 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_16,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_17,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X76: $i] :
( ( in @ X76
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X76 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_18,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_19,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X72: $i] :
( ( in @ X72
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X72 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,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_21,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_22,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_23,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_24,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X76: $i] :
( ( in @ X76
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X76 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
thf(c_0_25,plain,
( lamp
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_26,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
=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X34 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[lam2p]) ).
thf(c_0_27,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_20,c_0_18]) ).
thf(c_0_28,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 ) )
=> ? [X75: $i] :
( ( in @ X75
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X75 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_19]) ).
thf(c_0_29,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X74: $i] :
( ( in @ X74
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X74 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_19]) ).
thf(c_0_30,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X73: $i] :
( ( in @ X73
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X73 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_19]) ).
thf(c_0_31,axiom,
( app
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X77: $i] :
( ( in @ X77 @ X4 )
=> ? [X78: $i] :
( ( in @ X78
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X77 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X77 @ Z0 ) @ X30 ) )
= ( setadjoin @ X78 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[app,c_0_24]) ).
thf(c_0_32,plain,
( lamp
= ( ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( ( subset
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) )
@ ( cartprod @ X4 @ X5 ) )
& ! [X83: $i] :
( ( in @ X83 @ X4 )
=> ? [X84: $i] :
( ( in @ X84
@ ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X83 @ Z0 )
@ ( lam @ X4 @ X5
@ ^ [Z1: $i] : ( X33 @ Z1 ) ) ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X83 @ Z0 )
@ ( lam @ X4 @ X5
@ ^ [Z1: $i] : ( X33 @ Z1 ) ) ) )
= ( setadjoin @ X84 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_25,c_0_24]) ).
thf(c_0_33,axiom,
( funcinfuncset
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X81: $i] :
( ( in @ X81 @ X4 )
=> ? [X82: $i] :
( ( in @ X82
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X81 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X81 @ Z0 ) @ X30 ) )
= ( setadjoin @ X82 @ emptyset ) ) ) ) )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcinfuncset,c_0_24]) ).
thf(c_0_34,axiom,
( infuncsetfunc
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X79: $i] :
( ( in @ X79 @ X4 )
=> ? [X80: $i] :
( ( in @ X80
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X79 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X79 @ Z0 ) @ X30 ) )
= ( setadjoin @ X80 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[infuncsetfunc,c_0_24]) ).
thf(c_0_35,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
=> ( ! [X85: $i,X86: $i > $o] :
( ? [X87: $i] :
( ( in @ X87 @ ( dsetconstr @ X85 @ X86 ) )
& ( ( dsetconstr @ X85 @ X86 )
= ( setadjoin @ X87 @ emptyset ) ) )
=> ? [X88: $i] :
( ( in @ X88 @ X85 )
& ( X86 @ X88 ) ) )
=> ( ! [X89: $i,X90: $i > $o,X91: $i] :
( ( in @ X91 @ X89 )
=> ( ( X90 @ X91 )
=> ( ! [X92: $i] :
( ( in @ X92 @ X89 )
=> ( ( X90 @ X92 )
=> ( X92 = X91 ) ) )
=> ? [X93: $i] :
( ( in @ X93 @ ( dsetconstr @ X89 @ X90 ) )
& ( ( dsetconstr @ X89 @ X90 )
= ( setadjoin @ X93 @ emptyset ) ) ) ) ) )
=> ( ! [X94: $i,X95: $i > $o] :
( ! [X96: $i] :
( ( in @ X96 @ X94 )
=> ! [X97: $i] :
( ( in @ X97 @ X94 )
=> ( ( X95 @ X96 )
=> ( ( X95 @ X97 )
=> ( X96 = X97 ) ) ) ) )
=> ( ? [X98: $i] :
( ( in @ X98 @ X94 )
& ( X95 @ X98 ) )
=> ? [X99: $i] :
( ( in @ X99 @ ( dsetconstr @ X94 @ X95 ) )
& ( ( dsetconstr @ X94 @ X95 )
= ( setadjoin @ X99 @ emptyset ) ) ) ) )
=> ( 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
=> ( ! [X100: $i,X101: $i,X102: $i > $i > $o] : ( subset @ ( dpsetconstr @ X100 @ X101 @ X102 ) @ ( cartprod @ X100 @ X101 ) )
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( ! [X103: $i,X104: $i,X105: $i] :
( ( ( subset @ X105 @ ( cartprod @ X103 @ X104 ) )
& ! [X106: $i] :
( ( in @ X106 @ X103 )
=> ? [X107: $i] :
( ( in @ X107
@ ( dsetconstr @ X104
@ ^ [Z0: $i] : ( in @ ( kpair @ X106 @ Z0 ) @ X105 ) ) )
& ( ( dsetconstr @ X104
@ ^ [Z0: $i] : ( in @ ( kpair @ X106 @ Z0 ) @ X105 ) )
= ( setadjoin @ X107 @ emptyset ) ) ) ) )
=> ! [X108: $i] :
( ( in @ X108 @ X103 )
=> ( in @ ( ap @ X103 @ X104 @ X105 @ X108 ) @ X104 ) ) )
=> ( ! [X109: $i,X110: $i,X111: $i] :
( ( in @ X111 @ ( funcSet @ X109 @ X110 ) )
=> ( ( subset @ X111 @ ( cartprod @ X109 @ X110 ) )
& ! [X112: $i] :
( ( in @ X112 @ X109 )
=> ? [X113: $i] :
( ( in @ X113
@ ( dsetconstr @ X110
@ ^ [Z0: $i] : ( in @ ( kpair @ X112 @ Z0 ) @ X111 ) ) )
& ( ( dsetconstr @ X110
@ ^ [Z0: $i] : ( in @ ( kpair @ X112 @ Z0 ) @ X111 ) )
= ( setadjoin @ X113 @ emptyset ) ) ) ) ) )
=> ( ! [X114: $i,X115: $i,X116: $i] :
( ( in @ X116 @ ( funcSet @ X114 @ X115 ) )
=> ! [X117: $i] :
( ( in @ X117 @ X114 )
=> ( in @ ( ap @ X114 @ X115 @ X116 @ X117 ) @ X115 ) ) )
=> ( ! [X118: $i,X119: $i,X120: $i] :
( ( ( subset @ X120 @ ( cartprod @ X118 @ X119 ) )
& ! [X121: $i] :
( ( in @ X121 @ X118 )
=> ? [X122: $i] :
( ( in @ X122
@ ( dsetconstr @ X119
@ ^ [Z0: $i] : ( in @ ( kpair @ X121 @ Z0 ) @ X120 ) ) )
& ( ( dsetconstr @ X119
@ ^ [Z0: $i] : ( in @ ( kpair @ X121 @ Z0 ) @ X120 ) )
= ( setadjoin @ X122 @ emptyset ) ) ) ) )
=> ( in @ X120 @ ( funcSet @ X118 @ X119 ) ) )
=> ( lamProp
=> ( ! [X123: $i,X124: $i,X125: $i > $i] :
( ! [X126: $i] :
( ( in @ X126 @ X123 )
=> ( in @ ( X125 @ X126 ) @ X124 ) )
=> ( ( subset @ ( lam @ X123 @ X124 @ X125 ) @ ( cartprod @ X123 @ X124 ) )
& ! [X127: $i] :
( ( in @ X127 @ X123 )
=> ? [X128: $i] :
( ( in @ X128
@ ( dsetconstr @ X124
@ ^ [Z0: $i] : ( in @ ( kpair @ X127 @ Z0 ) @ ( lam @ X123 @ X124 @ X125 ) ) ) )
& ( ( dsetconstr @ X124
@ ^ [Z0: $i] : ( in @ ( kpair @ X127 @ Z0 ) @ ( lam @ X123 @ X124 @ X125 ) ) )
= ( setadjoin @ X128 @ emptyset ) ) ) ) ) )
=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in @ ( lam @ X4 @ X5 @ X34 ) @ ( funcSet @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),ap2p]),c_0_34])]) ).
thf(c_0_36,plain,
( lam
= ( ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( dpsetconstr @ Z0 @ Z1
@ ^ [Z3: $i] : ( $eq @ ( Z2 @ Z3 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[lam])]) ).
thf(c_0_37,negated_conjecture,
! [X129: $i,X130: $i > $o,X131: $i,X133: $i,X134: $i > $o,X135: $i,X138: $i,X139: $i > $o,X142: $i,X144: $i,X145: $i,X146: $i > $i > $o,X147: $i,X148: $i,X149: $i,X151: $i,X152: $i,X153: $i,X154: $i,X155: $i,X156: $i,X158: $i,X159: $i,X160: $i,X161: $i,X162: $i,X163: $i,X164: $i,X166: $i,X167: $i,X168: $i,X169: $i > $i,X171: $i,X176: $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
& ( ( in @ ( esk1_2 @ X129 @ X130 ) @ X129 )
| ~ ( in @ X131 @ ( dsetconstr @ X129 @ X130 ) )
| ( ( dsetconstr @ X129 @ X130 )
!= ( setadjoin @ X131 @ emptyset ) ) )
& ( ( X130 @ ( esk1_2 @ X129 @ X130 ) )
| ~ ( in @ X131 @ ( dsetconstr @ X129 @ X130 ) )
| ( ( dsetconstr @ X129 @ X130 )
!= ( setadjoin @ X131 @ emptyset ) ) )
& ( ( in @ ( esk3_3 @ X133 @ X134 @ X135 ) @ ( dsetconstr @ X133 @ X134 ) )
| ( in @ ( esk2_3 @ X133 @ X134 @ X135 ) @ X133 )
| ~ ( X134 @ X135 )
| ~ ( in @ X135 @ X133 ) )
& ( ( ( dsetconstr @ X133 @ X134 )
= ( setadjoin @ ( esk3_3 @ X133 @ X134 @ X135 ) @ emptyset ) )
| ( in @ ( esk2_3 @ X133 @ X134 @ X135 ) @ X133 )
| ~ ( X134 @ X135 )
| ~ ( in @ X135 @ X133 ) )
& ( ( in @ ( esk3_3 @ X133 @ X134 @ X135 ) @ ( dsetconstr @ X133 @ X134 ) )
| ( X134 @ ( esk2_3 @ X133 @ X134 @ X135 ) )
| ~ ( X134 @ X135 )
| ~ ( in @ X135 @ X133 ) )
& ( ( ( dsetconstr @ X133 @ X134 )
= ( setadjoin @ ( esk3_3 @ X133 @ X134 @ X135 ) @ emptyset ) )
| ( X134 @ ( esk2_3 @ X133 @ X134 @ X135 ) )
| ~ ( X134 @ X135 )
| ~ ( in @ X135 @ X133 ) )
& ( ( in @ ( esk3_3 @ X133 @ X134 @ X135 ) @ ( dsetconstr @ X133 @ X134 ) )
| ( ( esk2_3 @ X133 @ X134 @ X135 )
!= X135 )
| ~ ( X134 @ X135 )
| ~ ( in @ X135 @ X133 ) )
& ( ( ( dsetconstr @ X133 @ X134 )
= ( setadjoin @ ( esk3_3 @ X133 @ X134 @ X135 ) @ emptyset ) )
| ( ( esk2_3 @ X133 @ X134 @ X135 )
!= X135 )
| ~ ( X134 @ X135 )
| ~ ( in @ X135 @ X133 ) )
& ( ( in @ ( esk6_2 @ X138 @ X139 ) @ ( dsetconstr @ X138 @ X139 ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( in @ ( esk4_2 @ X138 @ X139 ) @ X138 ) )
& ( ( ( dsetconstr @ X138 @ X139 )
= ( setadjoin @ ( esk6_2 @ X138 @ X139 ) @ emptyset ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( in @ ( esk4_2 @ X138 @ X139 ) @ X138 ) )
& ( ( in @ ( esk6_2 @ X138 @ X139 ) @ ( dsetconstr @ X138 @ X139 ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( in @ ( esk5_2 @ X138 @ X139 ) @ X138 ) )
& ( ( ( dsetconstr @ X138 @ X139 )
= ( setadjoin @ ( esk6_2 @ X138 @ X139 ) @ emptyset ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( in @ ( esk5_2 @ X138 @ X139 ) @ X138 ) )
& ( ( in @ ( esk6_2 @ X138 @ X139 ) @ ( dsetconstr @ X138 @ X139 ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( X139 @ ( esk4_2 @ X138 @ X139 ) ) )
& ( ( ( dsetconstr @ X138 @ X139 )
= ( setadjoin @ ( esk6_2 @ X138 @ X139 ) @ emptyset ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( X139 @ ( esk4_2 @ X138 @ X139 ) ) )
& ( ( in @ ( esk6_2 @ X138 @ X139 ) @ ( dsetconstr @ X138 @ X139 ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( X139 @ ( esk5_2 @ X138 @ X139 ) ) )
& ( ( ( dsetconstr @ X138 @ X139 )
= ( setadjoin @ ( esk6_2 @ X138 @ X139 ) @ emptyset ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( X139 @ ( esk5_2 @ X138 @ X139 ) ) )
& ( ( in @ ( esk6_2 @ X138 @ X139 ) @ ( dsetconstr @ X138 @ X139 ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( ( esk4_2 @ X138 @ X139 )
!= ( esk5_2 @ X138 @ X139 ) ) )
& ( ( ( dsetconstr @ X138 @ X139 )
= ( setadjoin @ ( esk6_2 @ X138 @ X139 ) @ emptyset ) )
| ~ ( in @ X142 @ X138 )
| ~ ( X139 @ X142 )
| ( ( esk4_2 @ X138 @ X139 )
!= ( esk5_2 @ X138 @ X139 ) ) )
& 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
& ( subset @ ( dpsetconstr @ X144 @ X145 @ X146 ) @ ( cartprod @ X144 @ X145 ) )
& dpsetconstrERa
& dpsetconstrEL1
& dpsetconstrEL2
& dpsetconstrER
& funcImageSingleton
& apProp
& ( ( in @ ( esk7_3 @ X147 @ X148 @ X149 ) @ X147 )
| ~ ( subset @ X149 @ ( cartprod @ X147 @ X148 ) )
| ~ ( in @ X152 @ X147 )
| ( in @ ( ap @ X147 @ X148 @ X149 @ X152 ) @ X148 ) )
& ( ~ ( in @ X151
@ ( dsetconstr @ X148
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk7_3 @ X147 @ X148 @ X149 ) @ Z0 ) @ X149 ) ) )
| ( ( dsetconstr @ X148
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk7_3 @ X147 @ X148 @ X149 ) @ Z0 ) @ X149 ) )
!= ( setadjoin @ X151 @ emptyset ) )
| ~ ( subset @ X149 @ ( cartprod @ X147 @ X148 ) )
| ~ ( in @ X152 @ X147 )
| ( in @ ( ap @ X147 @ X148 @ X149 @ X152 ) @ X148 ) )
& ( ( subset @ X155 @ ( cartprod @ X153 @ X154 ) )
| ~ ( in @ X155 @ ( funcSet @ X153 @ X154 ) ) )
& ( ( in @ ( esk8_4 @ X153 @ X154 @ X155 @ X156 )
@ ( dsetconstr @ X154
@ ^ [Z0: $i] : ( in @ ( kpair @ X156 @ Z0 ) @ X155 ) ) )
| ~ ( in @ X156 @ X153 )
| ~ ( in @ X155 @ ( funcSet @ X153 @ X154 ) ) )
& ( ( ( dsetconstr @ X154
@ ^ [Z0: $i] : ( in @ ( kpair @ X156 @ Z0 ) @ X155 ) )
= ( setadjoin @ ( esk8_4 @ X153 @ X154 @ X155 @ X156 ) @ emptyset ) )
| ~ ( in @ X156 @ X153 )
| ~ ( in @ X155 @ ( funcSet @ X153 @ X154 ) ) )
& ( ~ ( in @ X160 @ ( funcSet @ X158 @ X159 ) )
| ~ ( in @ X161 @ X158 )
| ( in @ ( ap @ X158 @ X159 @ X160 @ X161 ) @ X159 ) )
& ( ( in @ ( esk9_3 @ X162 @ X163 @ X164 ) @ X162 )
| ~ ( subset @ X164 @ ( cartprod @ X162 @ X163 ) )
| ( in @ X164 @ ( funcSet @ X162 @ X163 ) ) )
& ( ~ ( in @ X166
@ ( dsetconstr @ X163
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk9_3 @ X162 @ X163 @ X164 ) @ Z0 ) @ X164 ) ) )
| ( ( dsetconstr @ X163
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk9_3 @ X162 @ X163 @ X164 ) @ Z0 ) @ X164 ) )
!= ( setadjoin @ X166 @ emptyset ) )
| ~ ( subset @ X164 @ ( cartprod @ X162 @ X163 ) )
| ( in @ X164 @ ( funcSet @ X162 @ X163 ) ) )
& lamProp
& ( ( subset @ ( lam @ X167 @ X168 @ X169 ) @ ( cartprod @ X167 @ X168 ) )
| ( in @ ( esk10_3 @ X167 @ X168 @ X169 ) @ X167 ) )
& ( ( in @ ( esk11_4 @ X167 @ X168 @ X169 @ X171 )
@ ( dsetconstr @ X168
@ ^ [Z0: $i] : ( in @ ( kpair @ X171 @ Z0 ) @ ( lam @ X167 @ X168 @ X169 ) ) ) )
| ~ ( in @ X171 @ X167 )
| ( in @ ( esk10_3 @ X167 @ X168 @ X169 ) @ X167 ) )
& ( ( ( dsetconstr @ X168
@ ^ [Z0: $i] : ( in @ ( kpair @ X171 @ Z0 ) @ ( lam @ X167 @ X168 @ X169 ) ) )
= ( setadjoin @ ( esk11_4 @ X167 @ X168 @ X169 @ X171 ) @ emptyset ) )
| ~ ( in @ X171 @ X167 )
| ( in @ ( esk10_3 @ X167 @ X168 @ X169 ) @ X167 ) )
& ( ( subset @ ( lam @ X167 @ X168 @ X169 ) @ ( cartprod @ X167 @ X168 ) )
| ~ ( in @ ( X169 @ ( esk10_3 @ X167 @ X168 @ X169 ) ) @ X168 ) )
& ( ( in @ ( esk11_4 @ X167 @ X168 @ X169 @ X171 )
@ ( dsetconstr @ X168
@ ^ [Z0: $i] : ( in @ ( kpair @ X171 @ Z0 ) @ ( lam @ X167 @ X168 @ X169 ) ) ) )
| ~ ( in @ X171 @ X167 )
| ~ ( in @ ( X169 @ ( esk10_3 @ X167 @ X168 @ X169 ) ) @ X168 ) )
& ( ( ( dsetconstr @ X168
@ ^ [Z0: $i] : ( in @ ( kpair @ X171 @ Z0 ) @ ( lam @ X167 @ X168 @ X169 ) ) )
= ( setadjoin @ ( esk11_4 @ X167 @ X168 @ X169 @ X171 ) @ emptyset ) )
| ~ ( in @ X171 @ X167 )
| ~ ( in @ ( X169 @ ( esk10_3 @ X167 @ X168 @ X169 ) ) @ X168 ) )
& ( ~ ( in @ X176 @ esk12_0 )
| ( in @ ( esk14_0 @ X176 ) @ esk13_0 ) )
& ~ ( in @ ( lam @ esk12_0 @ esk13_0 @ esk14_0 ) @ ( funcSet @ esk12_0 @ esk13_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_35])])])])])]) ).
thf(c_0_38,plain,
( lam
= ( ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( dpsetconstr @ Z0 @ Z1
@ ^ [Z3: $i] : ( $eq @ ( Z2 @ Z3 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_39,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_37]) ).
thf(c_0_40,plain,
! [X2: $i,X3: $i,X31: $i > $i] :
( ( dpsetconstr @ X2 @ X3
@ ^ [Z0: $i] : ( $eq @ ( X31 @ Z0 ) ) )
= ( lam @ X2 @ X3 @ X31 ) ),
inference(arg_cong,[status(thm)],[c_0_38]) ).
thf(c_0_41,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X3: $i] :
( ( in @ X5 @ ( funcSet @ X4 @ X3 ) )
| ~ ( in @ X2
@ ( dsetconstr @ X3
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk9_3 @ X4 @ X3 @ X5 ) @ Z0 ) @ X5 ) ) )
| ( ( dsetconstr @ X3
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk9_3 @ X4 @ X3 @ X5 ) @ Z0 ) @ X5 ) )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( subset @ X5 @ ( cartprod @ X4 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_42,negated_conjecture,
! [X2: $i,X4: $i,X31: $i > $i,X3: $i] :
( ( in @ ( esk11_4 @ X2 @ X3 @ X31 @ X4 )
@ ( dsetconstr @ X3
@ ^ [Z0: $i] : ( in @ ( kpair @ X4 @ Z0 ) @ ( lam @ X2 @ X3 @ X31 ) ) ) )
| ~ ( in @ X4 @ X2 )
| ~ ( in @ ( X31 @ ( esk10_3 @ X2 @ X3 @ X31 ) ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_43,negated_conjecture,
! [X4: $i,X31: $i > $i,X3: $i,X2: $i] :
( ( ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ ( lam @ X4 @ X2 @ X31 ) ) )
= ( setadjoin @ ( esk11_4 @ X4 @ X2 @ X31 @ X3 ) @ emptyset ) )
| ~ ( in @ X3 @ X4 )
| ~ ( in @ ( X31 @ ( esk10_3 @ X4 @ X2 @ X31 ) ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_44,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk9_3 @ X2 @ X3 @ X4 ) @ X2 )
| ( in @ X4 @ ( funcSet @ X2 @ X3 ) )
| ~ ( subset @ X4 @ ( cartprod @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_45,negated_conjecture,
! [X2: $i,X31: $i > $i,X3: $i] : ( subset @ ( lam @ X2 @ X3 @ X31 ) @ ( cartprod @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_46,negated_conjecture,
! [X2: $i,X31: $i > $i,X4: $i,X3: $i] :
( ( in @ ( lam @ X2 @ X3 @ X31 ) @ ( funcSet @ X4 @ X3 ) )
| ~ ( in @ ( esk9_3 @ X4 @ X3 @ ( lam @ X2 @ X3 @ X31 ) ) @ X2 )
| ~ ( subset @ ( lam @ X2 @ X3 @ X31 ) @ ( cartprod @ X4 @ X3 ) )
| ~ ( in @ ( X31 @ ( esk10_3 @ X2 @ X3 @ X31 ) ) @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
thf(c_0_47,negated_conjecture,
! [X2: $i,X31: $i > $i,X3: $i] :
( ( in @ ( esk9_3 @ X2 @ X3 @ ( lam @ X2 @ X3 @ X31 ) ) @ X2 )
| ( in @ ( lam @ X2 @ X3 @ X31 ) @ ( funcSet @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_48,negated_conjecture,
! [X3: $i,X31: $i > $i,X4: $i,X2: $i] :
( ( in @ ( esk11_4 @ X2 @ X3 @ X31 @ X4 )
@ ( dsetconstr @ X3
@ ^ [Z0: $i] : ( in @ ( kpair @ X4 @ Z0 ) @ ( lam @ X2 @ X3 @ X31 ) ) ) )
| ( in @ ( esk10_3 @ X2 @ X3 @ X31 ) @ X2 )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_49,negated_conjecture,
! [X2: $i,X3: $i,X31: $i > $i,X4: $i] :
( ( ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ ( lam @ X4 @ X2 @ X31 ) ) )
= ( setadjoin @ ( esk11_4 @ X4 @ X2 @ X31 @ X3 ) @ emptyset ) )
| ( in @ ( esk10_3 @ X4 @ X2 @ X31 ) @ X4 )
| ~ ( in @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_50,negated_conjecture,
! [X2: $i,X31: $i > $i,X3: $i] :
( ( in @ ( lam @ X2 @ X3 @ X31 ) @ ( funcSet @ X2 @ X3 ) )
| ~ ( in @ ( X31 @ ( esk10_3 @ X2 @ X3 @ X31 ) ) @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_45])]) ).
thf(c_0_51,negated_conjecture,
! [X2: $i] :
( ( in @ ( esk14_0 @ X2 ) @ esk13_0 )
| ~ ( in @ X2 @ esk12_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_52,negated_conjecture,
! [X2: $i,X31: $i > $i,X4: $i,X3: $i] :
( ( in @ ( lam @ X2 @ X3 @ X31 ) @ ( funcSet @ X4 @ X3 ) )
| ( in @ ( esk10_3 @ X2 @ X3 @ X31 ) @ X2 )
| ~ ( in @ ( esk9_3 @ X4 @ X3 @ ( lam @ X2 @ X3 @ X31 ) ) @ X2 )
| ~ ( subset @ ( lam @ X2 @ X3 @ X31 ) @ ( cartprod @ X4 @ X3 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_49]) ).
thf(c_0_53,negated_conjecture,
~ ( in @ ( lam @ esk12_0 @ esk13_0 @ esk14_0 ) @ ( funcSet @ esk12_0 @ esk13_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_54,negated_conjecture,
! [X2: $i] :
( ( in @ ( lam @ X2 @ esk13_0 @ esk14_0 ) @ ( funcSet @ X2 @ esk13_0 ) )
| ~ ( in @ ( esk10_3 @ X2 @ esk13_0 @ esk14_0 ) @ esk12_0 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_55,negated_conjecture,
! [X31: $i > $i,X3: $i,X2: $i] :
( ( in @ ( lam @ X2 @ X3 @ X31 ) @ ( funcSet @ X2 @ X3 ) )
| ( in @ ( esk10_3 @ X2 @ X3 @ X31 ) @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_47]),c_0_45])]) ).
thf(c_0_56,negated_conjecture,
~ ( in @ ( esk10_3 @ esk12_0 @ esk13_0 @ esk14_0 ) @ esk12_0 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_55]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU680^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n020.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 14:08:49 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.33 Running higher-order theorem proving
% 0.25/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.8nNWDAbnau/E---3.1_1109365.p
% 66.43/10.12 % Version: 3.5.1-ho
% 66.43/10.12 % Preprocessing class: HSLMSLSSLLLCHSA.
% 66.43/10.12 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 66.43/10.12 % Starting ho_unfolding_5 with 1200s (4) cores
% 66.43/10.12 % Starting pre_casc_3 with 300s (1) cores
% 66.43/10.12 % Starting new_ho_10_cnf2 with 300s (1) cores
% 66.43/10.12 % Starting full_lambda_10 with 300s (1) cores
% 66.43/10.12 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 66.43/10.12 % full_lambda_10 with pid 1109381 completed with status 0
% 66.43/10.12 % Result found by full_lambda_10
% 66.43/10.12 % Preprocessing class: HSLMSLSSLLLCHSA.
% 66.43/10.12 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 66.43/10.12 % Starting ho_unfolding_5 with 1200s (4) cores
% 66.43/10.12 % Starting pre_casc_3 with 300s (1) cores
% 66.43/10.12 % Starting new_ho_10_cnf2 with 300s (1) cores
% 66.43/10.12 % Starting full_lambda_10 with 300s (1) cores
% 66.43/10.12 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 66.43/10.12 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 66.43/10.12 % Search class: HGUSF-FFMM32-DHSMMFBN
% 66.43/10.12 % partial match(5): HGHSM-FMLM32-MHSMMFBN
% 66.43/10.12 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 66.43/10.12 % Starting SubtermCWHack with 28s (1) cores
% 66.43/10.12 % SubtermCWHack with pid 1109383 completed with status 0
% 66.43/10.12 % Result found by SubtermCWHack
% 66.43/10.12 % Preprocessing class: HSLMSLSSLLLCHSA.
% 66.43/10.12 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 66.43/10.12 % Starting ho_unfolding_5 with 1200s (4) cores
% 66.43/10.12 % Starting pre_casc_3 with 300s (1) cores
% 66.43/10.12 % Starting new_ho_10_cnf2 with 300s (1) cores
% 66.43/10.12 % Starting full_lambda_10 with 300s (1) cores
% 66.43/10.12 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 66.43/10.12 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 66.43/10.12 % Search class: HGUSF-FFMM32-DHSMMFBN
% 66.43/10.12 % partial match(5): HGHSM-FMLM32-MHSMMFBN
% 66.43/10.12 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 66.43/10.12 % Starting SubtermCWHack with 28s (1) cores
% 66.43/10.12 % Preprocessing time : 0.005 s
% 66.43/10.12
% 66.43/10.12 % Proof found!
% 66.43/10.12 % SZS status Theorem
% 66.43/10.12 % SZS output start CNFRefutation
% See solution above
% 66.43/10.12 % Parsed axioms : 438
% 66.43/10.12 % Removed by relevancy pruning/SinE : 422
% 66.43/10.12 % Initial clauses : 224
% 66.43/10.12 % Removed in clause preprocessing : 0
% 66.43/10.12 % Initial clauses in saturation : 224
% 66.43/10.12 % Processed clauses : 2003
% 66.43/10.12 % ...of these trivial : 5
% 66.43/10.12 % ...subsumed : 943
% 66.43/10.12 % ...remaining for further processing : 1055
% 66.43/10.12 % Other redundant clauses eliminated : 0
% 66.43/10.12 % Clauses deleted for lack of memory : 0
% 66.43/10.12 % Backward-subsumed : 31
% 66.43/10.12 % Backward-rewritten : 0
% 66.43/10.12 % Generated clauses : 62259
% 66.43/10.12 % ...of the previous two non-redundant : 62255
% 66.43/10.12 % ...aggressively subsumed : 0
% 66.43/10.12 % Contextual simplify-reflections : 18
% 66.43/10.12 % Paramodulations : 62237
% 66.43/10.12 % Factorizations : 0
% 66.43/10.12 % NegExts : 0
% 66.43/10.12 % Equation resolutions : 0
% 66.43/10.12 % Disequality decompositions : 0
% 66.43/10.12 % Total rewrite steps : 14
% 66.43/10.12 % ...of those cached : 7
% 66.43/10.12 % Propositional unsat checks : 0
% 66.43/10.12 % Propositional check models : 0
% 66.43/10.12 % Propositional check unsatisfiable : 0
% 66.43/10.12 % Propositional clauses : 0
% 66.43/10.12 % Propositional clauses after purity: 0
% 66.43/10.12 % Propositional unsat core size : 0
% 66.43/10.12 % Propositional preprocessing time : 0.000
% 66.43/10.12 % Propositional encoding time : 0.000
% 66.43/10.12 % Propositional solver time : 0.000
% 66.43/10.12 % Success case prop preproc time : 0.000
% 66.43/10.12 % Success case prop encoding time : 0.000
% 66.43/10.12 % Success case prop solver time : 0.000
% 66.43/10.12 % Current number of processed clauses : 1024
% 66.43/10.12 % Positive orientable unit clauses : 194
% 66.43/10.12 % Positive unorientable unit clauses: 8
% 66.43/10.12 % Negative unit clauses : 2
% 66.43/10.12 % Non-unit-clauses : 820
% 66.43/10.12 % Current number of unprocessed clauses: 60245
% 66.43/10.12 % ...number of literals in the above : 417656
% 66.43/10.12 % Current number of archived formulas : 0
% 66.43/10.12 % Current number of archived clauses : 31
% 66.43/10.12 % Clause-clause subsumption calls (NU) : 94948
% 66.43/10.12 % Rec. Clause-clause subsumption calls : 9053
% 66.43/10.12 % Non-unit clause-clause subsumptions : 951
% 66.43/10.12 % Unit Clause-clause subsumption calls : 120
% 66.43/10.12 % Rewrite failures with RHS unbound : 1362
% 66.43/10.12 % BW rewrite match attempts : 75
% 66.43/10.12 % BW rewrite match successes : 8
% 66.43/10.12 % Condensation attempts : 0
% 66.43/10.12 % Condensation successes : 0
% 66.43/10.12 % Termbank termtop insertions : 14756545
% 66.43/10.12 % Search garbage collected termcells : 6395
% 66.43/10.12
% 66.43/10.12 % -------------------------------------------------
% 66.43/10.12 % User time : 9.369 s
% 66.43/10.12 % System time : 0.143 s
% 66.43/10.12 % Total time : 9.512 s
% 66.43/10.12 % Maximum resident set size: 5576 pages
% 66.43/10.12
% 66.43/10.12 % -------------------------------------------------
% 66.43/10.12 % User time : 9.388 s
% 66.43/10.12 % System time : 0.152 s
% 66.43/10.12 % Total time : 9.540 s
% 66.43/10.12 % Maximum resident set size: 5376 pages
% 66.43/10.12 % E exiting
%------------------------------------------------------------------------------