%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU771^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:25:33 AM UTC 2026
% Result : Theorem 0.66s 0.49s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 40
% Syntax : Number of formulae : 70 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 1706 ( 73 equ; 0 cnn)
% Maximal formula atoms : 482 ( 24 avg)
% Number of connectives : 3961 ( 139 ~; 177 |; 345 &;2155 @)
% ( 51 <=>;1094 =>; 0 <=; 0 <~>)
% Maximal formula depth : 447 ( 29 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 94 ( 94 >; 0 *; 0 +; 0 <<)
% Number of symbols : 328 ( 325 usr; 291 con; 0-4 aty)
% Number of variables : 594 ( 76 ^; 508 !; 10 ?; 594 :)
% 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_246,type,
funcImageSingleton: $o ).
thf(decl_247,type,
apProp: $o ).
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_255,type,
lamp: $o ).
thf(decl_256,type,
lam2p: $o ).
thf(decl_257,type,
brelnall1: $o ).
thf(decl_258,type,
brelnall2: $o ).
thf(decl_259,type,
ex1E2: $o ).
thf(decl_260,type,
funcGraphProp1: $o ).
thf(decl_261,type,
funcGraphProp3: $o ).
thf(decl_262,type,
funcGraphProp2: $o ).
thf(decl_263,type,
funcextLem: $o ).
thf(decl_264,type,
funcGraphProp4: $o ).
thf(decl_265,type,
subbreln: $o ).
thf(decl_266,type,
eqbreln: $o ).
thf(decl_267,type,
funcext: $o ).
thf(decl_268,type,
funcext2: $o ).
thf(decl_269,type,
ap2apEq1: $o ).
thf(decl_270,type,
ap2apEq2: $o ).
thf(decl_271,type,
beta1: $o ).
thf(decl_272,type,
eta1: $o ).
thf(decl_273,type,
lam2lamEq: $o ).
thf(decl_274,type,
beta2: $o ).
thf(decl_275,type,
eta2: $o ).
thf(decl_276,type,
iffalseProp1: $o ).
thf(decl_277,type,
iffalseProp2: $o ).
thf(decl_278,type,
iftrueProp1: $o ).
thf(decl_279,type,
iftrueProp2: $o ).
thf(decl_280,type,
ifSingleton: $o ).
thf(decl_282,type,
ifp: $o ).
thf(decl_283,type,
theeq: $o ).
thf(decl_284,type,
iftrue: $o ).
thf(decl_285,type,
iffalse: $o ).
thf(decl_286,type,
iftrueorfalse: $o ).
thf(decl_287,type,
binintersectT_lem: $o ).
thf(decl_288,type,
binunionT_lem: $o ).
thf(decl_289,type,
powersetT_lem: $o ).
thf(decl_290,type,
setminusT_lem: $o ).
thf(decl_291,type,
complementT_lem: $o ).
thf(decl_292,type,
setextT: $o ).
thf(decl_293,type,
subsetTI: $o ).
thf(decl_294,type,
powersetTI1: $o ).
thf(decl_295,type,
powersetTE1: $o ).
thf(decl_296,type,
complementTI1: $o ).
thf(decl_297,type,
complementTE1: $o ).
thf(decl_298,type,
binintersectTELcontra: $o ).
thf(decl_299,type,
binintersectTERcontra: $o ).
thf(decl_300,type,
contrasubsetT: $o ).
thf(decl_301,type,
contrasubsetT1: $o ).
thf(decl_302,type,
contrasubsetT2: $o ).
thf(decl_303,type,
contrasubsetT3: $o ).
thf(decl_304,type,
doubleComplementI1: $o ).
thf(decl_305,type,
doubleComplementE1: $o ).
thf(decl_306,type,
doubleComplementSub1: $o ).
thf(decl_307,type,
doubleComplementSub2: $o ).
thf(decl_308,type,
doubleComplementEq: $o ).
thf(decl_309,type,
complementTnotintersectT: $o ).
thf(decl_310,type,
complementImpComplementIntersect: $o ).
thf(decl_311,type,
complementSubsetComplementIntersect: $o ).
thf(decl_312,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_313,type,
contraSubsetComplement: $o ).
thf(decl_314,type,
complementTcontraSubset: $o ).
thf(decl_315,type,
binunionTILcontra: $o ).
thf(decl_316,type,
binunionTIRcontra: $o ).
thf(decl_317,type,
inIntersectImpInUnion: $o ).
thf(decl_318,type,
inIntersectImpInUnion2: $o ).
thf(decl_319,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_320,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_321,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_322,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_323,type,
binunionTE: $o ).
thf(decl_324,type,
binunionTEcontra: $o ).
thf(decl_325,type,
demorgan2a1: $o ).
thf(decl_326,type,
complementUnionInPowersetComplement: $o ).
thf(decl_327,type,
demorgan2a2: $o ).
thf(decl_328,type,
demorgan1a: $o ).
thf(decl_329,type,
demorgan1b: $o ).
thf(decl_330,type,
demorgan1: $o ).
thf(decl_331,type,
demorgan2a: $o ).
thf(decl_332,type,
demorgan2b2: $o ).
thf(decl_333,type,
demorgan2b: $o ).
thf(decl_334,type,
demorgan2: $o ).
thf(decl_335,type,
woz13rule0: $o ).
thf(decl_336,type,
woz13rule1: $o ).
thf(decl_337,type,
woz13rule2: $o ).
thf(decl_338,type,
woz13rule3: $o ).
thf(decl_339,type,
woz13rule4: $o ).
thf(decl_340,type,
woz1_1: $o ).
thf(decl_341,type,
woz1_2: $o ).
thf(decl_342,type,
woz1_3: $o ).
thf(decl_343,type,
woz1_4: $o ).
thf(decl_344,type,
woz1_5: $o ).
thf(decl_345,type,
breln1: $i > $i > $o ).
thf(decl_346,type,
breln1all2: $o ).
thf(decl_347,type,
breln1Set: $i > $i ).
thf(decl_348,type,
breln1SetBreln1: $o ).
thf(decl_354,type,
reflwellordering: $i > $i > $o ).
thf(decl_355,type,
choice2fnsingleton: $o ).
thf(decl_356,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_357,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_358,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_359,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_360,type,
esk5_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_361,type,
esk6_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_362,type,
esk7_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_363,type,
esk8_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_364,type,
esk9_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_365,type,
esk10_4: $i > $i > $i > $i > $i ).
thf(decl_366,type,
esk11_4: $i > $i > $i > $i > $i ).
thf(decl_367,type,
esk12_4: $i > $i > $i > $i > $i ).
thf(decl_368,type,
esk13_4: $i > $i > $i > $i > $i ).
thf(decl_369,type,
esk14_4: $i > $i > $i > $i > $i ).
thf(decl_370,type,
esk15_4: $i > $i > $i > $i > $i ).
thf(decl_371,type,
esk16_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_372,type,
esk17_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_373,type,
esk18_3: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_374,type,
esk19_0: $i ).
thf(decl_375,type,
epred1_0: $i > $i > $o ).
thf(breln1,axiom,
( breln1
= ( ^ [X4: $i,X33: $i] : ( breln @ X4 @ X4 @ X33 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.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/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',setOfPairsIsBReln) ).
thf(setOfPairsIsBReln1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ! [X4: $i,X53: $i > $i > $o] :
( breln1 @ X4
@ ( dpsetconstr @ X4 @ X4
@ ^ [X2: $i,X3: $i] : ( X53 @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',setOfPairsIsBReln1) ).
thf(choice2fnsingleton,axiom,
( choice2fnsingleton
<=> ! [X4: $i,X5: $i,X52: $i > $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X52 @ X2 @ X3 ) ) )
=> ! [X33: $i] :
( ( in @ X33 @ ( breln1Set @ X5 ) )
=> ( ( reflwellordering @ X5 @ X33 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] :
( ( X52 @ X2 @ X3 )
& ! [X14: $i] :
( ( in @ X14 @ X5 )
=> ( ( X52 @ X2 @ X14 )
=> ( in @ ( kpair @ X3 @ X14 ) @ X33 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',choice2fnsingleton) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',eqbreln) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',subbreln) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',brelnall2) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.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/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.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/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',dpsetconstrER) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',dpsetconstrEL2) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',dpsetconstrEL1) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',dpsetconstrERa) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',ifSingleton) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',funcImageSingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',ksndsingleton) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',kfstsingleton) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',singletonprop) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',dpsetconstrSub) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',dpsetconstrI) ).
thf(breln1SetBreln1,axiom,
( breln1SetBreln1
<=> ! [X4: $i,X33: $i] :
( ( in @ X33 @ ( breln1Set @ X4 ) )
=> ( breln1 @ X4 @ X33 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',breln1SetBreln1) ).
thf(breln1all2,axiom,
( breln1all2
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',breln1all2) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodmempair) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodmempair1) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodpairin) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodsndpairEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',ksndpairEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodfstpairEq) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',kfstpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',kpairsurjEq) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',kpairp) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',kpairiskpair) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',theeq) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',theprop) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodpairsurjEq) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodpairmemER) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodpairmemEL) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodsndin) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p',cartprodfstin) ).
thf(c_0_40,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1]) ).
thf(c_0_41,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_42,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_43,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_44,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ! [X4: $i,X53: $i > $i > $o] :
( breln1 @ X4
@ ( dpsetconstr @ X4 @ X4
@ ^ [X2: $i,X3: $i] : ( X53 @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setOfPairsIsBReln1]) ).
thf(c_0_45,plain,
( choice2fnsingleton
<=> ! [X4: $i,X5: $i,X52: $i > $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X52 @ X2 @ X3 ) ) )
=> ! [X33: $i] :
( ( in @ X33 @ ( breln1Set @ X5 ) )
=> ( ( reflwellordering @ X5 @ X33 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] :
( ( X52 @ X2 @ Z0 )
& ! [X14: $i] :
( ( in @ X14 @ X5 )
=> ( ( X52 @ X2 @ X14 )
=> ( in @ ( kpair @ Z0 @ X14 ) @ X33 ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[choice2fnsingleton]) ).
thf(c_0_46,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_41]) ).
thf(c_0_47,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_41]) ).
thf(c_0_48,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_41]) ).
thf(c_0_49,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_41]) ).
thf(c_0_50,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_51,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_52,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_53,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_54,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_55,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_42,c_0_41]) ).
thf(c_0_56,plain,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X43
& ( Z0 = X2 ) )
| ( ~ X43
& ( Z0 = X3 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ifSingleton]) ).
thf(c_0_57,plain,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_58,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_59,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_60,plain,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singletonprop]) ).
thf(c_0_61,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_62,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_63,axiom,
( breln1SetBreln1
= ( ! [X4: $i,X33: $i] :
( ( in @ X33 @ ( breln1Set @ X4 ) )
=> ( subset @ X33 @ ( cartprod @ X4 @ X4 ) ) ) ) ),
inference(apply_def,[status(thm)],[breln1SetBreln1,c_0_43]) ).
thf(c_0_64,axiom,
( breln1all2
= ( ! [X4: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X4 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[breln1all2,c_0_43]) ).
thf(c_0_65,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
=> ( ! [X198: $i,X199: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X198 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X198 @ ( setadjoin @ X199 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X200: $i,X201: $i] : ( iskpair @ ( kpair @ X200 @ X201 ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( ! [X202: $i,X203: $i,X204: $i] :
( ( in @ X204 @ X202 )
=> ! [X205: $i] :
( ( in @ X205 @ X203 )
=> ( in @ ( kpair @ X204 @ X205 ) @ ( cartprod @ X202 @ X203 ) ) ) )
=> ( ! [X206: $i,X207: $i,X208: $i] :
( ( in @ X208 @ ( cartprod @ X206 @ X207 ) )
=> ? [X209: $i] :
( ( in @ X209 @ X206 )
& ? [X210: $i] :
( ( in @ X210 @ X207 )
& ( X208
= ( kpair @ X209 @ X210 ) ) ) ) )
=> ( ! [X211: $i,X212: $i,X213: $i] :
( ( in @ X213 @ ( cartprod @ X211 @ X212 ) )
=> ( iskpair @ X213 ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X214: $i,X215: $i > $o] :
( ! [X216: $i] :
( ( in @ X216 @ X214 )
=> ! [X217: $i] :
( ( in @ X217 @ X214 )
=> ( ( X215 @ X216 )
=> ( ( X215 @ X217 )
=> ( X216 = X217 ) ) ) ) )
=> ( ? [X218: $i] :
( ( in @ X218 @ X214 )
& ( X215 @ X218 ) )
=> ( singleton @ ( dsetconstr @ X214 @ X215 ) ) ) )
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X219: $i] :
( ( iskpair @ X219 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X219 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X219 ) ) ) )
=> ( ! [X220: $i] :
( ( singleton @ X220 )
=> ( in @ ( setunion @ X220 ) @ X220 ) )
=> ( ! [X221: $i,X222: $i] :
( ( kfst @ ( kpair @ X221 @ X222 ) )
= X221 )
=> ( ! [X223: $i,X224: $i,X225: $i] :
( ( in @ X225 @ ( cartprod @ X223 @ X224 ) )
=> ( in @ ( kfst @ X225 ) @ X223 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X226: $i] :
( ( iskpair @ X226 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X226 )
@ ^ [Z0: $i] :
( X226
= ( kpair @ ( kfst @ X226 ) @ Z0 ) ) ) ) )
=> ( ! [X227: $i,X228: $i] :
( ( ksnd @ ( kpair @ X227 @ X228 ) )
= X228 )
=> ( ! [X229: $i] :
( ( iskpair @ X229 )
=> ( ( kpair @ ( kfst @ X229 ) @ ( ksnd @ X229 ) )
= X229 ) )
=> ( ! [X230: $i,X231: $i,X232: $i] :
( ( in @ X232 @ ( cartprod @ X230 @ X231 ) )
=> ( in @ ( ksnd @ X232 ) @ X231 ) )
=> ( ! [X233: $i,X234: $i,X235: $i,X236: $i] :
( ( in @ ( kpair @ X235 @ X236 ) @ ( cartprod @ X233 @ X234 ) )
=> ( in @ X235 @ X233 ) )
=> ( ! [X237: $i,X238: $i,X239: $i,X240: $i] :
( ( in @ ( kpair @ X239 @ X240 ) @ ( cartprod @ X237 @ X238 ) )
=> ( in @ X240 @ X238 ) )
=> ( cartprodmempaircEq
=> ( ! [X241: $i,X242: $i,X243: $i] :
( ( in @ X243 @ X241 )
=> ! [X244: $i] :
( ( in @ X244 @ X242 )
=> ( ( kfst @ ( kpair @ X243 @ X244 ) )
= X243 ) ) )
=> ( ! [X245: $i,X246: $i,X247: $i] :
( ( in @ X247 @ X245 )
=> ! [X248: $i] :
( ( in @ X248 @ X246 )
=> ( ( ksnd @ ( kpair @ X247 @ X248 ) )
= X248 ) ) )
=> ( ! [X249: $i,X250: $i,X251: $i] :
( ( in @ X251 @ ( cartprod @ X249 @ X250 ) )
=> ( ( kpair @ ( kfst @ X251 ) @ ( ksnd @ X251 ) )
= X251 ) )
=> ( ! [X252: $i,X253: $i,X254: $i > $i > $o,X255: $i] :
( ( in @ X255 @ X252 )
=> ! [X256: $i] :
( ( in @ X256 @ X253 )
=> ( ( X254 @ X255 @ X256 )
=> ( in @ ( kpair @ X255 @ X256 ) @ ( dpsetconstr @ X252 @ X253 @ X254 ) ) ) ) )
=> ( ! [X257: $i,X258: $i,X259: $i > $i > $o] : ( subset @ ( dpsetconstr @ X257 @ X258 @ X259 ) @ ( cartprod @ X257 @ X258 ) )
=> ( ! [X260: $i,X261: $i,X262: $i > $i > $o] : ( subset @ ( dpsetconstr @ X260 @ X261 @ X262 ) @ ( cartprod @ X260 @ X261 ) )
=> ( ! [X263: $i,X264: $i,X265: $i > $i > $o,X266: $i] :
( ( in @ X266 @ X263 )
=> ! [X267: $i] :
( ( in @ X267 @ X264 )
=> ( ( in @ ( kpair @ X266 @ X267 ) @ ( dpsetconstr @ X263 @ X264 @ X265 ) )
=> ( X265 @ X266 @ X267 ) ) ) )
=> ( ! [X268: $i,X269: $i,X270: $i > $i > $o,X271: $i,X272: $i] :
( ( in @ ( kpair @ X271 @ X272 ) @ ( dpsetconstr @ X268 @ X269 @ X270 ) )
=> ( in @ X271 @ X268 ) )
=> ( ! [X273: $i,X274: $i,X275: $i > $i > $o,X276: $i,X277: $i] :
( ( in @ ( kpair @ X276 @ X277 ) @ ( dpsetconstr @ X273 @ X274 @ X275 ) )
=> ( in @ X277 @ X274 ) )
=> ( ! [X278: $i,X279: $i,X280: $i > $i > $o,X281: $i,X282: $i] :
( ( in @ ( kpair @ X281 @ X282 ) @ ( dpsetconstr @ X278 @ X279 @ X280 ) )
=> ( X280 @ X281 @ X282 ) )
=> ( ! [X283: $i,X284: $i,X285: $i] :
( ( func @ X283 @ X284 @ X285 )
=> ! [X286: $i] :
( ( in @ X286 @ X283 )
=> ( singleton
@ ( dsetconstr @ X284
@ ^ [Z0: $i] : ( in @ ( kpair @ X286 @ Z0 ) @ X285 ) ) ) ) )
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( ! [X287: $i,X288: $i,X289: $i > $i] :
( ! [X290: $i] :
( ( in @ X290 @ X287 )
=> ( in @ ( X289 @ X290 ) @ X288 ) )
=> ( func @ X287 @ X288
@ ( dpsetconstr @ X287 @ X288
@ ^ [Z0: $i] : ( $eq @ ( X289 @ Z0 ) ) ) ) )
=> ( lamp
=> ( lam2p
=> ( ! [X291: $i,X292: $i,X293: $i] :
( ( subset @ X293 @ ( cartprod @ X291 @ X292 ) )
=> ! [X294: $i > $o] :
( ! [X295: $i] :
( ( in @ X295 @ X291 )
=> ! [X296: $i] :
( ( in @ X296 @ X292 )
=> ( ( in @ ( kpair @ X295 @ X296 ) @ X293 )
=> ( X294 @ ( kpair @ X295 @ X296 ) ) ) ) )
=> ! [X297: $i] :
( ( in @ X297 @ X293 )
=> ( X294 @ X297 ) ) ) )
=> ( ! [X298: $i,X299: $i,X300: $i] :
( ( subset @ X300 @ ( cartprod @ X298 @ X299 ) )
=> ! [X301: $i > $o] :
( ! [X302: $i] :
( ( in @ X302 @ X298 )
=> ! [X303: $i] :
( ( in @ X303 @ X299 )
=> ( ( in @ ( kpair @ X302 @ X303 ) @ X300 )
=> ( X301 @ ( kpair @ X302 @ X303 ) ) ) ) )
=> ! [X304: $i] :
( ( in @ X304 @ X300 )
=> ( X301 @ X304 ) ) ) )
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( ! [X305: $i,X306: $i,X307: $i] :
( ( subset @ X307 @ ( cartprod @ X305 @ X306 ) )
=> ! [X308: $i] :
( ( subset @ X308 @ ( cartprod @ X305 @ X306 ) )
=> ( ! [X309: $i] :
( ( in @ X309 @ X305 )
=> ! [X310: $i] :
( ( in @ X310 @ X306 )
=> ( ( in @ ( kpair @ X309 @ X310 ) @ X307 )
=> ( in @ ( kpair @ X309 @ X310 ) @ X308 ) ) ) )
=> ( subset @ X307 @ X308 ) ) ) )
=> ( ! [X311: $i,X312: $i,X313: $i] :
( ( subset @ X313 @ ( cartprod @ X311 @ X312 ) )
=> ! [X314: $i] :
( ( subset @ X314 @ ( cartprod @ X311 @ X312 ) )
=> ( ! [X315: $i] :
( ( in @ X315 @ X311 )
=> ! [X316: $i] :
( ( in @ X316 @ X312 )
=> ( ( in @ ( kpair @ X315 @ X316 ) @ X313 )
=> ( in @ ( kpair @ X315 @ X316 ) @ X314 ) ) ) )
=> ( ! [X317: $i] :
( ( in @ X317 @ X311 )
=> ! [X318: $i] :
( ( in @ X318 @ X312 )
=> ( ( in @ ( kpair @ X317 @ X318 ) @ X314 )
=> ( in @ ( kpair @ X317 @ X318 ) @ X313 ) ) ) )
=> ( X313 = X314 ) ) ) ) )
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ! [X319: $i,X320: $o,X321: $i] :
( ( in @ X321 @ X319 )
=> ! [X322: $i] :
( ( in @ X322 @ X319 )
=> ( singleton
@ ( dsetconstr @ X319
@ ^ [Z0: $i] :
( ( X320
& ( Z0 = X321 ) )
| ( ~ X320
& ( Z0 = X322 ) ) ) ) ) ) )
=> ( ifp
=> ( ! [X323: $i] :
( ( singleton @ X323 )
=> ! [X324: $i] :
( ( in @ X324 @ X323 )
=> ( ( setunion @ X323 )
= X324 ) ) )
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( ! [X325: $i,X326: $i] :
( ( subset @ X326 @ ( cartprod @ X325 @ X325 ) )
=> ! [X327: $i > $o] :
( ! [X328: $i] :
( ( in @ X328 @ X325 )
=> ! [X329: $i] :
( ( in @ X329 @ X325 )
=> ( ( in @ ( kpair @ X328 @ X329 ) @ X326 )
=> ( X327 @ ( kpair @ X328 @ X329 ) ) ) ) )
=> ! [X330: $i] :
( ( in @ X330 @ X326 )
=> ( X327 @ X330 ) ) ) )
=> ( ! [X331: $i,X332: $i] :
( ( in @ X332 @ ( breln1Set @ X331 ) )
=> ( subset @ X332 @ ( cartprod @ X331 @ X331 ) ) )
=> ( ! [X333: $i,X334: $i,X335: $i > $i > $o] :
( ! [X336: $i] :
( ( in @ X336 @ X333 )
=> ? [X337: $i] :
( ( in @ X337 @ X334 )
& ( X335 @ X336 @ X337 ) ) )
=> ! [X338: $i] :
( ( in @ X338 @ ( breln1Set @ X334 ) )
=> ( ( reflwellordering @ X334 @ X338 )
=> ! [X339: $i] :
( ( in @ X339 @ X333 )
=> ( singleton
@ ( dsetconstr @ X334
@ ^ [Z0: $i] :
( ( X335 @ X339 @ Z0 )
& ! [X340: $i] :
( ( in @ X340 @ X334 )
=> ( ( X335 @ X339 @ X340 )
=> ( in @ ( kpair @ Z0 @ X340 ) @ X338 ) ) ) ) ) ) ) ) ) )
=> ! [X4: $i,X53: $i > $i > $o] : ( subset @ ( dpsetconstr @ X4 @ X4 @ X53 ) @ ( cartprod @ X4 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[c_0_44]),cartprodmempair]),cartprodmempair1]),cartprodpairin]),c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),c_0_52]),c_0_53]),c_0_54]),c_0_55]),cartprodsndpairEq]),ksndpairEq]),cartprodfstpairEq]),kfstpairEq]),kpairsurjEq]),kpairp]),kpairiskpair]),theeq]),c_0_56]),c_0_57]),c_0_58]),theprop]),c_0_59]),c_0_60]),cartprodpairsurjEq]),cartprodpairmemER]),cartprodpairmemEL]),cartprodsndin]),cartprodfstin]),c_0_61]),c_0_62]),c_0_63]),c_0_64]),c_0_43])]) ).
thf(c_0_66,negated_conjecture,
! [X341: $i,X342: $i,X343: $i,X344: $i,X345: $i,X346: $i,X347: $i,X348: $i,X349: $i,X350: $i,X351: $i,X354: $i,X355: $i,X356: $i,X357: $i,X358: $i > $o,X361: $i,X362: $i,X363: $i,X364: $i,X365: $i,X366: $i,X367: $i,X368: $i,X369: $i,X370: $i,X371: $i,X372: $i,X373: $i,X374: $i,X375: $i,X376: $i,X377: $i,X378: $i,X379: $i,X380: $i,X381: $i,X382: $i,X383: $i,X384: $i,X385: $i,X386: $i,X387: $i,X388: $i,X389: $i,X390: $i,X391: $i,X392: $i,X393: $i,X394: $i,X395: $i,X396: $i,X397: $i > $i > $o,X398: $i,X399: $i,X400: $i,X401: $i,X402: $i > $i > $o,X403: $i,X404: $i,X405: $i > $i > $o,X406: $i,X407: $i,X408: $i > $i > $o,X409: $i,X410: $i,X411: $i,X412: $i,X413: $i > $i > $o,X414: $i,X415: $i,X416: $i,X417: $i,X418: $i > $i > $o,X419: $i,X420: $i,X421: $i,X422: $i,X423: $i > $i > $o,X424: $i,X425: $i,X426: $i,X427: $i,X428: $i,X429: $i,X430: $i,X431: $i,X432: $i > $i,X434: $i,X435: $i,X436: $i,X437: $i > $o,X440: $i,X441: $i,X442: $i,X443: $i,X444: $i > $o,X447: $i,X448: $i,X449: $i,X450: $i,X451: $i,X454: $i,X455: $i,X456: $i,X457: $i,X462: $i,X463: $o,X464: $i,X465: $i,X466: $i,X467: $i,X468: $i,X469: $i,X470: $i > $o,X473: $i,X474: $i,X475: $i,X476: $i,X477: $i,X478: $i > $i > $o,X480: $i,X481: $i,X482: $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 @ X341 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X341 @ ( setadjoin @ X342 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X343 @ X344 ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& ( ~ ( in @ X347 @ X345 )
| ~ ( in @ X348 @ X346 )
| ( in @ ( kpair @ X347 @ X348 ) @ ( cartprod @ X345 @ X346 ) ) )
& ( ( in @ ( esk1_3 @ X349 @ X350 @ X351 ) @ X349 )
| ~ ( in @ X351 @ ( cartprod @ X349 @ X350 ) ) )
& ( ( in @ ( esk2_3 @ X349 @ X350 @ X351 ) @ X350 )
| ~ ( in @ X351 @ ( cartprod @ X349 @ X350 ) ) )
& ( ( X351
= ( kpair @ ( esk1_3 @ X349 @ X350 @ X351 ) @ ( esk2_3 @ X349 @ X350 @ X351 ) ) )
| ~ ( in @ X351 @ ( cartprod @ X349 @ X350 ) ) )
& ( ~ ( in @ X356 @ ( cartprod @ X354 @ X355 ) )
| ( iskpair @ X356 ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk3_2 @ X357 @ X358 ) @ X357 )
| ~ ( in @ X361 @ X357 )
| ~ ( X358 @ X361 )
| ( singleton @ ( dsetconstr @ X357 @ X358 ) ) )
& ( ( in @ ( esk4_2 @ X357 @ X358 ) @ X357 )
| ~ ( in @ X361 @ X357 )
| ~ ( X358 @ X361 )
| ( singleton @ ( dsetconstr @ X357 @ X358 ) ) )
& ( ( X358 @ ( esk3_2 @ X357 @ X358 ) )
| ~ ( in @ X361 @ X357 )
| ~ ( X358 @ X361 )
| ( singleton @ ( dsetconstr @ X357 @ X358 ) ) )
& ( ( X358 @ ( esk4_2 @ X357 @ X358 ) )
| ~ ( in @ X361 @ X357 )
| ~ ( X358 @ X361 )
| ( singleton @ ( dsetconstr @ X357 @ X358 ) ) )
& ( ( ( esk3_2 @ X357 @ X358 )
!= ( esk4_2 @ X357 @ X358 ) )
| ~ ( in @ X361 @ X357 )
| ~ ( X358 @ X361 )
| ( singleton @ ( dsetconstr @ X357 @ X358 ) ) )
& ex1E1
& ex1I
& ex1I2
& singletonsuniq
& setukpairinjL1
& ( ~ ( iskpair @ X362 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X362 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X362 ) ) ) )
& ( ~ ( singleton @ X363 )
| ( in @ ( setunion @ X363 ) @ X363 ) )
& ( ( kfst @ ( kpair @ X364 @ X365 ) )
= X364 )
& ( ~ ( in @ X368 @ ( cartprod @ X366 @ X367 ) )
| ( in @ ( kfst @ X368 ) @ X366 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ~ ( iskpair @ X369 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X369 )
@ ^ [Z0: $i] :
( X369
= ( kpair @ ( kfst @ X369 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X370 @ X371 ) )
= X371 )
& ( ~ ( iskpair @ X372 )
| ( ( kpair @ ( kfst @ X372 ) @ ( ksnd @ X372 ) )
= X372 ) )
& ( ~ ( in @ X375 @ ( cartprod @ X373 @ X374 ) )
| ( in @ ( ksnd @ X375 ) @ X374 ) )
& ( ~ ( in @ ( kpair @ X378 @ X379 ) @ ( cartprod @ X376 @ X377 ) )
| ( in @ X378 @ X376 ) )
& ( ~ ( in @ ( kpair @ X382 @ X383 ) @ ( cartprod @ X380 @ X381 ) )
| ( in @ X383 @ X381 ) )
& cartprodmempaircEq
& ( ~ ( in @ X386 @ X384 )
| ~ ( in @ X387 @ X385 )
| ( ( kfst @ ( kpair @ X386 @ X387 ) )
= X386 ) )
& ( ~ ( in @ X390 @ X388 )
| ~ ( in @ X391 @ X389 )
| ( ( ksnd @ ( kpair @ X390 @ X391 ) )
= X391 ) )
& ( ~ ( in @ X394 @ ( cartprod @ X392 @ X393 ) )
| ( ( kpair @ ( kfst @ X394 ) @ ( ksnd @ X394 ) )
= X394 ) )
& ( ~ ( in @ X398 @ X395 )
| ~ ( in @ X399 @ X396 )
| ~ ( X397 @ X398 @ X399 )
| ( in @ ( kpair @ X398 @ X399 ) @ ( dpsetconstr @ X395 @ X396 @ X397 ) ) )
& ( subset @ ( dpsetconstr @ X400 @ X401 @ X402 ) @ ( cartprod @ X400 @ X401 ) )
& ( subset @ ( dpsetconstr @ X403 @ X404 @ X405 ) @ ( cartprod @ X403 @ X404 ) )
& ( ~ ( in @ X409 @ X406 )
| ~ ( in @ X410 @ X407 )
| ~ ( in @ ( kpair @ X409 @ X410 ) @ ( dpsetconstr @ X406 @ X407 @ X408 ) )
| ( X408 @ X409 @ X410 ) )
& ( ~ ( in @ ( kpair @ X414 @ X415 ) @ ( dpsetconstr @ X411 @ X412 @ X413 ) )
| ( in @ X414 @ X411 ) )
& ( ~ ( in @ ( kpair @ X419 @ X420 ) @ ( dpsetconstr @ X416 @ X417 @ X418 ) )
| ( in @ X420 @ X417 ) )
& ( ~ ( in @ ( kpair @ X424 @ X425 ) @ ( dpsetconstr @ X421 @ X422 @ X423 ) )
| ( X423 @ X424 @ X425 ) )
& ( ~ ( func @ X426 @ X427 @ X428 )
| ~ ( in @ X429 @ X426 )
| ( singleton
@ ( dsetconstr @ X427
@ ^ [Z0: $i] : ( in @ ( kpair @ X429 @ Z0 ) @ X428 ) ) ) )
& apProp
& app
& infuncsetfunc
& ap2p
& funcinfuncset
& ( ( in @ ( esk5_3 @ X430 @ X431 @ X432 ) @ X430 )
| ( func @ X430 @ X431
@ ( dpsetconstr @ X430 @ X431
@ ^ [Z0: $i] : ( $eq @ ( X432 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X432 @ ( esk5_3 @ X430 @ X431 @ X432 ) ) @ X431 )
| ( func @ X430 @ X431
@ ( dpsetconstr @ X430 @ X431
@ ^ [Z0: $i] : ( $eq @ ( X432 @ Z0 ) ) ) ) )
& lamp
& lam2p
& ( ( in @ ( esk6_4 @ X434 @ X435 @ X436 @ X437 ) @ X434 )
| ~ ( in @ X440 @ X436 )
| ( X437 @ X440 )
| ~ ( subset @ X436 @ ( cartprod @ X434 @ X435 ) ) )
& ( ( in @ ( esk7_4 @ X434 @ X435 @ X436 @ X437 ) @ X435 )
| ~ ( in @ X440 @ X436 )
| ( X437 @ X440 )
| ~ ( subset @ X436 @ ( cartprod @ X434 @ X435 ) ) )
& ( ( in @ ( kpair @ ( esk6_4 @ X434 @ X435 @ X436 @ X437 ) @ ( esk7_4 @ X434 @ X435 @ X436 @ X437 ) ) @ X436 )
| ~ ( in @ X440 @ X436 )
| ( X437 @ X440 )
| ~ ( subset @ X436 @ ( cartprod @ X434 @ X435 ) ) )
& ( ~ ( X437 @ ( kpair @ ( esk6_4 @ X434 @ X435 @ X436 @ X437 ) @ ( esk7_4 @ X434 @ X435 @ X436 @ X437 ) ) )
| ~ ( in @ X440 @ X436 )
| ( X437 @ X440 )
| ~ ( subset @ X436 @ ( cartprod @ X434 @ X435 ) ) )
& ( ( in @ ( esk8_4 @ X441 @ X442 @ X443 @ X444 ) @ X441 )
| ~ ( in @ X447 @ X443 )
| ( X444 @ X447 )
| ~ ( subset @ X443 @ ( cartprod @ X441 @ X442 ) ) )
& ( ( in @ ( esk9_4 @ X441 @ X442 @ X443 @ X444 ) @ X442 )
| ~ ( in @ X447 @ X443 )
| ( X444 @ X447 )
| ~ ( subset @ X443 @ ( cartprod @ X441 @ X442 ) ) )
& ( ( in @ ( kpair @ ( esk8_4 @ X441 @ X442 @ X443 @ X444 ) @ ( esk9_4 @ X441 @ X442 @ X443 @ X444 ) ) @ X443 )
| ~ ( in @ X447 @ X443 )
| ( X444 @ X447 )
| ~ ( subset @ X443 @ ( cartprod @ X441 @ X442 ) ) )
& ( ~ ( X444 @ ( kpair @ ( esk8_4 @ X441 @ X442 @ X443 @ X444 ) @ ( esk9_4 @ X441 @ X442 @ X443 @ X444 ) ) )
| ~ ( in @ X447 @ X443 )
| ( X444 @ X447 )
| ~ ( subset @ X443 @ ( cartprod @ X441 @ X442 ) ) )
& ex1E2
& funcGraphProp1
& funcGraphProp3
& funcGraphProp2
& funcextLem
& funcGraphProp4
& ( ( in @ ( esk10_4 @ X448 @ X449 @ X450 @ X451 ) @ X448 )
| ( subset @ X450 @ X451 )
| ~ ( subset @ X451 @ ( cartprod @ X448 @ X449 ) )
| ~ ( subset @ X450 @ ( cartprod @ X448 @ X449 ) ) )
& ( ( in @ ( esk11_4 @ X448 @ X449 @ X450 @ X451 ) @ X449 )
| ( subset @ X450 @ X451 )
| ~ ( subset @ X451 @ ( cartprod @ X448 @ X449 ) )
| ~ ( subset @ X450 @ ( cartprod @ X448 @ X449 ) ) )
& ( ( in @ ( kpair @ ( esk10_4 @ X448 @ X449 @ X450 @ X451 ) @ ( esk11_4 @ X448 @ X449 @ X450 @ X451 ) ) @ X450 )
| ( subset @ X450 @ X451 )
| ~ ( subset @ X451 @ ( cartprod @ X448 @ X449 ) )
| ~ ( subset @ X450 @ ( cartprod @ X448 @ X449 ) ) )
& ( ~ ( in @ ( kpair @ ( esk10_4 @ X448 @ X449 @ X450 @ X451 ) @ ( esk11_4 @ X448 @ X449 @ X450 @ X451 ) ) @ X451 )
| ( subset @ X450 @ X451 )
| ~ ( subset @ X451 @ ( cartprod @ X448 @ X449 ) )
| ~ ( subset @ X450 @ ( cartprod @ X448 @ X449 ) ) )
& ( ( in @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ X454 )
| ( X456 = X457 )
| ( in @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ X454 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) @ X455 )
| ( X456 = X457 )
| ( in @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ X454 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( kpair @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X457 )
| ( X456 = X457 )
| ( in @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ X454 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ~ ( in @ ( kpair @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X456 )
| ( X456 = X457 )
| ( in @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ X454 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ X454 )
| ( X456 = X457 )
| ( in @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) @ X455 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) @ X455 )
| ( X456 = X457 )
| ( in @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) @ X455 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( kpair @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X457 )
| ( X456 = X457 )
| ( in @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) @ X455 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ~ ( in @ ( kpair @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X456 )
| ( X456 = X457 )
| ( in @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) @ X455 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ X454 )
| ( X456 = X457 )
| ( in @ ( kpair @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X456 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) @ X455 )
| ( X456 = X457 )
| ( in @ ( kpair @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X456 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( kpair @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X457 )
| ( X456 = X457 )
| ( in @ ( kpair @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X456 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ~ ( in @ ( kpair @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X456 )
| ( X456 = X457 )
| ( in @ ( kpair @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X456 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ X454 )
| ( X456 = X457 )
| ~ ( in @ ( kpair @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X457 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) @ X455 )
| ( X456 = X457 )
| ~ ( in @ ( kpair @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X457 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ( in @ ( kpair @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X457 )
| ( X456 = X457 )
| ~ ( in @ ( kpair @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X457 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& ( ~ ( in @ ( kpair @ ( esk14_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk15_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X456 )
| ( X456 = X457 )
| ~ ( in @ ( kpair @ ( esk12_4 @ X454 @ X455 @ X456 @ X457 ) @ ( esk13_4 @ X454 @ X455 @ X456 @ X457 ) ) @ X457 )
| ~ ( subset @ X457 @ ( cartprod @ X454 @ X455 ) )
| ~ ( subset @ X456 @ ( cartprod @ X454 @ X455 ) ) )
& funcext
& funcext2
& ap2apEq1
& ap2apEq2
& beta1
& eta1
& lam2lamEq
& beta2
& eta2
& iffalseProp1
& iffalseProp2
& iftrueProp1
& iftrueProp2
& ( ~ ( in @ X464 @ X462 )
| ~ ( in @ X465 @ X462 )
| ( singleton
@ ( dsetconstr @ X462
@ ^ [Z0: $i] :
( ( X463
& ( Z0 = X464 ) )
| ( ~ X463
& ( Z0 = X465 ) ) ) ) ) )
& ifp
& ( ~ ( singleton @ X466 )
| ~ ( in @ X467 @ X466 )
| ( ( setunion @ X466 )
= X467 ) )
& iftrue
& iffalse
& iftrueorfalse
& binintersectT_lem
& binunionT_lem
& powersetT_lem
& setminusT_lem
& complementT_lem
& setextT
& subsetTI
& powersetTI1
& powersetTE1
& complementTI1
& complementTE1
& binintersectTELcontra
& binintersectTERcontra
& contrasubsetT
& contrasubsetT1
& contrasubsetT2
& contrasubsetT3
& doubleComplementI1
& doubleComplementE1
& doubleComplementSub1
& doubleComplementSub2
& doubleComplementEq
& complementTnotintersectT
& complementImpComplementIntersect
& complementSubsetComplementIntersect
& complementInPowersetComplementIntersect
& contraSubsetComplement
& complementTcontraSubset
& binunionTILcontra
& binunionTIRcontra
& inIntersectImpInUnion
& inIntersectImpInUnion2
& inIntersectImpInIntersectUnions
& intersectInPowersetIntersectUnions
& inComplementUnionImpNotIn1
& inComplementUnionImpInComplement1
& binunionTE
& binunionTEcontra
& demorgan2a1
& complementUnionInPowersetComplement
& demorgan2a2
& demorgan1a
& demorgan1b
& demorgan1
& demorgan2a
& demorgan2b2
& demorgan2b
& demorgan2
& woz13rule0
& woz13rule1
& woz13rule2
& woz13rule3
& woz13rule4
& woz1_1
& woz1_2
& woz1_3
& woz1_4
& woz1_5
& ( ( in @ ( esk16_3 @ X468 @ X469 @ X470 ) @ X468 )
| ~ ( in @ X473 @ X469 )
| ( X470 @ X473 )
| ~ ( subset @ X469 @ ( cartprod @ X468 @ X468 ) ) )
& ( ( in @ ( esk17_3 @ X468 @ X469 @ X470 ) @ X468 )
| ~ ( in @ X473 @ X469 )
| ( X470 @ X473 )
| ~ ( subset @ X469 @ ( cartprod @ X468 @ X468 ) ) )
& ( ( in @ ( kpair @ ( esk16_3 @ X468 @ X469 @ X470 ) @ ( esk17_3 @ X468 @ X469 @ X470 ) ) @ X469 )
| ~ ( in @ X473 @ X469 )
| ( X470 @ X473 )
| ~ ( subset @ X469 @ ( cartprod @ X468 @ X468 ) ) )
& ( ~ ( X470 @ ( kpair @ ( esk16_3 @ X468 @ X469 @ X470 ) @ ( esk17_3 @ X468 @ X469 @ X470 ) ) )
| ~ ( in @ X473 @ X469 )
| ( X470 @ X473 )
| ~ ( subset @ X469 @ ( cartprod @ X468 @ X468 ) ) )
& ( ~ ( in @ X475 @ ( breln1Set @ X474 ) )
| ( subset @ X475 @ ( cartprod @ X474 @ X474 ) ) )
& ( ( in @ ( esk18_3 @ X476 @ X477 @ X478 ) @ X476 )
| ~ ( in @ X481 @ ( breln1Set @ X477 ) )
| ~ ( reflwellordering @ X477 @ X481 )
| ~ ( in @ X482 @ X476 )
| ( singleton
@ ( dsetconstr @ X477
@ ^ [Z0: $i] :
( ( X478 @ X482 @ Z0 )
& ! [X340: $i] :
( ( in @ X340 @ X477 )
=> ( ( X478 @ X482 @ X340 )
=> ( in @ ( kpair @ Z0 @ X340 ) @ X481 ) ) ) ) ) ) )
& ( ~ ( in @ X480 @ X477 )
| ~ ( X478 @ ( esk18_3 @ X476 @ X477 @ X478 ) @ X480 )
| ~ ( in @ X481 @ ( breln1Set @ X477 ) )
| ~ ( reflwellordering @ X477 @ X481 )
| ~ ( in @ X482 @ X476 )
| ( singleton
@ ( dsetconstr @ X477
@ ^ [Z0: $i] :
( ( X478 @ X482 @ Z0 )
& ! [X340: $i] :
( ( in @ X340 @ X477 )
=> ( ( X478 @ X482 @ X340 )
=> ( in @ ( kpair @ Z0 @ X340 ) @ X481 ) ) ) ) ) ) )
& ~ ( subset @ ( dpsetconstr @ esk19_0 @ esk19_0 @ epred1_0 ) @ ( cartprod @ esk19_0 @ esk19_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_65])])])])])]) ).
thf(c_0_67,negated_conjecture,
~ ( subset @ ( dpsetconstr @ esk19_0 @ esk19_0 @ epred1_0 ) @ ( cartprod @ esk19_0 @ esk19_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_68,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_66]) ).
thf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU771^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n015.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 14:27:32 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running higher-order theorem proving
% 0.34/0.40 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.nAKCjRA7Ch/E---3.1_3602908.p
% 0.66/0.49 % Version: 3.5.1-ho
% 0.66/0.49 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.66/0.49 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.49 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.66/0.49 % Starting pre_casc_3 with 300s (1) cores
% 0.66/0.49 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.66/0.49 % Starting full_lambda_10 with 300s (1) cores
% 0.66/0.49 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.66/0.49 % pre_casc_3 with pid 3602922 completed with status 0
% 0.66/0.49 % Result found by pre_casc_3
% 0.66/0.49 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.66/0.49 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.49 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.66/0.49 % Starting pre_casc_3 with 300s (1) cores
% 0.66/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.66/0.49 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.66/0.49 % Search class: HGUSM-FSLM32-MHSMMFBN
% 0.66/0.49 % partial match(2): HGHSM-FSLM32-MHSMMSBN
% 0.66/0.49 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.66/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.66/0.49 % SubtermCWHack with pid 3602927 completed with status 0
% 0.66/0.49 % Result found by SubtermCWHack
% 0.66/0.49 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.66/0.49 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.49 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.66/0.49 % Starting pre_casc_3 with 300s (1) cores
% 0.66/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.66/0.49 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.66/0.49 % Search class: HGUSM-FSLM32-MHSMMFBN
% 0.66/0.49 % partial match(2): HGHSM-FSLM32-MHSMMSBN
% 0.66/0.49 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.66/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.66/0.49 % Preprocessing time : 0.004 s
% 0.66/0.49
% 0.66/0.49 % Proof found!
% 0.66/0.49 % SZS status Theorem
% 0.66/0.49 % SZS output start CNFRefutation
% See solution above
% 0.66/0.49 % Parsed axioms : 625
% 0.66/0.49 % Removed by relevancy pruning/SinE : 585
% 0.66/0.49 % Initial clauses : 341
% 0.66/0.49 % Removed in clause preprocessing : 1
% 0.66/0.49 % Initial clauses in saturation : 340
% 0.66/0.49 % Processed clauses : 261
% 0.66/0.49 % ...of these trivial : 1
% 0.66/0.49 % ...subsumed : 0
% 0.66/0.49 % ...remaining for further processing : 259
% 0.66/0.49 % Other redundant clauses eliminated : 0
% 0.66/0.49 % Clauses deleted for lack of memory : 0
% 0.66/0.49 % Backward-subsumed : 0
% 0.66/0.49 % Backward-rewritten : 0
% 0.66/0.49 % Generated clauses : 3
% 0.66/0.49 % ...of the previous two non-redundant : 2
% 0.66/0.49 % ...aggressively subsumed : 0
% 0.66/0.49 % Contextual simplify-reflections : 0
% 0.66/0.49 % Paramodulations : 2
% 0.66/0.49 % Factorizations : 0
% 0.66/0.49 % NegExts : 0
% 0.66/0.49 % Equation resolutions : 0
% 0.66/0.49 % Disequality decompositions : 0
% 0.66/0.49 % Total rewrite steps : 2
% 0.66/0.49 % ...of those cached : 0
% 0.66/0.49 % Propositional unsat checks : 0
% 0.66/0.49 % Propositional check models : 0
% 0.66/0.49 % Propositional check unsatisfiable : 0
% 0.66/0.49 % Propositional clauses : 0
% 0.66/0.49 % Propositional clauses after purity: 0
% 0.66/0.49 % Propositional unsat core size : 0
% 0.66/0.49 % Propositional preprocessing time : 0.000
% 0.66/0.49 % Propositional encoding time : 0.000
% 0.66/0.49 % Propositional solver time : 0.000
% 0.66/0.49 % Success case prop preproc time : 0.000
% 0.66/0.49 % Success case prop encoding time : 0.000
% 0.66/0.49 % Success case prop solver time : 0.000
% 0.66/0.49 % Current number of processed clauses : 259
% 0.66/0.49 % Positive orientable unit clauses : 255
% 0.66/0.49 % Positive unorientable unit clauses: 0
% 0.66/0.49 % Negative unit clauses : 0
% 0.66/0.49 % Non-unit-clauses : 4
% 0.66/0.49 % Current number of unprocessed clauses: 81
% 0.66/0.49 % ...number of literals in the above : 273
% 0.66/0.49 % Current number of archived formulas : 0
% 0.66/0.49 % Current number of archived clauses : 0
% 0.66/0.49 % Clause-clause subsumption calls (NU) : 1
% 0.66/0.49 % Rec. Clause-clause subsumption calls : 0
% 0.66/0.49 % Non-unit clause-clause subsumptions : 0
% 0.66/0.49 % Unit Clause-clause subsumption calls : 0
% 0.66/0.49 % Rewrite failures with RHS unbound : 0
% 0.66/0.49 % BW rewrite match attempts : 0
% 0.66/0.49 % BW rewrite match successes : 0
% 0.66/0.49 % Condensation attempts : 0
% 0.66/0.49 % Condensation successes : 0
% 0.66/0.49 % Termbank termtop insertions : 27671
% 0.66/0.49 % Search garbage collected termcells : 11039
% 0.66/0.49
% 0.66/0.49 % -------------------------------------------------
% 0.66/0.49 % User time : 0.037 s
% 0.66/0.49 % System time : 0.007 s
% 0.66/0.49 % Total time : 0.044 s
% 0.66/0.49 % Maximum resident set size: 6896 pages
% 0.66/0.49
% 0.66/0.49 % -------------------------------------------------
% 0.66/0.49 % User time : 0.054 s
% 0.66/0.49 % System time : 0.015 s
% 0.66/0.49 % Total time : 0.069 s
% 0.66/0.49 % Maximum resident set size: 5632 pages
% 0.66/0.49 % E exiting
%------------------------------------------------------------------------------