%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU709^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:21 EDT 2024
% Result : Theorem 2.29s 0.97s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 552
% Syntax : Number of formulae : 615 ( 6 unt; 326 typ; 0 def)
% Number of atoms : 2688 ( 445 equ; 0 cnn)
% Maximal formula atoms : 829 ( 9 avg)
% Number of connectives : 10186 ( 637 ~; 654 |; 454 &;6819 @)
% ( 312 <=>;1310 =>; 0 <=; 0 <~>)
% Maximal formula depth : 965 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 497 ( 497 >; 0 *; 0 +; 0 <<)
% Number of symbols : 330 ( 326 usr; 235 con; 0-4 aty)
% Number of variables : 2353 ( 156 ^2117 !; 80 ?;2353 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
epred1_0: $o ).
thf(decl_286,type,
esk1_2: $i > $i > $i ).
thf(decl_287,type,
esk2_2: $i > $i > $i ).
thf(decl_288,type,
esk3_2: $i > $i > $i ).
thf(decl_289,type,
esk4_1: $i > $i ).
thf(decl_290,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_291,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_292,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_293,type,
esk8_1: $i > $i ).
thf(decl_294,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_295,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_296,type,
esk11_2: $i > $i > $i ).
thf(decl_297,type,
esk12_2: $i > $i > $i ).
thf(decl_298,type,
esk13_1: $i > $i ).
thf(decl_299,type,
esk14_1: $i > $i ).
thf(decl_300,type,
esk15_1: $i > $i ).
thf(decl_301,type,
esk16_2: $i > $i > $i ).
thf(decl_302,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_303,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_304,type,
esk19_1: $i > $i ).
thf(decl_305,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_306,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_307,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_308,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_309,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_310,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_311,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_312,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_313,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_314,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_315,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_316,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_317,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_318,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_319,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_320,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_321,type,
esk36_2: $i > $i > $i ).
thf(decl_322,type,
esk37_2: $i > $i > $i ).
thf(decl_323,type,
esk38_2: $i > $i > $i ).
thf(decl_324,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_325,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_326,type,
esk41_2: $i > $i > $i ).
thf(decl_327,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_328,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_329,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_330,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_331,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_332,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_333,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_334,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_335,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_336,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_337,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_338,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_339,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_340,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_341,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_342,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_343,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_344,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_345,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_346,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_347,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_348,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_349,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_350,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_351,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_352,type,
esk67_0: $i ).
thf(decl_353,type,
epred2_0: $o ).
thf(decl_354,type,
esk68_0: $i ).
thf(decl_355,type,
esk69_0: $i ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(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/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
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/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
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/benchmark/theBenchmark.p',ifSingleton) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(iftrueorfalse,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
=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
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/sandbox/benchmark/theBenchmark.p',app) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
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/benchmark/theBenchmark.p',brelnall1) ).
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/benchmark/theBenchmark.p',brelnall2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
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/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
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/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
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/benchmark/theBenchmark.p',subbreln) ).
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/benchmark/theBenchmark.p',eqbreln) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_225,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_226,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_227,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_228,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_229,plain,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuEu]) ).
thf(c_0_230,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_231,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_232,plain,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descr__Cong]) ).
thf(c_0_233,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_234,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_235,plain,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( dsetconstr @ X5
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).
thf(c_0_236,plain,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
@ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[apProp]) ).
thf(c_0_237,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_238,plain,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X31 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_239,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X32 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_240,plain,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E2]) ).
thf(c_0_241,plain,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X36 @ Z0 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[beta1]) ).
thf(c_0_242,plain,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
= X29 ) ) ),
inference(fof_simplification,[status(thm)],[eta1]) ).
thf(c_0_243,plain,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X37 @ Z0 ) )
= ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X37 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2lamEq]) ).
thf(c_0_244,plain,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X38 @ Z0 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[beta2]) ).
thf(c_0_245,plain,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
= X29 ) ) ),
inference(fof_simplification,[status(thm)],[eta2]) ).
thf(c_0_246,plain,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X39
& ( Z0 = X2 ) )
| ( ~ X39
& ( Z0 = X3 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iffalseProp1]) ).
thf(c_0_247,plain,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X40
& ( Z0 = X2 ) )
| ( ~ X40
& ( Z0 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iffalseProp2]) ).
thf(c_0_248,plain,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X41
& ( Z0 = X2 ) )
| ( ~ X41
& ( Z0 = X3 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp1]) ).
thf(c_0_249,plain,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X42
& ( Z0 = X2 ) )
| ( ~ X42
& ( Z0 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp2]) ).
thf(c_0_250,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_251,plain,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ ( powerset @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[sepInPowerset]) ).
thf(c_0_252,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_253,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_254,plain,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E1]) ).
thf(c_0_255,plain,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I]) ).
thf(c_0_256,plain,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_257,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_258,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_259,plain,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
<=> ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu__Cong]) ).
thf(c_0_260,plain,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE3u]) ).
thf(c_0_261,plain,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI2]) ).
thf(c_0_262,plain,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI3]) ).
thf(c_0_263,plain,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI1]) ).
thf(c_0_264,plain,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= emptyset )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[emptyE1]) ).
thf(c_0_265,plain,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE2]) ).
thf(c_0_266,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_267,plain,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[nonemptyI]) ).
thf(c_0_268,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_269,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_270,plain,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE1]) ).
thf(c_0_271,plain,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_272,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_273,plain,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_274,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_275,plain,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[replAx]) ).
thf(c_0_276,plain,
( epred1_0
<=> ! [X770: $i] :
? [X771: $i] :
( ! [X772: $i] :
( ( in @ X772 @ X771 )
=> ! [X773: $i] :
( ( in @ X773 @ X772 )
=> ( in @ X773 @ X770 ) ) )
& ! [X774: $i,X775: $i] :
( ( ( in @ X774 @ X770 )
& ( in @ X775 @ X770 ) )
=> ( ! [X776: $i] :
( ( in @ X776 @ X771 )
=> ( ( in @ X774 @ X776 )
<=> ( in @ X775 @ X776 ) ) )
=> ( X774 = X775 ) ) )
& ! [X777: $i,X778: $i] :
( ( ( in @ X777 @ X771 )
& ( in @ X778 @ X771 ) )
=> ( ! [X779: $i] :
( ( in @ X779 @ X777 )
=> ( in @ X779 @ X778 ) )
| ! [X780: $i] :
( ( in @ X780 @ X778 )
=> ( in @ X780 @ X777 ) ) ) )
& ! [X781: $i] :
( ( ! [X782: $i] :
( ( in @ X782 @ X781 )
=> ( in @ X782 @ X770 ) )
& ? [X783: $i] : ( in @ X783 @ X781 ) )
=> ? [X784: $i,X785: $i] :
( ( in @ X784 @ X771 )
& ( in @ X785 @ X781 )
& ~ ? [X786: $i] :
( ( in @ X786 @ X784 )
& ( in @ X786 @ X781 ) )
& ! [X787: $i] :
( ( in @ X787 @ X771 )
=> ( ! [X788: $i] :
( ( in @ X788 @ X787 )
=> ( in @ X788 @ X784 ) )
| ( in @ X785 @ X787 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_277,negated_conjecture,
~ ( ! [X743: $i,X744: $i] :
( ! [X745: $i] :
( ( in @ X745 @ X743 )
<=> ( in @ X745 @ X744 ) )
=> ( X743 = X744 ) )
=> ( ! [X746: $i] :
~ ( in @ X746 @ emptyset )
=> ( ! [X747: $i,X748: $i,X749: $i] :
( ( in @ X749 @ ( setadjoin @ X747 @ X748 ) )
<=> ( ( X749 = X747 )
| ( in @ X749 @ X748 ) ) )
=> ( ! [X750: $i,X751: $i] :
( ( in @ X751 @ ( powerset @ X750 ) )
<=> ! [X752: $i] :
( ( in @ X752 @ X751 )
=> ( in @ X752 @ X750 ) ) )
=> ( ! [X753: $i,X754: $i] :
( ( in @ X754 @ ( setunion @ X753 ) )
<=> ? [X755: $i] :
( ( in @ X754 @ X755 )
& ( in @ X755 @ X753 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X756: $i] :
( ( in @ X756 @ omega )
=> ( in @ ( setadjoin @ X756 @ X756 ) @ omega ) )
=> ( ! [X757: $i] :
( ( ( in @ emptyset @ X757 )
& ! [X758: $i] :
( ( ( in @ X758 @ omega )
& ( in @ X758 @ X757 ) )
=> ( in @ ( setadjoin @ X758 @ X758 ) @ X757 ) ) )
=> ! [X759: $i] :
( ( in @ X759 @ omega )
=> ( in @ X759 @ X757 ) ) )
=> ( ! [X760: $i > $i > $o,X761: $i] :
( ! [X762: $i] :
( ( in @ X762 @ X761 )
=> ( exu @ ( X760 @ X762 ) ) )
=> ? [X763: $i] :
! [X764: $i] :
( ( in @ X764 @ X763 )
<=> ? [X765: $i] :
( ( in @ X765 @ X761 )
& ( X760 @ X765 @ X764 ) ) ) )
=> ( ! [X766: $i] :
( ? [X767: $i] : ( in @ X767 @ X766 )
=> ? [X768: $i] :
( ( in @ X768 @ X766 )
& ~ ? [X769: $i] :
( ( in @ X769 @ X768 )
& ( in @ X769 @ X766 ) ) ) )
=> ( epred1_0
=> ( ! [X789: $i > $o] :
( ( exu @ X789 )
=> ( X789
@ ( descr
@ ^ [Z0: $i] : ( X789 @ Z0 ) ) ) )
=> ( ! [X790: $i,X791: $i > $o,X792: $i] :
( ( in @ X792 @ X790 )
=> ( ( X791 @ X792 )
=> ( in @ X792 @ ( dsetconstr @ X790 @ X791 ) ) ) )
=> ( ! [X793: $i,X794: $i > $o,X795: $i] :
( ( in @ X795 @ ( dsetconstr @ X793 @ X794 ) )
=> ( in @ X795 @ X793 ) )
=> ( ! [X796: $i,X797: $i > $o,X798: $i] :
( ( in @ X798 @ ( dsetconstr @ X796 @ X797 ) )
=> ( X797 @ X798 ) )
=> ( ! [X799: $i > $o] :
( ( exu @ X799 )
=> ? [X800: $i] :
( ( X799 @ X800 )
& ! [X801: $i] :
( ( X799 @ X801 )
=> ( X800 = X801 ) ) ) )
=> ( ! [X802: $o,X803: $i] :
( ( in @ X803 @ ( prop2set @ X802 ) )
=> X802 )
=> ( ! [X804: $i] :
( ( in @ X804 @ emptyset )
=> ! [X805: $o] : X805 )
=> ( ! [X806: $i] :
( ( in @ X806 @ emptyset )
=> ~ $true )
=> ( ! [X807: $i] :
~ ( in @ X807 @ emptyset )
=> ( ! [X808: $i > $o] :
( ( exu @ X808 )
=> ? [X809: $i] : ( X808 @ X809 ) )
=> ( ! [X810: $i,X811: $i] :
( ! [X812: $i] :
( ( in @ X812 @ X810 )
=> ( in @ X812 @ X811 ) )
=> ( ! [X813: $i] :
( ( in @ X813 @ X811 )
=> ( in @ X813 @ X810 ) )
=> ( X810 = X811 ) ) )
=> ( ! [X814: $i] :
( ! [X815: $i] :
~ ( in @ X815 @ X814 )
=> ( X814 = emptyset ) )
=> ( ! [X816: $i] :
( ! [X817: $i] :
~ ( in @ X817 @ X816 )
=> ( X816 = emptyset ) )
=> ( ! [X818: $i,X819: $i > $o,X820: $i] :
( ( in @ X820 @ X818 )
=> ( ( in @ X820 @ ( dsetconstr @ X818 @ X819 ) )
<=> ( X819 @ X820 ) ) )
=> ( ! [X821: $i] :
( ( nonempty @ X821 )
=> ? [X822: $i] : ( in @ X822 @ X821 ) )
=> ( ! [X823: $i,X824: $i > $o,X825: $i] :
( ( in @ X825 @ X823 )
=> ( ( X824 @ X825 )
=> ( nonempty @ ( dsetconstr @ X823 @ X824 ) ) ) )
=> ( ! [X826: $i] :
( ? [X827: $i] : ( in @ X827 @ X826 )
=> ( nonempty @ X826 ) )
=> ( ! [X828: $i,X829: $i] : ( in @ X828 @ ( setadjoin @ X828 @ X829 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X830: $i,X831: $i,X832: $i] :
( ( in @ X832 @ X831 )
=> ( in @ X832 @ ( setadjoin @ X830 @ X831 ) ) )
=> ( ! [X833: $i,X834: $i,X835: $i] :
( ( in @ X835 @ ( setadjoin @ X833 @ X834 ) )
=> ! [X836: $o] :
( ( ( X835 = X833 )
=> X836 )
=> ( ( ( in @ X835 @ X834 )
=> X836 )
=> X836 ) ) )
=> ( ! [X837: $i,X838: $i,X839: $i] :
( ( in @ X839 @ ( setadjoin @ X837 @ X838 ) )
=> ( ( X839 = X837 )
| ( in @ X839 @ X838 ) ) )
=> ( ! [X840: $i] :
( ( dsetconstr @ X840
@ ^ [Z0: $i] : $true )
= X840 )
=> ( ! [X841: $i,X842: $i] :
( ! [X843: $i] :
( ( in @ X843 @ X842 )
=> ( in @ X843 @ X841 ) )
=> ( in @ X842 @ ( powerset @ X841 ) ) )
=> ( ! [X844: $i] : ( in @ emptyset @ ( powerset @ X844 ) )
=> ( ! [X845: $i] : ( in @ emptyset @ ( powerset @ X845 ) )
=> ( ! [X846: $i,X847: $i,X848: $i] :
( ( in @ X847 @ ( powerset @ X846 ) )
=> ( ( in @ X848 @ X847 )
=> ( in @ X848 @ X846 ) ) )
=> ( ! [X849: $i,X850: $i,X851: $i] :
( ( in @ X850 @ X851 )
=> ( ( in @ X851 @ X849 )
=> ( in @ X850 @ ( setunion @ X849 ) ) ) )
=> ( ! [X852: $i,X853: $i] :
( ( in @ X853 @ ( setunion @ X852 ) )
=> ! [X854: $o] :
( ! [X855: $i] :
( ( in @ X853 @ X855 )
=> ( ( in @ X855 @ X852 )
=> X854 ) )
=> X854 ) )
=> ( ! [X856: $i,X857: $i] :
( ( in @ X857 @ X856 )
=> ( in @ X857 @ ( powerset @ ( setunion @ X856 ) ) ) )
=> ( ! [X858: $i > $o] :
( ( exu @ X858 )
=> ? [X859: $i] :
! [X860: $i] :
( ( X858 @ X860 )
<=> ( X860 = X859 ) ) )
=> ( ! [X861: $i] :
( ( nonempty @ X861 )
=> ? [X862: $i] :
( ( in @ X862 @ X861 )
& $true ) )
=> ( ! [X863: $i,X864: $i] :
( ( in @ X863 @ ( setadjoin @ X864 @ emptyset ) )
=> ( X863 = X864 ) )
=> ( ! [X865: $i,X866: $i] :
( ( X865 != X866 )
=> ~ ( in @ X866 @ ( setadjoin @ X865 @ emptyset ) ) )
=> ( ! [X867: $i,X868: $i] :
( ( X867 = X868 )
=> ( in @ X867 @ ( setadjoin @ X868 @ emptyset ) ) )
=> ( ! [X869: $i,X870: $i] :
( ( in @ X869 @ ( setadjoin @ X870 @ emptyset ) )
=> ( in @ X870 @ ( setadjoin @ X869 @ emptyset ) ) )
=> ( ! [X871: $i,X872: $i,X873: $i] :
( ( in @ X873 @ ( setadjoin @ X871 @ ( setadjoin @ X872 @ emptyset ) ) )
=> ( ( X873 = X871 )
| ( X873 = X872 ) ) )
=> ( ! [X874: $i,X875: $i] : ( in @ X874 @ ( setadjoin @ X874 @ ( setadjoin @ X875 @ emptyset ) ) )
=> ( ! [X876: $i,X877: $i] : ( in @ X877 @ ( setadjoin @ X876 @ ( setadjoin @ X877 @ emptyset ) ) )
=> ( ! [X878: $i,X879: $i > $o] :
( ? [X880: $i] :
( ( in @ X880 @ X878 )
& ( X879 @ X880 ) )
=> ( ( ( dsetconstr @ X878 @ X879 )
= emptyset )
=> ~ $true ) )
=> ( ! [X881: $i > $o,X882: $i] :
( ( in @ X882 @ emptyset )
=> ( X881 @ X882 ) )
=> ( ! [X883: $i,X884: $i > $o] :
( ~ ! [X885: $i] :
( ( in @ X885 @ X883 )
=> ( X884 @ X885 ) )
=> ? [X886: $i] :
( ( in @ X886 @ X883 )
& ~ ( X884 @ X886 ) ) )
=> ( ! [X887: $i,X888: $i > $o] :
( ! [X889: $i] :
( ( in @ X889 @ X887 )
=> ~ ( X888 @ X889 ) )
=> ~ ? [X890: $i] :
( ( in @ X890 @ X887 )
& ( X888 @ X890 ) ) )
=> ( ! [X891: $i,X892: $i > $o] :
( ~ ? [X893: $i] :
( ( in @ X893 @ X891 )
& ( X892 @ X893 ) )
=> ! [X894: $i] :
( ( in @ X894 @ X891 )
=> ~ ( X892 @ X894 ) ) )
=> ( ! [X895: $i,X896: $i > $o] :
( ? [X897: $i] :
( ( in @ X897 @ X895 )
& ~ ( X896 @ X897 ) )
=> ~ ! [X898: $i] :
( ( in @ X898 @ X895 )
=> ( X896 @ X898 ) ) )
=> ( ! [X899: $o] :
( X899
=> ( in @ emptyset @ ( prop2set @ X899 ) ) )
=> ( prop2set2propI
=> ( ! [X900: $i,X901: $i > $o] :
( ~ ? [X902: $i] :
( ( in @ X902 @ X900 )
& ( X901 @ X902 ) )
=> ! [X903: $i] :
( ( in @ X903 @ X900 )
=> ~ ( X901 @ X903 ) ) )
=> ( ! [X904: $i,X905: $i > $o] :
( ~ ! [X906: $i] :
( ( in @ X906 @ X904 )
=> ( X905 @ X906 ) )
=> ? [X907: $i] :
( ( in @ X907 @ X904 )
& ~ ( X905 @ X907 ) ) )
=> ( ! [X908: $i > $o] :
( ? [X909: $i] :
( ( X908 @ X909 )
& ! [X910: $i] :
( ( X908 @ X910 )
=> ( X909 = X910 ) ) )
=> ( exu @ X908 ) )
=> ( ! [X911: $i > $o] :
( ? [X912: $i] : ( X911 @ X912 )
=> ( ! [X913: $i,X914: $i] :
( ( X911 @ X913 )
=> ( ( X911 @ X914 )
=> ( X913 = X914 ) ) )
=> ( exu @ X911 ) ) )
=> ( ! [X915: $i > $o] :
( ? [X916: $i] :
! [X917: $i] :
( ( X915 @ X917 )
<=> ( X917 = X916 ) )
=> ( exu @ X915 ) )
=> ( ! [X918: $i,X919: $i] :
( ( X918 = X919 )
=> ! [X920: $i,X921: $i] :
( ( X920 = X921 )
=> ( ( in @ X920 @ X918 )
=> ( in @ X921 @ X919 ) ) ) )
=> ( ! [X922: $i,X923: $i] :
( ( X922 = X923 )
=> ! [X924: $i,X925: $i] :
( ( X924 = X925 )
=> ( ( in @ X924 @ X922 )
<=> ( in @ X925 @ X923 ) ) ) )
=> ( ! [X926: $i > $o] :
( ( exu @ X926 )
=> ! [X927: $i,X928: $i] :
( ( X926 @ X927 )
=> ( ( X926 @ X928 )
=> ( X927 = X928 ) ) ) )
=> ( ! [X929: $i > $o,X930: $i > $o] :
( ! [X931: $i,X932: $i] :
( ( X931 = X932 )
=> ( ( X929 @ X931 )
<=> ( X930 @ X932 ) ) )
=> ( ( exu @ X929 )
<=> ( exu @ X930 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X933: $i,X934: $i] :
( ( X933 = X934 )
=> ! [X935: $i,X936: $i] :
( ( X935 = X936 )
=> ( ( setadjoin @ X933 @ X935 )
= ( setadjoin @ X934 @ X936 ) ) ) )
=> ( ! [X937: $i,X938: $i] :
( ( X937 = X938 )
=> ( ( powerset @ X937 )
= ( powerset @ X938 ) ) )
=> ( ! [X939: $i,X940: $i] :
( ( X939 = X940 )
=> ( ( setunion @ X939 )
= ( setunion @ X940 ) ) )
=> ( ( omega = omega )
=> ( ! [X941: $i > $o] :
( ( exu @ X941 )
=> ! [X942: $i,X943: $i] :
( ( X941 @ X942 )
=> ( ( X941 @ X943 )
=> ( X942 = X943 ) ) ) )
=> ( ! [X944: $i > $o,X945: $i > $o] :
( ! [X946: $i,X947: $i] :
( ( X946 = X947 )
=> ( ( X944 @ X946 )
<=> ( X945 @ X947 ) ) )
=> ( ( exu @ X944 )
=> ( ( exu @ X945 )
=> ( ( descr @ X944 )
= ( descr @ X945 ) ) ) ) )
=> ( ! [X948: $i,X949: $i] :
( ( X948 = X949 )
=> ! [X950: $i > $o,X951: $i > $o] :
( ! [X952: $i] :
( ( in @ X952 @ X948 )
=> ! [X953: $i] :
( ( in @ X953 @ X949 )
=> ( ( X952 = X953 )
=> ( ( X950 @ X952 )
<=> ( X951 @ X953 ) ) ) ) )
=> ( ( dsetconstr @ X948 @ X950 )
= ( dsetconstr @ X949 @ X951 ) ) ) )
=> ( ! [X954: $i,X955: $i] :
( ! [X956: $i] :
( ( in @ X956 @ X954 )
=> ( in @ X956 @ X955 ) )
=> ( subset @ X954 @ X955 ) )
=> ( ! [X957: $i,X958: $i] :
( ( X957 = X958 )
=> ( subset @ X958 @ X957 ) )
=> ( ! [X959: $i,X960: $i] :
( ( X959 = X960 )
=> ( subset @ X959 @ X960 ) )
=> ( ! [X961: $i,X962: $i] :
( ! [X963: $i] :
( ( in @ X963 @ X961 )
=> ( in @ X963 @ X962 ) )
=> ( subset @ X961 @ X962 ) )
=> ( ! [X964: $i] : ( subset @ emptyset @ X964 )
=> ( ! [X965: $i,X966: $i,X967: $i] :
( ( subset @ X965 @ X966 )
=> ( ( in @ X967 @ X965 )
=> ( in @ X967 @ X966 ) ) )
=> ( ! [X968: $i,X969: $i,X970: $i] :
( ( subset @ X968 @ X969 )
=> ( ~ ( in @ X970 @ X969 )
=> ~ ( in @ X970 @ X968 ) ) )
=> ( ! [X971: $i,X972: $i,X973: $i] :
( ( in @ X973 @ X971 )
=> ( ~ ( in @ X973 @ X972 )
=> ~ ( subset @ X971 @ X972 ) ) )
=> ( ! [X974: $i,X975: $i] :
( ~ ( subset @ X974 @ X975 )
=> ( X974 != X975 ) )
=> ( ! [X976: $i,X977: $i,X978: $i] :
( ( in @ X978 @ X976 )
=> ( ~ ( in @ X978 @ X977 )
=> ( X976 != X977 ) ) )
=> ( ! [X979: $i] : ( subset @ X979 @ X979 )
=> ( ! [X980: $i,X981: $i,X982: $i] :
( ( subset @ X980 @ X981 )
=> ( ( subset @ X981 @ X982 )
=> ( subset @ X980 @ X982 ) ) )
=> ( ! [X983: $i,X984: $i] : ( subset @ X984 @ ( setadjoin @ X983 @ X984 ) )
=> ( ! [X985: $i,X986: $i,X987: $i] :
( ( subset @ X985 @ X987 )
=> ( subset @ X985 @ ( setadjoin @ X986 @ X987 ) ) )
=> ( ! [X988: $i,X989: $i] :
( ( subset @ X988 @ X989 )
=> ( in @ X988 @ ( powerset @ X989 ) ) )
=> ( ! [X990: $i,X991: $i] :
( ( subset @ X990 @ X991 )
=> ( ( subset @ X991 @ X990 )
=> ( X990 = X991 ) ) )
=> ( ! [X992: $i] :
( ( subset @ X992 @ emptyset )
=> ( X992 = emptyset ) )
=> ( ! [X993: $i,X994: $i] :
( ( subset @ X994 @ X993 )
=> ( in @ X994 @ ( powerset @ X993 ) ) )
=> ( ! [X995: $i,X996: $i] :
( ( in @ X996 @ ( powerset @ X995 ) )
=> ( subset @ X996 @ X995 ) )
=> ( ! [X997: $i] : ( in @ X997 @ ( powerset @ X997 ) )
=> ( ! [X998: $i,X999: $i] :
( ( subset @ X998 @ X999 )
=> ( subset @ ( powerset @ X998 ) @ ( powerset @ X999 ) ) )
=> ( ! [X1000: $i,X1001: $i > $o] : ( in @ ( dsetconstr @ X1000 @ X1001 ) @ ( powerset @ X1000 ) )
=> ( ! [X1002: $i,X1003: $i > $o] : ( subset @ ( dsetconstr @ X1002 @ X1003 ) @ X1002 )
=> ( ! [X1004: $i,X1005: $i,X1006: $i] :
( ( in @ X1006 @ X1004 )
=> ( in @ X1006 @ ( binunion @ X1004 @ X1005 ) ) )
=> ( ! [X1007: $i,X1008: $i] : ( in @ X1008 @ ( setadjoin @ X1007 @ ( setadjoin @ X1008 @ emptyset ) ) )
=> ( ! [X1009: $i,X1010: $i,X1011: $i] :
( ( in @ X1011 @ X1010 )
=> ( in @ X1011 @ ( binunion @ X1009 @ X1010 ) ) )
=> ( ! [X1012: $i,X1013: $i,X1014: $i,X1015: $o] :
( ( in @ X1014 @ ( binunion @ X1012 @ X1013 ) )
=> ( ( ( in @ X1014 @ X1012 )
=> X1015 )
=> ( ( ( in @ X1014 @ X1013 )
=> X1015 )
=> X1015 ) ) )
=> ( ! [X1016: $i,X1017: $i,X1018: $i] :
( ( in @ X1018 @ ( binunion @ X1016 @ X1017 ) )
=> ( ( in @ X1018 @ X1016 )
| ( in @ X1018 @ X1017 ) ) )
=> ( ! [X1019: $i,X1020: $i] : ( subset @ X1019 @ ( binunion @ X1019 @ X1020 ) )
=> ( ! [X1021: $i,X1022: $i] : ( subset @ X1022 @ ( binunion @ X1021 @ X1022 ) )
=> ( ! [X1023: $i,X1024: $i,X1025: $i] :
( ( in @ X1025 @ X1023 )
=> ( ( in @ X1025 @ X1024 )
=> ( in @ X1025 @ ( binintersect @ X1023 @ X1024 ) ) ) )
=> ( ! [X1026: $i,X1027: $i,X1028: $i] :
( ( subset @ X1028 @ X1026 )
=> ( ( subset @ X1028 @ X1027 )
=> ( subset @ X1028 @ ( binintersect @ X1026 @ X1027 ) ) ) )
=> ( ! [X1029: $i,X1030: $i,X1031: $i] :
( ( in @ X1031 @ ( binintersect @ X1029 @ X1030 ) )
=> ( in @ X1031 @ X1029 ) )
=> ( ! [X1032: $i,X1033: $i] : ( subset @ ( binintersect @ X1032 @ X1033 ) @ X1032 )
=> ( ! [X1034: $i,X1035: $i] :
( ( subset @ X1034 @ X1035 )
=> ( ( binintersect @ X1034 @ X1035 )
= X1034 ) )
=> ( ! [X1036: $i,X1037: $i] :
( ( ( binintersect @ X1036 @ X1037 )
= X1037 )
=> ( subset @ X1037 @ X1036 ) )
=> ( ! [X1038: $i,X1039: $i,X1040: $i] :
( ( in @ X1040 @ ( binintersect @ X1038 @ X1039 ) )
=> ( in @ X1040 @ X1039 ) )
=> ( ! [X1041: $i,X1042: $i] :
( ~ ? [X1043: $i] :
( ( in @ X1043 @ X1041 )
& ( in @ X1043 @ X1042 ) )
=> ( ( binintersect @ X1041 @ X1042 )
= emptyset ) )
=> ( ! [X1044: $i,X1045: $i] : ( subset @ ( binintersect @ X1044 @ X1045 ) @ X1045 )
=> ( ! [X1046: $i,X1047: $i] :
( ( subset @ X1047 @ X1046 )
=> ( ( binintersect @ X1046 @ X1047 )
= X1047 ) )
=> ( ! [X1048: $i,X1049: $i] :
( ( ( binintersect @ X1048 @ X1049 )
= X1048 )
=> ( subset @ X1048 @ X1049 ) )
=> ( ! [X1050: $i,X1051: $i,X1052: $i] :
( ( binintersect @ X1050 @ ( binunion @ X1051 @ X1052 ) )
= ( binunion @ ( binintersect @ X1050 @ X1051 ) @ ( binintersect @ X1050 @ X1052 ) ) )
=> ( ! [X1053: $i,X1054: $i,X1055: $i] :
( ( in @ X1055 @ X1053 )
=> ( ~ ( in @ X1055 @ X1054 )
=> ( in @ X1055 @ ( setminus @ X1053 @ X1054 ) ) ) )
=> ( ! [X1056: $i,X1057: $i,X1058: $i] :
( ( in @ X1058 @ ( setminus @ X1056 @ X1057 ) )
=> ( in @ X1058 @ X1056 ) )
=> ( ! [X1059: $i,X1060: $i,X1061: $i] :
( ( in @ X1061 @ ( setminus @ X1059 @ X1060 ) )
=> ~ ( in @ X1061 @ X1060 ) )
=> ( ! [X1062: $i,X1063: $i] :
( ( subset @ X1062 @ X1063 )
=> ( ( setminus @ X1062 @ X1063 )
= emptyset ) )
=> ( ! [X1064: $i,X1065: $i,X1066: $i] :
( ~ ( in @ X1066 @ ( setminus @ X1064 @ X1065 ) )
=> ( ( in @ X1066 @ X1064 )
=> ( in @ X1066 @ X1065 ) ) )
=> ( ! [X1067: $i,X1068: $i,X1069: $i] :
( ~ ( in @ X1069 @ ( setminus @ X1067 @ X1068 ) )
=> ( ~ ( in @ X1069 @ X1068 )
=> ~ ( in @ X1069 @ X1067 ) ) )
=> ( ! [X1070: $i,X1071: $i,X1072: $i] :
( ~ ( in @ X1072 @ X1070 )
=> ~ ( in @ X1072 @ ( setminus @ X1070 @ X1071 ) ) )
=> ( ! [X1073: $i,X1074: $i,X1075: $i] :
( ( in @ X1075 @ X1074 )
=> ~ ( in @ X1075 @ ( setminus @ X1073 @ X1074 ) ) )
=> ( ! [X1076: $i,X1077: $i] : ( subset @ ( setminus @ X1076 @ X1077 ) @ X1076 )
=> ( ! [X1078: $i,X1079: $i] :
( ( ( setminus @ X1078 @ X1079 )
= emptyset )
=> ( subset @ X1078 @ X1079 ) )
=> ( ! [X1080: $i,X1081: $i,X1082: $i] :
( ( in @ X1082 @ ( symdiff @ X1080 @ X1081 ) )
=> ! [X1083: $o] :
( ( ( in @ X1082 @ X1080 )
=> ( ~ ( in @ X1082 @ X1081 )
=> X1083 ) )
=> ( ( ~ ( in @ X1082 @ X1080 )
=> ( ( in @ X1082 @ X1081 )
=> X1083 ) )
=> X1083 ) ) )
=> ( ! [X1084: $i,X1085: $i,X1086: $i] :
( ( in @ X1086 @ X1084 )
=> ( ~ ( in @ X1086 @ X1085 )
=> ( in @ X1086 @ ( symdiff @ X1084 @ X1085 ) ) ) )
=> ( ! [X1087: $i,X1088: $i,X1089: $i] :
( ~ ( in @ X1089 @ X1087 )
=> ( ( in @ X1089 @ X1088 )
=> ( in @ X1089 @ ( symdiff @ X1087 @ X1088 ) ) ) )
=> ( ! [X1090: $i,X1091: $i,X1092: $i] :
( ( in @ X1092 @ X1090 )
=> ( ( in @ X1092 @ X1091 )
=> ~ ( in @ X1092 @ ( symdiff @ X1090 @ X1091 ) ) ) )
=> ( ! [X1093: $i,X1094: $i,X1095: $i] :
( ~ ( in @ X1095 @ X1093 )
=> ( ~ ( in @ X1095 @ X1094 )
=> ~ ( in @ X1095 @ ( symdiff @ X1093 @ X1094 ) ) ) )
=> ( ! [X1096: $i,X1097: $i] : ( in @ X1097 @ ( setadjoin @ X1096 @ ( setadjoin @ X1097 @ emptyset ) ) )
=> ( ! [X1098: $i,X1099: $i] : ( in @ X1098 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1098 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1098 @ ( setadjoin @ X1099 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1100: $i,X1101: $i] : ( in @ X1101 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1100 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1100 @ ( setadjoin @ X1101 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1102: $i,X1103: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1102 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1102 @ ( setadjoin @ X1103 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1104: $i,X1105: $i] : ( iskpair @ ( kpair @ X1104 @ X1105 ) )
=> ( ! [X1106: $i,X1107: $i] :
( ( in @ X1107 @ X1106 )
=> ( subset @ ( setadjoin @ X1107 @ emptyset ) @ X1106 ) )
=> ( ! [X1108: $i,X1109: $i] :
( ( in @ X1109 @ X1108 )
=> ( in @ ( setadjoin @ X1109 @ emptyset ) @ ( powerset @ X1108 ) ) )
=> ( ! [X1110: $i,X1111: $i,X1112: $i] :
( ( in @ X1112 @ X1110 )
=> ( in @ ( setadjoin @ X1112 @ emptyset ) @ ( powerset @ ( binunion @ X1110 @ X1111 ) ) ) )
=> ( ! [X1113: $i,X1114: $i,X1115: $i] :
( ( in @ X1115 @ ( setadjoin @ X1113 @ ( setadjoin @ X1114 @ emptyset ) ) )
=> ( ( X1115 = X1113 )
| ( X1115 = X1114 ) ) )
=> ( ! [X1116: $i,X1117: $i,X1118: $i] :
( ( in @ X1118 @ X1116 )
=> ! [X1119: $i] :
( ( in @ X1119 @ X1117 )
=> ( subset @ ( setadjoin @ X1118 @ ( setadjoin @ X1119 @ emptyset ) ) @ ( binunion @ X1116 @ X1117 ) ) ) )
=> ( ! [X1120: $i,X1121: $i,X1122: $i] :
( ( in @ X1122 @ X1120 )
=> ! [X1123: $i] :
( ( in @ X1123 @ X1121 )
=> ( in @ ( setadjoin @ X1122 @ ( setadjoin @ X1123 @ emptyset ) ) @ ( powerset @ ( binunion @ X1120 @ X1121 ) ) ) ) )
=> ( ! [X1124: $i,X1125: $i,X1126: $i] :
( ( in @ X1126 @ X1124 )
=> ! [X1127: $i] :
( ( in @ X1127 @ X1125 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1126 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1126 @ ( setadjoin @ X1127 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1124 @ X1125 ) ) ) ) )
=> ( ! [X1128: $i,X1129: $i,X1130: $i] :
( ( in @ X1130 @ X1128 )
=> ! [X1131: $i] :
( ( in @ X1131 @ X1129 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1130 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1130 @ ( setadjoin @ X1131 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1128 @ X1129 ) ) ) ) ) )
=> ( ! [X1132: $i,X1133: $i,X1134: $i] :
( ( in @ X1134 @ X1132 )
=> ! [X1135: $i] :
( ( in @ X1135 @ X1133 )
=> ( in @ ( kpair @ X1134 @ X1135 ) @ ( powerset @ ( powerset @ ( binunion @ X1132 @ X1133 ) ) ) ) ) )
=> ( ! [X1136: $i,X1137: $i,X1138: $i] :
( ( in @ X1138 @ X1136 )
=> ! [X1139: $i] :
( ( in @ X1139 @ X1137 )
=> ( in @ ( kpair @ X1138 @ X1139 ) @ ( cartprod @ X1136 @ X1137 ) ) ) )
=> ( ! [X1140: $i,X1141: $i,X1142: $i] :
( ( in @ X1142 @ ( cartprod @ X1140 @ X1141 ) )
=> ? [X1143: $i] :
( ( in @ X1143 @ X1140 )
& ? [X1144: $i] :
( ( in @ X1144 @ X1141 )
& ( X1142
= ( kpair @ X1143 @ X1144 ) ) ) ) )
=> ( ! [X1145: $i,X1146: $i,X1147: $i] :
( ( in @ X1147 @ ( cartprod @ X1145 @ X1146 ) )
=> ( iskpair @ X1147 ) )
=> ( ! [X1148: $i,X1149: $i] :
( ( in @ X1149 @ ( setunion @ X1148 ) )
=> ? [X1150: $i] :
( ( in @ X1150 @ X1148 )
& ( in @ X1149 @ X1150 ) ) )
=> ( ! [X1151: $i] : ( subset @ ( setunion @ ( setadjoin @ X1151 @ emptyset ) ) @ X1151 )
=> ( ! [X1152: $i] : ( subset @ X1152 @ ( setunion @ ( setadjoin @ X1152 @ emptyset ) ) )
=> ( ! [X1153: $i] :
( ( setunion @ ( setadjoin @ X1153 @ emptyset ) )
= X1153 )
=> ( ! [X1154: $i,X1155: $i > $o] :
( ! [X1156: $i] :
( ( in @ X1156 @ X1154 )
=> ! [X1157: $i] :
( ( in @ X1157 @ X1154 )
=> ( ( X1155 @ X1156 )
=> ( ( X1155 @ X1157 )
=> ( X1156 = X1157 ) ) ) ) )
=> ( ? [X1158: $i] :
( ( in @ X1158 @ X1154 )
& ( X1155 @ X1158 ) )
=> ( singleton @ ( dsetconstr @ X1154 @ X1155 ) ) ) )
=> ( ! [X1159: $i,X1160: $i > $o] :
( ( ex1 @ X1159 @ X1160 )
=> ? [X1161: $i] :
( ( in @ X1161 @ X1159 )
& ( X1160 @ X1161 ) ) )
=> ( ! [X1162: $i,X1163: $i > $o,X1164: $i] :
( ( in @ X1164 @ X1162 )
=> ( ( X1163 @ X1164 )
=> ( ! [X1165: $i] :
( ( in @ X1165 @ X1162 )
=> ( ( X1163 @ X1165 )
=> ( X1165 = X1164 ) ) )
=> ( ex1 @ X1162 @ X1163 ) ) ) )
=> ( ! [X1166: $i,X1167: $i > $o] :
( ! [X1168: $i] :
( ( in @ X1168 @ X1166 )
=> ! [X1169: $i] :
( ( in @ X1169 @ X1166 )
=> ( ( X1167 @ X1168 )
=> ( ( X1167 @ X1169 )
=> ( X1168 = X1169 ) ) ) ) )
=> ( ? [X1170: $i] :
( ( in @ X1170 @ X1166 )
& ( X1167 @ X1170 ) )
=> ( ex1 @ X1166 @ X1167 ) ) )
=> ( ! [X1171: $i,X1172: $i] :
( ( ( setadjoin @ X1171 @ emptyset )
= ( setadjoin @ X1172 @ emptyset ) )
=> ( X1171 = X1172 ) )
=> ( ! [X1173: $i,X1174: $i,X1175: $i] :
( ( in @ ( setadjoin @ X1175 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1173 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1173 @ ( setadjoin @ X1174 @ emptyset ) ) @ emptyset ) ) )
=> ( X1173 = X1175 ) )
=> ( ! [X1176: $i] :
( ( iskpair @ X1176 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1176 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1176 ) ) ) )
=> ( ! [X1177: $i] :
( ( singleton @ X1177 )
=> ( in @ ( setunion @ X1177 ) @ X1177 ) )
=> ( ! [X1178: $i,X1179: $i] :
( ( kfst @ ( kpair @ X1178 @ X1179 ) )
= X1178 )
=> ( ! [X1180: $i,X1181: $i,X1182: $i] :
( ( in @ X1182 @ ( cartprod @ X1180 @ X1181 ) )
=> ( in @ ( kfst @ X1182 ) @ X1180 ) )
=> ( ! [X1183: $i,X1184: $i,X1185: $i,X1186: $i] :
( ( ( setadjoin @ ( setadjoin @ X1183 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1183 @ ( setadjoin @ X1184 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1185 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1185 @ ( setadjoin @ X1186 @ emptyset ) ) @ emptyset ) ) )
=> ( X1183 = X1185 ) )
=> ( ! [X1187: $i,X1188: $i,X1189: $i,X1190: $i] :
( ( ( kpair @ X1187 @ X1188 )
= ( kpair @ X1189 @ X1190 ) )
=> ( X1187 = X1189 ) )
=> ( ! [X1191: $i,X1192: $i] :
( ( X1191 = X1192 )
=> ( ( setadjoin @ X1191 @ ( setadjoin @ X1192 @ emptyset ) )
= ( setadjoin @ X1191 @ emptyset ) ) )
=> ( ! [X1193: $i,X1194: $i] :
( ( X1193 = X1194 )
=> ( ( setadjoin @ ( setadjoin @ X1193 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1193 @ ( setadjoin @ X1194 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1193 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1195: $i,X1196: $i,X1197: $i,X1198: $i] :
( ( ( setadjoin @ ( setadjoin @ X1195 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1195 @ ( setadjoin @ X1196 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1197 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1197 @ ( setadjoin @ X1198 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1197 = X1198 )
=> ( X1196 = X1198 ) ) )
=> ( ! [X1199: $i,X1200: $i,X1201: $i] :
( ( ( setadjoin @ X1199 @ ( setadjoin @ X1200 @ emptyset ) )
= ( setadjoin @ X1201 @ emptyset ) )
=> ( X1199 = X1200 ) )
=> ( ! [X1202: $i,X1203: $i,X1204: $i,X1205: $i] :
( ( ( setadjoin @ ( setadjoin @ X1202 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1202 @ ( setadjoin @ X1203 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1204 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1204 @ ( setadjoin @ X1205 @ emptyset ) ) @ emptyset ) ) )
=> ( X1203 = X1205 ) )
=> ( ! [X1206: $i,X1207: $i,X1208: $i,X1209: $i] :
( ( ( kpair @ X1206 @ X1207 )
= ( kpair @ X1208 @ X1209 ) )
=> ( X1207 = X1209 ) )
=> ( ! [X1210: $i] :
( ( iskpair @ X1210 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1210 )
@ ^ [Z0: $i] :
( X1210
= ( kpair @ ( kfst @ X1210 ) @ Z0 ) ) ) ) )
=> ( ! [X1211: $i,X1212: $i] :
( ( ksnd @ ( kpair @ X1211 @ X1212 ) )
= X1212 )
=> ( ! [X1213: $i] :
( ( iskpair @ X1213 )
=> ( ( kpair @ ( kfst @ X1213 ) @ ( ksnd @ X1213 ) )
= X1213 ) )
=> ( ! [X1214: $i,X1215: $i,X1216: $i] :
( ( in @ X1216 @ ( cartprod @ X1214 @ X1215 ) )
=> ( in @ ( ksnd @ X1216 ) @ X1215 ) )
=> ( ! [X1217: $i,X1218: $i,X1219: $i,X1220: $i] :
( ( in @ ( kpair @ X1219 @ X1220 ) @ ( cartprod @ X1217 @ X1218 ) )
=> ( in @ X1219 @ X1217 ) )
=> ( ! [X1221: $i,X1222: $i,X1223: $i,X1224: $i] :
( ( in @ ( kpair @ X1223 @ X1224 ) @ ( cartprod @ X1221 @ X1222 ) )
=> ( in @ X1224 @ X1222 ) )
=> ( ! [X1225: $i,X1226: $i,X1227: $i] :
( ( in @ X1227 @ X1225 )
=> ! [X1228: $i] :
( ( in @ X1228 @ X1226 )
=> ( ( kpair @ X1227 @ X1228 )
= ( kpair @ X1227 @ X1228 ) ) ) )
=> ( ! [X1229: $i,X1230: $i,X1231: $i] :
( ( in @ X1231 @ X1229 )
=> ! [X1232: $i] :
( ( in @ X1232 @ X1230 )
=> ( ( kfst @ ( kpair @ X1231 @ X1232 ) )
= X1231 ) ) )
=> ( ! [X1233: $i,X1234: $i,X1235: $i] :
( ( in @ X1235 @ X1233 )
=> ! [X1236: $i] :
( ( in @ X1236 @ X1234 )
=> ( ( ksnd @ ( kpair @ X1235 @ X1236 ) )
= X1236 ) ) )
=> ( ! [X1237: $i,X1238: $i,X1239: $i] :
( ( in @ X1239 @ ( cartprod @ X1237 @ X1238 ) )
=> ( ( kpair @ ( kfst @ X1239 ) @ ( ksnd @ X1239 ) )
= X1239 ) )
=> ( ! [X1240: $i,X1241: $i,X1242: $i > $i > $o,X1243: $i] :
( ( in @ X1243 @ X1240 )
=> ! [X1244: $i] :
( ( in @ X1244 @ X1241 )
=> ( ( X1242 @ X1243 @ X1244 )
=> ( in @ ( kpair @ X1243 @ X1244 ) @ ( dpsetconstr @ X1240 @ X1241 @ X1242 ) ) ) ) )
=> ( ! [X1245: $i,X1246: $i,X1247: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1245 @ X1246 @ X1247 ) @ ( cartprod @ X1245 @ X1246 ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i > $i > $o] : ( breln @ X1248 @ X1249 @ ( dpsetconstr @ X1248 @ X1249 @ X1250 ) )
=> ( ! [X1251: $i,X1252: $i,X1253: $i > $i > $o,X1254: $i] :
( ( in @ X1254 @ X1251 )
=> ! [X1255: $i] :
( ( in @ X1255 @ X1252 )
=> ( ( in @ ( kpair @ X1254 @ X1255 ) @ ( dpsetconstr @ X1251 @ X1252 @ X1253 ) )
=> ( X1253 @ X1254 @ X1255 ) ) ) )
=> ( ! [X1256: $i,X1257: $i,X1258: $i > $i > $o,X1259: $i,X1260: $i] :
( ( in @ ( kpair @ X1259 @ X1260 ) @ ( dpsetconstr @ X1256 @ X1257 @ X1258 ) )
=> ( in @ X1259 @ X1256 ) )
=> ( ! [X1261: $i,X1262: $i,X1263: $i > $i > $o,X1264: $i,X1265: $i] :
( ( in @ ( kpair @ X1264 @ X1265 ) @ ( dpsetconstr @ X1261 @ X1262 @ X1263 ) )
=> ( in @ X1265 @ X1262 ) )
=> ( ! [X1266: $i,X1267: $i,X1268: $i > $i > $o,X1269: $i,X1270: $i] :
( ( in @ ( kpair @ X1269 @ X1270 ) @ ( dpsetconstr @ X1266 @ X1267 @ X1268 ) )
=> ( X1268 @ X1269 @ X1270 ) )
=> ( ! [X1271: $i,X1272: $i,X1273: $i] :
( ( func @ X1271 @ X1272 @ X1273 )
=> ! [X1274: $i] :
( ( in @ X1274 @ X1271 )
=> ( singleton
@ ( dsetconstr @ X1272
@ ^ [Z0: $i] : ( in @ ( kpair @ X1274 @ Z0 ) @ X1273 ) ) ) ) )
=> ( ! [X1275: $i,X1276: $i,X1277: $i] :
( ( func @ X1275 @ X1276 @ X1277 )
=> ! [X1278: $i] :
( ( in @ X1278 @ X1275 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1276
@ ^ [Z0: $i] : ( in @ ( kpair @ X1278 @ Z0 ) @ X1277 ) ) )
@ X1276 ) ) )
=> ( ! [X1279: $i,X1280: $i,X1281: $i] :
( ( func @ X1279 @ X1280 @ X1281 )
=> ! [X1282: $i] :
( ( in @ X1282 @ X1279 )
=> ( in @ ( ap @ X1279 @ X1280 @ X1281 @ X1282 ) @ X1280 ) ) )
=> ( ! [X1283: $i,X1284: $i,X1285: $i] :
( ( in @ X1285 @ ( funcSet @ X1283 @ X1284 ) )
=> ( func @ X1283 @ X1284 @ X1285 ) )
=> ( ! [X1286: $i,X1287: $i,X1288: $i] :
( ( in @ X1288 @ ( funcSet @ X1286 @ X1287 ) )
=> ! [X1289: $i] :
( ( in @ X1289 @ X1286 )
=> ( in @ ( ap @ X1286 @ X1287 @ X1288 @ X1289 ) @ X1287 ) ) )
=> ( ! [X1290: $i,X1291: $i,X1292: $i] :
( ( func @ X1290 @ X1291 @ X1292 )
=> ( in @ X1292 @ ( funcSet @ X1290 @ X1291 ) ) )
=> ( ! [X1293: $i,X1294: $i,X1295: $i > $i] :
( ! [X1296: $i] :
( ( in @ X1296 @ X1293 )
=> ( in @ ( X1295 @ X1296 ) @ X1294 ) )
=> ( func @ X1293 @ X1294
@ ( dpsetconstr @ X1293 @ X1294
@ ^ [Z0: $i] : ( $eq @ ( X1295 @ Z0 ) ) ) ) )
=> ( ! [X1297: $i,X1298: $i,X1299: $i > $i] :
( ! [X1300: $i] :
( ( in @ X1300 @ X1297 )
=> ( in @ ( X1299 @ X1300 ) @ X1298 ) )
=> ( func @ X1297 @ X1298 @ ( lam @ X1297 @ X1298 @ X1299 ) ) )
=> ( ! [X1301: $i,X1302: $i,X1303: $i > $i] :
( ! [X1304: $i] :
( ( in @ X1304 @ X1301 )
=> ( in @ ( X1303 @ X1304 ) @ X1302 ) )
=> ( in @ ( lam @ X1301 @ X1302 @ X1303 ) @ ( funcSet @ X1301 @ X1302 ) ) )
=> ( ! [X1305: $i,X1306: $i,X1307: $i] :
( ( breln @ X1305 @ X1306 @ X1307 )
=> ! [X1308: $i > $o] :
( ! [X1309: $i] :
( ( in @ X1309 @ X1305 )
=> ! [X1310: $i] :
( ( in @ X1310 @ X1306 )
=> ( ( in @ ( kpair @ X1309 @ X1310 ) @ X1307 )
=> ( X1308 @ ( kpair @ X1309 @ X1310 ) ) ) ) )
=> ! [X1311: $i] :
( ( in @ X1311 @ X1307 )
=> ( X1308 @ X1311 ) ) ) )
=> ( ! [X1312: $i,X1313: $i,X1314: $i] :
( ( breln @ X1312 @ X1313 @ X1314 )
=> ! [X1315: $i > $o] :
( ! [X1316: $i] :
( ( in @ X1316 @ X1312 )
=> ! [X1317: $i] :
( ( in @ X1317 @ X1313 )
=> ( ( in @ ( kpair @ X1316 @ X1317 ) @ X1314 )
=> ( X1315 @ ( kpair @ X1316 @ X1317 ) ) ) ) )
=> ! [X1318: $i] :
( ( in @ X1318 @ X1314 )
=> ( X1315 @ X1318 ) ) ) )
=> ( ! [X1319: $i,X1320: $i > $o] :
( ( ex1 @ X1319 @ X1320 )
=> ! [X1321: $i] :
( ( in @ X1321 @ X1319 )
=> ! [X1322: $i] :
( ( in @ X1322 @ X1319 )
=> ( ( X1320 @ X1321 )
=> ( ( X1320 @ X1322 )
=> ( X1321 = X1322 ) ) ) ) ) )
=> ( ! [X1323: $i,X1324: $i,X1325: $i] :
( ( func @ X1323 @ X1324 @ X1325 )
=> ! [X1326: $i] :
( ( in @ X1326 @ X1323 )
=> ( in @ ( kpair @ X1326 @ ( ap @ X1323 @ X1324 @ X1325 @ X1326 ) ) @ X1325 ) ) )
=> ( ! [X1327: $i,X1328: $i,X1329: $i] :
( ( in @ X1329 @ ( funcSet @ X1327 @ X1328 ) )
=> ! [X1330: $i] :
( ( in @ X1330 @ X1327 )
=> ( in @ ( kpair @ X1330 @ ( ap @ X1327 @ X1328 @ X1329 @ X1330 ) ) @ X1329 ) ) )
=> ( ! [X1331: $i,X1332: $i,X1333: $i] :
( ( func @ X1331 @ X1332 @ X1333 )
=> ! [X1334: $i] :
( ( in @ X1334 @ X1331 )
=> ! [X1335: $i] :
( ( in @ X1335 @ X1332 )
=> ( ( in @ ( kpair @ X1334 @ X1335 ) @ X1333 )
=> ( ( ap @ X1331 @ X1332 @ X1333 @ X1334 )
= X1335 ) ) ) ) )
=> ( ! [X1336: $i,X1337: $i,X1338: $i] :
( ( func @ X1336 @ X1337 @ X1338 )
=> ! [X1339: $i] :
( ( func @ X1336 @ X1337 @ X1339 )
=> ( ! [X1340: $i] :
( ( in @ X1340 @ X1336 )
=> ( ( ap @ X1336 @ X1337 @ X1338 @ X1340 )
= ( ap @ X1336 @ X1337 @ X1339 @ X1340 ) ) )
=> ! [X1341: $i] :
( ( in @ X1341 @ X1336 )
=> ! [X1342: $i] :
( ( in @ X1342 @ X1337 )
=> ( ( in @ ( kpair @ X1341 @ X1342 ) @ X1339 )
=> ( in @ ( kpair @ X1341 @ X1342 ) @ X1338 ) ) ) ) ) ) )
=> ( ! [X1343: $i,X1344: $i,X1345: $i] :
( ( in @ X1345 @ ( funcSet @ X1343 @ X1344 ) )
=> ! [X1346: $i] :
( ( in @ X1346 @ X1343 )
=> ! [X1347: $i] :
( ( in @ X1347 @ X1344 )
=> ( ( in @ ( kpair @ X1346 @ X1347 ) @ X1345 )
=> ( ( ap @ X1343 @ X1344 @ X1345 @ X1346 )
= X1347 ) ) ) ) )
=> ( ! [X1348: $i,X1349: $i,X1350: $i] :
( ( breln @ X1348 @ X1349 @ X1350 )
=> ! [X1351: $i] :
( ( breln @ X1348 @ X1349 @ X1351 )
=> ( ! [X1352: $i] :
( ( in @ X1352 @ X1348 )
=> ! [X1353: $i] :
( ( in @ X1353 @ X1349 )
=> ( ( in @ ( kpair @ X1352 @ X1353 ) @ X1350 )
=> ( in @ ( kpair @ X1352 @ X1353 ) @ X1351 ) ) ) )
=> ( subset @ X1350 @ X1351 ) ) ) )
=> ( ! [X1354: $i,X1355: $i,X1356: $i] :
( ( breln @ X1354 @ X1355 @ X1356 )
=> ! [X1357: $i] :
( ( breln @ X1354 @ X1355 @ X1357 )
=> ( ! [X1358: $i] :
( ( in @ X1358 @ X1354 )
=> ! [X1359: $i] :
( ( in @ X1359 @ X1355 )
=> ( ( in @ ( kpair @ X1358 @ X1359 ) @ X1356 )
=> ( in @ ( kpair @ X1358 @ X1359 ) @ X1357 ) ) ) )
=> ( ! [X1360: $i] :
( ( in @ X1360 @ X1354 )
=> ! [X1361: $i] :
( ( in @ X1361 @ X1355 )
=> ( ( in @ ( kpair @ X1360 @ X1361 ) @ X1357 )
=> ( in @ ( kpair @ X1360 @ X1361 ) @ X1356 ) ) ) )
=> ( X1356 = X1357 ) ) ) ) )
=> ( ! [X1362: $i,X1363: $i,X1364: $i] :
( ( func @ X1362 @ X1363 @ X1364 )
=> ! [X1365: $i] :
( ( func @ X1362 @ X1363 @ X1365 )
=> ( ! [X1366: $i] :
( ( in @ X1366 @ X1362 )
=> ( ( ap @ X1362 @ X1363 @ X1364 @ X1366 )
= ( ap @ X1362 @ X1363 @ X1365 @ X1366 ) ) )
=> ( X1364 = X1365 ) ) ) )
=> ( ! [X1367: $i,X1368: $i,X1369: $i] :
( ( in @ X1369 @ ( funcSet @ X1367 @ X1368 ) )
=> ! [X1370: $i] :
( ( in @ X1370 @ ( funcSet @ X1367 @ X1368 ) )
=> ( ! [X1371: $i] :
( ( in @ X1371 @ X1367 )
=> ( ( ap @ X1367 @ X1368 @ X1369 @ X1371 )
= ( ap @ X1367 @ X1368 @ X1370 @ X1371 ) ) )
=> ( X1369 = X1370 ) ) ) )
=> ( ! [X1372: $i,X1373: $i,X1374: $i] :
( ( in @ X1374 @ ( funcSet @ X1372 @ X1373 ) )
=> ! [X1375: $i] :
( ( in @ X1375 @ X1372 )
=> ( ( ap @ X1372 @ X1373 @ X1374 @ X1375 )
= ( ap @ X1372 @ X1373 @ X1374 @ X1375 ) ) ) )
=> ( ! [X1376: $i,X1377: $i,X1378: $i] :
( ( func @ X1376 @ X1377 @ X1378 )
=> ! [X1379: $i] :
( ( in @ X1379 @ X1376 )
=> ( ( ap @ X1376 @ X1377 @ X1378 @ X1379 )
= ( ap @ X1376 @ X1377 @ X1378 @ X1379 ) ) ) )
=> ( ! [X1380: $i,X1381: $i,X1382: $i > $i] :
( ! [X1383: $i] :
( ( in @ X1383 @ X1380 )
=> ( in @ ( X1382 @ X1383 ) @ X1381 ) )
=> ! [X1384: $i] :
( ( in @ X1384 @ X1380 )
=> ( ( ap @ X1380 @ X1381 @ ( lam @ X1380 @ X1381 @ X1382 ) @ X1384 )
= ( X1382 @ X1384 ) ) ) )
=> ( ! [X1385: $i,X1386: $i,X1387: $i] :
( ( func @ X1385 @ X1386 @ X1387 )
=> ( ( lam @ X1385 @ X1386 @ ( ap @ X1385 @ X1386 @ X1387 ) )
= X1387 ) )
=> ( ! [X1388: $i,X1389: $i,X1390: $i > $i] :
( ! [X1391: $i] :
( ( in @ X1391 @ X1388 )
=> ( in @ ( X1390 @ X1391 ) @ X1389 ) )
=> ( ( lam @ X1388 @ X1389 @ X1390 )
= ( lam @ X1388 @ X1389 @ X1390 ) ) )
=> ( ! [X1392: $i,X1393: $i,X1394: $i > $i] :
( ! [X1395: $i] :
( ( in @ X1395 @ X1392 )
=> ( in @ ( X1394 @ X1395 ) @ X1393 ) )
=> ! [X1396: $i] :
( ( in @ X1396 @ X1392 )
=> ( ( ap @ X1392 @ X1393 @ ( lam @ X1392 @ X1393 @ X1394 ) @ X1396 )
= ( X1394 @ X1396 ) ) ) )
=> ( ! [X1397: $i,X1398: $i,X1399: $i] :
( ( in @ X1399 @ ( funcSet @ X1397 @ X1398 ) )
=> ( ( lam @ X1397 @ X1398 @ ( ap @ X1397 @ X1398 @ X1399 ) )
= X1399 ) )
=> ( ! [X1400: $i,X1401: $o,X1402: $i] :
( ( in @ X1402 @ X1400 )
=> ! [X1403: $i] :
( ( in @ X1403 @ X1400 )
=> ( ~ X1401
=> ( in @ X1403
@ ( dsetconstr @ X1400
@ ^ [Z0: $i] :
( ( X1401
& ( Z0 = X1402 ) )
| ( ~ X1401
& ( Z0 = X1403 ) ) ) ) ) ) ) )
=> ( ! [X1404: $i,X1405: $o,X1406: $i] :
( ( in @ X1406 @ X1404 )
=> ! [X1407: $i] :
( ( in @ X1407 @ X1404 )
=> ( ~ X1405
=> ( ( dsetconstr @ X1404
@ ^ [Z0: $i] :
( ( X1405
& ( Z0 = X1406 ) )
| ( ~ X1405
& ( Z0 = X1407 ) ) ) )
= ( setadjoin @ X1407 @ emptyset ) ) ) ) )
=> ( ! [X1408: $i,X1409: $o,X1410: $i] :
( ( in @ X1410 @ X1408 )
=> ! [X1411: $i] :
( ( in @ X1411 @ X1408 )
=> ( X1409
=> ( in @ X1410
@ ( dsetconstr @ X1408
@ ^ [Z0: $i] :
( ( X1409
& ( Z0 = X1410 ) )
| ( ~ X1409
& ( Z0 = X1411 ) ) ) ) ) ) ) )
=> ( ! [X1412: $i,X1413: $o,X1414: $i] :
( ( in @ X1414 @ X1412 )
=> ! [X1415: $i] :
( ( in @ X1415 @ X1412 )
=> ( X1413
=> ( ( dsetconstr @ X1412
@ ^ [Z0: $i] :
( ( X1413
& ( Z0 = X1414 ) )
| ( ~ X1413
& ( Z0 = X1415 ) ) ) )
= ( setadjoin @ X1414 @ emptyset ) ) ) ) )
=> ( ! [X1416: $i,X1417: $o,X1418: $i] :
( ( in @ X1418 @ X1416 )
=> ! [X1419: $i] :
( ( in @ X1419 @ X1416 )
=> ( singleton
@ ( dsetconstr @ X1416
@ ^ [Z0: $i] :
( ( X1417
& ( Z0 = X1418 ) )
| ( ~ X1417
& ( Z0 = X1419 ) ) ) ) ) ) )
=> ( ! [X1420: $i,X1421: $o,X1422: $i] :
( ( in @ X1422 @ X1420 )
=> ! [X1423: $i] :
( ( in @ X1423 @ X1420 )
=> ( in @ ( if @ X1420 @ X1421 @ X1422 @ X1423 ) @ X1420 ) ) )
=> ( ! [X1424: $i] :
( ( singleton @ X1424 )
=> ! [X1425: $i] :
( ( in @ X1425 @ X1424 )
=> ( ( setunion @ X1424 )
= X1425 ) ) )
=> ( ! [X1426: $i,X1427: $o,X1428: $i] :
( ( in @ X1428 @ X1426 )
=> ! [X1429: $i] :
( ( in @ X1429 @ X1426 )
=> ( X1427
=> ( ( if @ X1426 @ X1427 @ X1428 @ X1429 )
= X1428 ) ) ) )
=> ( ! [X1430: $i,X1431: $o,X1432: $i] :
( ( in @ X1432 @ X1430 )
=> ! [X1433: $i] :
( ( in @ X1433 @ X1430 )
=> ( ~ X1431
=> ( ( if @ X1430 @ X1431 @ X1432 @ X1433 )
= X1433 ) ) ) )
=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[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)],[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)],[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)],[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)],[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)],[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(assume_negation,[status(cth)],[iftrueorfalse]),subsetE]),funcGraphProp3]),iffalse]),cartprodpairsurjEq]),c_0_225]),c_0_226]),omega__Cong]),c_0_227]),c_0_228]),c_0_229]),c_0_230]),c_0_231]),c_0_232]),c_0_233]),c_0_234]),c_0_235]),c_0_236]),app]),subsetI1]),infuncsetfunc]),ap2p]),eqimpsubset2]),funcinfuncset]),c_0_237]),eqimpsubset1]),c_0_238]),c_0_239]),subsetI2]),brelnall1]),brelnall2]),c_0_240]),emptysetsubset]),funcGraphProp1]),binunionIL]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subsetE2]),subbreln]),eqbreln]),notsubsetI]),funcext]),funcext2]),notequalI1]),ap2apEq1]),ap2apEq2]),c_0_241]),c_0_242]),notequalI2]),c_0_243]),c_0_244]),subsetRefl]),c_0_245]),c_0_246]),subsetTrans]),c_0_247]),c_0_248]),setadjoinSub]),c_0_249]),c_0_250]),setadjoinSub2]),ifp]),theeq]),subset2powerset]),iftrue]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_251]),c_0_252]),setukpairIR]),kpairiskpair]),kpairp]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),emptyset__Cong]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),setadjoin__Cong]),symdiffI2]),powerset__Cong]),symdiffIneg1]),setunion__Cong]),symdiffIneg2]),secondinupair]),setukpairIL]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_253]),c_0_254]),c_0_255]),c_0_256]),singletonsuniq]),setukpairinjL1]),c_0_257]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_258]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),c_0_259]),c_0_260]),in__Cong]),inCongP]),c_0_261]),c_0_262]),c_0_263]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_264]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_265]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_266]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_267]),nonemptyE1]),c_0_268]),noeltsimpempty]),emptyI]),setext]),c_0_269]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_270]),c_0_271]),c_0_272]),c_0_273]),c_0_274]),wellorderingAx]),foundationAx]),c_0_275]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_276]) ).
thf(c_0_278,negated_conjecture,
! [X1434: $i,X1435: $i,X1437: $i,X1438: $i,X1439: $i,X1440: $i,X1441: $i,X1442: $i,X1443: $i,X1444: $i,X1445: $i,X1447: $i,X1448: $i,X1450: $i,X1451: $i,X1452: $i,X1453: $i,X1454: $i,X1456: $i,X1457: $i > $i > $o,X1458: $i,X1461: $i,X1463: $i,X1464: $i,X1465: $i,X1466: $i,X1468: $i,X1469: $i > $o,X1470: $i,X1471: $i > $o,X1472: $i,X1473: $i,X1474: $i > $o,X1475: $i,X1476: $i,X1477: $i > $o,X1478: $i,X1479: $i > $o,X1481: $i,X1482: $o,X1483: $i,X1484: $i,X1485: $o,X1486: $i,X1487: $i,X1488: $i > $o,X1490: $i,X1491: $i,X1494: $i,X1496: $i,X1498: $i,X1499: $i > $o,X1500: $i,X1501: $i,X1503: $i,X1504: $i > $o,X1505: $i,X1506: $i,X1507: $i,X1508: $i,X1509: $i,X1510: $i,X1511: $i,X1512: $i,X1513: $i,X1514: $i,X1515: $i,X1516: $o,X1517: $i,X1518: $i,X1519: $i,X1520: $i,X1521: $i,X1522: $i,X1524: $i,X1525: $i,X1526: $i,X1527: $i,X1528: $i,X1529: $i,X1530: $i,X1531: $i,X1532: $i,X1533: $i,X1534: $o,X1536: $i,X1537: $i,X1538: $i > $o,X1540: $i,X1541: $i,X1542: $i,X1544: $i,X1545: $i,X1546: $i,X1547: $i,X1548: $i,X1549: $i,X1550: $i,X1551: $i,X1552: $i,X1553: $i,X1554: $i,X1555: $i,X1556: $i,X1557: $i,X1558: $i,X1559: $i,X1560: $i > $o,X1561: $i,X1562: $i > $o,X1563: $i,X1564: $i,X1565: $i > $o,X1566: $i,X1568: $i,X1569: $i > $o,X1571: $i,X1572: $i,X1573: $i > $o,X1575: $i,X1576: $i,X1577: $i > $o,X1578: $i,X1580: $o,X1581: $i,X1582: $i > $o,X1584: $i,X1585: $i,X1586: $i > $o,X1587: $i,X1589: $i > $o,X1590: $i,X1592: $i > $o,X1593: $i,X1596: $i > $o,X1597: $i,X1599: $i,X1600: $i,X1601: $i,X1602: $i,X1603: $i,X1604: $i,X1605: $i,X1606: $i,X1607: $i > $o,X1608: $i,X1609: $i,X1610: $i > $o,X1611: $i > $o,X1614: $i,X1615: $i,X1616: $i,X1617: $i,X1618: $i,X1619: $i,X1620: $i,X1621: $i,X1622: $i > $o,X1623: $i,X1624: $i,X1625: $i > $o,X1626: $i > $o,X1629: $i,X1630: $i,X1631: $i > $o,X1632: $i > $o,X1635: $i,X1636: $i,X1638: $i,X1639: $i,X1640: $i,X1641: $i,X1642: $i,X1643: $i,X1645: $i,X1646: $i,X1647: $i,X1648: $i,X1649: $i,X1650: $i,X1651: $i,X1652: $i,X1653: $i,X1654: $i,X1655: $i,X1656: $i,X1657: $i,X1658: $i,X1659: $i,X1660: $i,X1661: $i,X1662: $i,X1663: $i,X1664: $i,X1665: $i,X1666: $i,X1667: $i,X1668: $i,X1669: $i,X1670: $i,X1671: $i,X1672: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i,X1678: $i,X1679: $i,X1680: $i,X1681: $i,X1682: $i > $o,X1683: $i,X1684: $i > $o,X1685: $i,X1686: $i,X1687: $i,X1688: $i,X1689: $i,X1690: $i,X1691: $i,X1692: $i,X1693: $i,X1694: $i,X1695: $i,X1696: $o,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i,X1702: $i,X1703: $i,X1704: $i,X1705: $i,X1706: $i,X1707: $i,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i,X1713: $i,X1714: $i,X1715: $i,X1716: $i,X1717: $i,X1718: $i,X1719: $i,X1720: $i,X1721: $i,X1722: $i,X1723: $i,X1725: $i,X1726: $i,X1727: $i,X1728: $i,X1729: $i,X1730: $i,X1731: $i,X1732: $i,X1733: $i,X1734: $i,X1735: $i,X1736: $i,X1737: $i,X1738: $i,X1739: $i,X1740: $i,X1741: $i,X1742: $i,X1743: $i,X1744: $i,X1745: $i,X1746: $i,X1747: $i,X1748: $i,X1749: $i,X1750: $i,X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1756: $i,X1757: $i,X1758: $i,X1759: $i,X1760: $i,X1761: $i,X1762: $i,X1763: $i,X1764: $o,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1769: $i,X1770: $i,X1771: $i,X1772: $i,X1773: $i,X1774: $i,X1775: $i,X1776: $i,X1777: $i,X1778: $i,X1779: $i,X1780: $i,X1781: $i,X1782: $i,X1783: $i,X1784: $i,X1785: $i,X1786: $i,X1787: $i,X1788: $i,X1789: $i,X1790: $i,X1791: $i,X1792: $i,X1793: $i,X1794: $i,X1795: $i,X1796: $i,X1797: $i,X1798: $i,X1799: $i,X1800: $i,X1801: $i,X1802: $i,X1803: $i,X1804: $i,X1805: $i,X1806: $i,X1807: $i,X1808: $i,X1809: $i,X1810: $i,X1811: $i,X1812: $i,X1813: $i,X1814: $i,X1815: $i,X1816: $i,X1817: $i,X1818: $i,X1819: $i,X1820: $i,X1821: $i,X1822: $i,X1823: $i,X1826: $i,X1827: $i,X1828: $i,X1829: $i,X1830: $i,X1832: $i,X1833: $i,X1834: $i,X1835: $i,X1836: $i > $o,X1839: $i,X1840: $i,X1841: $i > $o,X1843: $i,X1844: $i > $o,X1845: $i,X1847: $i,X1848: $i > $o,X1851: $i,X1852: $i,X1853: $i,X1854: $i,X1855: $i,X1856: $i,X1857: $i,X1858: $i,X1859: $i,X1860: $i,X1861: $i,X1862: $i,X1863: $i,X1864: $i,X1865: $i,X1866: $i,X1867: $i,X1868: $i,X1869: $i,X1870: $i,X1871: $i,X1872: $i,X1873: $i,X1874: $i,X1875: $i,X1876: $i,X1877: $i,X1878: $i,X1879: $i,X1880: $i,X1881: $i,X1882: $i,X1883: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1888: $i,X1889: $i,X1890: $i,X1891: $i,X1892: $i,X1893: $i,X1894: $i,X1895: $i,X1896: $i,X1897: $i,X1898: $i,X1899: $i,X1900: $i,X1901: $i,X1902: $i,X1903: $i,X1904: $i,X1905: $i,X1906: $i,X1907: $i,X1908: $i,X1909: $i,X1910: $i,X1911: $i,X1912: $i,X1913: $i,X1914: $i,X1915: $i,X1916: $i,X1917: $i,X1918: $i,X1919: $i,X1920: $i,X1921: $i,X1922: $i,X1923: $i > $i > $o,X1924: $i,X1925: $i,X1926: $i,X1927: $i,X1928: $i > $i > $o,X1929: $i,X1930: $i,X1931: $i > $i > $o,X1932: $i,X1933: $i,X1934: $i > $i > $o,X1935: $i,X1936: $i,X1937: $i,X1938: $i,X1939: $i > $i > $o,X1940: $i,X1941: $i,X1942: $i,X1943: $i,X1944: $i > $i > $o,X1945: $i,X1946: $i,X1947: $i,X1948: $i,X1949: $i > $i > $o,X1950: $i,X1951: $i,X1952: $i,X1953: $i,X1954: $i,X1955: $i,X1956: $i,X1957: $i,X1958: $i,X1959: $i,X1960: $i,X1961: $i,X1962: $i,X1963: $i,X1964: $i,X1965: $i,X1966: $i,X1967: $i,X1968: $i,X1969: $i,X1970: $i,X1971: $i,X1972: $i,X1973: $i,X1974: $i,X1975: $i,X1976: $i > $i,X1978: $i,X1979: $i,X1980: $i > $i,X1982: $i,X1983: $i,X1984: $i > $i,X1986: $i,X1987: $i,X1988: $i,X1989: $i > $o,X1992: $i,X1993: $i,X1994: $i,X1995: $i,X1996: $i > $o,X1999: $i,X2000: $i,X2001: $i > $o,X2002: $i,X2003: $i,X2004: $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i,X2009: $i,X2010: $i,X2011: $i,X2012: $i,X2013: $i,X2014: $i,X2015: $i,X2016: $i,X2017: $i,X2018: $i,X2019: $i,X2020: $i,X2022: $i,X2023: $i,X2024: $i,X2025: $i,X2026: $i,X2027: $i,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2035: $i,X2036: $i,X2037: $i,X2038: $i,X2043: $i,X2044: $i,X2045: $i,X2046: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i > $i,X2065: $i,X2066: $i,X2067: $i,X2068: $i,X2069: $i,X2070: $i,X2071: $i > $i,X2073: $i,X2074: $i,X2075: $i > $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i,X2081: $i,X2082: $o,X2083: $i,X2084: $i,X2085: $i,X2086: $o,X2087: $i,X2088: $i,X2089: $i,X2090: $o,X2091: $i,X2092: $i,X2093: $i,X2094: $o,X2095: $i,X2096: $i,X2097: $i,X2098: $o,X2099: $i,X2100: $i,X2101: $i,X2102: $o,X2103: $i,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $o,X2109: $i,X2110: $i,X2111: $i,X2112: $o,X2113: $i,X2114: $i] :
( ( ~ ( in @ ( esk1_2 @ X1434 @ X1435 ) @ X1434 )
| ~ ( in @ ( esk1_2 @ X1434 @ X1435 ) @ X1435 )
| ( X1434 = X1435 ) )
& ( ( in @ ( esk1_2 @ X1434 @ X1435 ) @ X1434 )
| ( in @ ( esk1_2 @ X1434 @ X1435 ) @ X1435 )
| ( X1434 = X1435 ) )
& ~ ( in @ X1437 @ emptyset )
& ( ~ ( in @ X1440 @ ( setadjoin @ X1438 @ X1439 ) )
| ( X1440 = X1438 )
| ( in @ X1440 @ X1439 ) )
& ( ( X1440 != X1438 )
| ( in @ X1440 @ ( setadjoin @ X1438 @ X1439 ) ) )
& ( ~ ( in @ X1440 @ X1439 )
| ( in @ X1440 @ ( setadjoin @ X1438 @ X1439 ) ) )
& ( ~ ( in @ X1442 @ ( powerset @ X1441 ) )
| ~ ( in @ X1443 @ X1442 )
| ( in @ X1443 @ X1441 ) )
& ( ( in @ ( esk2_2 @ X1444 @ X1445 ) @ X1445 )
| ( in @ X1445 @ ( powerset @ X1444 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1444 @ X1445 ) @ X1444 )
| ( in @ X1445 @ ( powerset @ X1444 ) ) )
& ( ( in @ X1448 @ ( esk3_2 @ X1447 @ X1448 ) )
| ~ ( in @ X1448 @ ( setunion @ X1447 ) ) )
& ( ( in @ ( esk3_2 @ X1447 @ X1448 ) @ X1447 )
| ~ ( in @ X1448 @ ( setunion @ X1447 ) ) )
& ( ~ ( in @ X1451 @ X1452 )
| ~ ( in @ X1452 @ X1450 )
| ( in @ X1451 @ ( setunion @ X1450 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1453 @ omega )
| ( in @ ( setadjoin @ X1453 @ X1453 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1454 ) @ omega )
| ~ ( in @ emptyset @ X1454 )
| ~ ( in @ X1456 @ omega )
| ( in @ X1456 @ X1454 ) )
& ( ( in @ ( esk4_1 @ X1454 ) @ X1454 )
| ~ ( in @ emptyset @ X1454 )
| ~ ( in @ X1456 @ omega )
| ( in @ X1456 @ X1454 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1454 ) @ ( esk4_1 @ X1454 ) ) @ X1454 )
| ~ ( in @ emptyset @ X1454 )
| ~ ( in @ X1456 @ omega )
| ( in @ X1456 @ X1454 ) )
& ( ( in @ ( esk7_3 @ X1457 @ X1458 @ X1461 ) @ X1458 )
| ~ ( in @ X1461 @ ( esk6_2 @ X1457 @ X1458 ) )
| ( in @ ( esk5_2 @ X1457 @ X1458 ) @ X1458 ) )
& ( ( X1457 @ ( esk7_3 @ X1457 @ X1458 @ X1461 ) @ X1461 )
| ~ ( in @ X1461 @ ( esk6_2 @ X1457 @ X1458 ) )
| ( in @ ( esk5_2 @ X1457 @ X1458 ) @ X1458 ) )
& ( ~ ( in @ X1464 @ X1458 )
| ~ ( X1457 @ X1464 @ X1463 )
| ( in @ X1463 @ ( esk6_2 @ X1457 @ X1458 ) )
| ( in @ ( esk5_2 @ X1457 @ X1458 ) @ X1458 ) )
& ( ( in @ ( esk7_3 @ X1457 @ X1458 @ X1461 ) @ X1458 )
| ~ ( in @ X1461 @ ( esk6_2 @ X1457 @ X1458 ) )
| ~ ( exu @ ( X1457 @ ( esk5_2 @ X1457 @ X1458 ) ) ) )
& ( ( X1457 @ ( esk7_3 @ X1457 @ X1458 @ X1461 ) @ X1461 )
| ~ ( in @ X1461 @ ( esk6_2 @ X1457 @ X1458 ) )
| ~ ( exu @ ( X1457 @ ( esk5_2 @ X1457 @ X1458 ) ) ) )
& ( ~ ( in @ X1464 @ X1458 )
| ~ ( X1457 @ X1464 @ X1463 )
| ( in @ X1463 @ ( esk6_2 @ X1457 @ X1458 ) )
| ~ ( exu @ ( X1457 @ ( esk5_2 @ X1457 @ X1458 ) ) ) )
& ( ( in @ ( esk8_1 @ X1465 ) @ X1465 )
| ~ ( in @ X1466 @ X1465 ) )
& ( ~ ( in @ X1468 @ ( esk8_1 @ X1465 ) )
| ~ ( in @ X1468 @ X1465 )
| ~ ( in @ X1466 @ X1465 ) )
& epred1_0
& ( ~ ( exu @ X1469 )
| ( X1469 @ ( descr @ X1469 ) ) )
& ( ~ ( in @ X1472 @ X1470 )
| ~ ( X1471 @ X1472 )
| ( in @ X1472 @ ( dsetconstr @ X1470 @ X1471 ) ) )
& ( ~ ( in @ X1475 @ ( dsetconstr @ X1473 @ X1474 ) )
| ( in @ X1475 @ X1473 ) )
& ( ~ ( in @ X1478 @ ( dsetconstr @ X1476 @ X1477 ) )
| ( X1477 @ X1478 ) )
& ( ( X1479 @ ( esk9_1 @ X1479 ) )
| ~ ( exu @ X1479 ) )
& ( ~ ( X1479 @ X1481 )
| ( ( esk9_1 @ X1479 )
= X1481 )
| ~ ( exu @ X1479 ) )
& ( ~ ( in @ X1483 @ ( prop2set @ X1482 ) )
| X1482 )
& ( ~ ( in @ X1484 @ emptyset )
| X1485 )
& ( ~ ( in @ X1486 @ emptyset )
| ~ $true )
& ~ ( in @ X1487 @ emptyset )
& ( ~ ( exu @ X1488 )
| ( X1488 @ ( esk10_1 @ X1488 ) ) )
& ( ( in @ ( esk12_2 @ X1490 @ X1491 ) @ X1491 )
| ( X1490 = X1491 )
| ( in @ ( esk11_2 @ X1490 @ X1491 ) @ X1490 ) )
& ( ~ ( in @ ( esk12_2 @ X1490 @ X1491 ) @ X1490 )
| ( X1490 = X1491 )
| ( in @ ( esk11_2 @ X1490 @ X1491 ) @ X1490 ) )
& ( ( in @ ( esk12_2 @ X1490 @ X1491 ) @ X1491 )
| ( X1490 = X1491 )
| ~ ( in @ ( esk11_2 @ X1490 @ X1491 ) @ X1491 ) )
& ( ~ ( in @ ( esk12_2 @ X1490 @ X1491 ) @ X1490 )
| ( X1490 = X1491 )
| ~ ( in @ ( esk11_2 @ X1490 @ X1491 ) @ X1491 ) )
& ( ( in @ ( esk13_1 @ X1494 ) @ X1494 )
| ( X1494 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1496 ) @ X1496 )
| ( X1496 = emptyset ) )
& ( ~ ( in @ X1500 @ ( dsetconstr @ X1498 @ X1499 ) )
| ( X1499 @ X1500 )
| ~ ( in @ X1500 @ X1498 ) )
& ( ~ ( X1499 @ X1500 )
| ( in @ X1500 @ ( dsetconstr @ X1498 @ X1499 ) )
| ~ ( in @ X1500 @ X1498 ) )
& ( ~ ( nonempty @ X1501 )
| ( in @ ( esk15_1 @ X1501 ) @ X1501 ) )
& ( ~ ( in @ X1505 @ X1503 )
| ~ ( X1504 @ X1505 )
| ( nonempty @ ( dsetconstr @ X1503 @ X1504 ) ) )
& ( ~ ( in @ X1507 @ X1506 )
| ( nonempty @ X1506 ) )
& ( in @ X1508 @ ( setadjoin @ X1508 @ X1509 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1512 @ X1511 )
| ( in @ X1512 @ ( setadjoin @ X1510 @ X1511 ) ) )
& ( ( in @ X1515 @ X1514 )
| X1516
| ( X1515 = X1513 )
| ~ ( in @ X1515 @ ( setadjoin @ X1513 @ X1514 ) ) )
& ( ~ X1516
| X1516
| ( X1515 = X1513 )
| ~ ( in @ X1515 @ ( setadjoin @ X1513 @ X1514 ) ) )
& ( ( in @ X1515 @ X1514 )
| X1516
| ~ X1516
| ~ ( in @ X1515 @ ( setadjoin @ X1513 @ X1514 ) ) )
& ( ~ X1516
| X1516
| ~ X1516
| ~ ( in @ X1515 @ ( setadjoin @ X1513 @ X1514 ) ) )
& ( ~ ( in @ X1519 @ ( setadjoin @ X1517 @ X1518 ) )
| ( X1519 = X1517 )
| ( in @ X1519 @ X1518 ) )
& ( ( dsetconstr @ X1520
@ ^ [Z0: $i] : $true )
= X1520 )
& ( ( in @ ( esk16_2 @ X1521 @ X1522 ) @ X1522 )
| ( in @ X1522 @ ( powerset @ X1521 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1521 @ X1522 ) @ X1521 )
| ( in @ X1522 @ ( powerset @ X1521 ) ) )
& ( in @ emptyset @ ( powerset @ X1524 ) )
& ( in @ emptyset @ ( powerset @ X1525 ) )
& ( ~ ( in @ X1527 @ ( powerset @ X1526 ) )
| ~ ( in @ X1528 @ X1527 )
| ( in @ X1528 @ X1526 ) )
& ( ~ ( in @ X1530 @ X1531 )
| ~ ( in @ X1531 @ X1529 )
| ( in @ X1530 @ ( setunion @ X1529 ) ) )
& ( ( in @ X1533 @ ( esk17_3 @ X1532 @ X1533 @ X1534 ) )
| X1534
| ~ ( in @ X1533 @ ( setunion @ X1532 ) ) )
& ( ( in @ ( esk17_3 @ X1532 @ X1533 @ X1534 ) @ X1532 )
| X1534
| ~ ( in @ X1533 @ ( setunion @ X1532 ) ) )
& ( ~ X1534
| X1534
| ~ ( in @ X1533 @ ( setunion @ X1532 ) ) )
& ( ~ ( in @ X1537 @ X1536 )
| ( in @ X1537 @ ( powerset @ ( setunion @ X1536 ) ) ) )
& ( ~ ( X1538 @ X1540 )
| ( X1540
= ( esk18_1 @ X1538 ) )
| ~ ( exu @ X1538 ) )
& ( ( X1541
!= ( esk18_1 @ X1538 ) )
| ( X1538 @ X1541 )
| ~ ( exu @ X1538 ) )
& ( ( in @ ( esk19_1 @ X1542 ) @ X1542 )
| ~ ( nonempty @ X1542 ) )
& ( $true
| ~ ( nonempty @ X1542 ) )
& ( ~ ( in @ X1544 @ ( setadjoin @ X1545 @ emptyset ) )
| ( X1544 = X1545 ) )
& ( ( X1546 = X1547 )
| ~ ( in @ X1547 @ ( setadjoin @ X1546 @ emptyset ) ) )
& ( ( X1548 != X1549 )
| ( in @ X1548 @ ( setadjoin @ X1549 @ emptyset ) ) )
& ( ~ ( in @ X1550 @ ( setadjoin @ X1551 @ emptyset ) )
| ( in @ X1551 @ ( setadjoin @ X1550 @ emptyset ) ) )
& ( ~ ( in @ X1554 @ ( setadjoin @ X1552 @ ( setadjoin @ X1553 @ emptyset ) ) )
| ( X1554 = X1552 )
| ( X1554 = X1553 ) )
& ( in @ X1555 @ ( setadjoin @ X1555 @ ( setadjoin @ X1556 @ emptyset ) ) )
& ( in @ X1558 @ ( setadjoin @ X1557 @ ( setadjoin @ X1558 @ emptyset ) ) )
& ( ~ ( in @ X1561 @ X1559 )
| ~ ( X1560 @ X1561 )
| ( ( dsetconstr @ X1559 @ X1560 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1563 @ emptyset )
| ( X1562 @ X1563 ) )
& ( ( in @ ( esk20_2 @ X1564 @ X1565 ) @ X1564 )
| ~ ( in @ X1566 @ X1564 )
| ( X1565 @ X1566 ) )
& ( ~ ( X1565 @ ( esk20_2 @ X1564 @ X1565 ) )
| ~ ( in @ X1566 @ X1564 )
| ( X1565 @ X1566 ) )
& ( ( in @ ( esk21_2 @ X1568 @ X1569 ) @ X1568 )
| ~ ( in @ X1571 @ X1568 )
| ~ ( X1569 @ X1571 ) )
& ( ( X1569 @ ( esk21_2 @ X1568 @ X1569 ) )
| ~ ( in @ X1571 @ X1568 )
| ~ ( X1569 @ X1571 ) )
& ( ( in @ ( esk22_2 @ X1572 @ X1573 ) @ X1572 )
| ~ ( in @ X1575 @ X1572 )
| ~ ( X1573 @ X1575 ) )
& ( ( X1573 @ ( esk22_2 @ X1572 @ X1573 ) )
| ~ ( in @ X1575 @ X1572 )
| ~ ( X1573 @ X1575 ) )
& ( ( in @ ( esk23_2 @ X1576 @ X1577 ) @ X1576 )
| ~ ( in @ X1578 @ X1576 )
| ( X1577 @ X1578 ) )
& ( ~ ( X1577 @ ( esk23_2 @ X1576 @ X1577 ) )
| ~ ( in @ X1578 @ X1576 )
| ( X1577 @ X1578 ) )
& ( ~ X1580
| ( in @ emptyset @ ( prop2set @ X1580 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1581 @ X1582 ) @ X1581 )
| ~ ( in @ X1584 @ X1581 )
| ~ ( X1582 @ X1584 ) )
& ( ( X1582 @ ( esk24_2 @ X1581 @ X1582 ) )
| ~ ( in @ X1584 @ X1581 )
| ~ ( X1582 @ X1584 ) )
& ( ( in @ ( esk25_2 @ X1585 @ X1586 ) @ X1585 )
| ~ ( in @ X1587 @ X1585 )
| ( X1586 @ X1587 ) )
& ( ~ ( X1586 @ ( esk25_2 @ X1585 @ X1586 ) )
| ~ ( in @ X1587 @ X1585 )
| ( X1586 @ X1587 ) )
& ( ( X1589 @ ( esk26_2 @ X1589 @ X1590 ) )
| ~ ( X1589 @ X1590 )
| ( exu @ X1589 ) )
& ( ( X1590
!= ( esk26_2 @ X1589 @ X1590 ) )
| ~ ( X1589 @ X1590 )
| ( exu @ X1589 ) )
& ( ( X1592 @ ( esk27_1 @ X1592 ) )
| ( exu @ X1592 )
| ~ ( X1592 @ X1593 ) )
& ( ( X1592 @ ( esk28_1 @ X1592 ) )
| ( exu @ X1592 )
| ~ ( X1592 @ X1593 ) )
& ( ( ( esk27_1 @ X1592 )
!= ( esk28_1 @ X1592 ) )
| ( exu @ X1592 )
| ~ ( X1592 @ X1593 ) )
& ( ~ ( X1596 @ ( esk29_2 @ X1596 @ X1597 ) )
| ( ( esk29_2 @ X1596 @ X1597 )
!= X1597 )
| ( exu @ X1596 ) )
& ( ( X1596 @ ( esk29_2 @ X1596 @ X1597 ) )
| ( ( esk29_2 @ X1596 @ X1597 )
= X1597 )
| ( exu @ X1596 ) )
& ( ( X1599 != X1600 )
| ( X1601 != X1602 )
| ~ ( in @ X1601 @ X1599 )
| ( in @ X1602 @ X1600 ) )
& ( ~ ( in @ X1605 @ X1603 )
| ( in @ X1606 @ X1604 )
| ( X1605 != X1606 )
| ( X1603 != X1604 ) )
& ( ~ ( in @ X1606 @ X1604 )
| ( in @ X1605 @ X1603 )
| ( X1605 != X1606 )
| ( X1603 != X1604 ) )
& ( ~ ( exu @ X1607 )
| ~ ( X1607 @ X1608 )
| ~ ( X1607 @ X1609 )
| ( X1608 = X1609 ) )
& ( ~ ( exu @ X1610 )
| ( exu @ X1611 )
| ( ( esk30_2 @ X1610 @ X1611 )
= ( esk31_2 @ X1610 @ X1611 ) ) )
& ( ~ ( exu @ X1611 )
| ( exu @ X1610 )
| ( ( esk30_2 @ X1610 @ X1611 )
= ( esk31_2 @ X1610 @ X1611 ) ) )
& ( ~ ( exu @ X1610 )
| ( exu @ X1611 )
| ~ ( X1610 @ ( esk30_2 @ X1610 @ X1611 ) )
| ~ ( X1611 @ ( esk31_2 @ X1610 @ X1611 ) ) )
& ( ~ ( exu @ X1611 )
| ( exu @ X1610 )
| ~ ( X1610 @ ( esk30_2 @ X1610 @ X1611 ) )
| ~ ( X1611 @ ( esk31_2 @ X1610 @ X1611 ) ) )
& ( ~ ( exu @ X1610 )
| ( exu @ X1611 )
| ( X1610 @ ( esk30_2 @ X1610 @ X1611 ) )
| ( X1611 @ ( esk31_2 @ X1610 @ X1611 ) ) )
& ( ~ ( exu @ X1611 )
| ( exu @ X1610 )
| ( X1610 @ ( esk30_2 @ X1610 @ X1611 ) )
| ( X1611 @ ( esk31_2 @ X1610 @ X1611 ) ) )
& ( emptyset = emptyset )
& ( ( X1614 != X1615 )
| ( X1616 != X1617 )
| ( ( setadjoin @ X1614 @ X1616 )
= ( setadjoin @ X1615 @ X1617 ) ) )
& ( ( X1618 != X1619 )
| ( ( powerset @ X1618 )
= ( powerset @ X1619 ) ) )
& ( ( X1620 != X1621 )
| ( ( setunion @ X1620 )
= ( setunion @ X1621 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1622 )
| ~ ( X1622 @ X1623 )
| ~ ( X1622 @ X1624 )
| ( X1623 = X1624 ) )
& ( ( ( esk32_2 @ X1625 @ X1626 )
= ( esk33_2 @ X1625 @ X1626 ) )
| ~ ( exu @ X1625 )
| ~ ( exu @ X1626 )
| ( ( descr @ X1625 )
= ( descr @ X1626 ) ) )
& ( ~ ( X1625 @ ( esk32_2 @ X1625 @ X1626 ) )
| ~ ( X1626 @ ( esk33_2 @ X1625 @ X1626 ) )
| ~ ( exu @ X1625 )
| ~ ( exu @ X1626 )
| ( ( descr @ X1625 )
= ( descr @ X1626 ) ) )
& ( ( X1625 @ ( esk32_2 @ X1625 @ X1626 ) )
| ( X1626 @ ( esk33_2 @ X1625 @ X1626 ) )
| ~ ( exu @ X1625 )
| ~ ( exu @ X1626 )
| ( ( descr @ X1625 )
= ( descr @ X1626 ) ) )
& ( ( in @ ( esk34_4 @ X1629 @ X1630 @ X1631 @ X1632 ) @ X1629 )
| ( ( dsetconstr @ X1629 @ X1631 )
= ( dsetconstr @ X1630 @ X1632 ) )
| ( X1629 != X1630 ) )
& ( ( in @ ( esk35_4 @ X1629 @ X1630 @ X1631 @ X1632 ) @ X1630 )
| ( ( dsetconstr @ X1629 @ X1631 )
= ( dsetconstr @ X1630 @ X1632 ) )
| ( X1629 != X1630 ) )
& ( ( ( esk34_4 @ X1629 @ X1630 @ X1631 @ X1632 )
= ( esk35_4 @ X1629 @ X1630 @ X1631 @ X1632 ) )
| ( ( dsetconstr @ X1629 @ X1631 )
= ( dsetconstr @ X1630 @ X1632 ) )
| ( X1629 != X1630 ) )
& ( ~ ( X1631 @ ( esk34_4 @ X1629 @ X1630 @ X1631 @ X1632 ) )
| ~ ( X1632 @ ( esk35_4 @ X1629 @ X1630 @ X1631 @ X1632 ) )
| ( ( dsetconstr @ X1629 @ X1631 )
= ( dsetconstr @ X1630 @ X1632 ) )
| ( X1629 != X1630 ) )
& ( ( X1631 @ ( esk34_4 @ X1629 @ X1630 @ X1631 @ X1632 ) )
| ( X1632 @ ( esk35_4 @ X1629 @ X1630 @ X1631 @ X1632 ) )
| ( ( dsetconstr @ X1629 @ X1631 )
= ( dsetconstr @ X1630 @ X1632 ) )
| ( X1629 != X1630 ) )
& ( ( in @ ( esk36_2 @ X1635 @ X1636 ) @ X1635 )
| ( subset @ X1635 @ X1636 ) )
& ( ~ ( in @ ( esk36_2 @ X1635 @ X1636 ) @ X1636 )
| ( subset @ X1635 @ X1636 ) )
& ( ( X1638 != X1639 )
| ( subset @ X1639 @ X1638 ) )
& ( ( X1640 != X1641 )
| ( subset @ X1640 @ X1641 ) )
& ( ( in @ ( esk37_2 @ X1642 @ X1643 ) @ X1642 )
| ( subset @ X1642 @ X1643 ) )
& ( ~ ( in @ ( esk37_2 @ X1642 @ X1643 ) @ X1643 )
| ( subset @ X1642 @ X1643 ) )
& ( subset @ emptyset @ X1645 )
& ( ~ ( subset @ X1646 @ X1647 )
| ~ ( in @ X1648 @ X1646 )
| ( in @ X1648 @ X1647 ) )
& ( ~ ( subset @ X1649 @ X1650 )
| ( in @ X1651 @ X1650 )
| ~ ( in @ X1651 @ X1649 ) )
& ( ~ ( in @ X1654 @ X1652 )
| ( in @ X1654 @ X1653 )
| ~ ( subset @ X1652 @ X1653 ) )
& ( ( subset @ X1655 @ X1656 )
| ( X1655 != X1656 ) )
& ( ~ ( in @ X1659 @ X1657 )
| ( in @ X1659 @ X1658 )
| ( X1657 != X1658 ) )
& ( subset @ X1660 @ X1660 )
& ( ~ ( subset @ X1661 @ X1662 )
| ~ ( subset @ X1662 @ X1663 )
| ( subset @ X1661 @ X1663 ) )
& ( subset @ X1665 @ ( setadjoin @ X1664 @ X1665 ) )
& ( ~ ( subset @ X1666 @ X1668 )
| ( subset @ X1666 @ ( setadjoin @ X1667 @ X1668 ) ) )
& ( ~ ( subset @ X1669 @ X1670 )
| ( in @ X1669 @ ( powerset @ X1670 ) ) )
& ( ~ ( subset @ X1671 @ X1672 )
| ~ ( subset @ X1672 @ X1671 )
| ( X1671 = X1672 ) )
& ( ~ ( subset @ X1673 @ emptyset )
| ( X1673 = emptyset ) )
& ( ~ ( subset @ X1675 @ X1674 )
| ( in @ X1675 @ ( powerset @ X1674 ) ) )
& ( ~ ( in @ X1677 @ ( powerset @ X1676 ) )
| ( subset @ X1677 @ X1676 ) )
& ( in @ X1678 @ ( powerset @ X1678 ) )
& ( ~ ( subset @ X1679 @ X1680 )
| ( subset @ ( powerset @ X1679 ) @ ( powerset @ X1680 ) ) )
& ( in @ ( dsetconstr @ X1681 @ X1682 ) @ ( powerset @ X1681 ) )
& ( subset @ ( dsetconstr @ X1683 @ X1684 ) @ X1683 )
& ( ~ ( in @ X1687 @ X1685 )
| ( in @ X1687 @ ( binunion @ X1685 @ X1686 ) ) )
& ( in @ X1689 @ ( setadjoin @ X1688 @ ( setadjoin @ X1689 @ emptyset ) ) )
& ( ~ ( in @ X1692 @ X1691 )
| ( in @ X1692 @ ( binunion @ X1690 @ X1691 ) ) )
& ( ( in @ X1695 @ X1694 )
| X1696
| ( in @ X1695 @ X1693 )
| ~ ( in @ X1695 @ ( binunion @ X1693 @ X1694 ) ) )
& ( ~ X1696
| X1696
| ( in @ X1695 @ X1693 )
| ~ ( in @ X1695 @ ( binunion @ X1693 @ X1694 ) ) )
& ( ( in @ X1695 @ X1694 )
| X1696
| ~ X1696
| ~ ( in @ X1695 @ ( binunion @ X1693 @ X1694 ) ) )
& ( ~ X1696
| X1696
| ~ X1696
| ~ ( in @ X1695 @ ( binunion @ X1693 @ X1694 ) ) )
& ( ~ ( in @ X1699 @ ( binunion @ X1697 @ X1698 ) )
| ( in @ X1699 @ X1697 )
| ( in @ X1699 @ X1698 ) )
& ( subset @ X1700 @ ( binunion @ X1700 @ X1701 ) )
& ( subset @ X1703 @ ( binunion @ X1702 @ X1703 ) )
& ( ~ ( in @ X1706 @ X1704 )
| ~ ( in @ X1706 @ X1705 )
| ( in @ X1706 @ ( binintersect @ X1704 @ X1705 ) ) )
& ( ~ ( subset @ X1709 @ X1707 )
| ~ ( subset @ X1709 @ X1708 )
| ( subset @ X1709 @ ( binintersect @ X1707 @ X1708 ) ) )
& ( ~ ( in @ X1712 @ ( binintersect @ X1710 @ X1711 ) )
| ( in @ X1712 @ X1710 ) )
& ( subset @ ( binintersect @ X1713 @ X1714 ) @ X1713 )
& ( ~ ( subset @ X1715 @ X1716 )
| ( ( binintersect @ X1715 @ X1716 )
= X1715 ) )
& ( ( ( binintersect @ X1717 @ X1718 )
!= X1718 )
| ( subset @ X1718 @ X1717 ) )
& ( ~ ( in @ X1721 @ ( binintersect @ X1719 @ X1720 ) )
| ( in @ X1721 @ X1720 ) )
& ( ( in @ ( esk38_2 @ X1722 @ X1723 ) @ X1722 )
| ( ( binintersect @ X1722 @ X1723 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1722 @ X1723 ) @ X1723 )
| ( ( binintersect @ X1722 @ X1723 )
= emptyset ) )
& ( subset @ ( binintersect @ X1725 @ X1726 ) @ X1726 )
& ( ~ ( subset @ X1728 @ X1727 )
| ( ( binintersect @ X1727 @ X1728 )
= X1728 ) )
& ( ( ( binintersect @ X1729 @ X1730 )
!= X1729 )
| ( subset @ X1729 @ X1730 ) )
& ( ( binintersect @ X1731 @ ( binunion @ X1732 @ X1733 ) )
= ( binunion @ ( binintersect @ X1731 @ X1732 ) @ ( binintersect @ X1731 @ X1733 ) ) )
& ( ~ ( in @ X1736 @ X1734 )
| ( in @ X1736 @ X1735 )
| ( in @ X1736 @ ( setminus @ X1734 @ X1735 ) ) )
& ( ~ ( in @ X1739 @ ( setminus @ X1737 @ X1738 ) )
| ( in @ X1739 @ X1737 ) )
& ( ~ ( in @ X1742 @ ( setminus @ X1740 @ X1741 ) )
| ~ ( in @ X1742 @ X1741 ) )
& ( ~ ( subset @ X1743 @ X1744 )
| ( ( setminus @ X1743 @ X1744 )
= emptyset ) )
& ( ( in @ X1747 @ ( setminus @ X1745 @ X1746 ) )
| ~ ( in @ X1747 @ X1745 )
| ( in @ X1747 @ X1746 ) )
& ( ( in @ X1750 @ ( setminus @ X1748 @ X1749 ) )
| ( in @ X1750 @ X1749 )
| ~ ( in @ X1750 @ X1748 ) )
& ( ( in @ X1753 @ X1751 )
| ~ ( in @ X1753 @ ( setminus @ X1751 @ X1752 ) ) )
& ( ~ ( in @ X1756 @ X1755 )
| ~ ( in @ X1756 @ ( setminus @ X1754 @ X1755 ) ) )
& ( subset @ ( setminus @ X1757 @ X1758 ) @ X1757 )
& ( ( ( setminus @ X1759 @ X1760 )
!= emptyset )
| ( subset @ X1759 @ X1760 ) )
& ( ~ ( in @ X1763 @ X1761 )
| X1764
| ( in @ X1763 @ X1761 )
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ( in @ X1763 @ X1762 )
| X1764
| ( in @ X1763 @ X1761 )
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ~ X1764
| X1764
| ( in @ X1763 @ X1761 )
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ~ ( in @ X1763 @ X1761 )
| X1764
| ~ ( in @ X1763 @ X1762 )
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ( in @ X1763 @ X1762 )
| X1764
| ~ ( in @ X1763 @ X1762 )
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ~ X1764
| X1764
| ~ ( in @ X1763 @ X1762 )
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ~ ( in @ X1763 @ X1761 )
| X1764
| ~ X1764
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ( in @ X1763 @ X1762 )
| X1764
| ~ X1764
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ~ X1764
| X1764
| ~ X1764
| ~ ( in @ X1763 @ ( symdiff @ X1761 @ X1762 ) ) )
& ( ~ ( in @ X1767 @ X1765 )
| ( in @ X1767 @ X1766 )
| ( in @ X1767 @ ( symdiff @ X1765 @ X1766 ) ) )
& ( ( in @ X1770 @ X1768 )
| ~ ( in @ X1770 @ X1769 )
| ( in @ X1770 @ ( symdiff @ X1768 @ X1769 ) ) )
& ( ~ ( in @ X1773 @ X1771 )
| ~ ( in @ X1773 @ X1772 )
| ~ ( in @ X1773 @ ( symdiff @ X1771 @ X1772 ) ) )
& ( ( in @ X1776 @ X1774 )
| ( in @ X1776 @ X1775 )
| ~ ( in @ X1776 @ ( symdiff @ X1774 @ X1775 ) ) )
& ( in @ X1778 @ ( setadjoin @ X1777 @ ( setadjoin @ X1778 @ emptyset ) ) )
& ( in @ X1779 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1779 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1779 @ ( setadjoin @ X1780 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1782 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1781 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1781 @ ( setadjoin @ X1782 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1783 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1783 @ ( setadjoin @ X1784 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1785 @ X1786 ) )
& ( ~ ( in @ X1788 @ X1787 )
| ( subset @ ( setadjoin @ X1788 @ emptyset ) @ X1787 ) )
& ( ~ ( in @ X1790 @ X1789 )
| ( in @ ( setadjoin @ X1790 @ emptyset ) @ ( powerset @ X1789 ) ) )
& ( ~ ( in @ X1793 @ X1791 )
| ( in @ ( setadjoin @ X1793 @ emptyset ) @ ( powerset @ ( binunion @ X1791 @ X1792 ) ) ) )
& ( ~ ( in @ X1796 @ ( setadjoin @ X1794 @ ( setadjoin @ X1795 @ emptyset ) ) )
| ( X1796 = X1794 )
| ( X1796 = X1795 ) )
& ( ~ ( in @ X1799 @ X1797 )
| ~ ( in @ X1800 @ X1798 )
| ( subset @ ( setadjoin @ X1799 @ ( setadjoin @ X1800 @ emptyset ) ) @ ( binunion @ X1797 @ X1798 ) ) )
& ( ~ ( in @ X1803 @ X1801 )
| ~ ( in @ X1804 @ X1802 )
| ( in @ ( setadjoin @ X1803 @ ( setadjoin @ X1804 @ emptyset ) ) @ ( powerset @ ( binunion @ X1801 @ X1802 ) ) ) )
& ( ~ ( in @ X1807 @ X1805 )
| ~ ( in @ X1808 @ X1806 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1807 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1807 @ ( setadjoin @ X1808 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1805 @ X1806 ) ) ) )
& ( ~ ( in @ X1811 @ X1809 )
| ~ ( in @ X1812 @ X1810 )
| ( in @ ( setadjoin @ ( setadjoin @ X1811 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1811 @ ( setadjoin @ X1812 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1809 @ X1810 ) ) ) ) )
& ( ~ ( in @ X1815 @ X1813 )
| ~ ( in @ X1816 @ X1814 )
| ( in @ ( kpair @ X1815 @ X1816 ) @ ( powerset @ ( powerset @ ( binunion @ X1813 @ X1814 ) ) ) ) )
& ( ~ ( in @ X1819 @ X1817 )
| ~ ( in @ X1820 @ X1818 )
| ( in @ ( kpair @ X1819 @ X1820 ) @ ( cartprod @ X1817 @ X1818 ) ) )
& ( ( in @ ( esk39_3 @ X1821 @ X1822 @ X1823 ) @ X1821 )
| ~ ( in @ X1823 @ ( cartprod @ X1821 @ X1822 ) ) )
& ( ( in @ ( esk40_3 @ X1821 @ X1822 @ X1823 ) @ X1822 )
| ~ ( in @ X1823 @ ( cartprod @ X1821 @ X1822 ) ) )
& ( ( X1823
= ( kpair @ ( esk39_3 @ X1821 @ X1822 @ X1823 ) @ ( esk40_3 @ X1821 @ X1822 @ X1823 ) ) )
| ~ ( in @ X1823 @ ( cartprod @ X1821 @ X1822 ) ) )
& ( ~ ( in @ X1828 @ ( cartprod @ X1826 @ X1827 ) )
| ( iskpair @ X1828 ) )
& ( ( in @ ( esk41_2 @ X1829 @ X1830 ) @ X1829 )
| ~ ( in @ X1830 @ ( setunion @ X1829 ) ) )
& ( ( in @ X1830 @ ( esk41_2 @ X1829 @ X1830 ) )
| ~ ( in @ X1830 @ ( setunion @ X1829 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1832 @ emptyset ) ) @ X1832 )
& ( subset @ X1833 @ ( setunion @ ( setadjoin @ X1833 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1834 @ emptyset ) )
= X1834 )
& ( ( in @ ( esk42_2 @ X1835 @ X1836 ) @ X1835 )
| ~ ( in @ X1839 @ X1835 )
| ~ ( X1836 @ X1839 )
| ( singleton @ ( dsetconstr @ X1835 @ X1836 ) ) )
& ( ( in @ ( esk43_2 @ X1835 @ X1836 ) @ X1835 )
| ~ ( in @ X1839 @ X1835 )
| ~ ( X1836 @ X1839 )
| ( singleton @ ( dsetconstr @ X1835 @ X1836 ) ) )
& ( ( X1836 @ ( esk42_2 @ X1835 @ X1836 ) )
| ~ ( in @ X1839 @ X1835 )
| ~ ( X1836 @ X1839 )
| ( singleton @ ( dsetconstr @ X1835 @ X1836 ) ) )
& ( ( X1836 @ ( esk43_2 @ X1835 @ X1836 ) )
| ~ ( in @ X1839 @ X1835 )
| ~ ( X1836 @ X1839 )
| ( singleton @ ( dsetconstr @ X1835 @ X1836 ) ) )
& ( ( ( esk42_2 @ X1835 @ X1836 )
!= ( esk43_2 @ X1835 @ X1836 ) )
| ~ ( in @ X1839 @ X1835 )
| ~ ( X1836 @ X1839 )
| ( singleton @ ( dsetconstr @ X1835 @ X1836 ) ) )
& ( ( in @ ( esk44_2 @ X1840 @ X1841 ) @ X1840 )
| ~ ( ex1 @ X1840 @ X1841 ) )
& ( ( X1841 @ ( esk44_2 @ X1840 @ X1841 ) )
| ~ ( ex1 @ X1840 @ X1841 ) )
& ( ( in @ ( esk45_3 @ X1843 @ X1844 @ X1845 ) @ X1843 )
| ( ex1 @ X1843 @ X1844 )
| ~ ( X1844 @ X1845 )
| ~ ( in @ X1845 @ X1843 ) )
& ( ( X1844 @ ( esk45_3 @ X1843 @ X1844 @ X1845 ) )
| ( ex1 @ X1843 @ X1844 )
| ~ ( X1844 @ X1845 )
| ~ ( in @ X1845 @ X1843 ) )
& ( ( ( esk45_3 @ X1843 @ X1844 @ X1845 )
!= X1845 )
| ( ex1 @ X1843 @ X1844 )
| ~ ( X1844 @ X1845 )
| ~ ( in @ X1845 @ X1843 ) )
& ( ( in @ ( esk46_2 @ X1847 @ X1848 ) @ X1847 )
| ~ ( in @ X1851 @ X1847 )
| ~ ( X1848 @ X1851 )
| ( ex1 @ X1847 @ X1848 ) )
& ( ( in @ ( esk47_2 @ X1847 @ X1848 ) @ X1847 )
| ~ ( in @ X1851 @ X1847 )
| ~ ( X1848 @ X1851 )
| ( ex1 @ X1847 @ X1848 ) )
& ( ( X1848 @ ( esk46_2 @ X1847 @ X1848 ) )
| ~ ( in @ X1851 @ X1847 )
| ~ ( X1848 @ X1851 )
| ( ex1 @ X1847 @ X1848 ) )
& ( ( X1848 @ ( esk47_2 @ X1847 @ X1848 ) )
| ~ ( in @ X1851 @ X1847 )
| ~ ( X1848 @ X1851 )
| ( ex1 @ X1847 @ X1848 ) )
& ( ( ( esk46_2 @ X1847 @ X1848 )
!= ( esk47_2 @ X1847 @ X1848 ) )
| ~ ( in @ X1851 @ X1847 )
| ~ ( X1848 @ X1851 )
| ( ex1 @ X1847 @ X1848 ) )
& ( ( ( setadjoin @ X1852 @ emptyset )
!= ( setadjoin @ X1853 @ emptyset ) )
| ( X1852 = X1853 ) )
& ( ~ ( in @ ( setadjoin @ X1856 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1854 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1854 @ ( setadjoin @ X1855 @ emptyset ) ) @ emptyset ) ) )
| ( X1854 = X1856 ) )
& ( ~ ( iskpair @ X1857 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1857 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1857 ) ) ) )
& ( ~ ( singleton @ X1858 )
| ( in @ ( setunion @ X1858 ) @ X1858 ) )
& ( ( kfst @ ( kpair @ X1859 @ X1860 ) )
= X1859 )
& ( ~ ( in @ X1863 @ ( cartprod @ X1861 @ X1862 ) )
| ( in @ ( kfst @ X1863 ) @ X1861 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1864 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1864 @ ( setadjoin @ X1865 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1866 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1866 @ ( setadjoin @ X1867 @ emptyset ) ) @ emptyset ) ) )
| ( X1864 = X1866 ) )
& ( ( ( kpair @ X1868 @ X1869 )
!= ( kpair @ X1870 @ X1871 ) )
| ( X1868 = X1870 ) )
& ( ( X1872 != X1873 )
| ( ( setadjoin @ X1872 @ ( setadjoin @ X1873 @ emptyset ) )
= ( setadjoin @ X1872 @ emptyset ) ) )
& ( ( X1874 != X1875 )
| ( ( setadjoin @ ( setadjoin @ X1874 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1874 @ ( setadjoin @ X1875 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1874 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1876 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1876 @ ( setadjoin @ X1877 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1878 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1878 @ ( setadjoin @ X1879 @ emptyset ) ) @ emptyset ) ) )
| ( X1878 != X1879 )
| ( X1877 = X1879 ) )
& ( ( ( setadjoin @ X1880 @ ( setadjoin @ X1881 @ emptyset ) )
!= ( setadjoin @ X1882 @ emptyset ) )
| ( X1880 = X1881 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1883 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1883 @ ( setadjoin @ X1884 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1885 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1885 @ ( setadjoin @ X1886 @ emptyset ) ) @ emptyset ) ) )
| ( X1884 = X1886 ) )
& ( ( ( kpair @ X1887 @ X1888 )
!= ( kpair @ X1889 @ X1890 ) )
| ( X1888 = X1890 ) )
& ( ~ ( iskpair @ X1891 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1891 )
@ ^ [Z0: $i] :
( X1891
= ( kpair @ ( kfst @ X1891 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X1892 @ X1893 ) )
= X1893 )
& ( ~ ( iskpair @ X1894 )
| ( ( kpair @ ( kfst @ X1894 ) @ ( ksnd @ X1894 ) )
= X1894 ) )
& ( ~ ( in @ X1897 @ ( cartprod @ X1895 @ X1896 ) )
| ( in @ ( ksnd @ X1897 ) @ X1896 ) )
& ( ~ ( in @ ( kpair @ X1900 @ X1901 ) @ ( cartprod @ X1898 @ X1899 ) )
| ( in @ X1900 @ X1898 ) )
& ( ~ ( in @ ( kpair @ X1904 @ X1905 ) @ ( cartprod @ X1902 @ X1903 ) )
| ( in @ X1905 @ X1903 ) )
& ( ~ ( in @ X1908 @ X1906 )
| ~ ( in @ X1909 @ X1907 )
| ( ( kpair @ X1908 @ X1909 )
= ( kpair @ X1908 @ X1909 ) ) )
& ( ~ ( in @ X1912 @ X1910 )
| ~ ( in @ X1913 @ X1911 )
| ( ( kfst @ ( kpair @ X1912 @ X1913 ) )
= X1912 ) )
& ( ~ ( in @ X1916 @ X1914 )
| ~ ( in @ X1917 @ X1915 )
| ( ( ksnd @ ( kpair @ X1916 @ X1917 ) )
= X1917 ) )
& ( ~ ( in @ X1920 @ ( cartprod @ X1918 @ X1919 ) )
| ( ( kpair @ ( kfst @ X1920 ) @ ( ksnd @ X1920 ) )
= X1920 ) )
& ( ~ ( in @ X1924 @ X1921 )
| ~ ( in @ X1925 @ X1922 )
| ~ ( X1923 @ X1924 @ X1925 )
| ( in @ ( kpair @ X1924 @ X1925 ) @ ( dpsetconstr @ X1921 @ X1922 @ X1923 ) ) )
& ( subset @ ( dpsetconstr @ X1926 @ X1927 @ X1928 ) @ ( cartprod @ X1926 @ X1927 ) )
& ( breln @ X1929 @ X1930 @ ( dpsetconstr @ X1929 @ X1930 @ X1931 ) )
& ( ~ ( in @ X1935 @ X1932 )
| ~ ( in @ X1936 @ X1933 )
| ~ ( in @ ( kpair @ X1935 @ X1936 ) @ ( dpsetconstr @ X1932 @ X1933 @ X1934 ) )
| ( X1934 @ X1935 @ X1936 ) )
& ( ~ ( in @ ( kpair @ X1940 @ X1941 ) @ ( dpsetconstr @ X1937 @ X1938 @ X1939 ) )
| ( in @ X1940 @ X1937 ) )
& ( ~ ( in @ ( kpair @ X1945 @ X1946 ) @ ( dpsetconstr @ X1942 @ X1943 @ X1944 ) )
| ( in @ X1946 @ X1943 ) )
& ( ~ ( in @ ( kpair @ X1950 @ X1951 ) @ ( dpsetconstr @ X1947 @ X1948 @ X1949 ) )
| ( X1949 @ X1950 @ X1951 ) )
& ( ~ ( func @ X1952 @ X1953 @ X1954 )
| ~ ( in @ X1955 @ X1952 )
| ( singleton
@ ( dsetconstr @ X1953
@ ^ [Z0: $i] : ( in @ ( kpair @ X1955 @ Z0 ) @ X1954 ) ) ) )
& ( ~ ( func @ X1956 @ X1957 @ X1958 )
| ~ ( in @ X1959 @ X1956 )
| ( in
@ ( setunion
@ ( dsetconstr @ X1957
@ ^ [Z0: $i] : ( in @ ( kpair @ X1959 @ Z0 ) @ X1958 ) ) )
@ X1957 ) )
& ( ~ ( func @ X1960 @ X1961 @ X1962 )
| ~ ( in @ X1963 @ X1960 )
| ( in @ ( ap @ X1960 @ X1961 @ X1962 @ X1963 ) @ X1961 ) )
& ( ~ ( in @ X1966 @ ( funcSet @ X1964 @ X1965 ) )
| ( func @ X1964 @ X1965 @ X1966 ) )
& ( ~ ( in @ X1969 @ ( funcSet @ X1967 @ X1968 ) )
| ~ ( in @ X1970 @ X1967 )
| ( in @ ( ap @ X1967 @ X1968 @ X1969 @ X1970 ) @ X1968 ) )
& ( ~ ( func @ X1971 @ X1972 @ X1973 )
| ( in @ X1973 @ ( funcSet @ X1971 @ X1972 ) ) )
& ( ( in @ ( esk48_3 @ X1974 @ X1975 @ X1976 ) @ X1974 )
| ( func @ X1974 @ X1975
@ ( dpsetconstr @ X1974 @ X1975
@ ^ [Z0: $i] : ( $eq @ ( X1976 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X1976 @ ( esk48_3 @ X1974 @ X1975 @ X1976 ) ) @ X1975 )
| ( func @ X1974 @ X1975
@ ( dpsetconstr @ X1974 @ X1975
@ ^ [Z0: $i] : ( $eq @ ( X1976 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X1978 @ X1979 @ X1980 ) @ X1978 )
| ( func @ X1978 @ X1979 @ ( lam @ X1978 @ X1979 @ X1980 ) ) )
& ( ~ ( in @ ( X1980 @ ( esk49_3 @ X1978 @ X1979 @ X1980 ) ) @ X1979 )
| ( func @ X1978 @ X1979 @ ( lam @ X1978 @ X1979 @ X1980 ) ) )
& ( ( in @ ( esk50_3 @ X1982 @ X1983 @ X1984 ) @ X1982 )
| ( in @ ( lam @ X1982 @ X1983 @ X1984 ) @ ( funcSet @ X1982 @ X1983 ) ) )
& ( ~ ( in @ ( X1984 @ ( esk50_3 @ X1982 @ X1983 @ X1984 ) ) @ X1983 )
| ( in @ ( lam @ X1982 @ X1983 @ X1984 ) @ ( funcSet @ X1982 @ X1983 ) ) )
& ( ( in @ ( esk51_4 @ X1986 @ X1987 @ X1988 @ X1989 ) @ X1986 )
| ~ ( in @ X1992 @ X1988 )
| ( X1989 @ X1992 )
| ~ ( breln @ X1986 @ X1987 @ X1988 ) )
& ( ( in @ ( esk52_4 @ X1986 @ X1987 @ X1988 @ X1989 ) @ X1987 )
| ~ ( in @ X1992 @ X1988 )
| ( X1989 @ X1992 )
| ~ ( breln @ X1986 @ X1987 @ X1988 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X1986 @ X1987 @ X1988 @ X1989 ) @ ( esk52_4 @ X1986 @ X1987 @ X1988 @ X1989 ) ) @ X1988 )
| ~ ( in @ X1992 @ X1988 )
| ( X1989 @ X1992 )
| ~ ( breln @ X1986 @ X1987 @ X1988 ) )
& ( ~ ( X1989 @ ( kpair @ ( esk51_4 @ X1986 @ X1987 @ X1988 @ X1989 ) @ ( esk52_4 @ X1986 @ X1987 @ X1988 @ X1989 ) ) )
| ~ ( in @ X1992 @ X1988 )
| ( X1989 @ X1992 )
| ~ ( breln @ X1986 @ X1987 @ X1988 ) )
& ( ( in @ ( esk53_4 @ X1993 @ X1994 @ X1995 @ X1996 ) @ X1993 )
| ~ ( in @ X1999 @ X1995 )
| ( X1996 @ X1999 )
| ~ ( breln @ X1993 @ X1994 @ X1995 ) )
& ( ( in @ ( esk54_4 @ X1993 @ X1994 @ X1995 @ X1996 ) @ X1994 )
| ~ ( in @ X1999 @ X1995 )
| ( X1996 @ X1999 )
| ~ ( breln @ X1993 @ X1994 @ X1995 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X1993 @ X1994 @ X1995 @ X1996 ) @ ( esk54_4 @ X1993 @ X1994 @ X1995 @ X1996 ) ) @ X1995 )
| ~ ( in @ X1999 @ X1995 )
| ( X1996 @ X1999 )
| ~ ( breln @ X1993 @ X1994 @ X1995 ) )
& ( ~ ( X1996 @ ( kpair @ ( esk53_4 @ X1993 @ X1994 @ X1995 @ X1996 ) @ ( esk54_4 @ X1993 @ X1994 @ X1995 @ X1996 ) ) )
| ~ ( in @ X1999 @ X1995 )
| ( X1996 @ X1999 )
| ~ ( breln @ X1993 @ X1994 @ X1995 ) )
& ( ~ ( ex1 @ X2000 @ X2001 )
| ~ ( in @ X2002 @ X2000 )
| ~ ( in @ X2003 @ X2000 )
| ~ ( X2001 @ X2002 )
| ~ ( X2001 @ X2003 )
| ( X2002 = X2003 ) )
& ( ~ ( func @ X2004 @ X2005 @ X2006 )
| ~ ( in @ X2007 @ X2004 )
| ( in @ ( kpair @ X2007 @ ( ap @ X2004 @ X2005 @ X2006 @ X2007 ) ) @ X2006 ) )
& ( ~ ( in @ X2010 @ ( funcSet @ X2008 @ X2009 ) )
| ~ ( in @ X2011 @ X2008 )
| ( in @ ( kpair @ X2011 @ ( ap @ X2008 @ X2009 @ X2010 @ X2011 ) ) @ X2010 ) )
& ( ~ ( func @ X2012 @ X2013 @ X2014 )
| ~ ( in @ X2015 @ X2012 )
| ~ ( in @ X2016 @ X2013 )
| ~ ( in @ ( kpair @ X2015 @ X2016 ) @ X2014 )
| ( ( ap @ X2012 @ X2013 @ X2014 @ X2015 )
= X2016 ) )
& ( ( in @ ( esk55_4 @ X2017 @ X2018 @ X2019 @ X2020 ) @ X2017 )
| ~ ( in @ X2022 @ X2017 )
| ~ ( in @ X2023 @ X2018 )
| ~ ( in @ ( kpair @ X2022 @ X2023 ) @ X2020 )
| ( in @ ( kpair @ X2022 @ X2023 ) @ X2019 )
| ~ ( func @ X2017 @ X2018 @ X2020 )
| ~ ( func @ X2017 @ X2018 @ X2019 ) )
& ( ( ( ap @ X2017 @ X2018 @ X2019 @ ( esk55_4 @ X2017 @ X2018 @ X2019 @ X2020 ) )
!= ( ap @ X2017 @ X2018 @ X2020 @ ( esk55_4 @ X2017 @ X2018 @ X2019 @ X2020 ) ) )
| ~ ( in @ X2022 @ X2017 )
| ~ ( in @ X2023 @ X2018 )
| ~ ( in @ ( kpair @ X2022 @ X2023 ) @ X2020 )
| ( in @ ( kpair @ X2022 @ X2023 ) @ X2019 )
| ~ ( func @ X2017 @ X2018 @ X2020 )
| ~ ( func @ X2017 @ X2018 @ X2019 ) )
& ( ~ ( in @ X2026 @ ( funcSet @ X2024 @ X2025 ) )
| ~ ( in @ X2027 @ X2024 )
| ~ ( in @ X2028 @ X2025 )
| ~ ( in @ ( kpair @ X2027 @ X2028 ) @ X2026 )
| ( ( ap @ X2024 @ X2025 @ X2026 @ X2027 )
= X2028 ) )
& ( ( in @ ( esk56_4 @ X2029 @ X2030 @ X2031 @ X2032 ) @ X2029 )
| ( subset @ X2031 @ X2032 )
| ~ ( breln @ X2029 @ X2030 @ X2032 )
| ~ ( breln @ X2029 @ X2030 @ X2031 ) )
& ( ( in @ ( esk57_4 @ X2029 @ X2030 @ X2031 @ X2032 ) @ X2030 )
| ( subset @ X2031 @ X2032 )
| ~ ( breln @ X2029 @ X2030 @ X2032 )
| ~ ( breln @ X2029 @ X2030 @ X2031 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2029 @ X2030 @ X2031 @ X2032 ) @ ( esk57_4 @ X2029 @ X2030 @ X2031 @ X2032 ) ) @ X2031 )
| ( subset @ X2031 @ X2032 )
| ~ ( breln @ X2029 @ X2030 @ X2032 )
| ~ ( breln @ X2029 @ X2030 @ X2031 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2029 @ X2030 @ X2031 @ X2032 ) @ ( esk57_4 @ X2029 @ X2030 @ X2031 @ X2032 ) ) @ X2032 )
| ( subset @ X2031 @ X2032 )
| ~ ( breln @ X2029 @ X2030 @ X2032 )
| ~ ( breln @ X2029 @ X2030 @ X2031 ) )
& ( ( in @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2035 )
| ( X2037 = X2038 )
| ( in @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2035 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2036 )
| ( X2037 = X2038 )
| ( in @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2035 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2038 )
| ( X2037 = X2038 )
| ( in @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2035 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2037 )
| ( X2037 = X2038 )
| ( in @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2035 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2035 )
| ( X2037 = X2038 )
| ( in @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2036 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2036 )
| ( X2037 = X2038 )
| ( in @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2036 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2038 )
| ( X2037 = X2038 )
| ( in @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2036 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2037 )
| ( X2037 = X2038 )
| ( in @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2036 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2035 )
| ( X2037 = X2038 )
| ( in @ ( kpair @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2037 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2036 )
| ( X2037 = X2038 )
| ( in @ ( kpair @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2037 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2038 )
| ( X2037 = X2038 )
| ( in @ ( kpair @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2037 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2037 )
| ( X2037 = X2038 )
| ( in @ ( kpair @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2037 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2035 )
| ( X2037 = X2038 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ X2036 )
| ( X2037 = X2038 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2038 )
| ( X2037 = X2038 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk61_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2037 )
| ( X2037 = X2038 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2035 @ X2036 @ X2037 @ X2038 ) @ ( esk59_4 @ X2035 @ X2036 @ X2037 @ X2038 ) ) @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2038 )
| ~ ( breln @ X2035 @ X2036 @ X2037 ) )
& ( ( in @ ( esk62_4 @ X2043 @ X2044 @ X2045 @ X2046 ) @ X2043 )
| ( X2045 = X2046 )
| ~ ( func @ X2043 @ X2044 @ X2046 )
| ~ ( func @ X2043 @ X2044 @ X2045 ) )
& ( ( ( ap @ X2043 @ X2044 @ X2045 @ ( esk62_4 @ X2043 @ X2044 @ X2045 @ X2046 ) )
!= ( ap @ X2043 @ X2044 @ X2046 @ ( esk62_4 @ X2043 @ X2044 @ X2045 @ X2046 ) ) )
| ( X2045 = X2046 )
| ~ ( func @ X2043 @ X2044 @ X2046 )
| ~ ( func @ X2043 @ X2044 @ X2045 ) )
& ( ( in @ ( esk63_4 @ X2048 @ X2049 @ X2050 @ X2051 ) @ X2048 )
| ( X2050 = X2051 )
| ~ ( in @ X2051 @ ( funcSet @ X2048 @ X2049 ) )
| ~ ( in @ X2050 @ ( funcSet @ X2048 @ X2049 ) ) )
& ( ( ( ap @ X2048 @ X2049 @ X2050 @ ( esk63_4 @ X2048 @ X2049 @ X2050 @ X2051 ) )
!= ( ap @ X2048 @ X2049 @ X2051 @ ( esk63_4 @ X2048 @ X2049 @ X2050 @ X2051 ) ) )
| ( X2050 = X2051 )
| ~ ( in @ X2051 @ ( funcSet @ X2048 @ X2049 ) )
| ~ ( in @ X2050 @ ( funcSet @ X2048 @ X2049 ) ) )
& ( ~ ( in @ X2055 @ ( funcSet @ X2053 @ X2054 ) )
| ~ ( in @ X2056 @ X2053 )
| ( ( ap @ X2053 @ X2054 @ X2055 @ X2056 )
= ( ap @ X2053 @ X2054 @ X2055 @ X2056 ) ) )
& ( ~ ( func @ X2057 @ X2058 @ X2059 )
| ~ ( in @ X2060 @ X2057 )
| ( ( ap @ X2057 @ X2058 @ X2059 @ X2060 )
= ( ap @ X2057 @ X2058 @ X2059 @ X2060 ) ) )
& ( ( in @ ( esk64_3 @ X2061 @ X2062 @ X2063 ) @ X2061 )
| ~ ( in @ X2065 @ X2061 )
| ( ( ap @ X2061 @ X2062 @ ( lam @ X2061 @ X2062 @ X2063 ) @ X2065 )
= ( X2063 @ X2065 ) ) )
& ( ~ ( in @ ( X2063 @ ( esk64_3 @ X2061 @ X2062 @ X2063 ) ) @ X2062 )
| ~ ( in @ X2065 @ X2061 )
| ( ( ap @ X2061 @ X2062 @ ( lam @ X2061 @ X2062 @ X2063 ) @ X2065 )
= ( X2063 @ X2065 ) ) )
& ( ~ ( func @ X2066 @ X2067 @ X2068 )
| ( ( lam @ X2066 @ X2067 @ ( ap @ X2066 @ X2067 @ X2068 ) )
= X2068 ) )
& ( ( in @ ( esk65_3 @ X2069 @ X2070 @ X2071 ) @ X2069 )
| ( ( lam @ X2069 @ X2070 @ X2071 )
= ( lam @ X2069 @ X2070 @ X2071 ) ) )
& ( ~ ( in @ ( X2071 @ ( esk65_3 @ X2069 @ X2070 @ X2071 ) ) @ X2070 )
| ( ( lam @ X2069 @ X2070 @ X2071 )
= ( lam @ X2069 @ X2070 @ X2071 ) ) )
& ( ( in @ ( esk66_3 @ X2073 @ X2074 @ X2075 ) @ X2073 )
| ~ ( in @ X2077 @ X2073 )
| ( ( ap @ X2073 @ X2074 @ ( lam @ X2073 @ X2074 @ X2075 ) @ X2077 )
= ( X2075 @ X2077 ) ) )
& ( ~ ( in @ ( X2075 @ ( esk66_3 @ X2073 @ X2074 @ X2075 ) ) @ X2074 )
| ~ ( in @ X2077 @ X2073 )
| ( ( ap @ X2073 @ X2074 @ ( lam @ X2073 @ X2074 @ X2075 ) @ X2077 )
= ( X2075 @ X2077 ) ) )
& ( ~ ( in @ X2080 @ ( funcSet @ X2078 @ X2079 ) )
| ( ( lam @ X2078 @ X2079 @ ( ap @ X2078 @ X2079 @ X2080 ) )
= X2080 ) )
& ( ~ ( in @ X2083 @ X2081 )
| ~ ( in @ X2084 @ X2081 )
| X2082
| ( in @ X2084
@ ( dsetconstr @ X2081
@ ^ [Z0: $i] :
( ( X2082
& ( Z0 = X2083 ) )
| ( ~ X2082
& ( Z0 = X2084 ) ) ) ) ) )
& ( ~ ( in @ X2087 @ X2085 )
| ~ ( in @ X2088 @ X2085 )
| X2086
| ( ( dsetconstr @ X2085
@ ^ [Z0: $i] :
( ( X2086
& ( Z0 = X2087 ) )
| ( ~ X2086
& ( Z0 = X2088 ) ) ) )
= ( setadjoin @ X2088 @ emptyset ) ) )
& ( ~ ( in @ X2091 @ X2089 )
| ~ ( in @ X2092 @ X2089 )
| ~ X2090
| ( in @ X2091
@ ( dsetconstr @ X2089
@ ^ [Z0: $i] :
( ( X2090
& ( Z0 = X2091 ) )
| ( ~ X2090
& ( Z0 = X2092 ) ) ) ) ) )
& ( ~ ( in @ X2095 @ X2093 )
| ~ ( in @ X2096 @ X2093 )
| ~ X2094
| ( ( dsetconstr @ X2093
@ ^ [Z0: $i] :
( ( X2094
& ( Z0 = X2095 ) )
| ( ~ X2094
& ( Z0 = X2096 ) ) ) )
= ( setadjoin @ X2095 @ emptyset ) ) )
& ( ~ ( in @ X2099 @ X2097 )
| ~ ( in @ X2100 @ X2097 )
| ( singleton
@ ( dsetconstr @ X2097
@ ^ [Z0: $i] :
( ( X2098
& ( Z0 = X2099 ) )
| ( ~ X2098
& ( Z0 = X2100 ) ) ) ) ) )
& ( ~ ( in @ X2103 @ X2101 )
| ~ ( in @ X2104 @ X2101 )
| ( in @ ( if @ X2101 @ X2102 @ X2103 @ X2104 ) @ X2101 ) )
& ( ~ ( singleton @ X2105 )
| ~ ( in @ X2106 @ X2105 )
| ( ( setunion @ X2105 )
= X2106 ) )
& ( ~ ( in @ X2109 @ X2107 )
| ~ ( in @ X2110 @ X2107 )
| ~ X2108
| ( ( if @ X2107 @ X2108 @ X2109 @ X2110 )
= X2109 ) )
& ( ~ ( in @ X2113 @ X2111 )
| ~ ( in @ X2114 @ X2111 )
| X2112
| ( ( if @ X2111 @ X2112 @ X2113 @ X2114 )
= X2114 ) )
& ( in @ esk68_0 @ esk67_0 )
& ( in @ esk69_0 @ esk67_0 )
& ( ~ epred2_0
| epred2_0 )
& ( ~ ( in @ ( if @ esk67_0 @ $false @ esk68_0 @ esk69_0 ) @ ( setadjoin @ esk68_0 @ ( setadjoin @ esk69_0 @ emptyset ) ) )
| epred2_0 )
& ( ~ epred2_0
| ~ ( in @ ( if @ esk67_0 @ $true @ esk68_0 @ esk69_0 ) @ ( setadjoin @ esk68_0 @ ( setadjoin @ esk69_0 @ emptyset ) ) ) )
& ( ~ ( in @ ( if @ esk67_0 @ $false @ esk68_0 @ esk69_0 ) @ ( setadjoin @ esk68_0 @ ( setadjoin @ esk69_0 @ emptyset ) ) )
| ~ ( in @ ( if @ esk67_0 @ $true @ esk68_0 @ esk69_0 ) @ ( setadjoin @ esk68_0 @ ( setadjoin @ esk69_0 @ emptyset ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_277])])])])])])])]) ).
thf(c_0_279,negated_conjecture,
( ~ epred2_0
| ~ ( in @ ( if @ esk67_0 @ $true @ esk68_0 @ esk69_0 ) @ ( setadjoin @ esk68_0 @ ( setadjoin @ esk69_0 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
thf(c_0_280,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( ( if @ X3 @ $true @ X2 @ X4 )
= X2 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X3 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_278])])]) ).
thf(c_0_281,negated_conjecture,
! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
thf(c_0_282,negated_conjecture,
in @ esk69_0 @ esk67_0,
inference(split_conjunct,[status(thm)],[c_0_278]) ).
thf(c_0_283,negated_conjecture,
in @ esk68_0 @ esk67_0,
inference(split_conjunct,[status(thm)],[c_0_278]) ).
thf(c_0_284,negated_conjecture,
( epred2_0
| ~ ( in @ ( if @ esk67_0 @ ~ $true @ esk68_0 @ esk69_0 ) @ ( setadjoin @ esk68_0 @ ( setadjoin @ esk69_0 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
thf(c_0_285,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( ( if @ X3 @ ~ $true @ X2 @ X4 )
= X4 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X3 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_278])])]) ).
thf(c_0_286,negated_conjecture,
! [X3: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
thf(c_0_287,negated_conjecture,
~ epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_281]),c_0_282]),c_0_283])]) ).
thf(c_0_288,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_285]),c_0_286]),c_0_282]),c_0_283])]),c_0_287]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU709^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 16:24:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.22/0.51 Running higher-order theorem proving
% 0.22/0.51 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.29/0.97 # Version: 3.1.0-ho
% 2.29/0.97 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.29/0.97 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.97 # Starting ehoh_best5 with 300s (1) cores
% 2.29/0.97 # Starting almost_fo_3_lam with 300s (1) cores
% 2.29/0.97 # Starting new_bool_5 with 300s (1) cores
% 2.29/0.97 # Starting pre_casc_3 with 300s (1) cores
% 2.29/0.97 # Starting ho_unfolding_8 with 300s (1) cores
% 2.29/0.97 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.29/0.97 # Starting new_bool_3 with 300s (1) cores
% 2.29/0.97 # Starting new_ho_5 with 300s (1) cores
% 2.29/0.97 # new_bool_5 with pid 409 completed with status 0
% 2.29/0.97 # Result found by new_bool_5
% 2.29/0.97 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.29/0.97 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.97 # Starting ehoh_best5 with 300s (1) cores
% 2.29/0.97 # Starting almost_fo_3_lam with 300s (1) cores
% 2.29/0.97 # Starting new_bool_5 with 300s (1) cores
% 2.29/0.97 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.29/0.97 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.29/0.97 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.29/0.97 # Starting ho_unfolding_8 with 55s (1) cores
% 2.29/0.97 # ho_unfolding_8 with pid 419 completed with status 0
% 2.29/0.97 # Result found by ho_unfolding_8
% 2.29/0.97 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.29/0.97 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.97 # Starting ehoh_best5 with 300s (1) cores
% 2.29/0.97 # Starting almost_fo_3_lam with 300s (1) cores
% 2.29/0.97 # Starting new_bool_5 with 300s (1) cores
% 2.29/0.97 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.29/0.97 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.29/0.97 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.29/0.97 # Starting ho_unfolding_8 with 55s (1) cores
% 2.29/0.97 # Preprocessing time : 0.086 s
% 2.29/0.97 # Presaturation interreduction done
% 2.29/0.97
% 2.29/0.97 # Proof found!
% 2.29/0.97 # SZS status Theorem
% 2.29/0.97 # SZS output start CNFRefutation
% See solution above
% 2.29/0.97 # Parsed axioms : 493
% 2.29/0.97 # Removed by relevancy pruning/SinE : 268
% 2.29/0.97 # Initial clauses : 376
% 2.29/0.97 # Removed in clause preprocessing : 35
% 2.29/0.97 # Initial clauses in saturation : 341
% 2.29/0.97 # Processed clauses : 657
% 2.29/0.97 # ...of these trivial : 9
% 2.29/0.97 # ...subsumed : 28
% 2.29/0.97 # ...remaining for further processing : 619
% 2.29/0.97 # Other redundant clauses eliminated : 53
% 2.29/0.97 # Clauses deleted for lack of memory : 0
% 2.29/0.97 # Backward-subsumed : 1
% 2.29/0.97 # Backward-rewritten : 1
% 2.29/0.97 # Generated clauses : 6123
% 2.29/0.97 # ...of the previous two non-redundant : 5918
% 2.29/0.97 # ...aggressively subsumed : 0
% 2.29/0.97 # Contextual simplify-reflections : 0
% 2.29/0.97 # Paramodulations : 6031
% 2.29/0.97 # Factorizations : 2
% 2.29/0.97 # NegExts : 0
% 2.29/0.97 # Equation resolutions : 60
% 2.29/0.97 # Disequality decompositions : 0
% 2.29/0.97 # Total rewrite steps : 173
% 2.29/0.97 # ...of those cached : 117
% 2.29/0.97 # Propositional unsat checks : 0
% 2.29/0.97 # Propositional check models : 0
% 2.29/0.97 # Propositional check unsatisfiable : 0
% 2.29/0.97 # Propositional clauses : 0
% 2.29/0.97 # Propositional clauses after purity: 0
% 2.29/0.97 # Propositional unsat core size : 0
% 2.29/0.97 # Propositional preprocessing time : 0.000
% 2.29/0.97 # Propositional encoding time : 0.000
% 2.29/0.97 # Propositional solver time : 0.000
% 2.29/0.97 # Success case prop preproc time : 0.000
% 2.29/0.97 # Success case prop encoding time : 0.000
% 2.29/0.97 # Success case prop solver time : 0.000
% 2.29/0.97 # Current number of processed clauses : 301
% 2.29/0.97 # Positive orientable unit clauses : 37
% 2.29/0.97 # Positive unorientable unit clauses: 0
% 2.29/0.97 # Negative unit clauses : 5
% 2.29/0.97 # Non-unit-clauses : 259
% 2.29/0.97 # Current number of unprocessed clauses: 5901
% 2.29/0.97 # ...number of literals in the above : 23636
% 2.29/0.97 # Current number of archived formulas : 0
% 2.29/0.97 # Current number of archived clauses : 302
% 2.29/0.97 # Clause-clause subsumption calls (NU) : 37811
% 2.29/0.97 # Rec. Clause-clause subsumption calls : 17715
% 2.29/0.97 # Non-unit clause-clause subsumptions : 23
% 2.29/0.97 # Unit Clause-clause subsumption calls : 682
% 2.29/0.97 # Rewrite failures with RHS unbound : 0
% 2.29/0.97 # BW rewrite match attempts : 38
% 2.29/0.97 # BW rewrite match successes : 1
% 2.29/0.97 # Condensation attempts : 0
% 2.29/0.97 # Condensation successes : 0
% 2.29/0.97 # Termbank termtop insertions : 153574
% 2.29/0.97 # Search garbage collected termcells : 23530
% 2.29/0.97
% 2.29/0.97 # -------------------------------------------------
% 2.29/0.97 # User time : 0.393 s
% 2.29/0.97 # System time : 0.022 s
% 2.29/0.97 # Total time : 0.415 s
% 2.29/0.97 # Maximum resident set size: 7556 pages
% 2.29/0.97
% 2.29/0.97 # -------------------------------------------------
% 2.29/0.97 # User time : 0.403 s
% 2.29/0.97 # System time : 0.030 s
% 2.29/0.97 # Total time : 0.432 s
% 2.29/0.97 # Maximum resident set size: 2364 pages
% 2.29/0.97 % E---3.1 exiting
% 2.29/0.98 % E exiting
%------------------------------------------------------------------------------