%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU823^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:31:44 AM UTC 2026
% Result : Theorem 0.37s 0.32s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 6348 (1756 equ; 0 cnn)
% Maximal formula atoms : 342 ( 154 avg)
% Number of connectives : 2931 ( 49 ~; 27 |;1029 &; 110 @)
% ( 7 <=>;1709 =>; 0 <=; 0 <~>)
% Maximal formula depth : 348 ( 70 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 630 ( 627 usr; 372 con; 0-6 aty)
% Number of variables : 40 ( 0 sgn 32 !; 8 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_279,type,
contrasubsetT1: $o ).
thf(func_def_280,type,
contrasubsetT2: $o ).
thf(func_def_281,type,
contrasubsetT3: $o ).
thf(func_def_282,type,
doubleComplementI1: $o ).
thf(func_def_283,type,
doubleComplementE1: $o ).
thf(func_def_284,type,
doubleComplementSub1: $o ).
thf(func_def_285,type,
doubleComplementSub2: $o ).
thf(func_def_286,type,
doubleComplementEq: $o ).
thf(func_def_287,type,
complementTnotintersectT: $o ).
thf(func_def_288,type,
complementImpComplementIntersect: $o ).
thf(func_def_289,type,
complementSubsetComplementIntersect: $o ).
thf(func_def_290,type,
complementInPowersetComplementIntersect: $o ).
thf(func_def_291,type,
contraSubsetComplement: $o ).
thf(func_def_292,type,
complementTcontraSubset: $o ).
thf(func_def_293,type,
binunionTILcontra: $o ).
thf(func_def_294,type,
binunionTIRcontra: $o ).
thf(func_def_295,type,
inIntersectImpInUnion: $o ).
thf(func_def_296,type,
inIntersectImpInUnion2: $o ).
thf(func_def_297,type,
inIntersectImpInIntersectUnions: $o ).
thf(func_def_298,type,
intersectInPowersetIntersectUnions: $o ).
thf(func_def_299,type,
inComplementUnionImpNotIn1: $o ).
thf(func_def_300,type,
inComplementUnionImpInComplement1: $o ).
thf(func_def_301,type,
binunionTE: $o ).
thf(func_def_302,type,
binunionTEcontra: $o ).
thf(func_def_303,type,
demorgan2a1: $o ).
thf(func_def_304,type,
complementUnionInPowersetComplement: $o ).
thf(func_def_305,type,
demorgan2a2: $o ).
thf(func_def_306,type,
demorgan1a: $o ).
thf(func_def_307,type,
demorgan1b: $o ).
thf(func_def_308,type,
demorgan1: $o ).
thf(func_def_309,type,
demorgan2a: $o ).
thf(func_def_310,type,
demorgan2b2: $o ).
thf(func_def_311,type,
demorgan2b: $o ).
thf(func_def_312,type,
demorgan2: $o ).
thf(func_def_313,type,
woz13rule0: $o ).
thf(func_def_314,type,
woz13rule1: $o ).
thf(func_def_315,type,
woz13rule2: $o ).
thf(func_def_316,type,
woz13rule3: $o ).
thf(func_def_317,type,
woz13rule4: $o ).
thf(func_def_318,type,
woz1_1: $o ).
thf(func_def_319,type,
woz1_2: $o ).
thf(func_def_320,type,
woz1_3: $o ).
thf(func_def_321,type,
woz1_4: $o ).
thf(func_def_322,type,
woz1_5: $o ).
thf(func_def_323,type,
breln1: $i > $i > $o ).
thf(func_def_324,type,
breln1all2: $o ).
thf(func_def_325,type,
breln1Set: $i > $i ).
thf(func_def_326,type,
breln1SetBreln1: $o ).
thf(func_def_327,type,
transitive: $i > $i > $o ).
thf(func_def_328,type,
antisymmetric: $i > $i > $o ).
thf(func_def_329,type,
reflexive: $i > $i > $o ).
thf(func_def_330,type,
refltransitive: $i > $i > $o ).
thf(func_def_331,type,
refllinearorder: $i > $i > $o ).
thf(func_def_332,type,
reflwellordering: $i > $i > $o ).
thf(func_def_333,type,
choice2fnsingleton: $o ).
thf(func_def_334,type,
setOfPairsIsBReln1: $o ).
thf(func_def_335,type,
breln1all1: $o ).
thf(func_def_336,type,
subbreln1: $o ).
thf(func_def_337,type,
eqbreln1: $o ).
thf(func_def_338,type,
breln1invset: $i > $i > $i ).
thf(func_def_339,type,
breln1invprop: $o ).
thf(func_def_340,type,
breln1invI: $o ).
thf(func_def_341,type,
breln1invE: $o ).
thf(func_def_342,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_343,type,
breln1compprop: $o ).
thf(func_def_344,type,
breln1compI: $o ).
thf(func_def_345,type,
breln1compE: $o ).
thf(func_def_346,type,
breln1compEex: $o ).
thf(func_def_347,type,
breln1unionprop: $o ).
thf(func_def_348,type,
breln1unionIL: $o ).
thf(func_def_349,type,
breln1unionIR: $o ).
thf(func_def_350,type,
breln1unionI: $o ).
thf(func_def_351,type,
breln1unionE: $o ).
thf(func_def_352,type,
breln1unionEcases: $o ).
thf(func_def_353,type,
breln1unionCommutes: $o ).
thf(func_def_354,type,
woz2Ex: $o ).
thf(func_def_355,type,
woz2W: $o ).
thf(func_def_356,type,
woz2A: $o ).
thf(func_def_357,type,
woz2B: $o ).
thf(func_def_358,type,
image1Ex: $o ).
thf(func_def_359,type,
image1Ex1: $o ).
thf(func_def_360,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_361,type,
image1Equiv: $o ).
thf(func_def_362,type,
image1E: $o ).
thf(func_def_363,type,
image1I: $o ).
thf(func_def_364,type,
injective: $i > $i > $i > $o ).
thf(func_def_365,type,
injFuncSet: $i > $i > $i ).
thf(func_def_366,type,
injFuncInInjFuncSet: $o ).
thf(func_def_367,type,
injFuncSetFuncIn: $o ).
thf(func_def_368,type,
injFuncSetFuncInj: $o ).
thf(func_def_369,type,
surjective: $i > $i > $i > $o ).
thf(func_def_370,type,
surjFuncSet: $i > $i > $i ).
thf(func_def_371,type,
surjFuncSetFuncIn: $o ).
thf(func_def_372,type,
surjFuncSetFuncSurj: $o ).
thf(func_def_373,type,
leftInvIsSurj: $o ).
thf(func_def_374,type,
surjCantorThm: $o ).
thf(func_def_375,type,
foundation2: $o ).
thf(func_def_376,type,
notinself: $o ).
thf(func_def_377,type,
notinself2: $o ).
thf(func_def_378,type,
omegaS: $i > $i ).
thf(func_def_379,type,
omegaSp: $o ).
thf(func_def_380,type,
omegaSclos: $o ).
thf(func_def_381,type,
peano0notS: $o ).
thf(func_def_382,type,
peano3: $i > $i > $i > $o ).
thf(func_def_383,type,
peano4: $i > $i > $i > $o ).
thf(func_def_384,type,
peano5: $i > $i > $i > $o ).
thf(func_def_385,type,
peanoSinj: $o ).
thf(func_def_386,type,
peano: $i > $i > $i > $o ).
thf(func_def_387,type,
transitiveset: $i > $o ).
thf(func_def_388,type,
transitivesetOp1: $o ).
thf(func_def_389,type,
binintTransitive: $o ).
thf(func_def_390,type,
transitivesetOp2: $o ).
thf(func_def_391,type,
setunionTransitive: $o ).
thf(func_def_392,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_393,type,
wellorderedByIn: $i > $o ).
thf(func_def_394,type,
ordinal: $i > $o ).
thf(func_def_395,type,
limitOrdinal: $i > $o ).
thf(func_def_396,type,
ordinalMinLem1: $o ).
thf(func_def_397,type,
ordinalTransSet: $o ).
thf(func_def_398,type,
ordinalTransSet1: $o ).
thf(func_def_399,type,
setunionOrdinalLem1: $o ).
thf(func_def_400,type,
succOrdinal: $i > $o ).
thf(func_def_401,type,
emptysetOrdinal: $o ).
thf(func_def_402,type,
ordinalIrrefl: $o ).
thf(func_def_403,type,
ordinalIrrefl2: $o ).
thf(func_def_406,type,
vOR: $o > $o > $o ).
thf(func_def_407,type,
vAND: $o > $o > $o ).
thf(func_def_408,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_409,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_410,type,
vNOT: $o > $o ).
thf(func_def_411,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_412,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_413,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_414,type,
vIMP: $o > $o > $o ).
thf(func_def_415,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_416,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_417,type,
vIFF: $o > $o > $o ).
thf(func_def_418,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_419,type,
sP0: $o ).
thf(func_def_420,type,
sP1: $i > $i > $o ).
thf(func_def_421,type,
sP2: $i > $o ).
thf(func_def_422,type,
sP3: $o ).
thf(func_def_423,type,
sP4: $o ).
thf(func_def_431,type,
sK12: $i > $i > $o ).
thf(func_def_432,type,
sK13: $i > $o ).
thf(func_def_435,type,
sK16: $i > ( $i > $o ) > $i ).
thf(func_def_436,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_441,type,
sK22: $i > $i > $i > $i > $i ).
thf(func_def_444,type,
sK25: $i > $o ).
thf(func_def_445,type,
sK26: $i > $i ).
thf(func_def_446,type,
sK27: ( $i > $o ) > $i ).
thf(func_def_483,type,
sK64: $i > $i > $i > $i ).
thf(func_def_484,type,
sK65: $i > $i > $i > $i ).
thf(func_def_485,type,
sK66: $i > $i > $i > $i ).
thf(func_def_486,type,
sK67: $i > $i > $i > $i ).
thf(func_def_488,type,
sK69: $o ).
thf(func_def_489,type,
sK70: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_490,type,
sK71: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_494,type,
sK75: $i > $o ).
thf(func_def_497,type,
sK78: $o ).
thf(func_def_503,type,
sK84: $i > $o ).
thf(func_def_504,type,
sK85: $i > $i ).
thf(func_def_505,type,
sK86: ( $i > $o ) > $i ).
thf(func_def_510,type,
sK91: $i > $i > $i ).
thf(func_def_511,type,
sK92: $i > $i > $i ).
thf(func_def_516,type,
sK97: $i > $o ).
thf(func_def_517,type,
sK98: $i > $o ).
thf(func_def_518,type,
sK99: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_519,type,
sK100: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_529,type,
sK110: $i > $o ).
thf(func_def_532,type,
sK113: $i > ( $i > $o ) > $i ).
thf(func_def_549,type,
sK130: $i > $i ).
thf(func_def_552,type,
sK133: $i > $i ).
thf(func_def_571,type,
sK152: $i > $i > ( $i > $i ) > $i > $i ).
thf(func_def_572,type,
sK153: $i > ( $i > $i ) > $i > $i ).
thf(func_def_574,type,
sK155: $i > $i ).
thf(func_def_579,type,
sK160: $i > $i ).
thf(func_def_581,type,
sK162: ( $i > $i ) > $i > $i > $i ).
thf(func_def_585,type,
sK166: $i > $i > $i > $i ).
thf(func_def_586,type,
sK167: $i > $i > $i > $i ).
thf(func_def_601,type,
sK182: ( $i > $o ) > $i > $i ).
thf(func_def_603,type,
sK184: $i > $o ).
thf(func_def_609,type,
sK190: $o ).
thf(func_def_610,type,
sK191: $o > $i > $i > $i ).
thf(func_def_616,type,
sK197: $i > $o ).
thf(func_def_631,type,
sK212: $i > $i ).
thf(func_def_635,type,
sK216: $i > $i > $i ).
thf(func_def_662,type,
sK243: $i > $o ).
thf(func_def_664,type,
sK245: $i > $i > $i > $i > $i ).
thf(func_def_669,type,
sK250: $i > $o ).
thf(func_def_672,type,
sK253: $i > ( $i > $o ) > $i ).
thf(func_def_682,type,
sK263: $i > $i > $i > $i ).
thf(func_def_683,type,
sK264: $i > $o ).
thf(func_def_687,type,
sK268: $i > $i ).
thf(func_def_688,type,
sK269: $o ).
thf(func_def_690,type,
sK271: ( $i > $i ) > $i > $i > $i ).
thf(func_def_693,type,
sK274: $i > $i ).
thf(func_def_698,type,
sK279: $o ).
thf(func_def_710,type,
sK291: $i > $o ).
thf(func_def_711,type,
sK292: ( $i > $o ) > $i ).
thf(func_def_720,type,
sK301: $o ).
thf(func_def_725,type,
sK306: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_726,type,
sK307: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_730,type,
sK311: $i > $o ).
thf(func_def_747,type,
sK328: $i > $i > $i ).
thf(func_def_753,type,
sK334: $i > $i ).
thf(func_def_756,type,
sK337: $i > $o ).
thf(func_def_773,type,
sK354: $o ).
thf(func_def_776,type,
sK357: $i > $i > $o ).
thf(func_def_807,type,
sK388: $o ).
thf(func_def_809,type,
sK390: ( $i > $o ) > $i > $i ).
thf(func_def_810,type,
sK391: ( $i > $o ) > $i > $i ).
thf(func_def_812,type,
sK393: $i > $o ).
thf(func_def_814,type,
sK395: $i > $o ).
thf(func_def_823,type,
sK404: $o > $i > $i > $i > $i > $i > $i ).
thf(func_def_829,type,
sK410: $o ).
thf(func_def_831,type,
sK412: $i > $i > $o ).
thf(func_def_839,type,
sK420: $i > $i > $i ).
thf(func_def_843,type,
sK424: $o ).
thf(func_def_855,type,
sK436: $i > $i > $i > $i > $i ).
thf(func_def_859,type,
sK440: $i > $o ).
thf(func_def_861,type,
sK442: $i > ( $i > $o ) > $i ).
thf(func_def_863,type,
sK444: $i > $i ).
thf(func_def_864,type,
sK445: $i > $o ).
thf(func_def_865,type,
sK446: $i > $o ).
thf(func_def_866,type,
sK447: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_867,type,
sK448: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_873,type,
sK454: ( $i > $o ) > $i > $i > $i ).
thf(func_def_874,type,
sK455: ( $i > $o ) > $i > $i > $i ).
thf(func_def_877,type,
sK458: $i > $o ).
thf(func_def_891,type,
sK472: $i > $o ).
thf(func_def_902,type,
sK483: $i > $i ).
thf(func_def_918,type,
sK499: $i > $i > $o ).
thf(func_def_919,type,
sK500: $i > $i ).
thf(func_def_920,type,
sK501: $i > $i ).
thf(func_def_921,type,
sK502: ( $i > $i > $o ) > $i > $i ).
thf(func_def_922,type,
sK503: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_923,type,
sK504: ( $i > $i > $o ) > $i > $i ).
thf(func_def_929,type,
sK510: $i > $o ).
thf(func_def_933,type,
sK514: $i > $o ).
thf(func_def_937,type,
sK518: $i > $i ).
thf(func_def_939,type,
sK520: $i > ( $i > $i ) > $i > $i ).
thf(func_def_948,type,
sK529: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_951,type,
sK532: $i > $i > $o ).
thf(func_def_954,type,
sK535: $i > $i ).
thf(func_def_956,type,
sK537: $i > $i ).
thf(func_def_957,type,
sK538: $i > $i ).
thf(func_def_958,type,
sK539: $i > $i ).
thf(func_def_959,type,
sK540: $i > $i ).
thf(func_def_960,type,
sK541: $i > $i ).
thf(func_def_961,type,
sK542: $i > $i > $i > $i ).
thf(func_def_962,type,
sK543: $i > $i ).
thf(func_def_963,type,
sK544: $i > $i ).
thf(func_def_964,type,
sK545: $i > $i ).
thf(func_def_965,type,
sK546: $i > $i ).
thf(func_def_966,type,
sK547: $i > $i > $i ).
thf(func_def_967,type,
sK548: $i > $i > $i ).
thf(func_def_968,type,
sK549: $i > $i > $i > $i ).
thf(func_def_969,type,
sK550: $i > $i > $i > $i ).
thf(func_def_970,type,
sK551: $i > $i > $i > $i ).
thf(func_def_971,type,
sK552: $i > $i > $i ).
thf(func_def_972,type,
sK553: $i > $i > $i ).
thf(func_def_973,type,
sK554: $i > $i > $i ).
thf(func_def_994,type,
sK575: $i > $i > $i > $i ).
thf(func_def_995,type,
sK576: $i > $i > $i > $i ).
thf(func_def_1000,type,
sK581: ( $i > $o ) > $i > $i ).
thf(func_def_1002,type,
sK583: $i > $o ).
thf(func_def_1007,type,
sK588: $o ).
thf(func_def_1012,type,
sK593: $i > $i > $i ).
thf(func_def_1017,type,
sK598: $i > $i ).
thf(func_def_1027,type,
sK608: $i > $i > $o ).
thf(func_def_1036,type,
sK617: $i > $o ).
thf(func_def_1038,type,
sK619: ( $i > $o ) > $i > $i ).
thf(func_def_1073,type,
sK654: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1075,type,
sK656: $i > $i ).
thf(func_def_1080,type,
sK661: $i > $i > $i > $i ).
thf(func_def_1087,type,
sK668: $o ).
thf(func_def_1101,type,
sK682: $i > $i > $i ).
thf(func_def_1131,type,
sK712: $i > $i > $o ).
thf(func_def_1145,type,
sK726: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1148,type,
sK729: $i > $i ).
thf(func_def_1171,type,
sK752: $i > $i > $i > $i > $i > $i ).
thf(func_def_1179,type,
sK760: $i > $i > $i ).
thf(func_def_1180,type,
sK761: $o ).
thf(func_def_1197,type,
sK778: $i > $o ).
thf(func_def_1200,type,
sK781: $i > $i ).
thf(func_def_1201,type,
sK782: $i > ( $i > $o ) > $i ).
thf(func_def_1202,type,
sK783: $i > $o ).
thf(func_def_1205,type,
sK786: $i > $o ).
thf(func_def_1207,type,
sK788: ( $i > $o ) > $i ).
thf(func_def_1208,type,
sK789: ( $i > $o ) > $i ).
thf(func_def_1236,type,
sK817: $i > $i ).
thf(func_def_1237,type,
sK818: $i > ( $i > $o ) > $i ).
thf(func_def_1238,type,
sK819: $i > $o ).
thf(func_def_1247,type,
sK828: $i > $i > $i > $i > $i ).
thf(func_def_1248,type,
sK829: $i > $i > $i > $i > $i ).
thf(func_def_1256,type,
sK837: $i > $i > $o ).
thf(func_def_1258,type,
sK839: $o ).
thf(func_def_1262,type,
sK843: $i > $o ).
thf(func_def_1269,type,
sK850: $o ).
thf(func_def_1280,type,
sK861: $o ).
thf(func_def_1290,type,
sK871: $i > $o ).
thf(func_def_1297,type,
sK878: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1298,type,
sK879: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1301,type,
sK882: $i > $o ).
thf(func_def_1305,type,
sK886: $i > $i > $i > $i ).
thf(func_def_1306,type,
sK887: $i > $i > $i > $i ).
thf(func_def_1315,type,
sK896: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1317,type,
sK898: $i > $i ).
thf(func_def_1330,type,
sK911: $i > $i ).
thf(func_def_1335,type,
sK916: $i > $i > $i > $i > $i ).
thf(func_def_1336,type,
sK917: $i > $i > $i > $i > $i ).
thf(func_def_1337,type,
sK918: $i > $i > $i > $i > $i ).
thf(func_def_1338,type,
sK919: $i > $i > $i > $i > $i ).
thf(func_def_1340,type,
sK921: $i > $i ).
thf(func_def_1343,type,
sK924: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1379,type,
sK960: $i > $o ).
thf(func_def_1383,type,
sK964: $i > $i ).
thf(func_def_1384,type,
sK965: $i > $i ).
thf(func_def_1385,type,
sK966: $i > $i ).
thf(func_def_1386,type,
sK967: ( $i > $i ) > $i > $i ).
thf(func_def_1387,type,
sK968: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1388,type,
sK969: $i > $o ).
thf(func_def_1390,type,
sK971: $i > ( $i > $o ) > $i ).
thf(func_def_1395,type,
sK976: $i > $i > $o ).
thf(func_def_1408,type,
sK989: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1410,type,
sK991: $i > $i ).
thf(func_def_1416,type,
sK997: $o ).
thf(func_def_1439,type,
sK1020: $o ).
thf(func_def_1449,type,
sK1030: $o ).
thf(func_def_1468,type,
sK1049: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1471,type,
sK1052: $i > $o ).
thf(func_def_1475,type,
sK1056: $i > $i > $o ).
thf(func_def_1479,type,
sK1060: $o ).
thf(func_def_1481,type,
sK1062: $i > $o ).
thf(func_def_1487,type,
sK1068: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1488,type,
sK1069: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1489,type,
sK1070: $i > $o ).
thf(func_def_1490,type,
sK1071: $i > $o ).
thf(func_def_1514,type,
sK1095: $i > $i ).
thf(func_def_1517,type,
sK1098: $i > $i > $i ).
thf(func_def_1520,type,
sK1101: $i > $i > $i ).
thf(f325,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) )
= notinself2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself2) ).
thf(f344,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
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ( transitivesetOp2
=> ( setunionTransitive
=> ( ordinalMinLem1
=> ( ordinalTransSet
=> ( ordinalTransSet1
=> ( setunionOrdinalLem1
=> ( emptysetOrdinal
=> ( ordinalIrrefl
=> ( ordinalIrrefl2
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalNoCycle) ).
thf(f345,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
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ( transitivesetOp2
=> ( setunionTransitive
=> ( ordinalMinLem1
=> ( ordinalTransSet
=> ( ordinalTransSet1
=> ( setunionOrdinalLem1
=> ( emptysetOrdinal
=> ( ordinalIrrefl
=> ( ordinalIrrefl2
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f344]) ).
thf(f701,plain,
~ ( 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
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ( transitivesetOp2
=> ( setunionTransitive
=> ( ordinalMinLem1
=> ( ordinalTransSet
=> ( ordinalTransSet1
=> ( setunionOrdinalLem1
=> ( emptysetOrdinal
=> ( ordinalIrrefl
=> ( ordinalIrrefl2
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f345]) ).
thf(f702,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ( ( image1E = $true )
=> ( ( image1I = $true )
=> ( ( injFuncInInjFuncSet = $true )
=> ( ( injFuncSetFuncIn = $true )
=> ( ( injFuncSetFuncInj = $true )
=> ( ( surjFuncSetFuncIn = $true )
=> ( ( surjFuncSetFuncSurj = $true )
=> ( ( leftInvIsSurj = $true )
=> ( ( surjCantorThm = $true )
=> ( ( foundation2 = $true )
=> ( ( notinself = $true )
=> ( ( notinself2 = $true )
=> ( ( omegaSp = $true )
=> ( ( omegaSclos = $true )
=> ( ( peano0notS = $true )
=> ( ( peanoSinj = $true )
=> ( ( transitivesetOp1 = $true )
=> ( ( binintTransitive = $true )
=> ( ( transitivesetOp2 = $true )
=> ( ( setunionTransitive = $true )
=> ( ( ordinalMinLem1 = $true )
=> ( ( ordinalTransSet = $true )
=> ( ( ordinalTransSet1 = $true )
=> ( ( setunionOrdinalLem1 = $true )
=> ( ( emptysetOrdinal = $true )
=> ( ( ordinalIrrefl = $true )
=> ( ( ordinalIrrefl2 = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f701]) ).
thf(f939,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
=> ~ ( in @ X0 @ X1 ) )
= notinself2 ),
inference(rectify,[],[f325]) ).
thf(f940,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( notinself2 = $true ) ),
inference(fool_elimination,[],[f939]) ).
thf(f1054,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ( ( image1E = $true )
=> ( ( image1I = $true )
=> ( ( injFuncInInjFuncSet = $true )
=> ( ( injFuncSetFuncIn = $true )
=> ( ( injFuncSetFuncInj = $true )
=> ( ( surjFuncSetFuncIn = $true )
=> ( ( surjFuncSetFuncSurj = $true )
=> ( ( leftInvIsSurj = $true )
=> ( ( surjCantorThm = $true )
=> ( ( foundation2 = $true )
=> ( ( notinself = $true )
=> ( ( notinself2 = $true )
=> ( ( omegaSp = $true )
=> ( ( omegaSclos = $true )
=> ( ( peano0notS = $true )
=> ( ( peanoSinj = $true )
=> ( ( transitivesetOp1 = $true )
=> ( ( binintTransitive = $true )
=> ( ( transitivesetOp2 = $true )
=> ( ( setunionTransitive = $true )
=> ( ( ordinalMinLem1 = $true )
=> ( ( ordinalTransSet = $true )
=> ( ( ordinalTransSet1 = $true )
=> ( ( setunionOrdinalLem1 = $true )
=> ( ( emptysetOrdinal = $true )
=> ( ( ordinalIrrefl = $true )
=> ( ( ordinalIrrefl2 = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f702]) ).
thf(f1074,plain,
( ( notinself2 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f940]) ).
thf(f1231,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( ordinalIrrefl2 = $true )
& ( ordinalIrrefl = $true )
& ( emptysetOrdinal = $true )
& ( setunionOrdinalLem1 = $true )
& ( ordinalTransSet1 = $true )
& ( ordinalTransSet = $true )
& ( ordinalMinLem1 = $true )
& ( setunionTransitive = $true )
& ( transitivesetOp2 = $true )
& ( binintTransitive = $true )
& ( transitivesetOp1 = $true )
& ( peanoSinj = $true )
& ( peano0notS = $true )
& ( omegaSclos = $true )
& ( omegaSp = $true )
& ( notinself2 = $true )
& ( notinself = $true )
& ( foundation2 = $true )
& ( surjCantorThm = $true )
& ( leftInvIsSurj = $true )
& ( surjFuncSetFuncSurj = $true )
& ( surjFuncSetFuncIn = $true )
& ( injFuncSetFuncInj = $true )
& ( injFuncSetFuncIn = $true )
& ( injFuncInInjFuncSet = $true )
& ( image1I = $true )
& ( image1E = $true )
& ( image1Equiv = $true )
& ( image1Ex1 = $true )
& ( image1Ex = $true )
& ( woz2B = $true )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1unionEcases = $true )
& ( breln1unionE = $true )
& ( breln1unionI = $true )
& ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ( breln1unionprop = $true )
& ( breln1compEex = $true )
& ( breln1compE = $true )
& ( breln1compI = $true )
& ( breln1compprop = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $true )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $true )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f1054]) ).
thf(f1232,plain,
( ( notequalI1 = $true )
& ( setadjoinIR = $true )
& ( binunionRsub = $true )
& ( breln1unionIL = $true )
& ( singletonsuniq = $true )
& ( complementSubsetComplementIntersect = $true )
& ( eta2 = $true )
& ( emptysetAx = $true )
& ( kfstpairEq = $true )
& ( peano0notS = $true )
& ( woz1_3 = $true )
& ( ksndpairEq = $true )
& ( funcGraphProp2 = $true )
& ( binunionTIRcontra = $true )
& ( notinemptyset = $true )
& ( emptyinPowerset = $true )
& ( ap2p = $true )
& ( image1Ex1 = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodpairin = $true )
& ( woz2Ex = $true )
& ( doubleComplementSub2 = $true )
& ( quantDeMorgan1 = $true )
& ( setunionAx = $true )
& ( binintersectT_lem = $true )
& ( funcGraphProp1 = $true )
& ( powersetsubset = $true )
& ( upairsetIR = $true )
& ( setunionE2 = $true )
& ( foundation2 = $true )
& ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( singletoninpowerset = $true )
& ( cartprodsndpairEq = $true )
& ( setminusILneg = $true )
& ( demorgan1 = $true )
& ( subsetE = $true )
& ( subsetRefl = $true )
& ( binintTransitive = $true )
& ( peanoSinj = $true )
& ( binunionIR = $true )
& ( dsetconstr__Cong = $true )
& ( setminusT_lem = $true )
& ( setukpairinjL1 = $true )
& ( ifp = $true )
& ( setminusI = $true )
& ( setukpairinjR11 = $true )
& ( iffalse = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( woz2A = $true )
& ( ex1I2 = $true )
& ( demorgan2 = $true )
& ( setunionsingleton = $true )
& ( beta2 = $true )
& ( complementT_lem = $true )
& ( upairequniteq = $true )
& ( woz1_4 = $true )
& ( nonemptyImpWitness = $true )
& ( iffalseProp1 = $true )
& ( dpsetconstrER = $true )
& ( woz13rule2 = $true )
& ( funcinfuncset = $true )
& ( cartprodmempaircEq = $true )
& ( lamp = $true )
& ( setukpairinjR12 = $true )
& ( cartprodfstpairEq = $true )
& ( binintersectTELcontra = $true )
& ( ordinalIrrefl = $true )
& ( funcext2 = $true )
& ( brelnall1 = $true )
& ( omegaSclos = $true )
& ( breln1invprop = $true )
& ( ubforcartprodlem1 = $true )
& ( lam2lamEq = $true )
& ( prop2setE = $true )
& ( ex1E2 = $true )
& ( binunionTEcontra = $true )
& ( setOfPairsIsBReln1 = $true )
& ( breln1invI = $true )
& ( symdiffIneg2 = $true )
& ( exuI3 = $true )
& ( powersetE = $true )
& ( kpairiskpair = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( woz13rule4 = $true )
& ( theeq = $true )
& ( wellorderingAx = $true )
& ( ap2apEq1 = $true )
& ( iftrueProp1 = $true )
& ( exuE3u = $true )
& ( setextAx = $true )
& ( in__Cong = $true )
& ( complementTE1 = $true )
& ( breln1all1 = $true )
& ( image1Equiv = $true )
& ( setminusLsub = $true )
& ( demorgan2a = $true )
& ( binunionTILcontra = $true )
& ( notinsingleton = $true )
& ( upairsubunion = $true )
& ( binintersectSubset5 = $true )
& ( breln1all2 = $true )
& ( emptyinunitempty = $true )
& ( apProp = $true )
& ( lamProp = $true )
& ( binunionE = $true )
& ( quantDeMorgan2 = $true )
& ( woz13rule3 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( ordinalTransSet = $true )
& ( kfstsingleton = $true )
& ( exuE3e = $true )
& ( setminusSubset1 = $true )
& ( uniqinunit = $true )
& ( vacuousDall = $true )
& ( woz1_2 = $true )
& ( descrp = $true )
& ( breln1unionE = $true )
& ( breln1unionprop = $true )
& ( setminusELneg = $true )
& ( theprop = $true )
& ( demorgan2b2 = $true )
& ( subsetI1 = $true )
& ( brelnall2 = $true )
& ( app = $true )
& ( setadjoin__Cong = $true )
& ( contrasubsetT = $true )
& ( ordinalTransSet1 = $true )
& ( eqimpsubset2 = $true )
& ( breln1compEex = $true )
& ( binintersectSubset3 = $true )
& ( emptyInPowerset = $true )
& ( upairsetE = $true )
& ( setunionsingleton1 = $true )
& ( breln1compI = $true )
& ( setadjoinAx = $true )
& ( powersetTI1 = $true )
& ( demorgan1a = $true )
& ( setukpairinjR1 = $true )
& ( binintersectSubset4 = $true )
& ( setext = $true )
& ( contrasubsetT2 = $true )
& ( setadjoinIL = $true )
& ( prop2set2propI = $true )
& ( cartprodpairsurjEq = $true )
& ( injFuncSetFuncInj = $true )
& ( image1I = $true )
& ( setukpairIR = $true )
& ( replAx = $true )
& ( subsetE2 = $true )
& ( powersetT_lem = $true )
& ( notinself = $true )
& ( secondinupair = $true )
& ( funcGraphProp3 = $true )
& ( upairset2E = $true )
& ( bs114d = $true )
& ( setukpairIL = $true )
& ( symdiffI1 = $true )
& ( ordinalMinLem1 = $true )
& ( ubforcartprodlem2 = $true )
& ( notdallE = $true )
& ( emptyE1 = $true )
& ( binintersectER = $true )
& ( setOfPairsIsBReln = $true )
& ( ubforcartprodlem3 = $true )
& ( complementImpComplementIntersect = $true )
& ( cartprodpairmemEL = $true )
& ( subsetTI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( woz1_1 = $true )
& ( beta1 = $true )
& ( binintersectSubset1 = $true )
& ( breln1unionIR = $true )
& ( choice2fnsingleton = $true )
& ( dpsetconstrEL1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( ksndsingleton = $true )
& ( eqbreln1 = $true )
& ( binunionT_lem = $true )
& ( binunionTE = $true )
& ( exu__Cong = $true )
& ( emptysetOrdinal = $true )
& ( foundationAx = $true )
& ( cartprodmempair1 = $true )
& ( omegaSAx = $true )
& ( setadjoinOr = $true )
& ( demorgan2a1 = $true )
& ( breln1unionCommutes = $true )
& ( omega0Ax = $true )
& ( inCongP = $true )
& ( binintersectTERcontra = $true )
& ( inIntersectImpInUnion2 = $true )
& ( singletonprop = $true )
& ( binintersectEL = $true )
& ( eqinunit = $true )
& ( eqimpsubset1 = $true )
& ( singletonsubset = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrI = $true )
& ( dsetconstrI = $true )
& ( woz13rule1 = $true )
& ( image1E = $true )
& ( powersetTE1 = $true )
& ( subsetI2 = $true )
& ( doubleComplementSub1 = $true )
& ( ap2apEq2 = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( funcImageSingleton = $true )
& ( binintersectLsub = $true )
& ( cartprodsndin = $true )
& ( funcext = $true )
& ( subsetemptysetimpeq = $true )
& ( upairset2IR = $true )
& ( setextsub = $true )
& ( setminusSubset2 = $true )
& ( complementTcontraSubset = $true )
& ( setunionE = $true )
& ( doubleComplementEq = $true )
& ( setoftrueEq = $true )
& ( surjFuncSetFuncIn = $true )
& ( omegaIndAx = $true )
& ( sepInPowerset = $true )
& ( powersetE1 = $true )
& ( setminusIRneg = $true )
& ( ordinalIrrefl2 = $true )
& ( setukpairinjR = $true )
& ( iftrueorfalse = $true )
& ( setukpairinjL2 = $true )
& ( demorgan1b = $true )
& ( dpsetconstrSub = $true )
& ( transitivesetOp2 = $true )
& ( setukpairinjR2 = $true )
& ( complementTI1 = $true )
& ( funcGraphProp4 = $true )
& ( lam2p = $true )
& ( singletoninpowunion = $true )
& ( complementUnionInPowersetComplement = $true )
& ( noeltsimpempty = $true )
& ( upairsetIL = $true )
& ( cartprodmempair = $true )
& ( descr__Cong = $true )
& ( setminusERneg = $true )
& ( omegaSp = $true )
& ( disjointsetsI1 = $true )
& ( breln1compE = $true )
& ( notsubsetI = $true )
& ( notequalI2 = $true )
& ( notdexE = $true )
& ( exuEu = $true )
& ( iftrueProp2 = $true )
& ( symdiffE = $true )
& ( powerset__Cong = $true )
& ( subPowSU = $true )
& ( binunionIL = $true )
& ( injFuncSetFuncIn = $true )
& ( contraSubsetComplement = $true )
& ( exuI1 = $true )
& ( eqbreln = $true )
& ( nonemptyI = $true )
& ( demorgan2a2 = $true )
& ( emptyI = $true )
& ( emptyset__Cong = $true )
& ( woz1_5 = $true )
& ( prop2setI = $true )
& ( doubleComplementE1 = $true )
& ( nonemptyI1 = $true )
& ( breln1unionI = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan4 = $true )
& ( breln1unionEcases = $true )
& ( omega__Cong = $true )
& ( exuE1 = $true )
& ( notinself2 = $true )
& ( woz2W = $true )
& ( setukpairinjL = $true )
& ( setminusER = $true )
& ( woz13rule0 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( complementTnotintersectT = $true )
& ( eta1 = $true )
& ( binunionLsub = $true )
& ( symdiffI2 = $true )
& ( breln1SetBreln1 = $true )
& ( symdiffIneg1 = $true )
& ( dpsetconstrERa = $true )
& ( breln1compprop = $true )
& ( contrasubsetT1 = $true )
& ( setunionI = $true )
& ( iftrue = $true )
& ( funcextLem = $true )
& ( contrasubsetT3 = $true )
& ( binintersectI = $true )
& ( dsetconstrEL = $true )
& ( kpairp = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset2 = $true )
& ( binunionEcases = $true )
& ( emptysetimpfalse = $true )
& ( subbreln1 = $true )
& ( transitivesetOp1 = $true )
& ( iffalseProp2 = $true )
& ( setunionOrdinalLem1 = $true )
& ( binintersectRsub = $true )
& ( ex1I = $true )
& ( image1Ex = $true )
& ( upairinpowunion = $true )
& ( leftInvIsSurj = $true )
& ( setunionsingleton2 = $true )
& ( sepSubset = $true )
& ( infuncsetfunc = $true )
& ( kpairsurjEq = $true )
& ( inIntersectImpInUnion = $true )
& ( ifSingleton = $true )
& ( setadjoinE = $true )
& ( setadjoinSub = $true )
& ( exuI2 = $true )
& ( surjCantorThm = $true )
& ( setminusEL = $true )
& ( setextT = $true )
& ( singletonsswitch = $true )
& ( demorgan2b = $true )
& ( setunion__Cong = $true )
& ( dsetconstrER = $true )
& ( inPowerset = $true )
& ( exuE2 = $true )
& ( injFuncInInjFuncSet = $true )
& ( subbreln = $true )
& ( setunionTransitive = $true )
& ( powersetI1 = $true )
& ( breln1invE = $true )
& ( setadjoinSub2 = $true )
& ( cartprodfstin = $true )
& ( ex1E1 = $true )
& ( emptysetE = $true )
& ( doubleComplementI1 = $true )
& ( powersetAx = $true )
& ( subsetTrans = $true )
& ( woz2B = $true ) ),
inference(flattening,[],[f1231]) ).
thf(f1481,plain,
( ( notinself2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f1074]) ).
thf(f1537,plain,
( ( ( notinself2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( notinself2 != $true ) ) ),
inference(nnf_transformation,[],[f1481]) ).
thf(f1538,plain,
( ( ( notinself2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X2 @ X3 )
!= $true ) )
| ( notinself2 != $true ) ) ),
inference(rectify,[],[f1537]) ).
thf(f1539,plain,
( ( ( notinself2 = $true )
| ( ( ( in @ sK43 @ sK42 )
= $true )
& ( $true
= ( in @ sK42 @ sK43 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X2 @ X3 )
!= $true ) )
| ( notinself2 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42,sK43]),skolemize(X0,sK42),skolemize(X1,sK43)],[f1538]) ).
thf(f1817,plain,
( ( notequalI1 = $true )
& ( setadjoinIR = $true )
& ( binunionRsub = $true )
& ( breln1unionIL = $true )
& ( singletonsuniq = $true )
& ( complementSubsetComplementIntersect = $true )
& ( eta2 = $true )
& ( emptysetAx = $true )
& ( kfstpairEq = $true )
& ( peano0notS = $true )
& ( woz1_3 = $true )
& ( ksndpairEq = $true )
& ( funcGraphProp2 = $true )
& ( binunionTIRcontra = $true )
& ( notinemptyset = $true )
& ( emptyinPowerset = $true )
& ( ap2p = $true )
& ( image1Ex1 = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodpairin = $true )
& ( woz2Ex = $true )
& ( doubleComplementSub2 = $true )
& ( quantDeMorgan1 = $true )
& ( setunionAx = $true )
& ( binintersectT_lem = $true )
& ( funcGraphProp1 = $true )
& ( powersetsubset = $true )
& ( upairsetIR = $true )
& ( setunionE2 = $true )
& ( foundation2 = $true )
& ( $true
= ( in @ sK340 @ sK341 ) )
& ( ( in @ sK341 @ sK340 )
= $true )
& ( ( ordinal @ sK340 )
= $true )
& ( singletoninpowerset = $true )
& ( cartprodsndpairEq = $true )
& ( setminusILneg = $true )
& ( demorgan1 = $true )
& ( subsetE = $true )
& ( subsetRefl = $true )
& ( binintTransitive = $true )
& ( peanoSinj = $true )
& ( binunionIR = $true )
& ( dsetconstr__Cong = $true )
& ( setminusT_lem = $true )
& ( setukpairinjL1 = $true )
& ( ifp = $true )
& ( setminusI = $true )
& ( setukpairinjR11 = $true )
& ( iffalse = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( woz2A = $true )
& ( ex1I2 = $true )
& ( demorgan2 = $true )
& ( setunionsingleton = $true )
& ( beta2 = $true )
& ( complementT_lem = $true )
& ( upairequniteq = $true )
& ( woz1_4 = $true )
& ( nonemptyImpWitness = $true )
& ( iffalseProp1 = $true )
& ( dpsetconstrER = $true )
& ( woz13rule2 = $true )
& ( funcinfuncset = $true )
& ( cartprodmempaircEq = $true )
& ( lamp = $true )
& ( setukpairinjR12 = $true )
& ( cartprodfstpairEq = $true )
& ( binintersectTELcontra = $true )
& ( ordinalIrrefl = $true )
& ( funcext2 = $true )
& ( brelnall1 = $true )
& ( omegaSclos = $true )
& ( breln1invprop = $true )
& ( ubforcartprodlem1 = $true )
& ( lam2lamEq = $true )
& ( prop2setE = $true )
& ( ex1E2 = $true )
& ( binunionTEcontra = $true )
& ( setOfPairsIsBReln1 = $true )
& ( breln1invI = $true )
& ( symdiffIneg2 = $true )
& ( exuI3 = $true )
& ( powersetE = $true )
& ( kpairiskpair = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( woz13rule4 = $true )
& ( theeq = $true )
& ( wellorderingAx = $true )
& ( ap2apEq1 = $true )
& ( iftrueProp1 = $true )
& ( exuE3u = $true )
& ( setextAx = $true )
& ( in__Cong = $true )
& ( complementTE1 = $true )
& ( breln1all1 = $true )
& ( image1Equiv = $true )
& ( setminusLsub = $true )
& ( demorgan2a = $true )
& ( binunionTILcontra = $true )
& ( notinsingleton = $true )
& ( upairsubunion = $true )
& ( binintersectSubset5 = $true )
& ( breln1all2 = $true )
& ( emptyinunitempty = $true )
& ( apProp = $true )
& ( lamProp = $true )
& ( binunionE = $true )
& ( quantDeMorgan2 = $true )
& ( woz13rule3 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( ordinalTransSet = $true )
& ( kfstsingleton = $true )
& ( exuE3e = $true )
& ( setminusSubset1 = $true )
& ( uniqinunit = $true )
& ( vacuousDall = $true )
& ( woz1_2 = $true )
& ( descrp = $true )
& ( breln1unionE = $true )
& ( breln1unionprop = $true )
& ( setminusELneg = $true )
& ( theprop = $true )
& ( demorgan2b2 = $true )
& ( subsetI1 = $true )
& ( brelnall2 = $true )
& ( app = $true )
& ( setadjoin__Cong = $true )
& ( contrasubsetT = $true )
& ( ordinalTransSet1 = $true )
& ( eqimpsubset2 = $true )
& ( breln1compEex = $true )
& ( binintersectSubset3 = $true )
& ( emptyInPowerset = $true )
& ( upairsetE = $true )
& ( setunionsingleton1 = $true )
& ( breln1compI = $true )
& ( setadjoinAx = $true )
& ( powersetTI1 = $true )
& ( demorgan1a = $true )
& ( setukpairinjR1 = $true )
& ( binintersectSubset4 = $true )
& ( setext = $true )
& ( contrasubsetT2 = $true )
& ( setadjoinIL = $true )
& ( prop2set2propI = $true )
& ( cartprodpairsurjEq = $true )
& ( injFuncSetFuncInj = $true )
& ( image1I = $true )
& ( setukpairIR = $true )
& ( replAx = $true )
& ( subsetE2 = $true )
& ( powersetT_lem = $true )
& ( notinself = $true )
& ( secondinupair = $true )
& ( funcGraphProp3 = $true )
& ( upairset2E = $true )
& ( bs114d = $true )
& ( setukpairIL = $true )
& ( symdiffI1 = $true )
& ( ordinalMinLem1 = $true )
& ( ubforcartprodlem2 = $true )
& ( notdallE = $true )
& ( emptyE1 = $true )
& ( binintersectER = $true )
& ( setOfPairsIsBReln = $true )
& ( ubforcartprodlem3 = $true )
& ( complementImpComplementIntersect = $true )
& ( cartprodpairmemEL = $true )
& ( subsetTI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( woz1_1 = $true )
& ( beta1 = $true )
& ( binintersectSubset1 = $true )
& ( breln1unionIR = $true )
& ( choice2fnsingleton = $true )
& ( dpsetconstrEL1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( ksndsingleton = $true )
& ( eqbreln1 = $true )
& ( binunionT_lem = $true )
& ( binunionTE = $true )
& ( exu__Cong = $true )
& ( emptysetOrdinal = $true )
& ( foundationAx = $true )
& ( cartprodmempair1 = $true )
& ( omegaSAx = $true )
& ( setadjoinOr = $true )
& ( demorgan2a1 = $true )
& ( breln1unionCommutes = $true )
& ( omega0Ax = $true )
& ( inCongP = $true )
& ( binintersectTERcontra = $true )
& ( inIntersectImpInUnion2 = $true )
& ( singletonprop = $true )
& ( binintersectEL = $true )
& ( eqinunit = $true )
& ( eqimpsubset1 = $true )
& ( singletonsubset = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrI = $true )
& ( dsetconstrI = $true )
& ( woz13rule1 = $true )
& ( image1E = $true )
& ( powersetTE1 = $true )
& ( subsetI2 = $true )
& ( doubleComplementSub1 = $true )
& ( ap2apEq2 = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( funcImageSingleton = $true )
& ( binintersectLsub = $true )
& ( cartprodsndin = $true )
& ( funcext = $true )
& ( subsetemptysetimpeq = $true )
& ( upairset2IR = $true )
& ( setextsub = $true )
& ( setminusSubset2 = $true )
& ( complementTcontraSubset = $true )
& ( setunionE = $true )
& ( doubleComplementEq = $true )
& ( setoftrueEq = $true )
& ( surjFuncSetFuncIn = $true )
& ( omegaIndAx = $true )
& ( sepInPowerset = $true )
& ( powersetE1 = $true )
& ( setminusIRneg = $true )
& ( ordinalIrrefl2 = $true )
& ( setukpairinjR = $true )
& ( iftrueorfalse = $true )
& ( setukpairinjL2 = $true )
& ( demorgan1b = $true )
& ( dpsetconstrSub = $true )
& ( transitivesetOp2 = $true )
& ( setukpairinjR2 = $true )
& ( complementTI1 = $true )
& ( funcGraphProp4 = $true )
& ( lam2p = $true )
& ( singletoninpowunion = $true )
& ( complementUnionInPowersetComplement = $true )
& ( noeltsimpempty = $true )
& ( upairsetIL = $true )
& ( cartprodmempair = $true )
& ( descr__Cong = $true )
& ( setminusERneg = $true )
& ( omegaSp = $true )
& ( disjointsetsI1 = $true )
& ( breln1compE = $true )
& ( notsubsetI = $true )
& ( notequalI2 = $true )
& ( notdexE = $true )
& ( exuEu = $true )
& ( iftrueProp2 = $true )
& ( symdiffE = $true )
& ( powerset__Cong = $true )
& ( subPowSU = $true )
& ( binunionIL = $true )
& ( injFuncSetFuncIn = $true )
& ( contraSubsetComplement = $true )
& ( exuI1 = $true )
& ( eqbreln = $true )
& ( nonemptyI = $true )
& ( demorgan2a2 = $true )
& ( emptyI = $true )
& ( emptyset__Cong = $true )
& ( woz1_5 = $true )
& ( prop2setI = $true )
& ( doubleComplementE1 = $true )
& ( nonemptyI1 = $true )
& ( breln1unionI = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan4 = $true )
& ( breln1unionEcases = $true )
& ( omega__Cong = $true )
& ( exuE1 = $true )
& ( notinself2 = $true )
& ( woz2W = $true )
& ( setukpairinjL = $true )
& ( setminusER = $true )
& ( woz13rule0 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( complementTnotintersectT = $true )
& ( eta1 = $true )
& ( binunionLsub = $true )
& ( symdiffI2 = $true )
& ( breln1SetBreln1 = $true )
& ( symdiffIneg1 = $true )
& ( dpsetconstrERa = $true )
& ( breln1compprop = $true )
& ( contrasubsetT1 = $true )
& ( setunionI = $true )
& ( iftrue = $true )
& ( funcextLem = $true )
& ( contrasubsetT3 = $true )
& ( binintersectI = $true )
& ( dsetconstrEL = $true )
& ( kpairp = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset2 = $true )
& ( binunionEcases = $true )
& ( emptysetimpfalse = $true )
& ( subbreln1 = $true )
& ( transitivesetOp1 = $true )
& ( iffalseProp2 = $true )
& ( setunionOrdinalLem1 = $true )
& ( binintersectRsub = $true )
& ( ex1I = $true )
& ( image1Ex = $true )
& ( upairinpowunion = $true )
& ( leftInvIsSurj = $true )
& ( setunionsingleton2 = $true )
& ( sepSubset = $true )
& ( infuncsetfunc = $true )
& ( kpairsurjEq = $true )
& ( inIntersectImpInUnion = $true )
& ( ifSingleton = $true )
& ( setadjoinE = $true )
& ( setadjoinSub = $true )
& ( exuI2 = $true )
& ( surjCantorThm = $true )
& ( setminusEL = $true )
& ( setextT = $true )
& ( singletonsswitch = $true )
& ( demorgan2b = $true )
& ( setunion__Cong = $true )
& ( dsetconstrER = $true )
& ( inPowerset = $true )
& ( exuE2 = $true )
& ( injFuncInInjFuncSet = $true )
& ( subbreln = $true )
& ( setunionTransitive = $true )
& ( powersetI1 = $true )
& ( breln1invE = $true )
& ( setadjoinSub2 = $true )
& ( cartprodfstin = $true )
& ( ex1E1 = $true )
& ( emptysetE = $true )
& ( doubleComplementI1 = $true )
& ( powersetAx = $true )
& ( subsetTrans = $true )
& ( woz2B = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK340,sK341]),skolemize(X0,sK340),skolemize(X1,sK341)],[f1232]) ).
thf(f2566,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
!= $true )
| ( notinself2 != $true )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f1539]) ).
thf(f3051,plain,
notinself2 = $true,
inference(cnf_transformation,[],[f1817]) ).
thf(f3296,plain,
( ( in @ sK341 @ sK340 )
= $true ),
inference(cnf_transformation,[],[f1817]) ).
thf(f3297,plain,
( $true
= ( in @ sK340 @ sK341 ) ),
inference(cnf_transformation,[],[f1817]) ).
thf(f4682,definition,
( spl1104_8
<=> ( notinself2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl1104_8])],[avatar_definition]) ).
thf(f4686,definition,
( spl1104_9
<=> ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl1104_9])],[avatar_definition]) ).
thf(f4687,plain,
( ! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X2 @ X3 )
!= $true ) )
| ~ spl1104_9 ),
inference(avatar_component_clause,[],[f4686]) ).
thf(f4688,plain,
( ~ spl1104_8
| spl1104_9 ),
inference(avatar_split_clause,[],[f2566,f4686,f4682]) ).
thf(f10309,plain,
spl1104_8,
inference(avatar_split_clause,[],[f3051,f4682]) ).
thf(f11465,definition,
( spl1104_1467
<=> ( ( in @ sK341 @ sK340 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1104_1467])],[avatar_definition]) ).
thf(f11467,plain,
( ( ( in @ sK341 @ sK340 )
= $true )
| ~ spl1104_1467 ),
inference(avatar_component_clause,[],[f11465]) ).
thf(f11468,plain,
spl1104_1467,
inference(avatar_split_clause,[],[f3296,f11465]) ).
thf(f12163,definition,
( spl1104_1608
<=> ( $true
= ( in @ sK340 @ sK341 ) ) ),
introduced(definition,[new_symbols(definition,[spl1104_1608])],[avatar_definition]) ).
thf(f12166,plain,
spl1104_1608,
inference(avatar_split_clause,[],[f3297,f12163]) ).
thf(f13259,plain,
( ( $true
!= ( in @ sK340 @ sK341 ) )
| ( $true != $true )
| ~ spl1104_9
| ~ spl1104_1467 ),
inference(superposition,[],[f4687,f11467]) ).
thf(f13260,plain,
( ( $true
!= ( in @ sK340 @ sK341 ) )
| ~ spl1104_9
| ~ spl1104_1467 ),
inference(trivial_inequality_removal,[],[f13259]) ).
thf(f13261,plain,
( ~ spl1104_1608
| ~ spl1104_9
| ~ spl1104_1467 ),
inference(avatar_split_clause,[],[f13260,f11465,f4686,f12163]) ).
cnf(s5,plain,
( ~ spl1104_8
| spl1104_9 ),
inference(sat_conversion,[],[f4688]) ).
cnf(s1086,plain,
spl1104_8,
inference(sat_conversion,[],[f10309]) ).
cnf(s1366,plain,
spl1104_1467,
inference(sat_conversion,[],[f11468]) ).
cnf(s1558,plain,
spl1104_1608,
inference(sat_conversion,[],[f12166]) ).
cnf(s1846,plain,
( ~ spl1104_9
| ~ spl1104_1467
| ~ spl1104_1608 ),
inference(sat_conversion,[],[f13261]) ).
cnf(s1869,plain,
~ spl1104_9,
inference(rat,[],[s1846,s1558,s1366]) ).
cnf(s2284,plain,
$false,
inference(rat,[],[s5,s1869,s1086]) ).
thf(f13262,plain,
$false,
inference(avatar_sat_refutation,[],[s2284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU823^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/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 14:34:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running higher-order theorem proving
% 0.09/0.16 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.25 % (189649)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.37/0.25 % (189660)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.37/0.25 % (189660)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.37/0.25 % (189654)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2844168512:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.37/0.25 % (189656)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1366158560:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.37/0.25 % (189655)lrs+10_16_si=on:nwc=1.5:random_seed=413840529:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.37/0.25 % (189658)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2382978006:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.37/0.25 % (189657)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2666636034:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.37/0.25 % (189659)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2822290982:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.37/0.25 % (189660)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3729534502:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.37/0.25 % (189656)Instruction limit reached!
% 0.37/0.25 % (189656)------------------------------
% 0.37/0.25 % (189656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.25 % (189656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.25 % (189656)CaDiCaL version: 2.1.3
% 0.37/0.25 % (189656)Termination reason: Instruction limit
% 0.37/0.25 % (189656)Termination phase: shuffling
% 0.37/0.25 % (189656)Time elapsed: 0.002 s
% 0.37/0.25 % (189656)Peak memory usage: 10 MB
% 0.37/0.25 % (189656)Instructions burned: 7 (million)
% 0.37/0.25 % (189655)Instruction limit reached!
% 0.37/0.25 % (189655)------------------------------
% 0.37/0.25 % (189655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.25 % (189655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.25 % (189655)CaDiCaL version: 2.1.3
% 0.37/0.25 % (189655)Termination reason: Instruction limit
% 0.37/0.25 % (189655)Termination phase: shuffling
% 0.37/0.25 % (189655)Time elapsed: 0.005 s
% 0.37/0.25 % (189655)Peak memory usage: 10 MB
% 0.37/0.25 % (189655)Instructions burned: 19 (million)
% 0.37/0.25 % (189658)Instruction limit reached!
% 0.37/0.25 % (189658)------------------------------
% 0.37/0.25 % (189658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.25 % (189658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.25 % (189658)CaDiCaL version: 2.1.3
% 0.37/0.25 % (189658)Termination reason: Instruction limit
% 0.37/0.25 % (189658)Termination phase: shuffling
% 0.37/0.25 % (189658)Time elapsed: 0.006 s
% 0.37/0.25 % (189658)Peak memory usage: 11 MB
% 0.37/0.25 % (189658)Instructions burned: 25 (million)
% 0.37/0.25 % (189668)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2213884794:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.37/0.25 % (189670)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.37/0.25 % (189668)Instruction limit reached!
% 0.37/0.25 % (189668)------------------------------
% 0.37/0.25 % (189668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.25 % (189668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.25 % (189668)CaDiCaL version: 2.1.3
% 0.37/0.25 % (189668)Termination reason: Instruction limit
% 0.37/0.25 % (189668)Termination phase: shuffling
% 0.37/0.25 % (189668)Time elapsed: 0.001 s
% 0.37/0.25 % (189668)Peak memory usage: 10 MB
% 0.37/0.25 % (189668)Instructions burned: 2 (million)
% 0.37/0.25 % (189669)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1616701663:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.37/0.27 % (189659)Instruction limit reached!
% 0.37/0.27 % (189659)------------------------------
% 0.37/0.27 % (189659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.27 % (189659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.27 % (189659)CaDiCaL version: 2.1.3
% 0.37/0.27 % (189659)Termination reason: Instruction limit
% 0.37/0.27 % (189659)Termination phase: SInE selection
% 0.37/0.27 % (189659)Time elapsed: 0.017 s
% 0.37/0.27 % (189659)Peak memory usage: 11 MB
% 0.37/0.27 % (189659)Instructions burned: 75 (million)
% 0.37/0.27 % (189670)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3843589095:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.37/0.27 % (189669)Instruction limit reached!
% 0.37/0.27 % (189669)------------------------------
% 0.37/0.27 % (189669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.27 % (189669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.27 % (189669)CaDiCaL version: 2.1.3
% 0.37/0.27 % (189669)Termination reason: Instruction limit
% 0.37/0.27 % (189669)Termination phase: shuffling
% 0.37/0.27 % (189669)Time elapsed: 0.005 s
% 0.37/0.27 % (189669)Peak memory usage: 10 MB
% 0.37/0.27 % (189669)Instructions burned: 16 (million)
% 0.37/0.27 % (189670)Instruction limit reached!
% 0.37/0.27 % (189670)------------------------------
% 0.37/0.27 % (189670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.27 % (189670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.27 % (189670)CaDiCaL version: 2.1.3
% 0.37/0.27 % (189670)Termination reason: Instruction limit
% 0.37/0.27 % (189670)Termination phase: shuffling
% 0.37/0.27 % (189670)Time elapsed: 0.003 s
% 0.37/0.27 % (189670)Peak memory usage: 10 MB
% 0.37/0.27 % (189670)Instructions burned: 14 (million)
% 0.37/0.27 % (189654)Instruction limit reached!
% 0.37/0.27 % (189654)------------------------------
% 0.37/0.27 % (189654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.27 % (189654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.27 % (189654)CaDiCaL version: 2.1.3
% 0.37/0.27 % (189654)Termination reason: Instruction limit
% 0.37/0.27 % (189654)Termination phase: Preprocessing 3
% 0.37/0.27 % (189654)Time elapsed: 0.021 s
% 0.37/0.27 % (189654)Peak memory usage: 12 MB
% 0.37/0.27 % (189654)Instructions burned: 90 (million)
% 0.37/0.27 % (189675)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.37/0.27 % (189675)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.37/0.27 % (189672)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3977585897:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.37/0.27 % (189675)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2875846841:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.37/0.27 % (189672)Instruction limit reached!
% 0.37/0.27 % (189672)------------------------------
% 0.37/0.27 % (189672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.27 % (189672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.27 % (189672)CaDiCaL version: 2.1.3
% 0.37/0.27 % (189672)Termination reason: Instruction limit
% 0.37/0.27 % (189672)Termination phase: shuffling
% 0.37/0.27 % (189672)Time elapsed: 0.004 s
% 0.37/0.27 % (189672)Peak memory usage: 10 MB
% 0.37/0.27 % (189672)Instructions burned: 14 (million)
% 0.37/0.27 % (189678)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.37/0.27 % (189677)lrs+10_1_si=on:cs=on:random_seed=663002933:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.37/0.27 % (189676)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1491133683:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.37/0.30 % (189678)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=576402840:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.37/0.30 % (189678)Instruction limit reached!
% 0.37/0.30 % (189678)------------------------------
% 0.37/0.30 % (189678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.30 % (189678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.30 % (189678)CaDiCaL version: 2.1.3
% 0.37/0.30 % (189678)Termination reason: Instruction limit
% 0.37/0.30 % (189678)Termination phase: shuffling
% 0.37/0.30 % (189678)Time elapsed: 0.001 s
% 0.37/0.30 % (189678)Peak memory usage: 10 MB
% 0.37/0.30 % (189678)Instructions burned: 2 (million)
% 0.37/0.30 % (189677)Instruction limit reached!
% 0.37/0.30 % (189677)------------------------------
% 0.37/0.30 % (189677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.30 % (189677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.30 % (189677)CaDiCaL version: 2.1.3
% 0.37/0.30 % (189677)Termination reason: Instruction limit
% 0.37/0.30 % (189677)Termination phase: shuffling
% 0.37/0.30 % (189677)Time elapsed: 0.002 s
% 0.37/0.30 % (189677)Peak memory usage: 10 MB
% 0.37/0.30 % (189677)Instructions burned: 9 (million)
% 0.37/0.30 % (189660)Instruction limit reached!
% 0.37/0.30 % (189660)------------------------------
% 0.37/0.30 % (189660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.30 % (189660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.30 % (189660)CaDiCaL version: 2.1.3
% 0.37/0.30 % (189660)Termination reason: Instruction limit
% 0.37/0.30 % (189660)Termination phase: Twee Goal Transformation
% 0.37/0.30 % (189660)Time elapsed: 0.035 s
% 0.37/0.30 % (189660)Peak memory usage: 13 MB
% 0.37/0.30 % (189660)Instructions burned: 158 (million)
% 0.37/0.30 % (189675)Instruction limit reached!
% 0.37/0.30 % (189675)------------------------------
% 0.37/0.30 % (189675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.30 % (189675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.30 % (189675)CaDiCaL version: 2.1.3
% 0.37/0.30 % (189675)Termination reason: Instruction limit
% 0.37/0.30 % (189675)Termination phase: shuffling
% 0.37/0.30 % (189675)Time elapsed: 0.007 s
% 0.37/0.30 % (189675)Peak memory usage: 11 MB
% 0.37/0.30 % (189675)Instructions burned: 33 (million)
% 0.37/0.30 % (189681)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3153721045:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.37/0.30 % (189685)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2584788300:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.37/0.30 % (189686)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3326934088:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.37/0.30 % (189687)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1703104242:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.37/0.30 % (189688)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=958893309:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.37/0.30 % (189681)Instruction limit reached!
% 0.37/0.30 % (189681)------------------------------
% 0.37/0.30 % (189681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.30 % (189681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.30 % (189681)CaDiCaL version: 2.1.3
% 0.37/0.30 % (189681)Termination reason: Instruction limit
% 0.37/0.30 % (189681)Termination phase: Property scanning
% 0.37/0.30 % (189681)Time elapsed: 0.009 s
% 0.37/0.30 % (189681)Peak memory usage: 11 MB
% 0.37/0.30 % (189681)Instructions burned: 39 (million)
% 0.37/0.30 % (189687)Instruction limit reached!
% 0.37/0.30 % (189687)------------------------------
% 0.37/0.30 % (189687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.30 % (189687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.30 % (189687)CaDiCaL version: 2.1.3
% 0.37/0.30 % (189687)Termination reason: Instruction limit
% 0.37/0.30 % (189687)Termination phase: shuffling
% 0.37/0.30 % (189687)Time elapsed: 0.004 s
% 0.37/0.32 % (189687)Peak memory usage: 10 MB
% 0.37/0.32 % (189687)Instructions burned: 16 (million)
% 0.37/0.32 % (189686)Instruction limit reached!
% 0.37/0.32 % (189686)------------------------------
% 0.37/0.32 % (189686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189686)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189686)Termination reason: Instruction limit
% 0.37/0.32 % (189686)Termination phase: shuffling
% 0.37/0.32 % (189686)Time elapsed: 0.006 s
% 0.37/0.32 % (189686)Peak memory usage: 11 MB
% 0.37/0.32 % (189686)Instructions burned: 26 (million)
% 0.37/0.32 % (189676)Instruction limit reached!
% 0.37/0.32 % (189676)------------------------------
% 0.37/0.32 % (189676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189676)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189676)Termination reason: Instruction limit
% 0.37/0.32 % (189676)Termination phase: Property scanning
% 0.37/0.32 % (189676)Time elapsed: 0.020 s
% 0.37/0.32 % (189676)Peak memory usage: 11 MB
% 0.37/0.32 % (189676)Instructions burned: 89 (million)
% 0.37/0.32 % (189694)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3744524105:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.37/0.32 % (189695)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3239798291:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.37/0.32 % (189695)Instruction limit reached!
% 0.37/0.32 % (189695)------------------------------
% 0.37/0.32 % (189695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189695)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189695)Termination reason: Instruction limit
% 0.37/0.32 % (189695)Termination phase: shuffling
% 0.37/0.32 % (189695)Time elapsed: 0.001 s
% 0.37/0.32 % (189695)Peak memory usage: 10 MB
% 0.37/0.32 % (189695)Instructions burned: 2 (million)
% 0.37/0.32 % (189696)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3633861263:i=26:ep=R:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/26Mi)
% 0.37/0.32 % (189697)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=966311175:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/23Mi)
% 0.37/0.32 % (189694)Instruction limit reached!
% 0.37/0.32 % (189694)------------------------------
% 0.37/0.32 % (189694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189694)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189694)Termination reason: Instruction limit
% 0.37/0.32 % (189694)Termination phase: shuffling
% 0.37/0.32 % (189694)Time elapsed: 0.004 s
% 0.37/0.32 % (189694)Peak memory usage: 10 MB
% 0.37/0.32 % (189694)Instructions burned: 16 (million)
% 0.37/0.32 % (189697)Instruction limit reached!
% 0.37/0.32 % (189697)------------------------------
% 0.37/0.32 % (189697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189697)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189697)Termination reason: Instruction limit
% 0.37/0.32 % (189697)Termination phase: shuffling
% 0.37/0.32 % (189697)Time elapsed: 0.006 s
% 0.37/0.32 % (189697)Peak memory usage: 11 MB
% 0.37/0.32 % (189697)Instructions burned: 24 (million)
% 0.37/0.32 % (189696)Instruction limit reached!
% 0.37/0.32 % (189696)------------------------------
% 0.37/0.32 % (189696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189696)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189696)Termination reason: Instruction limit
% 0.37/0.32 % (189696)Termination phase: shuffling
% 0.37/0.32 % (189696)Time elapsed: 0.007 s
% 0.37/0.32 % (189696)Peak memory usage: 11 MB
% 0.37/0.32 % (189696)Instructions burned: 30 (million)
% 0.37/0.32 % (189703)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.37/0.32 % (189703)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.37/0.32 % (189702)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3164236583:cond=on:i=60:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/60Mi)
% 0.37/0.32 % (189703)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=581943879:i=14:add=off:nm=40:rtra=on:rawr=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.37/0.32 % (189704)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.37/0.32 % (189703)Instruction limit reached!
% 0.37/0.32 % (189703)------------------------------
% 0.37/0.32 % (189703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189703)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189703)Termination reason: Instruction limit
% 0.37/0.32 % (189703)Termination phase: shuffling
% 0.37/0.32 % (189703)Time elapsed: 0.004 s
% 0.37/0.32 % (189703)Peak memory usage: 10 MB
% 0.37/0.32 % (189703)Instructions burned: 16 (million)
% 0.37/0.32 % (189704)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=321463027:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.37/0.32 % (189705)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=861709657:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.37/0.32 % (189704)Instruction limit reached!
% 0.37/0.32 % (189704)------------------------------
% 0.37/0.32 % (189704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189704)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189704)Termination reason: Instruction limit
% 0.37/0.32 % (189704)Termination phase: shuffling
% 0.37/0.32 % (189704)Time elapsed: 0.003 s
% 0.37/0.32 % (189704)Peak memory usage: 10 MB
% 0.37/0.32 % (189704)Instructions burned: 12 (million)
% 0.37/0.32 % (189702)Instruction limit reached!
% 0.37/0.32 % (189702)------------------------------
% 0.37/0.32 % (189702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189702)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189702)Termination reason: Instruction limit
% 0.37/0.32 % (189702)Termination phase: Unused predicate definition removal
% 0.37/0.32 % (189702)Time elapsed: 0.014 s
% 0.37/0.32 % (189702)Peak memory usage: 11 MB
% 0.37/0.32 % (189702)Instructions burned: 63 (million)
% 0.37/0.32 % (189705)Instruction limit reached!
% 0.37/0.32 % (189705)------------------------------
% 0.37/0.32 % (189705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189705)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189705)Termination reason: Instruction limit
% 0.37/0.32 % (189705)Termination phase: shuffling
% 0.37/0.32 % (189705)Time elapsed: 0.008 s
% 0.37/0.32 % (189705)Peak memory usage: 11 MB
% 0.37/0.32 % (189705)Instructions burned: 35 (million)
% 0.37/0.32 % (189708)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4057492195:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.37/0.32 % (189708)Instruction limit reached!
% 0.37/0.32 % (189708)------------------------------
% 0.37/0.32 % (189708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189708)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189708)Termination reason: Instruction limit
% 0.37/0.32 % (189708)Termination phase: shuffling
% 0.37/0.32 % (189708)Time elapsed: 0.002 s
% 0.37/0.32 % (189708)Peak memory usage: 10 MB
% 0.37/0.32 % (189708)Instructions burned: 7 (million)
% 0.37/0.32 % (189711)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=100453706:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.37/0.32 % (189712)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3120934599:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 0.37/0.32 % (189714)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2486997474:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 0.37/0.32 % (189711)Instruction limit reached!
% 0.37/0.32 % (189711)------------------------------
% 0.37/0.32 % (189711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189711)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189711)Termination reason: Instruction limit
% 0.37/0.32 % (189711)Termination phase: shuffling
% 0.37/0.32 % (189711)Time elapsed: 0.006 s
% 0.37/0.32 % (189711)Peak memory usage: 11 MB
% 0.37/0.32 % (189711)Instructions burned: 26 (million)
% 0.37/0.32 % (189685)Instruction limit reached!
% 0.37/0.32 % (189685)------------------------------
% 0.37/0.32 % (189685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189685)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189685)Termination reason: Instruction limit
% 0.37/0.32 % (189685)Termination phase: Saturation
% 0.37/0.32 % (189685)Time elapsed: 0.057 s
% 0.37/0.32 % (189685)Peak memory usage: 15 MB
% 0.37/0.32 % (189685)Instructions burned: 253 (million)
% 0.37/0.32 % (189715)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=586560610:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 0.37/0.32 % (189712)Instruction limit reached!
% 0.37/0.32 % (189712)------------------------------
% 0.37/0.32 % (189712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189712)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189712)Termination reason: Instruction limit
% 0.37/0.32 % (189712)Termination phase: shuffling
% 0.37/0.32 % (189712)Time elapsed: 0.006 s
% 0.37/0.32 % (189712)Peak memory usage: 11 MB
% 0.37/0.32 % (189712)Instructions burned: 24 (million)
% 0.37/0.32 % (189719)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=207245246:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 0.37/0.32 % (189720)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3395057264:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 0.37/0.32 % (189657) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-189649-189657"...
% 0.37/0.32 % (189722)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.37/0.32 % (189722)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2851796607:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 0.37/0.32 % (189657)...printing done.
% 0.37/0.32 % (189722)Instruction limit reached!
% 0.37/0.32 % (189722)------------------------------
% 0.37/0.32 % (189722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189722)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189722)Termination reason: Instruction limit
% 0.37/0.32 % (189722)Termination phase: shuffling
% 0.37/0.32 % (189722)Time elapsed: 0.002 s
% 0.37/0.32 % (189722)Peak memory usage: 10 MB
% 0.37/0.32 % (189722)Instructions burned: 9 (million)
% 0.37/0.32 % (189657)Refutation found. Thanks to Tanya!
% 0.37/0.32 % SZS status Theorem for theBenchmark
% 0.37/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.32 % (189657)------------------------------
% 0.37/0.32 % (189657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.32 % (189657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.32 % (189657)CaDiCaL version: 2.1.3
% 0.37/0.32 % (189657)Termination reason: Refutation
% 0.37/0.32 % (189657)Time elapsed: 0.119 s
% 0.37/0.32 % (189657)Peak memory usage: 22 MB
% 0.37/0.32 % (189657)Instructions burned: 465 (million)
% 0.37/0.32 % (189649)Success in time 0.155 s
% 0.37/0.32 % Vampire exiting
%------------------------------------------------------------------------------