%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU809^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:27:53 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 1414 ( 33 equ; 0 cnn)
% Maximal formula atoms : 349 ( 54 avg)
% Number of connectives : 1621 ( 31 ~; 20 |; 340 &; 211 @)
% ( 11 <=>;1008 =>; 0 <=; 0 <~>)
% Maximal formula depth : 344 ( 56 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 341 ( 338 usr; 330 con; 0-2 aty)
% Number of variables : 67 ( 5 ^; 50 !; 12 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_25,type,
setextAx: $o ).
thf(decl_26,type,
emptyset: $i ).
thf(decl_27,type,
emptysetAx: $o ).
thf(decl_28,type,
setadjoin: $i > $i > $i ).
thf(decl_29,type,
setadjoinAx: $o ).
thf(decl_31,type,
powersetAx: $o ).
thf(decl_33,type,
setunionAx: $o ).
thf(decl_34,type,
omega: $i ).
thf(decl_35,type,
omega0Ax: $o ).
thf(decl_36,type,
omegaSAx: $o ).
thf(decl_37,type,
omegaIndAx: $o ).
thf(decl_38,type,
replAx: $o ).
thf(decl_39,type,
foundationAx: $o ).
thf(decl_40,type,
wellorderingAx: $o ).
thf(decl_42,type,
descrp: $o ).
thf(decl_43,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_44,type,
dsetconstrI: $o ).
thf(decl_45,type,
dsetconstrEL: $o ).
thf(decl_46,type,
dsetconstrER: $o ).
thf(decl_47,type,
exuE1: $o ).
thf(decl_49,type,
prop2setE: $o ).
thf(decl_50,type,
emptysetE: $o ).
thf(decl_51,type,
emptysetimpfalse: $o ).
thf(decl_52,type,
notinemptyset: $o ).
thf(decl_53,type,
exuE3e: $o ).
thf(decl_54,type,
setext: $o ).
thf(decl_55,type,
emptyI: $o ).
thf(decl_56,type,
noeltsimpempty: $o ).
thf(decl_57,type,
setbeta: $o ).
thf(decl_58,type,
nonempty: $i > $o ).
thf(decl_59,type,
nonemptyE1: $o ).
thf(decl_60,type,
nonemptyI: $o ).
thf(decl_61,type,
nonemptyI1: $o ).
thf(decl_62,type,
setadjoinIL: $o ).
thf(decl_63,type,
emptyinunitempty: $o ).
thf(decl_64,type,
setadjoinIR: $o ).
thf(decl_65,type,
setadjoinE: $o ).
thf(decl_66,type,
setadjoinOr: $o ).
thf(decl_67,type,
setoftrueEq: $o ).
thf(decl_68,type,
powersetI: $o ).
thf(decl_69,type,
emptyinPowerset: $o ).
thf(decl_70,type,
emptyInPowerset: $o ).
thf(decl_71,type,
powersetE: $o ).
thf(decl_72,type,
setunionI: $o ).
thf(decl_73,type,
setunionE: $o ).
thf(decl_74,type,
subPowSU: $o ).
thf(decl_75,type,
exuE2: $o ).
thf(decl_76,type,
nonemptyImpWitness: $o ).
thf(decl_77,type,
uniqinunit: $o ).
thf(decl_78,type,
notinsingleton: $o ).
thf(decl_79,type,
eqinunit: $o ).
thf(decl_80,type,
singletonsswitch: $o ).
thf(decl_81,type,
upairsetE: $o ).
thf(decl_82,type,
upairsetIL: $o ).
thf(decl_83,type,
upairsetIR: $o ).
thf(decl_84,type,
emptyE1: $o ).
thf(decl_85,type,
vacuousDall: $o ).
thf(decl_86,type,
quantDeMorgan1: $o ).
thf(decl_87,type,
quantDeMorgan2: $o ).
thf(decl_88,type,
quantDeMorgan3: $o ).
thf(decl_89,type,
quantDeMorgan4: $o ).
thf(decl_90,type,
prop2setI: $o ).
thf(decl_92,type,
prop2set2propI: $o ).
thf(decl_93,type,
notdexE: $o ).
thf(decl_94,type,
notdallE: $o ).
thf(decl_95,type,
exuI1: $o ).
thf(decl_96,type,
exuI3: $o ).
thf(decl_97,type,
exuI2: $o ).
thf(decl_98,type,
inCongP: $o ).
thf(decl_99,type,
in__Cong: $o ).
thf(decl_100,type,
exuE3u: $o ).
thf(decl_101,type,
exu__Cong: $o ).
thf(decl_102,type,
emptyset__Cong: $o ).
thf(decl_103,type,
setadjoin__Cong: $o ).
thf(decl_104,type,
powerset__Cong: $o ).
thf(decl_105,type,
setunion__Cong: $o ).
thf(decl_106,type,
omega__Cong: $o ).
thf(decl_107,type,
exuEu: $o ).
thf(decl_108,type,
descr__Cong: $o ).
thf(decl_109,type,
dsetconstr__Cong: $o ).
thf(decl_113,type,
subsetI1: $o ).
thf(decl_114,type,
eqimpsubset2: $o ).
thf(decl_115,type,
eqimpsubset1: $o ).
thf(decl_116,type,
subsetI2: $o ).
thf(decl_117,type,
emptysetsubset: $o ).
thf(decl_118,type,
subsetE: $o ).
thf(decl_119,type,
subsetE2: $o ).
thf(decl_120,type,
notsubsetI: $o ).
thf(decl_121,type,
notequalI1: $o ).
thf(decl_122,type,
notequalI2: $o ).
thf(decl_123,type,
subsetRefl: $o ).
thf(decl_124,type,
subsetTrans: $o ).
thf(decl_125,type,
setadjoinSub: $o ).
thf(decl_126,type,
setadjoinSub2: $o ).
thf(decl_127,type,
subset2powerset: $o ).
thf(decl_128,type,
setextsub: $o ).
thf(decl_129,type,
subsetemptysetimpeq: $o ).
thf(decl_130,type,
powersetI1: $o ).
thf(decl_131,type,
powersetE1: $o ).
thf(decl_132,type,
inPowerset: $o ).
thf(decl_133,type,
powersetsubset: $o ).
thf(decl_134,type,
sepInPowerset: $o ).
thf(decl_135,type,
sepSubset: $o ).
thf(decl_137,type,
binunionIL: $o ).
thf(decl_138,type,
upairset2IR: $o ).
thf(decl_139,type,
binunionIR: $o ).
thf(decl_140,type,
binunionEcases: $o ).
thf(decl_141,type,
binunionE: $o ).
thf(decl_142,type,
binunionLsub: $o ).
thf(decl_143,type,
binunionRsub: $o ).
thf(decl_144,type,
binintersect: $i > $i > $i ).
thf(decl_145,type,
binintersectI: $o ).
thf(decl_146,type,
binintersectSubset5: $o ).
thf(decl_147,type,
binintersectEL: $o ).
thf(decl_148,type,
binintersectLsub: $o ).
thf(decl_149,type,
binintersectSubset2: $o ).
thf(decl_150,type,
binintersectSubset3: $o ).
thf(decl_151,type,
binintersectER: $o ).
thf(decl_152,type,
disjointsetsI1: $o ).
thf(decl_153,type,
binintersectRsub: $o ).
thf(decl_154,type,
binintersectSubset4: $o ).
thf(decl_155,type,
binintersectSubset1: $o ).
thf(decl_156,type,
bs114d: $o ).
thf(decl_159,type,
setminusI: $o ).
thf(decl_160,type,
setminusEL: $o ).
thf(decl_161,type,
setminusER: $o ).
thf(decl_162,type,
setminusSubset2: $o ).
thf(decl_163,type,
setminusERneg: $o ).
thf(decl_164,type,
setminusELneg: $o ).
thf(decl_165,type,
setminusILneg: $o ).
thf(decl_166,type,
setminusIRneg: $o ).
thf(decl_167,type,
setminusLsub: $o ).
thf(decl_168,type,
setminusSubset1: $o ).
thf(decl_170,type,
symdiffE: $o ).
thf(decl_171,type,
symdiffI1: $o ).
thf(decl_172,type,
symdiffI2: $o ).
thf(decl_173,type,
symdiffIneg1: $o ).
thf(decl_174,type,
symdiffIneg2: $o ).
thf(decl_176,type,
secondinupair: $o ).
thf(decl_177,type,
setukpairIL: $o ).
thf(decl_178,type,
setukpairIR: $o ).
thf(decl_179,type,
kpairiskpair: $o ).
thf(decl_181,type,
kpairp: $o ).
thf(decl_183,type,
singletonsubset: $o ).
thf(decl_184,type,
singletoninpowerset: $o ).
thf(decl_185,type,
singletoninpowunion: $o ).
thf(decl_186,type,
upairset2E: $o ).
thf(decl_187,type,
upairsubunion: $o ).
thf(decl_188,type,
upairinpowunion: $o ).
thf(decl_189,type,
ubforcartprodlem1: $o ).
thf(decl_190,type,
ubforcartprodlem2: $o ).
thf(decl_191,type,
ubforcartprodlem3: $o ).
thf(decl_192,type,
cartprodpairin: $o ).
thf(decl_193,type,
cartprodmempair1: $o ).
thf(decl_194,type,
cartprodmempair: $o ).
thf(decl_195,type,
setunionE2: $o ).
thf(decl_196,type,
setunionsingleton1: $o ).
thf(decl_197,type,
setunionsingleton2: $o ).
thf(decl_198,type,
setunionsingleton: $o ).
thf(decl_200,type,
singletonprop: $o ).
thf(decl_202,type,
ex1E1: $o ).
thf(decl_203,type,
ex1I: $o ).
thf(decl_204,type,
ex1I2: $o ).
thf(decl_205,type,
singletonsuniq: $o ).
thf(decl_210,type,
setukpairinjL1: $o ).
thf(decl_211,type,
kfstsingleton: $o ).
thf(decl_212,type,
theprop: $o ).
thf(decl_214,type,
kfstpairEq: $o ).
thf(decl_215,type,
cartprodfstin: $o ).
thf(decl_216,type,
setukpairinjL2: $o ).
thf(decl_217,type,
setukpairinjL: $o ).
thf(decl_218,type,
setukpairinjR11: $o ).
thf(decl_219,type,
setukpairinjR12: $o ).
thf(decl_220,type,
setukpairinjR1: $o ).
thf(decl_221,type,
upairequniteq: $o ).
thf(decl_222,type,
setukpairinjR2: $o ).
thf(decl_223,type,
setukpairinjR: $o ).
thf(decl_224,type,
ksndsingleton: $o ).
thf(decl_226,type,
ksndpairEq: $o ).
thf(decl_227,type,
kpairsurjEq: $o ).
thf(decl_228,type,
cartprodsndin: $o ).
thf(decl_229,type,
cartprodpairmemEL: $o ).
thf(decl_230,type,
cartprodpairmemER: $o ).
thf(decl_231,type,
cartprodmempaircEq: $o ).
thf(decl_232,type,
cartprodfstpairEq: $o ).
thf(decl_233,type,
cartprodsndpairEq: $o ).
thf(decl_234,type,
cartprodpairsurjEq: $o ).
thf(decl_237,type,
dpsetconstrI: $o ).
thf(decl_238,type,
dpsetconstrSub: $o ).
thf(decl_239,type,
setOfPairsIsBReln: $o ).
thf(decl_240,type,
dpsetconstrERa: $o ).
thf(decl_241,type,
dpsetconstrEL1: $o ).
thf(decl_242,type,
dpsetconstrEL2: $o ).
thf(decl_243,type,
dpsetconstrER: $o ).
thf(decl_246,type,
funcImageSingleton: $o ).
thf(decl_247,type,
apProp: $o ).
thf(decl_249,type,
app: $o ).
thf(decl_250,type,
infuncsetfunc: $o ).
thf(decl_251,type,
ap2p: $o ).
thf(decl_252,type,
funcinfuncset: $o ).
thf(decl_253,type,
lamProp: $o ).
thf(decl_255,type,
lamp: $o ).
thf(decl_256,type,
lam2p: $o ).
thf(decl_257,type,
brelnall1: $o ).
thf(decl_258,type,
brelnall2: $o ).
thf(decl_259,type,
ex1E2: $o ).
thf(decl_260,type,
funcGraphProp1: $o ).
thf(decl_261,type,
funcGraphProp3: $o ).
thf(decl_262,type,
funcGraphProp2: $o ).
thf(decl_263,type,
funcextLem: $o ).
thf(decl_264,type,
funcGraphProp4: $o ).
thf(decl_265,type,
subbreln: $o ).
thf(decl_266,type,
eqbreln: $o ).
thf(decl_267,type,
funcext: $o ).
thf(decl_268,type,
funcext2: $o ).
thf(decl_269,type,
ap2apEq1: $o ).
thf(decl_270,type,
ap2apEq2: $o ).
thf(decl_271,type,
beta1: $o ).
thf(decl_272,type,
eta1: $o ).
thf(decl_273,type,
lam2lamEq: $o ).
thf(decl_274,type,
beta2: $o ).
thf(decl_275,type,
eta2: $o ).
thf(decl_276,type,
iffalseProp1: $o ).
thf(decl_277,type,
iffalseProp2: $o ).
thf(decl_278,type,
iftrueProp1: $o ).
thf(decl_279,type,
iftrueProp2: $o ).
thf(decl_280,type,
ifSingleton: $o ).
thf(decl_282,type,
ifp: $o ).
thf(decl_283,type,
theeq: $o ).
thf(decl_284,type,
iftrue: $o ).
thf(decl_285,type,
iffalse: $o ).
thf(decl_286,type,
iftrueorfalse: $o ).
thf(decl_287,type,
binintersectT_lem: $o ).
thf(decl_288,type,
binunionT_lem: $o ).
thf(decl_289,type,
powersetT_lem: $o ).
thf(decl_290,type,
setminusT_lem: $o ).
thf(decl_291,type,
complementT_lem: $o ).
thf(decl_292,type,
setextT: $o ).
thf(decl_293,type,
subsetTI: $o ).
thf(decl_294,type,
powersetTI1: $o ).
thf(decl_295,type,
powersetTE1: $o ).
thf(decl_296,type,
complementTI1: $o ).
thf(decl_297,type,
complementTE1: $o ).
thf(decl_298,type,
binintersectTELcontra: $o ).
thf(decl_299,type,
binintersectTERcontra: $o ).
thf(decl_300,type,
contrasubsetT: $o ).
thf(decl_301,type,
contrasubsetT1: $o ).
thf(decl_302,type,
contrasubsetT2: $o ).
thf(decl_303,type,
contrasubsetT3: $o ).
thf(decl_304,type,
doubleComplementI1: $o ).
thf(decl_305,type,
doubleComplementE1: $o ).
thf(decl_306,type,
doubleComplementSub1: $o ).
thf(decl_307,type,
doubleComplementSub2: $o ).
thf(decl_308,type,
doubleComplementEq: $o ).
thf(decl_309,type,
complementTnotintersectT: $o ).
thf(decl_310,type,
complementImpComplementIntersect: $o ).
thf(decl_311,type,
complementSubsetComplementIntersect: $o ).
thf(decl_312,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_313,type,
contraSubsetComplement: $o ).
thf(decl_314,type,
complementTcontraSubset: $o ).
thf(decl_315,type,
binunionTILcontra: $o ).
thf(decl_316,type,
binunionTIRcontra: $o ).
thf(decl_317,type,
inIntersectImpInUnion: $o ).
thf(decl_318,type,
inIntersectImpInUnion2: $o ).
thf(decl_319,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_320,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_321,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_322,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_323,type,
binunionTE: $o ).
thf(decl_324,type,
binunionTEcontra: $o ).
thf(decl_325,type,
demorgan2a1: $o ).
thf(decl_326,type,
complementUnionInPowersetComplement: $o ).
thf(decl_327,type,
demorgan2a2: $o ).
thf(decl_328,type,
demorgan1a: $o ).
thf(decl_329,type,
demorgan1b: $o ).
thf(decl_330,type,
demorgan1: $o ).
thf(decl_331,type,
demorgan2a: $o ).
thf(decl_332,type,
demorgan2b2: $o ).
thf(decl_333,type,
demorgan2b: $o ).
thf(decl_334,type,
demorgan2: $o ).
thf(decl_335,type,
woz13rule0: $o ).
thf(decl_336,type,
woz13rule1: $o ).
thf(decl_337,type,
woz13rule2: $o ).
thf(decl_338,type,
woz13rule3: $o ).
thf(decl_339,type,
woz13rule4: $o ).
thf(decl_340,type,
woz1_1: $o ).
thf(decl_341,type,
woz1_2: $o ).
thf(decl_342,type,
woz1_3: $o ).
thf(decl_343,type,
woz1_4: $o ).
thf(decl_344,type,
woz1_5: $o ).
thf(decl_346,type,
breln1all2: $o ).
thf(decl_348,type,
breln1SetBreln1: $o ).
thf(decl_355,type,
choice2fnsingleton: $o ).
thf(decl_356,type,
setOfPairsIsBReln1: $o ).
thf(decl_357,type,
breln1all1: $o ).
thf(decl_358,type,
subbreln1: $o ).
thf(decl_359,type,
eqbreln1: $o ).
thf(decl_361,type,
breln1invprop: $o ).
thf(decl_362,type,
breln1invI: $o ).
thf(decl_363,type,
breln1invE: $o ).
thf(decl_365,type,
breln1compprop: $o ).
thf(decl_366,type,
breln1compI: $o ).
thf(decl_367,type,
breln1compE: $o ).
thf(decl_368,type,
breln1compEex: $o ).
thf(decl_369,type,
breln1unionprop: $o ).
thf(decl_370,type,
breln1unionIL: $o ).
thf(decl_371,type,
breln1unionIR: $o ).
thf(decl_372,type,
breln1unionI: $o ).
thf(decl_373,type,
breln1unionE: $o ).
thf(decl_374,type,
breln1unionEcases: $o ).
thf(decl_375,type,
breln1unionCommutes: $o ).
thf(decl_376,type,
woz2Ex: $o ).
thf(decl_377,type,
woz2W: $o ).
thf(decl_378,type,
woz2A: $o ).
thf(decl_379,type,
woz2B: $o ).
thf(decl_380,type,
image1Ex: $o ).
thf(decl_381,type,
image1Ex1: $o ).
thf(decl_383,type,
image1Equiv: $o ).
thf(decl_384,type,
image1E: $o ).
thf(decl_385,type,
image1I: $o ).
thf(decl_388,type,
injFuncInInjFuncSet: $o ).
thf(decl_389,type,
injFuncSetFuncIn: $o ).
thf(decl_390,type,
injFuncSetFuncInj: $o ).
thf(decl_393,type,
surjFuncSetFuncIn: $o ).
thf(decl_394,type,
surjFuncSetFuncSurj: $o ).
thf(decl_395,type,
leftInvIsSurj: $o ).
thf(decl_396,type,
surjCantorThm: $o ).
thf(decl_397,type,
foundation2: $o ).
thf(decl_398,type,
notinself: $o ).
thf(decl_399,type,
notinself2: $o ).
thf(decl_400,type,
omegaS: $i > $i ).
thf(decl_401,type,
omegaSp: $o ).
thf(decl_402,type,
esk1_1: $i > $i ).
thf(decl_403,type,
esk2_1: $i > $i ).
thf(decl_404,type,
esk3_1: $i > $i ).
thf(decl_405,type,
esk4_1: $i > $i ).
thf(decl_406,type,
esk5_0: $i ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',nonempty) ).
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/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',nonemptyI) ).
thf(omegaSclos,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',omegaSclos) ).
thf(foundation2,axiom,
( foundation2
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( ( binintersect @ X21 @ X4 )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',foundation2) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',nonemptyImpWitness) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',nonemptyE1) ).
thf(omegaSp,axiom,
( omegaSp
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( omegaS @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',omegaSp) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',omega__Cong) ).
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/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p',omega0Ax) ).
thf(c_0_12,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_13,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_14,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[omegaSclos]) ).
thf(c_0_15,axiom,
( foundation2
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( ( binintersect @ X21 @ X4 )
= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[foundation2,c_0_12]) ).
thf(c_0_16,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_12]) ).
thf(c_0_17,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_12]) ).
thf(c_0_18,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_19,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_12]) ).
thf(c_0_20,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( ! [X80: $i] :
( ( in @ X80 @ omega )
=> ( in @ ( setadjoin @ X80 @ X80 ) @ omega ) )
=> ( ! [X81: $i] :
( ( ( in @ emptyset @ X81 )
& ! [X82: $i] :
( ( ( in @ X82 @ omega )
& ( in @ X82 @ X81 ) )
=> ( in @ ( setadjoin @ X82 @ X82 ) @ X81 ) ) )
=> ! [X83: $i] :
( ( in @ X83 @ omega )
=> ( in @ X83 @ X81 ) ) )
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( ! [X84: $i] :
( ( X84 != emptyset )
=> ? [X85: $i] : ( in @ X85 @ X84 ) )
=> ( ! [X86: $i,X87: $i > $o,X88: $i] :
( ( in @ X88 @ X86 )
=> ( ( X87 @ X88 )
=> ( ( dsetconstr @ X86 @ X87 )
!= emptyset ) ) )
=> ( ! [X89: $i] :
( ? [X90: $i] : ( in @ X90 @ X89 )
=> ( X89 != emptyset ) )
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( ! [X91: $i] :
( ( X91 != emptyset )
=> ? [X92: $i] :
( ( in @ X92 @ X91 )
& $true ) )
=> ( 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 = omega )
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( ! [X93: $i] :
( ( X93 != emptyset )
=> ? [X94: $i] :
( ( in @ X94 @ X93 )
& ( ( binintersect @ X94 @ X93 )
= emptyset ) ) )
=> ( notinself
=> ( notinself2
=> ( ! [X95: $i] :
( ( in @ X95 @ omega )
=> ( in @ ( omegaS @ X95 ) @ omega ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_19]),omegaSp]),omega__Cong]),omegaIndAx]),omegaSAx]),omega0Ax])])]) ).
thf(c_0_21,negated_conjecture,
! [X97: $i,X98: $i,X100: $i,X101: $i,X103: $i,X104: $i > $o,X105: $i,X106: $i,X107: $i,X108: $i,X110: $i,X112: $i] :
( setextAx
& emptysetAx
& setadjoinAx
& powersetAx
& setunionAx
& ( in @ emptyset @ omega )
& ( ~ ( in @ X97 @ omega )
| ( in @ ( setadjoin @ X97 @ X97 ) @ omega ) )
& ( ( in @ ( esk1_1 @ X98 ) @ omega )
| ~ ( in @ emptyset @ X98 )
| ~ ( in @ X100 @ omega )
| ( in @ X100 @ X98 ) )
& ( ( in @ ( esk1_1 @ X98 ) @ X98 )
| ~ ( in @ emptyset @ X98 )
| ~ ( in @ X100 @ omega )
| ( in @ X100 @ X98 ) )
& ( ~ ( in @ ( setadjoin @ ( esk1_1 @ X98 ) @ ( esk1_1 @ X98 ) ) @ X98 )
| ~ ( in @ emptyset @ X98 )
| ~ ( in @ X100 @ omega )
| ( in @ X100 @ X98 ) )
& replAx
& foundationAx
& wellorderingAx
& descrp
& dsetconstrI
& dsetconstrEL
& dsetconstrER
& exuE1
& prop2setE
& emptysetE
& emptysetimpfalse
& notinemptyset
& exuE3e
& setext
& emptyI
& noeltsimpempty
& setbeta
& ( ( X101 = emptyset )
| ( in @ ( esk2_1 @ X101 ) @ X101 ) )
& ( ~ ( in @ X105 @ X103 )
| ~ ( X104 @ X105 )
| ( ( dsetconstr @ X103 @ X104 )
!= emptyset ) )
& ( ~ ( in @ X107 @ X106 )
| ( X106 != emptyset ) )
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& setoftrueEq
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& setunionI
& setunionE
& subPowSU
& exuE2
& ( ( in @ ( esk3_1 @ X108 ) @ X108 )
| ( X108 = emptyset ) )
& ( $true
| ( X108 = emptyset ) )
& 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 = omega )
& exuEu
& descr__Cong
& dsetconstr__Cong
& subsetI1
& eqimpsubset2
& eqimpsubset1
& subsetI2
& emptysetsubset
& subsetE
& subsetE2
& notsubsetI
& notequalI1
& notequalI2
& subsetRefl
& subsetTrans
& setadjoinSub
& setadjoinSub2
& subset2powerset
& setextsub
& subsetemptysetimpeq
& powersetI1
& powersetE1
& inPowerset
& powersetsubset
& sepInPowerset
& sepSubset
& binunionIL
& upairset2IR
& binunionIR
& binunionEcases
& binunionE
& binunionLsub
& binunionRsub
& binintersectI
& binintersectSubset5
& binintersectEL
& binintersectLsub
& binintersectSubset2
& binintersectSubset3
& binintersectER
& disjointsetsI1
& binintersectRsub
& binintersectSubset4
& binintersectSubset1
& bs114d
& setminusI
& setminusEL
& setminusER
& setminusSubset2
& setminusERneg
& setminusELneg
& setminusILneg
& setminusIRneg
& setminusLsub
& setminusSubset1
& symdiffE
& symdiffI1
& symdiffI2
& symdiffIneg1
& symdiffIneg2
& secondinupair
& setukpairIL
& setukpairIR
& kpairiskpair
& kpairp
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& cartprodpairin
& cartprodmempair1
& cartprodmempair
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& singletonprop
& ex1E1
& ex1I
& ex1I2
& singletonsuniq
& setukpairinjL1
& kfstsingleton
& theprop
& kfstpairEq
& cartprodfstin
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ksndsingleton
& ksndpairEq
& kpairsurjEq
& cartprodsndin
& cartprodpairmemEL
& cartprodpairmemER
& cartprodmempaircEq
& cartprodfstpairEq
& cartprodsndpairEq
& cartprodpairsurjEq
& dpsetconstrI
& dpsetconstrSub
& setOfPairsIsBReln
& dpsetconstrERa
& dpsetconstrEL1
& dpsetconstrEL2
& dpsetconstrER
& funcImageSingleton
& apProp
& app
& infuncsetfunc
& ap2p
& funcinfuncset
& lamProp
& lamp
& lam2p
& brelnall1
& brelnall2
& ex1E2
& funcGraphProp1
& funcGraphProp3
& funcGraphProp2
& funcextLem
& funcGraphProp4
& subbreln
& eqbreln
& funcext
& funcext2
& ap2apEq1
& ap2apEq2
& beta1
& eta1
& lam2lamEq
& beta2
& eta2
& iffalseProp1
& iffalseProp2
& iftrueProp1
& iftrueProp2
& ifSingleton
& ifp
& theeq
& iftrue
& iffalse
& iftrueorfalse
& binintersectT_lem
& binunionT_lem
& powersetT_lem
& setminusT_lem
& complementT_lem
& setextT
& subsetTI
& powersetTI1
& powersetTE1
& complementTI1
& complementTE1
& binintersectTELcontra
& binintersectTERcontra
& contrasubsetT
& contrasubsetT1
& contrasubsetT2
& contrasubsetT3
& doubleComplementI1
& doubleComplementE1
& doubleComplementSub1
& doubleComplementSub2
& doubleComplementEq
& complementTnotintersectT
& complementImpComplementIntersect
& complementSubsetComplementIntersect
& complementInPowersetComplementIntersect
& contraSubsetComplement
& complementTcontraSubset
& binunionTILcontra
& binunionTIRcontra
& inIntersectImpInUnion
& inIntersectImpInUnion2
& inIntersectImpInIntersectUnions
& intersectInPowersetIntersectUnions
& inComplementUnionImpNotIn1
& inComplementUnionImpInComplement1
& binunionTE
& binunionTEcontra
& demorgan2a1
& complementUnionInPowersetComplement
& demorgan2a2
& demorgan1a
& demorgan1b
& demorgan1
& demorgan2a
& demorgan2b2
& demorgan2b
& demorgan2
& woz13rule0
& woz13rule1
& woz13rule2
& woz13rule3
& woz13rule4
& woz1_1
& woz1_2
& woz1_3
& woz1_4
& woz1_5
& breln1all2
& breln1SetBreln1
& choice2fnsingleton
& setOfPairsIsBReln1
& breln1all1
& subbreln1
& eqbreln1
& breln1invprop
& breln1invI
& breln1invE
& breln1compprop
& breln1compI
& breln1compE
& breln1compEex
& breln1unionprop
& breln1unionIL
& breln1unionIR
& breln1unionI
& breln1unionE
& breln1unionEcases
& breln1unionCommutes
& woz2Ex
& woz2W
& woz2A
& woz2B
& image1Ex
& image1Ex1
& image1Equiv
& image1E
& image1I
& injFuncInInjFuncSet
& injFuncSetFuncIn
& injFuncSetFuncInj
& surjFuncSetFuncIn
& surjFuncSetFuncSurj
& leftInvIsSurj
& surjCantorThm
& ( ( in @ ( esk4_1 @ X110 ) @ X110 )
| ( X110 = emptyset ) )
& ( ( ( binintersect @ ( esk4_1 @ X110 ) @ X110 )
= emptyset )
| ( X110 = emptyset ) )
& notinself
& notinself2
& ( ~ ( in @ X112 @ omega )
| ( in @ ( omegaS @ X112 ) @ omega ) )
& ( in @ esk5_0 @ omega )
& ~ ( in @ ( setadjoin @ esk5_0 @ esk5_0 ) @ omega ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_20])])])])])])]) ).
thf(c_0_22,negated_conjecture,
~ ( in @ ( setadjoin @ esk5_0 @ esk5_0 ) @ omega ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X2: $i] :
( ( in @ ( setadjoin @ X2 @ X2 ) @ omega )
| ~ ( in @ X2 @ omega ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
in @ esk5_0 @ omega,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU809^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:32:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.16 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.6NmseYZk5Y/E---3.1_185231.p
% 0.08/0.20 % Version: 3.5.1-ho
% 0.08/0.20 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.20 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.20 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.20 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.20 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.20 % Starting ho_unfolding_8 with 300s (1) cores
% 0.08/0.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.20 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.20 % Starting new_ho_5 with 300s (1) cores
% 0.08/0.20 % pre_casc_3 with pid 185247 completed with status 0
% 0.08/0.20 % Result found by pre_casc_3
% 0.08/0.20 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.20 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.20 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.20 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.20 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.08/0.20 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.08/0.20 % Search class: HGHSF-FFMM21-SHFMMFBN
% 0.08/0.20 % partial match(2): HGHSF-FFMM21-SHFFFFBN
% 0.08/0.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % SubtermCWHack with pid 185254 completed with status 0
% 0.08/0.20 % Result found by SubtermCWHack
% 0.08/0.20 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.20 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.20 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.20 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.20 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.08/0.20 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.08/0.20 % Search class: HGHSF-FFMM21-SHFMMFBN
% 0.08/0.20 % partial match(2): HGHSF-FFMM21-SHFFFFBN
% 0.08/0.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % Preprocessing time : 0.002 s
% 0.08/0.20
% 0.08/0.20 % Proof found!
% 0.08/0.20 % SZS status Theorem
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20 % Parsed axioms : 708
% 0.08/0.20 % Removed by relevancy pruning/SinE : 695
% 0.08/0.20 % Initial clauses : 332
% 0.08/0.20 % Removed in clause preprocessing : 2
% 0.08/0.20 % Initial clauses in saturation : 330
% 0.08/0.20 % Processed clauses : 326
% 0.08/0.20 % ...of these trivial : 0
% 0.08/0.20 % ...subsumed : 0
% 0.08/0.20 % ...remaining for further processing : 326
% 0.08/0.20 % Other redundant clauses eliminated : 1
% 0.08/0.20 % Clauses deleted for lack of memory : 0
% 0.08/0.20 % Backward-subsumed : 0
% 0.08/0.20 % Backward-rewritten : 0
% 0.08/0.20 % Generated clauses : 4
% 0.08/0.20 % ...of the previous two non-redundant : 2
% 0.08/0.20 % ...aggressively subsumed : 0
% 0.08/0.20 % Contextual simplify-reflections : 0
% 0.08/0.20 % Paramodulations : 3
% 0.08/0.20 % Factorizations : 0
% 0.08/0.20 % NegExts : 0
% 0.08/0.20 % Equation resolutions : 1
% 0.08/0.20 % Disequality decompositions : 0
% 0.08/0.20 % Total rewrite steps : 1
% 0.08/0.20 % ...of those cached : 0
% 0.08/0.20 % Propositional unsat checks : 0
% 0.08/0.20 % Propositional check models : 0
% 0.08/0.20 % Propositional check unsatisfiable : 0
% 0.08/0.20 % Propositional clauses : 0
% 0.08/0.20 % Propositional clauses after purity: 0
% 0.08/0.20 % Propositional unsat core size : 0
% 0.08/0.20 % Propositional preprocessing time : 0.000
% 0.08/0.20 % Propositional encoding time : 0.000
% 0.08/0.20 % Propositional solver time : 0.000
% 0.08/0.20 % Success case prop preproc time : 0.000
% 0.08/0.20 % Success case prop encoding time : 0.000
% 0.08/0.20 % Success case prop solver time : 0.000
% 0.08/0.20 % Current number of processed clauses : 325
% 0.08/0.20 % Positive orientable unit clauses : 317
% 0.08/0.20 % Positive unorientable unit clauses: 1
% 0.08/0.20 % Negative unit clauses : 2
% 0.08/0.20 % Non-unit-clauses : 5
% 0.08/0.20 % Current number of unprocessed clauses: 6
% 0.08/0.20 % ...number of literals in the above : 19
% 0.08/0.20 % Current number of archived formulas : 0
% 0.08/0.20 % Current number of archived clauses : 0
% 0.08/0.20 % Clause-clause subsumption calls (NU) : 3
% 0.08/0.20 % Rec. Clause-clause subsumption calls : 3
% 0.08/0.20 % Non-unit clause-clause subsumptions : 0
% 0.08/0.20 % Unit Clause-clause subsumption calls : 0
% 0.08/0.20 % Rewrite failures with RHS unbound : 0
% 0.08/0.20 % BW rewrite match attempts : 1
% 0.08/0.20 % BW rewrite match successes : 1
% 0.08/0.20 % Condensation attempts : 0
% 0.08/0.20 % Condensation successes : 0
% 0.08/0.20 % Termbank termtop insertions : 21211
% 0.08/0.20 % Search garbage collected termcells : 8319
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.012 s
% 0.08/0.20 % System time : 0.006 s
% 0.08/0.20 % Total time : 0.018 s
% 0.08/0.20 % Maximum resident set size: 5476 pages
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.022 s
% 0.08/0.20 % System time : 0.009 s
% 0.08/0.20 % Total time : 0.031 s
% 0.08/0.20 % Maximum resident set size: 5376 pages
% 0.08/0.20 % E exiting
%------------------------------------------------------------------------------