%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU692^1 : 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 : n007.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 08:25:13 AM UTC 2026
% Result : Theorem 117.27s 17.54s
% Output : CNFRefutation 117.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 43
% Syntax : Number of formulae : 76 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 1406 ( 84 equ; 0 cnn)
% Maximal formula atoms : 404 ( 18 avg)
% Number of connectives : 3889 ( 147 ~; 181 |; 246 &;2405 @)
% ( 53 <=>; 857 =>; 0 <=; 0 <~>)
% Maximal formula depth : 390 ( 23 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 250 ( 247 usr; 215 con; 0-4 aty)
% Number of variables : 632 ( 55 ^; 573 !; 4 ?; 632 :)
% 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_32,type,
setunion: $i > $i ).
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_175,type,
iskpair: $i > $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_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_213,type,
kfst: $i > $i ).
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_225,type,
ksnd: $i > $i ).
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,
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,
esk1_3: $i > $i > $i > $i ).
thf(decl_269,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_270,type,
esk3_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_271,type,
esk4_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_272,type,
esk5_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_273,type,
esk6_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_274,type,
esk7_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_275,type,
esk8_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_276,type,
esk9_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_277,type,
esk10_4: $i > $i > $i > $i > $i ).
thf(decl_278,type,
esk11_4: $i > $i > $i > $i > $i ).
thf(decl_279,type,
esk12_4: $i > $i > $i > $i > $i ).
thf(decl_280,type,
esk13_4: $i > $i > $i > $i > $i ).
thf(decl_281,type,
esk14_4: $i > $i > $i > $i > $i ).
thf(decl_282,type,
esk15_4: $i > $i > $i > $i > $i ).
thf(decl_283,type,
esk16_4: $i > $i > $i > $i > $i ).
thf(decl_284,type,
esk17_4: $i > $i > $i > $i > $i ).
thf(decl_285,type,
esk18_0: $i ).
thf(decl_286,type,
esk19_0: $i ).
thf(decl_287,type,
esk20_0: $i ).
thf(decl_288,type,
esk21_0: $i ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.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.xJ2tyjYAEF/E---3.1_3423716.p',setOfPairsIsBReln) ).
thf(funcext2,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
=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( in @ X35 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ( X29 = X35 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',funcext2) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',ksndsingleton) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',kfstsingleton) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X34: $i] :
( ( breln @ X4 @ X5 @ X34 )
=> ! [X36: $i] :
( ( breln @ X4 @ X5 @ X36 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X36 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X36 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X34 ) ) ) )
=> ( X34 = X36 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',eqbreln) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X34: $i] :
( ( breln @ X4 @ X5 @ X34 )
=> ! [X36: $i] :
( ( breln @ X4 @ X5 @ X36 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X36 ) ) ) )
=> ( subset @ X34 @ X36 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',subbreln) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X34: $i] :
( ( breln @ X4 @ X5 @ X34 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X34 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',brelnall2) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X34: $i] :
( ( breln @ X4 @ X5 @ X34 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X34 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',brelnall1) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',lamProp) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',dpsetconstrER) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',dpsetconstrEL2) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',dpsetconstrEL1) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',dpsetconstrERa) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',dpsetconstrSub) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',dpsetconstrI) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X33 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',lam2p) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodsndpairEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',ksndpairEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodfstpairEq) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',kfstpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',kpairsurjEq) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',kpairp) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',kpairiskpair) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodpairsurjEq) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodpairmemER) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodpairmemEL) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodsndin) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodfstin) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodmempair) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodmempair1) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',cartprodpairin) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',funcinfuncset) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',infuncsetfunc) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X35: $i] :
( ( func @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ( X29 = X35 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',funcext) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',funcGraphProp4) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X35: $i] :
( ( func @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',funcextLem) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',funcGraphProp2) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',funcGraphProp3) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',funcGraphProp1) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',ap2p) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xJ2tyjYAEF/E---3.1_3423716.p',app) ).
thf(c_0_43,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_44,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_45,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
=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( in @ X35 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ( X29 = X35 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcext2]) ).
thf(c_0_46,plain,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ksndsingleton]) ).
thf(c_0_47,plain,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_48,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X34: $i] :
( ( subset @ X34 @ ( cartprod @ X4 @ X5 ) )
=> ! [X36: $i] :
( ( subset @ X36 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X36 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X36 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X34 ) ) ) )
=> ( X34 = X36 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_43]) ).
thf(c_0_49,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X34: $i] :
( ( subset @ X34 @ ( cartprod @ X4 @ X5 ) )
=> ! [X36: $i] :
( ( subset @ X36 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X36 ) ) ) )
=> ( subset @ X34 @ X36 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_43]) ).
thf(c_0_50,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X34: $i] :
( ( subset @ X34 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X34 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_43]) ).
thf(c_0_51,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X34: $i] :
( ( subset @ X34 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X34 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_43]) ).
thf(c_0_52,plain,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X30 @ Z0 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamProp]) ).
thf(c_0_53,plain,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X28 @ Z0 @ Z1 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrER]) ).
thf(c_0_54,plain,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X27 @ Z0 @ Z1 ) ) )
=> ( in @ X3 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL2]) ).
thf(c_0_55,plain,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X26 @ Z0 @ Z1 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL1]) ).
thf(c_0_56,plain,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X25 @ Z0 @ Z1 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrERa]) ).
thf(c_0_57,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_44,c_0_43]) ).
thf(c_0_58,plain,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X23 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrSub]) ).
thf(c_0_59,plain,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X22 @ Z0 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrI]) ).
thf(c_0_60,plain,
( lamp
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X32 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_61,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_62,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
=> ( ! [X205: $i,X206: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X205 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X205 @ ( setadjoin @ X206 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X207: $i,X208: $i] : ( iskpair @ ( kpair @ X207 @ X208 ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( ! [X209: $i,X210: $i,X211: $i] :
( ( in @ X211 @ X209 )
=> ! [X212: $i] :
( ( in @ X212 @ X210 )
=> ( in @ ( kpair @ X211 @ X212 ) @ ( cartprod @ X209 @ X210 ) ) ) )
=> ( ! [X213: $i,X214: $i,X215: $i] :
( ( in @ X215 @ ( cartprod @ X213 @ X214 ) )
=> ? [X216: $i] :
( ( in @ X216 @ X213 )
& ? [X217: $i] :
( ( in @ X217 @ X214 )
& ( X215
= ( kpair @ X216 @ X217 ) ) ) ) )
=> ( ! [X218: $i,X219: $i,X220: $i] :
( ( in @ X220 @ ( cartprod @ X218 @ X219 ) )
=> ( iskpair @ X220 ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X221: $i] :
( ( iskpair @ X221 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X221 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X221 ) ) ) )
=> ( theprop
=> ( ! [X222: $i,X223: $i] :
( ( kfst @ ( kpair @ X222 @ X223 ) )
= X222 )
=> ( ! [X224: $i,X225: $i,X226: $i] :
( ( in @ X226 @ ( cartprod @ X224 @ X225 ) )
=> ( in @ ( kfst @ X226 ) @ X224 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X227: $i] :
( ( iskpair @ X227 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X227 )
@ ^ [Z0: $i] :
( X227
= ( kpair @ ( kfst @ X227 ) @ Z0 ) ) ) ) )
=> ( ! [X228: $i,X229: $i] :
( ( ksnd @ ( kpair @ X228 @ X229 ) )
= X229 )
=> ( ! [X230: $i] :
( ( iskpair @ X230 )
=> ( ( kpair @ ( kfst @ X230 ) @ ( ksnd @ X230 ) )
= X230 ) )
=> ( ! [X231: $i,X232: $i,X233: $i] :
( ( in @ X233 @ ( cartprod @ X231 @ X232 ) )
=> ( in @ ( ksnd @ X233 ) @ X232 ) )
=> ( ! [X234: $i,X235: $i,X236: $i,X237: $i] :
( ( in @ ( kpair @ X236 @ X237 ) @ ( cartprod @ X234 @ X235 ) )
=> ( in @ X236 @ X234 ) )
=> ( ! [X238: $i,X239: $i,X240: $i,X241: $i] :
( ( in @ ( kpair @ X240 @ X241 ) @ ( cartprod @ X238 @ X239 ) )
=> ( in @ X241 @ X239 ) )
=> ( cartprodmempaircEq
=> ( ! [X242: $i,X243: $i,X244: $i] :
( ( in @ X244 @ X242 )
=> ! [X245: $i] :
( ( in @ X245 @ X243 )
=> ( ( kfst @ ( kpair @ X244 @ X245 ) )
= X244 ) ) )
=> ( ! [X246: $i,X247: $i,X248: $i] :
( ( in @ X248 @ X246 )
=> ! [X249: $i] :
( ( in @ X249 @ X247 )
=> ( ( ksnd @ ( kpair @ X248 @ X249 ) )
= X249 ) ) )
=> ( ! [X250: $i,X251: $i,X252: $i] :
( ( in @ X252 @ ( cartprod @ X250 @ X251 ) )
=> ( ( kpair @ ( kfst @ X252 ) @ ( ksnd @ X252 ) )
= X252 ) )
=> ( ! [X253: $i,X254: $i,X255: $i > $i > $o,X256: $i] :
( ( in @ X256 @ X253 )
=> ! [X257: $i] :
( ( in @ X257 @ X254 )
=> ( ( X255 @ X256 @ X257 )
=> ( in @ ( kpair @ X256 @ X257 ) @ ( dpsetconstr @ X253 @ X254 @ X255 ) ) ) ) )
=> ( ! [X258: $i,X259: $i,X260: $i > $i > $o] : ( subset @ ( dpsetconstr @ X258 @ X259 @ X260 ) @ ( cartprod @ X258 @ X259 ) )
=> ( ! [X261: $i,X262: $i,X263: $i > $i > $o] : ( subset @ ( dpsetconstr @ X261 @ X262 @ X263 ) @ ( cartprod @ X261 @ X262 ) )
=> ( ! [X264: $i,X265: $i,X266: $i > $i > $o,X267: $i] :
( ( in @ X267 @ X264 )
=> ! [X268: $i] :
( ( in @ X268 @ X265 )
=> ( ( in @ ( kpair @ X267 @ X268 ) @ ( dpsetconstr @ X264 @ X265 @ X266 ) )
=> ( X266 @ X267 @ X268 ) ) ) )
=> ( ! [X269: $i,X270: $i,X271: $i > $i > $o,X272: $i,X273: $i] :
( ( in @ ( kpair @ X272 @ X273 ) @ ( dpsetconstr @ X269 @ X270 @ X271 ) )
=> ( in @ X272 @ X269 ) )
=> ( ! [X274: $i,X275: $i,X276: $i > $i > $o,X277: $i,X278: $i] :
( ( in @ ( kpair @ X277 @ X278 ) @ ( dpsetconstr @ X274 @ X275 @ X276 ) )
=> ( in @ X278 @ X275 ) )
=> ( ! [X279: $i,X280: $i,X281: $i > $i > $o,X282: $i,X283: $i] :
( ( in @ ( kpair @ X282 @ X283 ) @ ( dpsetconstr @ X279 @ X280 @ X281 ) )
=> ( X281 @ X282 @ X283 ) )
=> ( funcImageSingleton
=> ( apProp
=> ( ! [X284: $i,X285: $i,X286: $i] :
( ( func @ X284 @ X285 @ X286 )
=> ! [X287: $i] :
( ( in @ X287 @ X284 )
=> ( in @ ( ap @ X284 @ X285 @ X286 @ X287 ) @ X285 ) ) )
=> ( ! [X288: $i,X289: $i,X290: $i] :
( ( in @ X290 @ ( funcSet @ X288 @ X289 ) )
=> ( func @ X288 @ X289 @ X290 ) )
=> ( ! [X291: $i,X292: $i,X293: $i] :
( ( in @ X293 @ ( funcSet @ X291 @ X292 ) )
=> ! [X294: $i] :
( ( in @ X294 @ X291 )
=> ( in @ ( ap @ X291 @ X292 @ X293 @ X294 ) @ X292 ) ) )
=> ( ! [X295: $i,X296: $i,X297: $i] :
( ( func @ X295 @ X296 @ X297 )
=> ( in @ X297 @ ( funcSet @ X295 @ X296 ) ) )
=> ( ! [X298: $i,X299: $i,X300: $i > $i] :
( ! [X301: $i] :
( ( in @ X301 @ X298 )
=> ( in @ ( X300 @ X301 ) @ X299 ) )
=> ( func @ X298 @ X299
@ ( dpsetconstr @ X298 @ X299
@ ^ [Z0: $i] : ( $eq @ ( X300 @ Z0 ) ) ) ) )
=> ( ! [X302: $i,X303: $i,X304: $i > $i] :
( ! [X305: $i] :
( ( in @ X305 @ X302 )
=> ( in @ ( X304 @ X305 ) @ X303 ) )
=> ( func @ X302 @ X303 @ ( lam @ X302 @ X303 @ X304 ) ) )
=> ( ! [X306: $i,X307: $i,X308: $i > $i] :
( ! [X309: $i] :
( ( in @ X309 @ X306 )
=> ( in @ ( X308 @ X309 ) @ X307 ) )
=> ( in @ ( lam @ X306 @ X307 @ X308 ) @ ( funcSet @ X306 @ X307 ) ) )
=> ( ! [X310: $i,X311: $i,X312: $i] :
( ( subset @ X312 @ ( cartprod @ X310 @ X311 ) )
=> ! [X313: $i > $o] :
( ! [X314: $i] :
( ( in @ X314 @ X310 )
=> ! [X315: $i] :
( ( in @ X315 @ X311 )
=> ( ( in @ ( kpair @ X314 @ X315 ) @ X312 )
=> ( X313 @ ( kpair @ X314 @ X315 ) ) ) ) )
=> ! [X316: $i] :
( ( in @ X316 @ X312 )
=> ( X313 @ X316 ) ) ) )
=> ( ! [X317: $i,X318: $i,X319: $i] :
( ( subset @ X319 @ ( cartprod @ X317 @ X318 ) )
=> ! [X320: $i > $o] :
( ! [X321: $i] :
( ( in @ X321 @ X317 )
=> ! [X322: $i] :
( ( in @ X322 @ X318 )
=> ( ( in @ ( kpair @ X321 @ X322 ) @ X319 )
=> ( X320 @ ( kpair @ X321 @ X322 ) ) ) ) )
=> ! [X323: $i] :
( ( in @ X323 @ X319 )
=> ( X320 @ X323 ) ) ) )
=> ( ex1E2
=> ( ! [X324: $i,X325: $i,X326: $i] :
( ( func @ X324 @ X325 @ X326 )
=> ! [X327: $i] :
( ( in @ X327 @ X324 )
=> ( in @ ( kpair @ X327 @ ( ap @ X324 @ X325 @ X326 @ X327 ) ) @ X326 ) ) )
=> ( ! [X328: $i,X329: $i,X330: $i] :
( ( in @ X330 @ ( funcSet @ X328 @ X329 ) )
=> ! [X331: $i] :
( ( in @ X331 @ X328 )
=> ( in @ ( kpair @ X331 @ ( ap @ X328 @ X329 @ X330 @ X331 ) ) @ X330 ) ) )
=> ( ! [X332: $i,X333: $i,X334: $i] :
( ( func @ X332 @ X333 @ X334 )
=> ! [X335: $i] :
( ( in @ X335 @ X332 )
=> ! [X336: $i] :
( ( in @ X336 @ X333 )
=> ( ( in @ ( kpair @ X335 @ X336 ) @ X334 )
=> ( ( ap @ X332 @ X333 @ X334 @ X335 )
= X336 ) ) ) ) )
=> ( ! [X337: $i,X338: $i,X339: $i] :
( ( func @ X337 @ X338 @ X339 )
=> ! [X340: $i] :
( ( func @ X337 @ X338 @ X340 )
=> ( ! [X341: $i] :
( ( in @ X341 @ X337 )
=> ( ( ap @ X337 @ X338 @ X339 @ X341 )
= ( ap @ X337 @ X338 @ X340 @ X341 ) ) )
=> ! [X342: $i] :
( ( in @ X342 @ X337 )
=> ! [X343: $i] :
( ( in @ X343 @ X338 )
=> ( ( in @ ( kpair @ X342 @ X343 ) @ X340 )
=> ( in @ ( kpair @ X342 @ X343 ) @ X339 ) ) ) ) ) ) )
=> ( ! [X344: $i,X345: $i,X346: $i] :
( ( in @ X346 @ ( funcSet @ X344 @ X345 ) )
=> ! [X347: $i] :
( ( in @ X347 @ X344 )
=> ! [X348: $i] :
( ( in @ X348 @ X345 )
=> ( ( in @ ( kpair @ X347 @ X348 ) @ X346 )
=> ( ( ap @ X344 @ X345 @ X346 @ X347 )
= X348 ) ) ) ) )
=> ( ! [X349: $i,X350: $i,X351: $i] :
( ( subset @ X351 @ ( cartprod @ X349 @ X350 ) )
=> ! [X352: $i] :
( ( subset @ X352 @ ( cartprod @ X349 @ X350 ) )
=> ( ! [X353: $i] :
( ( in @ X353 @ X349 )
=> ! [X354: $i] :
( ( in @ X354 @ X350 )
=> ( ( in @ ( kpair @ X353 @ X354 ) @ X351 )
=> ( in @ ( kpair @ X353 @ X354 ) @ X352 ) ) ) )
=> ( subset @ X351 @ X352 ) ) ) )
=> ( ! [X355: $i,X356: $i,X357: $i] :
( ( subset @ X357 @ ( cartprod @ X355 @ X356 ) )
=> ! [X358: $i] :
( ( subset @ X358 @ ( cartprod @ X355 @ X356 ) )
=> ( ! [X359: $i] :
( ( in @ X359 @ X355 )
=> ! [X360: $i] :
( ( in @ X360 @ X356 )
=> ( ( in @ ( kpair @ X359 @ X360 ) @ X357 )
=> ( in @ ( kpair @ X359 @ X360 ) @ X358 ) ) ) )
=> ( ! [X361: $i] :
( ( in @ X361 @ X355 )
=> ! [X362: $i] :
( ( in @ X362 @ X356 )
=> ( ( in @ ( kpair @ X361 @ X362 ) @ X358 )
=> ( in @ ( kpair @ X361 @ X362 ) @ X357 ) ) ) )
=> ( X357 = X358 ) ) ) ) )
=> ( ! [X363: $i,X364: $i,X365: $i] :
( ( func @ X363 @ X364 @ X365 )
=> ! [X366: $i] :
( ( func @ X363 @ X364 @ X366 )
=> ( ! [X367: $i] :
( ( in @ X367 @ X363 )
=> ( ( ap @ X363 @ X364 @ X365 @ X367 )
= ( ap @ X363 @ X364 @ X366 @ X367 ) ) )
=> ( X365 = X366 ) ) ) )
=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( in @ X35 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X35 @ X2 ) ) )
=> ( X29 = X35 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_45,cartprodsndpairEq]),ksndpairEq]),cartprodfstpairEq]),kfstpairEq]),kpairsurjEq]),c_0_46]),c_0_47]),kpairp]),kpairiskpair]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),cartprodpairsurjEq]),cartprodpairmemER]),cartprodpairmemEL]),cartprodsndin]),cartprodfstin]),cartprodmempair]),cartprodmempair1]),cartprodpairin]),c_0_52]),c_0_53]),c_0_54]),c_0_55]),c_0_56]),c_0_57]),c_0_58]),c_0_59]),c_0_60]),c_0_61]),funcinfuncset]),infuncsetfunc]),funcext]),funcGraphProp4]),funcextLem]),funcGraphProp2]),funcGraphProp3]),funcGraphProp1]),ap2p]),app])]) ).
thf(c_0_63,negated_conjecture,
! [X371: $i,X372: $i,X373: $i,X374: $i,X375: $i,X376: $i,X377: $i,X378: $i,X379: $i,X380: $i,X381: $i,X384: $i,X385: $i,X386: $i,X387: $i,X388: $i,X389: $i,X390: $i,X391: $i,X392: $i,X393: $i,X394: $i,X395: $i,X396: $i,X397: $i,X398: $i,X399: $i,X400: $i,X401: $i,X402: $i,X403: $i,X404: $i,X405: $i,X406: $i,X407: $i,X408: $i,X409: $i,X410: $i,X411: $i,X412: $i,X413: $i,X414: $i,X415: $i,X416: $i,X417: $i,X418: $i,X419: $i,X420: $i,X421: $i > $i > $o,X422: $i,X423: $i,X424: $i,X425: $i,X426: $i > $i > $o,X427: $i,X428: $i,X429: $i > $i > $o,X430: $i,X431: $i,X432: $i > $i > $o,X433: $i,X434: $i,X435: $i,X436: $i,X437: $i > $i > $o,X438: $i,X439: $i,X440: $i,X441: $i,X442: $i > $i > $o,X443: $i,X444: $i,X445: $i,X446: $i,X447: $i > $i > $o,X448: $i,X449: $i,X450: $i,X451: $i,X452: $i,X453: $i,X454: $i,X455: $i,X456: $i,X457: $i,X458: $i,X459: $i,X460: $i,X461: $i,X462: $i,X463: $i,X464: $i,X465: $i,X466: $i > $i,X468: $i,X469: $i,X470: $i > $i,X472: $i,X473: $i,X474: $i > $i,X476: $i,X477: $i,X478: $i,X479: $i > $o,X482: $i,X483: $i,X484: $i,X485: $i,X486: $i > $o,X489: $i,X490: $i,X491: $i,X492: $i,X493: $i,X494: $i,X495: $i,X496: $i,X497: $i,X498: $i,X499: $i,X500: $i,X501: $i,X502: $i,X503: $i,X504: $i,X505: $i,X506: $i,X508: $i,X509: $i,X510: $i,X511: $i,X512: $i,X513: $i,X514: $i,X515: $i,X516: $i,X517: $i,X518: $i,X521: $i,X522: $i,X523: $i,X524: $i,X529: $i,X530: $i,X531: $i,X532: $i,X538: $i] :
( setextAx
& emptysetAx
& setadjoinAx
& powersetAx
& setunionAx
& omega0Ax
& omegaSAx
& omegaIndAx
& replAx
& foundationAx
& wellorderingAx
& descrp
& dsetconstrI
& dsetconstrEL
& dsetconstrER
& exuE1
& prop2setE
& emptysetE
& emptysetimpfalse
& notinemptyset
& exuE3e
& setext
& emptyI
& noeltsimpempty
& setbeta
& nonemptyE1
& nonemptyI
& nonemptyI1
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& setoftrueEq
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& setunionI
& setunionE
& subPowSU
& exuE2
& nonemptyImpWitness
& uniqinunit
& notinsingleton
& eqinunit
& singletonsswitch
& upairsetE
& upairsetIL
& upairsetIR
& emptyE1
& vacuousDall
& quantDeMorgan1
& quantDeMorgan2
& quantDeMorgan3
& quantDeMorgan4
& prop2setI
& prop2set2propI
& notdexE
& notdallE
& exuI1
& exuI3
& exuI2
& inCongP
& in__Cong
& exuE3u
& exu__Cong
& emptyset__Cong
& setadjoin__Cong
& powerset__Cong
& setunion__Cong
& omega__Cong
& exuEu
& descr__Cong
& dsetconstr__Cong
& subsetI1
& eqimpsubset2
& eqimpsubset1
& subsetI2
& emptysetsubset
& subsetE
& subsetE2
& notsubsetI
& notequalI1
& notequalI2
& subsetRefl
& subsetTrans
& setadjoinSub
& setadjoinSub2
& subset2powerset
& setextsub
& subsetemptysetimpeq
& powersetI1
& powersetE1
& inPowerset
& powersetsubset
& sepInPowerset
& sepSubset
& binunionIL
& upairset2IR
& binunionIR
& binunionEcases
& binunionE
& binunionLsub
& binunionRsub
& binintersectI
& binintersectSubset5
& binintersectEL
& binintersectLsub
& binintersectSubset2
& binintersectSubset3
& binintersectER
& disjointsetsI1
& binintersectRsub
& binintersectSubset4
& binintersectSubset1
& bs114d
& setminusI
& setminusEL
& setminusER
& setminusSubset2
& setminusERneg
& setminusELneg
& setminusILneg
& setminusIRneg
& setminusLsub
& setminusSubset1
& symdiffE
& symdiffI1
& symdiffI2
& symdiffIneg1
& symdiffIneg2
& secondinupair
& setukpairIL
& setukpairIR
& ( iskpair @ ( setadjoin @ ( setadjoin @ X371 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X371 @ ( setadjoin @ X372 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X373 @ X374 ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& ( ~ ( in @ X377 @ X375 )
| ~ ( in @ X378 @ X376 )
| ( in @ ( kpair @ X377 @ X378 ) @ ( cartprod @ X375 @ X376 ) ) )
& ( ( in @ ( esk1_3 @ X379 @ X380 @ X381 ) @ X379 )
| ~ ( in @ X381 @ ( cartprod @ X379 @ X380 ) ) )
& ( ( in @ ( esk2_3 @ X379 @ X380 @ X381 ) @ X380 )
| ~ ( in @ X381 @ ( cartprod @ X379 @ X380 ) ) )
& ( ( X381
= ( kpair @ ( esk1_3 @ X379 @ X380 @ X381 ) @ ( esk2_3 @ X379 @ X380 @ X381 ) ) )
| ~ ( in @ X381 @ ( cartprod @ X379 @ X380 ) ) )
& ( ~ ( in @ X386 @ ( cartprod @ X384 @ X385 ) )
| ( iskpair @ X386 ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& singletonprop
& ex1E1
& ex1I
& ex1I2
& singletonsuniq
& setukpairinjL1
& ( ~ ( iskpair @ X387 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X387 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X387 ) ) ) )
& theprop
& ( ( kfst @ ( kpair @ X388 @ X389 ) )
= X388 )
& ( ~ ( in @ X392 @ ( cartprod @ X390 @ X391 ) )
| ( in @ ( kfst @ X392 ) @ X390 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ~ ( iskpair @ X393 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X393 )
@ ^ [Z0: $i] :
( X393
= ( kpair @ ( kfst @ X393 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X394 @ X395 ) )
= X395 )
& ( ~ ( iskpair @ X396 )
| ( ( kpair @ ( kfst @ X396 ) @ ( ksnd @ X396 ) )
= X396 ) )
& ( ~ ( in @ X399 @ ( cartprod @ X397 @ X398 ) )
| ( in @ ( ksnd @ X399 ) @ X398 ) )
& ( ~ ( in @ ( kpair @ X402 @ X403 ) @ ( cartprod @ X400 @ X401 ) )
| ( in @ X402 @ X400 ) )
& ( ~ ( in @ ( kpair @ X406 @ X407 ) @ ( cartprod @ X404 @ X405 ) )
| ( in @ X407 @ X405 ) )
& cartprodmempaircEq
& ( ~ ( in @ X410 @ X408 )
| ~ ( in @ X411 @ X409 )
| ( ( kfst @ ( kpair @ X410 @ X411 ) )
= X410 ) )
& ( ~ ( in @ X414 @ X412 )
| ~ ( in @ X415 @ X413 )
| ( ( ksnd @ ( kpair @ X414 @ X415 ) )
= X415 ) )
& ( ~ ( in @ X418 @ ( cartprod @ X416 @ X417 ) )
| ( ( kpair @ ( kfst @ X418 ) @ ( ksnd @ X418 ) )
= X418 ) )
& ( ~ ( in @ X422 @ X419 )
| ~ ( in @ X423 @ X420 )
| ~ ( X421 @ X422 @ X423 )
| ( in @ ( kpair @ X422 @ X423 ) @ ( dpsetconstr @ X419 @ X420 @ X421 ) ) )
& ( subset @ ( dpsetconstr @ X424 @ X425 @ X426 ) @ ( cartprod @ X424 @ X425 ) )
& ( subset @ ( dpsetconstr @ X427 @ X428 @ X429 ) @ ( cartprod @ X427 @ X428 ) )
& ( ~ ( in @ X433 @ X430 )
| ~ ( in @ X434 @ X431 )
| ~ ( in @ ( kpair @ X433 @ X434 ) @ ( dpsetconstr @ X430 @ X431 @ X432 ) )
| ( X432 @ X433 @ X434 ) )
& ( ~ ( in @ ( kpair @ X438 @ X439 ) @ ( dpsetconstr @ X435 @ X436 @ X437 ) )
| ( in @ X438 @ X435 ) )
& ( ~ ( in @ ( kpair @ X443 @ X444 ) @ ( dpsetconstr @ X440 @ X441 @ X442 ) )
| ( in @ X444 @ X441 ) )
& ( ~ ( in @ ( kpair @ X448 @ X449 ) @ ( dpsetconstr @ X445 @ X446 @ X447 ) )
| ( X447 @ X448 @ X449 ) )
& funcImageSingleton
& apProp
& ( ~ ( func @ X450 @ X451 @ X452 )
| ~ ( in @ X453 @ X450 )
| ( in @ ( ap @ X450 @ X451 @ X452 @ X453 ) @ X451 ) )
& ( ~ ( in @ X456 @ ( funcSet @ X454 @ X455 ) )
| ( func @ X454 @ X455 @ X456 ) )
& ( ~ ( in @ X459 @ ( funcSet @ X457 @ X458 ) )
| ~ ( in @ X460 @ X457 )
| ( in @ ( ap @ X457 @ X458 @ X459 @ X460 ) @ X458 ) )
& ( ~ ( func @ X461 @ X462 @ X463 )
| ( in @ X463 @ ( funcSet @ X461 @ X462 ) ) )
& ( ( in @ ( esk3_3 @ X464 @ X465 @ X466 ) @ X464 )
| ( func @ X464 @ X465
@ ( dpsetconstr @ X464 @ X465
@ ^ [Z0: $i] : ( $eq @ ( X466 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X466 @ ( esk3_3 @ X464 @ X465 @ X466 ) ) @ X465 )
| ( func @ X464 @ X465
@ ( dpsetconstr @ X464 @ X465
@ ^ [Z0: $i] : ( $eq @ ( X466 @ Z0 ) ) ) ) )
& ( ( in @ ( esk4_3 @ X468 @ X469 @ X470 ) @ X468 )
| ( func @ X468 @ X469 @ ( lam @ X468 @ X469 @ X470 ) ) )
& ( ~ ( in @ ( X470 @ ( esk4_3 @ X468 @ X469 @ X470 ) ) @ X469 )
| ( func @ X468 @ X469 @ ( lam @ X468 @ X469 @ X470 ) ) )
& ( ( in @ ( esk5_3 @ X472 @ X473 @ X474 ) @ X472 )
| ( in @ ( lam @ X472 @ X473 @ X474 ) @ ( funcSet @ X472 @ X473 ) ) )
& ( ~ ( in @ ( X474 @ ( esk5_3 @ X472 @ X473 @ X474 ) ) @ X473 )
| ( in @ ( lam @ X472 @ X473 @ X474 ) @ ( funcSet @ X472 @ X473 ) ) )
& ( ( in @ ( esk6_4 @ X476 @ X477 @ X478 @ X479 ) @ X476 )
| ~ ( in @ X482 @ X478 )
| ( X479 @ X482 )
| ~ ( subset @ X478 @ ( cartprod @ X476 @ X477 ) ) )
& ( ( in @ ( esk7_4 @ X476 @ X477 @ X478 @ X479 ) @ X477 )
| ~ ( in @ X482 @ X478 )
| ( X479 @ X482 )
| ~ ( subset @ X478 @ ( cartprod @ X476 @ X477 ) ) )
& ( ( in @ ( kpair @ ( esk6_4 @ X476 @ X477 @ X478 @ X479 ) @ ( esk7_4 @ X476 @ X477 @ X478 @ X479 ) ) @ X478 )
| ~ ( in @ X482 @ X478 )
| ( X479 @ X482 )
| ~ ( subset @ X478 @ ( cartprod @ X476 @ X477 ) ) )
& ( ~ ( X479 @ ( kpair @ ( esk6_4 @ X476 @ X477 @ X478 @ X479 ) @ ( esk7_4 @ X476 @ X477 @ X478 @ X479 ) ) )
| ~ ( in @ X482 @ X478 )
| ( X479 @ X482 )
| ~ ( subset @ X478 @ ( cartprod @ X476 @ X477 ) ) )
& ( ( in @ ( esk8_4 @ X483 @ X484 @ X485 @ X486 ) @ X483 )
| ~ ( in @ X489 @ X485 )
| ( X486 @ X489 )
| ~ ( subset @ X485 @ ( cartprod @ X483 @ X484 ) ) )
& ( ( in @ ( esk9_4 @ X483 @ X484 @ X485 @ X486 ) @ X484 )
| ~ ( in @ X489 @ X485 )
| ( X486 @ X489 )
| ~ ( subset @ X485 @ ( cartprod @ X483 @ X484 ) ) )
& ( ( in @ ( kpair @ ( esk8_4 @ X483 @ X484 @ X485 @ X486 ) @ ( esk9_4 @ X483 @ X484 @ X485 @ X486 ) ) @ X485 )
| ~ ( in @ X489 @ X485 )
| ( X486 @ X489 )
| ~ ( subset @ X485 @ ( cartprod @ X483 @ X484 ) ) )
& ( ~ ( X486 @ ( kpair @ ( esk8_4 @ X483 @ X484 @ X485 @ X486 ) @ ( esk9_4 @ X483 @ X484 @ X485 @ X486 ) ) )
| ~ ( in @ X489 @ X485 )
| ( X486 @ X489 )
| ~ ( subset @ X485 @ ( cartprod @ X483 @ X484 ) ) )
& ex1E2
& ( ~ ( func @ X490 @ X491 @ X492 )
| ~ ( in @ X493 @ X490 )
| ( in @ ( kpair @ X493 @ ( ap @ X490 @ X491 @ X492 @ X493 ) ) @ X492 ) )
& ( ~ ( in @ X496 @ ( funcSet @ X494 @ X495 ) )
| ~ ( in @ X497 @ X494 )
| ( in @ ( kpair @ X497 @ ( ap @ X494 @ X495 @ X496 @ X497 ) ) @ X496 ) )
& ( ~ ( func @ X498 @ X499 @ X500 )
| ~ ( in @ X501 @ X498 )
| ~ ( in @ X502 @ X499 )
| ~ ( in @ ( kpair @ X501 @ X502 ) @ X500 )
| ( ( ap @ X498 @ X499 @ X500 @ X501 )
= X502 ) )
& ( ( in @ ( esk10_4 @ X503 @ X504 @ X505 @ X506 ) @ X503 )
| ~ ( in @ X508 @ X503 )
| ~ ( in @ X509 @ X504 )
| ~ ( in @ ( kpair @ X508 @ X509 ) @ X506 )
| ( in @ ( kpair @ X508 @ X509 ) @ X505 )
| ~ ( func @ X503 @ X504 @ X506 )
| ~ ( func @ X503 @ X504 @ X505 ) )
& ( ( ( ap @ X503 @ X504 @ X505 @ ( esk10_4 @ X503 @ X504 @ X505 @ X506 ) )
!= ( ap @ X503 @ X504 @ X506 @ ( esk10_4 @ X503 @ X504 @ X505 @ X506 ) ) )
| ~ ( in @ X508 @ X503 )
| ~ ( in @ X509 @ X504 )
| ~ ( in @ ( kpair @ X508 @ X509 ) @ X506 )
| ( in @ ( kpair @ X508 @ X509 ) @ X505 )
| ~ ( func @ X503 @ X504 @ X506 )
| ~ ( func @ X503 @ X504 @ X505 ) )
& ( ~ ( in @ X512 @ ( funcSet @ X510 @ X511 ) )
| ~ ( in @ X513 @ X510 )
| ~ ( in @ X514 @ X511 )
| ~ ( in @ ( kpair @ X513 @ X514 ) @ X512 )
| ( ( ap @ X510 @ X511 @ X512 @ X513 )
= X514 ) )
& ( ( in @ ( esk11_4 @ X515 @ X516 @ X517 @ X518 ) @ X515 )
| ( subset @ X517 @ X518 )
| ~ ( subset @ X518 @ ( cartprod @ X515 @ X516 ) )
| ~ ( subset @ X517 @ ( cartprod @ X515 @ X516 ) ) )
& ( ( in @ ( esk12_4 @ X515 @ X516 @ X517 @ X518 ) @ X516 )
| ( subset @ X517 @ X518 )
| ~ ( subset @ X518 @ ( cartprod @ X515 @ X516 ) )
| ~ ( subset @ X517 @ ( cartprod @ X515 @ X516 ) ) )
& ( ( in @ ( kpair @ ( esk11_4 @ X515 @ X516 @ X517 @ X518 ) @ ( esk12_4 @ X515 @ X516 @ X517 @ X518 ) ) @ X517 )
| ( subset @ X517 @ X518 )
| ~ ( subset @ X518 @ ( cartprod @ X515 @ X516 ) )
| ~ ( subset @ X517 @ ( cartprod @ X515 @ X516 ) ) )
& ( ~ ( in @ ( kpair @ ( esk11_4 @ X515 @ X516 @ X517 @ X518 ) @ ( esk12_4 @ X515 @ X516 @ X517 @ X518 ) ) @ X518 )
| ( subset @ X517 @ X518 )
| ~ ( subset @ X518 @ ( cartprod @ X515 @ X516 ) )
| ~ ( subset @ X517 @ ( cartprod @ X515 @ X516 ) ) )
& ( ( in @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ X521 )
| ( X523 = X524 )
| ( in @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ X521 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) @ X522 )
| ( X523 = X524 )
| ( in @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ X521 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( kpair @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X524 )
| ( X523 = X524 )
| ( in @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ X521 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ~ ( in @ ( kpair @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X523 )
| ( X523 = X524 )
| ( in @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ X521 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ X521 )
| ( X523 = X524 )
| ( in @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) @ X522 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) @ X522 )
| ( X523 = X524 )
| ( in @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) @ X522 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( kpair @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X524 )
| ( X523 = X524 )
| ( in @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) @ X522 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ~ ( in @ ( kpair @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X523 )
| ( X523 = X524 )
| ( in @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) @ X522 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ X521 )
| ( X523 = X524 )
| ( in @ ( kpair @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X523 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) @ X522 )
| ( X523 = X524 )
| ( in @ ( kpair @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X523 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( kpair @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X524 )
| ( X523 = X524 )
| ( in @ ( kpair @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X523 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ~ ( in @ ( kpair @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X523 )
| ( X523 = X524 )
| ( in @ ( kpair @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X523 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ X521 )
| ( X523 = X524 )
| ~ ( in @ ( kpair @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X524 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) @ X522 )
| ( X523 = X524 )
| ~ ( in @ ( kpair @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X524 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( kpair @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X524 )
| ( X523 = X524 )
| ~ ( in @ ( kpair @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X524 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ~ ( in @ ( kpair @ ( esk15_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk16_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X523 )
| ( X523 = X524 )
| ~ ( in @ ( kpair @ ( esk13_4 @ X521 @ X522 @ X523 @ X524 ) @ ( esk14_4 @ X521 @ X522 @ X523 @ X524 ) ) @ X524 )
| ~ ( subset @ X524 @ ( cartprod @ X521 @ X522 ) )
| ~ ( subset @ X523 @ ( cartprod @ X521 @ X522 ) ) )
& ( ( in @ ( esk17_4 @ X529 @ X530 @ X531 @ X532 ) @ X529 )
| ( X531 = X532 )
| ~ ( func @ X529 @ X530 @ X532 )
| ~ ( func @ X529 @ X530 @ X531 ) )
& ( ( ( ap @ X529 @ X530 @ X531 @ ( esk17_4 @ X529 @ X530 @ X531 @ X532 ) )
!= ( ap @ X529 @ X530 @ X532 @ ( esk17_4 @ X529 @ X530 @ X531 @ X532 ) ) )
| ( X531 = X532 )
| ~ ( func @ X529 @ X530 @ X532 )
| ~ ( func @ X529 @ X530 @ X531 ) )
& ( in @ esk20_0 @ ( funcSet @ esk18_0 @ esk19_0 ) )
& ( in @ esk21_0 @ ( funcSet @ esk18_0 @ esk19_0 ) )
& ( ~ ( in @ X538 @ esk18_0 )
| ( ( ap @ esk18_0 @ esk19_0 @ esk20_0 @ X538 )
= ( ap @ esk18_0 @ esk19_0 @ esk21_0 @ X538 ) ) )
& ( esk20_0 != esk21_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_62])])])])])]) ).
thf(c_0_64,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( func @ X3 @ X4 @ X2 )
| ~ ( in @ X2 @ ( funcSet @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_65,negated_conjecture,
in @ esk21_0 @ ( funcSet @ esk18_0 @ esk19_0 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_66,negated_conjecture,
! [X2: $i,X3: $i,X5: $i,X4: $i] :
( ( X4 = X5 )
| ( ( ap @ X2 @ X3 @ X4 @ ( esk17_4 @ X2 @ X3 @ X4 @ X5 ) )
!= ( ap @ X2 @ X3 @ X5 @ ( esk17_4 @ X2 @ X3 @ X4 @ X5 ) ) )
| ~ ( func @ X2 @ X3 @ X5 )
| ~ ( func @ X2 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_67,negated_conjecture,
! [X2: $i] :
( ( ( ap @ esk18_0 @ esk19_0 @ esk20_0 @ X2 )
= ( ap @ esk18_0 @ esk19_0 @ esk21_0 @ X2 ) )
| ~ ( in @ X2 @ esk18_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_68,negated_conjecture,
func @ esk18_0 @ esk19_0 @ esk21_0,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_69,negated_conjecture,
in @ esk20_0 @ ( funcSet @ esk18_0 @ esk19_0 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_70,negated_conjecture,
! [X2: $i] :
( ( X2 = esk21_0 )
| ( ( ap @ esk18_0 @ esk19_0 @ X2 @ ( esk17_4 @ esk18_0 @ esk19_0 @ X2 @ esk21_0 ) )
!= ( ap @ esk18_0 @ esk19_0 @ esk20_0 @ ( esk17_4 @ esk18_0 @ esk19_0 @ X2 @ esk21_0 ) ) )
| ~ ( in @ ( esk17_4 @ esk18_0 @ esk19_0 @ X2 @ esk21_0 ) @ esk18_0 )
| ~ ( func @ esk18_0 @ esk19_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
thf(c_0_71,negated_conjecture,
func @ esk18_0 @ esk19_0 @ esk20_0,
inference(spm,[status(thm)],[c_0_64,c_0_69]) ).
thf(c_0_72,negated_conjecture,
esk20_0 != esk21_0,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_73,negated_conjecture,
~ ( in @ ( esk17_4 @ esk18_0 @ esk19_0 @ esk20_0 @ esk21_0 ) @ esk18_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_70]),c_0_71])]),c_0_72]) ).
thf(c_0_74,negated_conjecture,
! [X2: $i,X3: $i,X5: $i,X4: $i] :
( ( in @ ( esk17_4 @ X2 @ X3 @ X4 @ X5 ) @ X2 )
| ( X4 = X5 )
| ~ ( func @ X2 @ X3 @ X5 )
| ~ ( func @ X2 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_68]),c_0_71])]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU692^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n007.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 14:09:08 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.33 Running higher-order theorem proving
% 0.38/0.42 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.xJ2tyjYAEF/E---3.1_3423716.p
% 117.27/17.54 % Version: 3.5.1-ho
% 117.27/17.54 % Preprocessing class: HSLMSLSSLLLCHFA.
% 117.27/17.54 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 117.27/17.54 % Starting ehoh_best5 with 300s (1) cores
% 117.27/17.54 % Starting almost_fo_3_lam with 300s (1) cores
% 117.27/17.54 % Starting new_bool_5 with 300s (1) cores
% 117.27/17.54 % Starting pre_casc_3 with 300s (1) cores
% 117.27/17.54 % Starting ho_unfolding_8 with 300s (1) cores
% 117.27/17.54 % Starting new_ho_10_cnf2 with 300s (1) cores
% 117.27/17.54 % Starting new_bool_3 with 300s (1) cores
% 117.27/17.54 % Starting new_ho_5 with 300s (1) cores
% 117.27/17.54 % pre_casc_3 with pid 3423732 completed with status 0
% 117.27/17.54 % Result found by pre_casc_3
% 117.27/17.54 % Preprocessing class: HSLMSLSSLLLCHFA.
% 117.27/17.54 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 117.27/17.54 % Starting ehoh_best5 with 300s (1) cores
% 117.27/17.54 % Starting almost_fo_3_lam with 300s (1) cores
% 117.27/17.54 % Starting new_bool_5 with 300s (1) cores
% 117.27/17.54 % Starting pre_casc_3 with 300s (1) cores
% 117.27/17.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 117.27/17.54 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 117.27/17.54 % Search class: HGUSM-FSLM33-MHFMMFBN
% 117.27/17.54 % partial match(3): HGHSM-FSLM32-MHFMMSBN
% 117.27/17.54 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 117.27/17.54 % Starting SubtermCWHack with 31s (1) cores
% 117.27/17.54 % SubtermCWHack with pid 3423737 completed with status 0
% 117.27/17.54 % Result found by SubtermCWHack
% 117.27/17.54 % Preprocessing class: HSLMSLSSLLLCHFA.
% 117.27/17.54 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 117.27/17.54 % Starting ehoh_best5 with 300s (1) cores
% 117.27/17.54 % Starting almost_fo_3_lam with 300s (1) cores
% 117.27/17.54 % Starting new_bool_5 with 300s (1) cores
% 117.27/17.54 % Starting pre_casc_3 with 300s (1) cores
% 117.27/17.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 117.27/17.54 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 117.27/17.54 % Search class: HGUSM-FSLM33-MHFMMFBN
% 117.27/17.54 % partial match(3): HGHSM-FSLM32-MHFMMSBN
% 117.27/17.54 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 117.27/17.54 % Starting SubtermCWHack with 31s (1) cores
% 117.27/17.54 % Preprocessing time : 0.003 s
% 117.27/17.54
% 117.27/17.54 % Proof found!
% 117.27/17.54 % SZS status Theorem
% 117.27/17.54 % SZS output start CNFRefutation
% See solution above
% 117.27/17.55 % Parsed axioms : 460
% 117.27/17.55 % Removed by relevancy pruning/SinE : 416
% 117.27/17.55 % Initial clauses : 249
% 117.27/17.55 % Removed in clause preprocessing : 0
% 117.27/17.55 % Initial clauses in saturation : 249
% 117.27/17.55 % Processed clauses : 12904
% 117.27/17.55 % ...of these trivial : 3
% 117.27/17.55 % ...subsumed : 6209
% 117.27/17.55 % ...remaining for further processing : 6692
% 117.27/17.55 % Other redundant clauses eliminated : 1
% 117.27/17.55 % Clauses deleted for lack of memory : 0
% 117.27/17.55 % Backward-subsumed : 325
% 117.27/17.55 % Backward-rewritten : 0
% 117.27/17.55 % Generated clauses : 843416
% 117.27/17.55 % ...of the previous two non-redundant : 842477
% 117.27/17.55 % ...aggressively subsumed : 0
% 117.27/17.55 % Contextual simplify-reflections : 60
% 117.27/17.55 % Paramodulations : 843410
% 117.27/17.55 % Factorizations : 0
% 117.27/17.55 % NegExts : 0
% 117.27/17.55 % Equation resolutions : 3
% 117.27/17.55 % Disequality decompositions : 0
% 117.27/17.55 % Total rewrite steps : 11434
% 117.27/17.55 % ...of those cached : 10885
% 117.27/17.55 % Propositional unsat checks : 0
% 117.27/17.55 % Propositional check models : 0
% 117.27/17.55 % Propositional check unsatisfiable : 0
% 117.27/17.55 % Propositional clauses : 0
% 117.27/17.55 % Propositional clauses after purity: 0
% 117.27/17.55 % Propositional unsat core size : 0
% 117.27/17.55 % Propositional preprocessing time : 0.000
% 117.27/17.55 % Propositional encoding time : 0.000
% 117.27/17.55 % Propositional solver time : 0.000
% 117.27/17.55 % Success case prop preproc time : 0.000
% 117.27/17.55 % Success case prop encoding time : 0.000
% 117.27/17.55 % Success case prop solver time : 0.000
% 117.27/17.55 % Current number of processed clauses : 6366
% 117.27/17.55 % Positive orientable unit clauses : 184
% 117.27/17.55 % Positive unorientable unit clauses: 0
% 117.27/17.55 % Negative unit clauses : 2
% 117.27/17.55 % Non-unit-clauses : 6180
% 117.27/17.55 % Current number of unprocessed clauses: 829252
% 117.27/17.55 % ...number of literals in the above : 3893403
% 117.27/17.55 % Current number of archived formulas : 0
% 117.27/17.55 % Current number of archived clauses : 326
% 117.27/17.55 % Clause-clause subsumption calls (NU) : 2383168
% 117.27/17.55 % Rec. Clause-clause subsumption calls : 1410519
% 117.27/17.55 % Non-unit clause-clause subsumptions : 6594
% 117.27/17.55 % Unit Clause-clause subsumption calls : 3864
% 117.27/17.55 % Rewrite failures with RHS unbound : 0
% 117.27/17.55 % BW rewrite match attempts : 3
% 117.27/17.55 % BW rewrite match successes : 0
% 117.27/17.55 % Condensation attempts : 0
% 117.27/17.55 % Condensation successes : 0
% 117.27/17.55 % Termbank termtop insertions : 21735961
% 117.27/17.55 % Search garbage collected termcells : 8627
% 117.27/17.55
% 117.27/17.55 % -------------------------------------------------
% 117.27/17.55 % User time : 16.234 s
% 117.27/17.55 % System time : 0.509 s
% 117.27/17.55 % Total time : 16.743 s
% 117.27/17.55 % Maximum resident set size: 6368 pages
% 117.27/17.55
% 117.27/17.55 % -------------------------------------------------
% 117.27/17.55 % User time : 16.257 s
% 117.27/17.55 % System time : 0.516 s
% 117.27/17.55 % Total time : 16.773 s
% 117.27/17.55 % Maximum resident set size: 5376 pages
% 117.27/17.55 % E exiting
%------------------------------------------------------------------------------