%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU739^1 : 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 : n003.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 08:31:03 AM UTC 2026
% Result : Theorem 0.47s 0.46s
% Output : Refutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 5664 (1604 equ; 0 cnn)
% Maximal formula atoms : 260 ( 128 avg)
% Number of connectives : 2656 ( 53 ~; 31 |;1042 &; 226 @)
% ( 6 <=>;1298 =>; 0 <=; 0 <~>)
% Maximal formula depth : 269 ( 57 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 : 482 ( 479 usr; 287 con; 0-4 aty)
% Number of variables : 68 ( 0 sgn 50 !; 18 ?; 68 :)
% 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_296,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_297,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_298,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_299,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_300,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_301,type,
vOR: $o > $o > $o ).
thf(func_def_302,type,
vAND: $o > $o > $o ).
thf(func_def_303,type,
vNOT: $o > $o ).
thf(func_def_304,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_305,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_306,type,
vIMP: $o > $o > $o ).
thf(func_def_307,type,
sP0: $i > $i > $o ).
thf(func_def_308,type,
sP1: $i > $o ).
thf(func_def_309,type,
sP2: $o ).
thf(func_def_310,type,
sP3: $o ).
thf(func_def_311,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_313,type,
sK6: $i > $o ).
thf(func_def_316,type,
sK9: $o ).
thf(func_def_319,type,
sK12: $o ).
thf(func_def_350,type,
sK43: $o ).
thf(func_def_352,type,
sK45: $o ).
thf(func_def_357,type,
sK50: $i > $o ).
thf(func_def_359,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_366,type,
sK59: $i > $o ).
thf(func_def_369,type,
sK62: ( $i > $i ) > $i > $i > $i ).
thf(func_def_372,type,
sK65: $i > $i ).
thf(func_def_382,type,
sK75: $i > $o ).
thf(func_def_384,type,
sK77: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_385,type,
sK78: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_391,type,
sK84: $i > $o ).
thf(func_def_410,type,
sK103: $i > $i > $o ).
thf(func_def_423,type,
sK116: $i > $i > $i ).
thf(func_def_424,type,
sK117: $i > $o ).
thf(func_def_448,type,
sK141: $o ).
thf(func_def_451,type,
sK144: $i > $o ).
thf(func_def_452,type,
sK145: $i > $o ).
thf(func_def_453,type,
sK146: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_454,type,
sK147: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_459,type,
sK152: $i > $o ).
thf(func_def_464,type,
sK157: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_465,type,
sK158: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_469,type,
sK162: $i > $o ).
thf(func_def_475,type,
sK168: $i > $i > $i > $i ).
thf(func_def_484,type,
sK177: $i > $i > $i > $i > $i ).
thf(func_def_494,type,
sK187: $i > $o ).
thf(func_def_496,type,
sK189: $i > ( $i > $o ) > $i ).
thf(func_def_503,type,
sK196: $i > $o ).
thf(func_def_505,type,
sK198: ( $i > $o ) > $i > $i ).
thf(func_def_507,type,
sK200: $i > $i ).
thf(func_def_508,type,
sK201: $i > $i > $o ).
thf(func_def_519,type,
sK212: $i > $o ).
thf(func_def_522,type,
sK215: $i > $i > ( $i > $o ) > $i ).
thf(func_def_539,type,
sK232: $i > $i > $o ).
thf(func_def_543,type,
sK236: $o > $i > $i > $i ).
thf(func_def_546,type,
sK239: $o ).
thf(func_def_547,type,
sK240: $i > $o ).
thf(func_def_555,type,
sK248: $i > ( $i > $o ) > $i ).
thf(func_def_556,type,
sK249: $i > ( $i > $o ) > $i ).
thf(func_def_557,type,
sK250: $i > $o ).
thf(func_def_560,type,
sK253: $i > ( $i > $o ) > $i ).
thf(func_def_561,type,
sK254: $i > ( $i > $o ) > $i ).
thf(func_def_562,type,
sK255: $i > $o ).
thf(func_def_594,type,
sK287: $i > $i ).
thf(func_def_599,type,
sK292: $i > $i > $o ).
thf(func_def_602,type,
sK295: ( $i > $i > $o ) > $i > $i ).
thf(func_def_603,type,
sK296: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_604,type,
sK297: ( $i > $i > $o ) > $i > $i ).
thf(func_def_606,type,
sK299: $i > $i > $o ).
thf(func_def_607,type,
sK300: $i > $i ).
thf(func_def_608,type,
sK301: $i > $i ).
thf(func_def_613,type,
sK306: $i > $o ).
thf(func_def_615,type,
sK308: $i > $i ).
thf(func_def_616,type,
sK309: $i > $i ).
thf(func_def_617,type,
sK310: $i > $i ).
thf(func_def_618,type,
sK311: $i > $i ).
thf(func_def_619,type,
sK312: $i > $i ).
thf(func_def_620,type,
sK313: $i > $i > $i > $i ).
thf(func_def_621,type,
sK314: $i > $i ).
thf(func_def_622,type,
sK315: $i > $i ).
thf(func_def_623,type,
sK316: $i > $i ).
thf(func_def_624,type,
sK317: $i > $i ).
thf(func_def_625,type,
sK318: $i > $i > $i ).
thf(func_def_626,type,
sK319: $i > $i > $i > $i ).
thf(func_def_627,type,
sK320: $i > $i > $i > $i ).
thf(func_def_628,type,
sK321: $i > $i > $i > $i ).
thf(func_def_629,type,
sK322: $i > $i > $i ).
thf(func_def_630,type,
sK323: $i > $i > $i ).
thf(func_def_631,type,
sK324: $i > $i > $i ).
thf(func_def_632,type,
sK325: $i > $i > $i ).
thf(func_def_635,type,
sK328: $i > $i ).
thf(func_def_636,type,
sK329: $i > $i ).
thf(func_def_641,type,
sK334: $i > $i > $i > $i > $i ).
thf(func_def_654,type,
sK347: $i > $i > $i > $i > $i ).
thf(func_def_655,type,
sK348: $i > $i > $i > $i > $i ).
thf(func_def_656,type,
sK349: $i > $i > $i > $i > $i ).
thf(func_def_657,type,
sK350: $i > $i > $i > $i > $i ).
thf(func_def_662,type,
sK355: $o ).
thf(func_def_663,type,
sK356: $i > $o ).
thf(func_def_664,type,
sK357: ( $i > $o ) > $i ).
thf(func_def_665,type,
sK358: $i > $i > $i > $i > $i ).
thf(func_def_671,type,
sK364: $i > $i ).
thf(func_def_681,type,
sK374: $i > $o ).
thf(func_def_683,type,
sK376: ( $i > $i ) > $i > $i > $i ).
thf(func_def_686,type,
sK379: $i > $i ).
thf(func_def_728,type,
sK421: $i > $o ).
thf(func_def_730,type,
sK423: ( $i > $o ) > $i > $i ).
thf(func_def_735,type,
sK428: $i > $i > $i ).
thf(func_def_736,type,
sK429: $i > $i > $i ).
thf(func_def_755,type,
sK448: $i > $i ).
thf(func_def_757,type,
sK450: $i > ( $i > $i ) > $i > $i ).
thf(func_def_776,type,
sK469: $i > $i > $i > $i ).
thf(func_def_777,type,
sK470: $i > $i > $i > $i ).
thf(func_def_784,type,
sK477: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_785,type,
sK478: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_786,type,
sK479: $i > $o ).
thf(func_def_787,type,
sK480: $i > $o ).
thf(func_def_789,type,
sK482: $i > $i ).
thf(func_def_791,type,
sK484: $i > ( $i > $i ) > $i > $i ).
thf(func_def_800,type,
sK493: $o ).
thf(func_def_803,type,
sK496: ( $i > $o ) > $i > $i ).
thf(func_def_805,type,
sK498: $i > $o ).
thf(func_def_815,type,
sK508: $i > $o ).
thf(func_def_823,type,
sK516: ( $i > $o ) > $i ).
thf(func_def_824,type,
sK517: $i > $o ).
thf(func_def_825,type,
sK518: $i > $i ).
thf(func_def_826,type,
sK519: $i > $o ).
thf(func_def_841,type,
sK534: $i > $i > $o ).
thf(func_def_848,type,
sK541: $i > $i ).
thf(func_def_851,type,
sK544: $i > ( $i > $i ) > $i > $i ).
thf(func_def_855,type,
sK548: $i > $i > $i ).
thf(func_def_862,type,
sK555: $i > $o ).
thf(func_def_868,type,
sK561: $i > $o ).
thf(func_def_869,type,
sK562: $i > $i ).
thf(func_def_870,type,
sK563: ( $i > $o ) > $i ).
thf(func_def_871,type,
sK564: $o ).
thf(func_def_879,type,
sK572: $i > $i > $i ).
thf(func_def_886,type,
sK579: $i > $i > $i ).
thf(func_def_899,type,
sK592: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_900,type,
sK593: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_903,type,
sK596: $i > $o ).
thf(func_def_904,type,
sK597: $i > $o ).
thf(func_def_913,type,
sK606: $o ).
thf(func_def_915,type,
sK608: $i > $o ).
thf(func_def_926,type,
sK619: $o ).
thf(func_def_943,type,
sK636: $i > $i ).
thf(func_def_945,type,
sK638: $i > $i > $i > $i > $i ).
thf(func_def_946,type,
sK639: $i > $i > $i > $i > $i ).
thf(func_def_956,type,
sK649: $o ).
thf(func_def_964,type,
sK657: $i > $i ).
thf(func_def_971,type,
sK664: $i > $i > $o ).
thf(func_def_978,type,
sK671: $i > ( $i > $o ) > $i ).
thf(func_def_979,type,
sK672: $i > $o ).
thf(func_def_994,type,
sK687: $i > ( $i > $o ) > $i ).
thf(func_def_995,type,
sK688: $i > $o ).
thf(func_def_1004,type,
sK697: $i > $i > $i > $i ).
thf(func_def_1013,type,
sK706: $i > $i > $i > $i ).
thf(func_def_1014,type,
sK707: $i > $i > $i > $i ).
thf(func_def_1018,type,
sK711: $i > $o ).
thf(func_def_1020,type,
sK713: $i > ( $i > $o ) > $i ).
thf(func_def_1021,type,
sK714: $i > $o ).
thf(func_def_1025,type,
sK718: $o ).
thf(func_def_1039,type,
sK732: $i > $i ).
thf(func_def_1041,type,
sK734: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1042,type,
sK735: $o ).
thf(func_def_1046,type,
sK739: $o ).
thf(func_def_1050,type,
sK743: $i > $i > $i ).
thf(func_def_1070,type,
sK763: $i > $i > $o ).
thf(func_def_1075,type,
sK768: $i > $i > $i ).
thf(func_def_1078,type,
sK771: $i > $o ).
thf(func_def_1079,type,
sK772: $i > $i > $i ).
thf(func_def_1084,type,
sK777: $o ).
thf(func_def_1095,type,
sK788: $o ).
thf(func_def_1100,type,
sK793: ( $i > $o ) > $i ).
thf(func_def_1101,type,
sK794: ( $i > $o ) > $i ).
thf(func_def_1102,type,
sK795: $i > $o ).
thf(func_def_1108,type,
sK801: $i > $i > $i ).
thf(f103,axiom,
( binunionIR
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(f260,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
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(f261,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
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f260]) ).
thf(f509,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
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f261]) ).
thf(f510,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f509]) ).
thf(f732,plain,
( binunionIR
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f103]) ).
thf(f733,plain,
( ( binunionIR = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f732]) ).
thf(f792,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 )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f510]) ).
thf(f961,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $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,[],[f792]) ).
thf(f962,plain,
( ( dsetconstr__Cong = $true )
& ( setukpairIR = $true )
& ( eta1 = $true )
& ( dpsetconstrERa = $true )
& ( setbeta = $true )
& ( inCongP = $true )
& ( setukpairinjR1 = $true )
& ( lam2p = $true )
& ( notdallE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( subPowSU = $true )
& ( upairset2E = $true )
& ( powersetI = $true )
& ( setminusI = $true )
& ( ubforcartprodlem1 = $true )
& ( setextT = $true )
& ( cartprodmempair = $true )
& ( cartprodmempaircEq = $true )
& ( binunionRsub = $true )
& ( setextAx = $true )
& ( eqbreln = $true )
& ( omegaSAx = $true )
& ( complementTI1 = $true )
& ( powersetAx = $true )
& ( exuE3e = $true )
& ( cartprodpairsurjEq = $true )
& ( binunionE = $true )
& ( quantDeMorgan1 = $true )
& ( binunionTILcontra = $true )
& ( singletonsswitch = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( exuE2 = $true )
& ( setukpairinjL2 = $true )
& ( setunionsingleton = $true )
& ( upairsetE = $true )
& ( setukpairinjR2 = $true )
& ( setunionE = $true )
& ( subsetE = $true )
& ( omegaIndAx = $true )
& ( funcGraphProp4 = $true )
& ( exuI1 = $true )
& ( contrasubsetT3 = $true )
& ( iftrueorfalse = $true )
& ( ap2apEq1 = $true )
& ( doubleComplementSub2 = $true )
& ( iffalseProp2 = $true )
& ( upairsubunion = $true )
& ( binintersectSubset5 = $true )
& ( ex1I = $true )
& ( funcextLem = $true )
& ( complementTcontraSubset = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( binintersectER = $true )
& ( setOfPairsIsBReln = $true )
& ( descr__Cong = $true )
& ( complementT_lem = $true )
& ( setunionsingleton1 = $true )
& ( kpairiskpair = $true )
& ( kpairsurjEq = $true )
& ( beta2 = $true )
& ( binintersectSubset4 = $true )
& ( cartprodpairmemEL = $true )
& ( binintersectSubset2 = $true )
& ( setminusSubset2 = $true )
& ( setminusERneg = $true )
& ( secondinupair = $true )
& ( emptysetsubset = $true )
& ( powersetsubset = $true )
& ( setminusLsub = $true )
& ( inPowerset = $true )
& ( ifp = $true )
& ( emptysetimpfalse = $true )
& ( lam2lamEq = $true )
& ( subsetI2 = $true )
& ( setoftrueEq = $true )
& ( setunionI = $true )
& ( binintersectTELcontra = $true )
& ( contraSubsetComplement = $true )
& ( powersetE1 = $true )
& ( singletonsuniq = $true )
& ( setadjoinAx = $true )
& ( doubleComplementI1 = $true )
& ( ap2apEq2 = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( notinsingleton = $true )
& ( singletonprop = $true )
& ( theeq = $true )
& ( lamProp = $true )
& ( doubleComplementSub1 = $true )
& ( sepSubset = $true )
& ( notsubsetI = $true )
& ( binintersectSubset1 = $true )
& ( cartprodpairin = $true )
& ( setukpairIL = $true )
& ( setadjoinOr = $true )
& ( iftrueProp1 = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjL1 = $true )
& ( funcext2 = $true )
& ( setukpairinjR11 = $true )
& ( setadjoinE = $true )
& ( powersetE = $true )
& ( symdiffE = $true )
& ( foundationAx = $true )
& ( notequalI1 = $true )
& ( infuncsetfunc = $true )
& ( exuI3 = $true )
& ( ksndsingleton = $true )
& ( binintersectI = $true )
& ( powersetTE1 = $true )
& ( setadjoinIL = $true )
& ( complementTnotintersectT = $true )
& ( setminusSubset1 = $true )
& ( nonemptyE1 = $true )
& ( ifSingleton = $true )
& ( vacuousDall = $true )
& ( binintersectEL = $true )
& ( funcGraphProp3 = $true )
& ( symdiffIneg1 = $true )
& ( complementImpComplementIntersect = $true )
& ( setadjoinSub2 = $true )
& ( brelnall1 = $true )
& ( nonemptyI1 = $true )
& ( cartprodpairmemER = $true )
& ( binunionEcases = $true )
& ( notequalI2 = $true )
& ( setminusELneg = $true )
& ( sepInPowerset = $true )
& ( kfstpairEq = $true )
& ( upairequniteq = $true )
& ( lamp = $true )
& ( setukpairinjR12 = $true )
& ( kfstsingleton = $true )
& ( disjointsetsI1 = $true )
& ( powersetTI1 = $true )
& ( powersetI1 = $true )
& ( dpsetconstrER = $true )
& ( funcGraphProp2 = $true )
& ( ap2p = $true )
& ( ex1I2 = $true )
& ( dsetconstrEL = $true )
& ( setunion__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( brelnall2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setunionE2 = $true )
& ( funcImageSingleton = $true )
& ( setadjoinIR = $true )
& ( subsetRefl = $true )
& ( setukpairinjR = $true )
& ( quantDeMorgan2 = $true )
& ( iftrue = $true )
& ( nonemptyI = $true )
& ( ex1E1 = $true )
& ( iffalseProp1 = $true )
& ( emptysetAx = $true )
& ( wellorderingAx = $true )
& ( binintersectTERcontra = $true )
& ( binunionIL = $true )
& ( ex1E2 = $true )
& ( setukpairinjL = $true )
& ( funcext = $true )
& ( emptyset__Cong = $true )
& ( subsetTI = $true )
& ( setadjoinSub = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( setextsub = $true )
& ( upairsetIL = $true )
& ( contrasubsetT1 = $true )
& ( binunionLsub = $true )
& ( dsetconstrER = $true )
& ( subbreln = $true )
& ( kpairp = $true )
& ( setminusEL = $true )
& ( contrasubsetT2 = $true )
& ( noeltsimpempty = $true )
& ( apProp = $true )
& ( eqimpsubset2 = $true )
& ( emptysetE = $true )
& ( cartprodmempair1 = $true )
& ( contrasubsetT = $true )
& ( setminusER = $true )
& ( setminusILneg = $true )
& ( exuE1 = $true )
& ( beta1 = $true )
& ( setadjoin__Cong = $true )
& ( ksndpairEq = $true )
& ( doubleComplementE1 = $true )
& ( cartprodsndpairEq = $true )
& ( funcinfuncset = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( subsetI1 = $true )
& ( theprop = $true )
& ( cartprodfstin = $true )
& ( cartprodsndin = $true )
& ( omega0Ax = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectT_lem = $true )
& ( singletoninpowunion = $true )
& ( subsetTrans = $true )
& ( setminusIRneg = $true )
& ( upairsetIR = $true )
& ( dpsetconstrEL2 = $true )
& ( notdexE = $true )
& ( symdiffI2 = $true )
& ( exuE3u = $true )
& ( prop2set2propI = $true )
& ( emptyE1 = $true )
& ( replAx = $true )
& ( iffalse = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( notinemptyset = $true )
& ( app = $true )
& ( emptyinunitempty = $true )
& ( exuEu = $true )
& ( complementTE1 = $true )
& ( dpsetconstrEL1 = $true )
& ( exu__Cong = $true )
& ( omega__Cong = $true )
& ( upairset2IR = $true )
& ( setminusT_lem = $true )
& ( iftrueProp2 = $true )
& ( bs114d = $true )
& ( ubforcartprodlem3 = $true )
& ( dpsetconstrSub = $true )
& ( singletonsubset = $true )
& ( binintersectSubset3 = $true )
& ( doubleComplementEq = $true )
& ( eta2 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( upairinpowunion = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( subset2powerset = $true )
& ( cartprodfstpairEq = $true )
& ( singletoninpowerset = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( setunionsingleton2 = $true )
& ( prop2setE = $true )
& ( exuI2 = $true )
& ( subsetE2 = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true ) ),
inference(flattening,[],[f961]) ).
thf(f1089,plain,
( ( binunionIR = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f733]) ).
thf(f1606,plain,
( ( ( binunionIR = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( binunionIR != $true ) ) ),
inference(nnf_transformation,[],[f1089]) ).
thf(f1607,plain,
( ( ( binunionIR = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ( binunionIR != $true ) ) ),
inference(rectify,[],[f1606]) ).
thf(f1608,plain,
( ( ( binunionIR = $true )
| ( ( $true
!= ( in @ sK523 @ ( binunion @ sK522 @ sK524 ) ) )
& ( ( in @ sK523 @ sK524 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ( binunionIR != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK522,sK523,sK524]),skolemize(X0,sK522),skolemize(X1,sK523),skolemize(X2,sK524)],[f1607]) ).
thf(f1756,plain,
( ( dsetconstr__Cong = $true )
& ( setukpairIR = $true )
& ( eta1 = $true )
& ( dpsetconstrERa = $true )
& ( setbeta = $true )
& ( inCongP = $true )
& ( setukpairinjR1 = $true )
& ( lam2p = $true )
& ( notdallE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( subPowSU = $true )
& ( upairset2E = $true )
& ( powersetI = $true )
& ( setminusI = $true )
& ( ubforcartprodlem1 = $true )
& ( setextT = $true )
& ( cartprodmempair = $true )
& ( cartprodmempaircEq = $true )
& ( binunionRsub = $true )
& ( setextAx = $true )
& ( eqbreln = $true )
& ( omegaSAx = $true )
& ( complementTI1 = $true )
& ( powersetAx = $true )
& ( exuE3e = $true )
& ( cartprodpairsurjEq = $true )
& ( binunionE = $true )
& ( quantDeMorgan1 = $true )
& ( binunionTILcontra = $true )
& ( singletonsswitch = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( exuE2 = $true )
& ( setukpairinjL2 = $true )
& ( setunionsingleton = $true )
& ( upairsetE = $true )
& ( setukpairinjR2 = $true )
& ( setunionE = $true )
& ( subsetE = $true )
& ( omegaIndAx = $true )
& ( funcGraphProp4 = $true )
& ( exuI1 = $true )
& ( contrasubsetT3 = $true )
& ( iftrueorfalse = $true )
& ( ap2apEq1 = $true )
& ( doubleComplementSub2 = $true )
& ( iffalseProp2 = $true )
& ( upairsubunion = $true )
& ( binintersectSubset5 = $true )
& ( ex1I = $true )
& ( funcextLem = $true )
& ( complementTcontraSubset = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( binintersectER = $true )
& ( setOfPairsIsBReln = $true )
& ( descr__Cong = $true )
& ( complementT_lem = $true )
& ( setunionsingleton1 = $true )
& ( kpairiskpair = $true )
& ( kpairsurjEq = $true )
& ( beta2 = $true )
& ( binintersectSubset4 = $true )
& ( cartprodpairmemEL = $true )
& ( binintersectSubset2 = $true )
& ( setminusSubset2 = $true )
& ( setminusERneg = $true )
& ( secondinupair = $true )
& ( emptysetsubset = $true )
& ( powersetsubset = $true )
& ( setminusLsub = $true )
& ( inPowerset = $true )
& ( ifp = $true )
& ( emptysetimpfalse = $true )
& ( lam2lamEq = $true )
& ( subsetI2 = $true )
& ( setoftrueEq = $true )
& ( setunionI = $true )
& ( binintersectTELcontra = $true )
& ( contraSubsetComplement = $true )
& ( powersetE1 = $true )
& ( singletonsuniq = $true )
& ( setadjoinAx = $true )
& ( doubleComplementI1 = $true )
& ( ap2apEq2 = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( notinsingleton = $true )
& ( singletonprop = $true )
& ( theeq = $true )
& ( lamProp = $true )
& ( doubleComplementSub1 = $true )
& ( sepSubset = $true )
& ( notsubsetI = $true )
& ( binintersectSubset1 = $true )
& ( cartprodpairin = $true )
& ( setukpairIL = $true )
& ( setadjoinOr = $true )
& ( iftrueProp1 = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjL1 = $true )
& ( funcext2 = $true )
& ( setukpairinjR11 = $true )
& ( setadjoinE = $true )
& ( powersetE = $true )
& ( symdiffE = $true )
& ( foundationAx = $true )
& ( notequalI1 = $true )
& ( infuncsetfunc = $true )
& ( exuI3 = $true )
& ( ksndsingleton = $true )
& ( binintersectI = $true )
& ( powersetTE1 = $true )
& ( setadjoinIL = $true )
& ( complementTnotintersectT = $true )
& ( setminusSubset1 = $true )
& ( nonemptyE1 = $true )
& ( ifSingleton = $true )
& ( vacuousDall = $true )
& ( binintersectEL = $true )
& ( funcGraphProp3 = $true )
& ( symdiffIneg1 = $true )
& ( complementImpComplementIntersect = $true )
& ( setadjoinSub2 = $true )
& ( brelnall1 = $true )
& ( nonemptyI1 = $true )
& ( cartprodpairmemER = $true )
& ( binunionEcases = $true )
& ( notequalI2 = $true )
& ( setminusELneg = $true )
& ( sepInPowerset = $true )
& ( kfstpairEq = $true )
& ( upairequniteq = $true )
& ( lamp = $true )
& ( setukpairinjR12 = $true )
& ( kfstsingleton = $true )
& ( disjointsetsI1 = $true )
& ( powersetTI1 = $true )
& ( powersetI1 = $true )
& ( dpsetconstrER = $true )
& ( funcGraphProp2 = $true )
& ( ap2p = $true )
& ( ex1I2 = $true )
& ( dsetconstrEL = $true )
& ( setunion__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( brelnall2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setunionE2 = $true )
& ( funcImageSingleton = $true )
& ( setadjoinIR = $true )
& ( subsetRefl = $true )
& ( setukpairinjR = $true )
& ( quantDeMorgan2 = $true )
& ( iftrue = $true )
& ( nonemptyI = $true )
& ( ex1E1 = $true )
& ( iffalseProp1 = $true )
& ( emptysetAx = $true )
& ( wellorderingAx = $true )
& ( binintersectTERcontra = $true )
& ( binunionIL = $true )
& ( ex1E2 = $true )
& ( setukpairinjL = $true )
& ( funcext = $true )
& ( emptyset__Cong = $true )
& ( subsetTI = $true )
& ( setadjoinSub = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( setextsub = $true )
& ( upairsetIL = $true )
& ( contrasubsetT1 = $true )
& ( binunionLsub = $true )
& ( dsetconstrER = $true )
& ( subbreln = $true )
& ( kpairp = $true )
& ( setminusEL = $true )
& ( contrasubsetT2 = $true )
& ( noeltsimpempty = $true )
& ( apProp = $true )
& ( eqimpsubset2 = $true )
& ( emptysetE = $true )
& ( cartprodmempair1 = $true )
& ( contrasubsetT = $true )
& ( setminusER = $true )
& ( setminusILneg = $true )
& ( exuE1 = $true )
& ( beta1 = $true )
& ( setadjoin__Cong = $true )
& ( ksndpairEq = $true )
& ( doubleComplementE1 = $true )
& ( cartprodsndpairEq = $true )
& ( funcinfuncset = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( subsetI1 = $true )
& ( theprop = $true )
& ( cartprodfstin = $true )
& ( cartprodsndin = $true )
& ( omega0Ax = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectT_lem = $true )
& ( singletoninpowunion = $true )
& ( subsetTrans = $true )
& ( setminusIRneg = $true )
& ( upairsetIR = $true )
& ( dpsetconstrEL2 = $true )
& ( notdexE = $true )
& ( symdiffI2 = $true )
& ( exuE3u = $true )
& ( prop2set2propI = $true )
& ( emptyE1 = $true )
& ( replAx = $true )
& ( iffalse = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( notinemptyset = $true )
& ( app = $true )
& ( emptyinunitempty = $true )
& ( exuEu = $true )
& ( complementTE1 = $true )
& ( dpsetconstrEL1 = $true )
& ( exu__Cong = $true )
& ( omega__Cong = $true )
& ( upairset2IR = $true )
& ( setminusT_lem = $true )
& ( iftrueProp2 = $true )
& ( bs114d = $true )
& ( ubforcartprodlem3 = $true )
& ( dpsetconstrSub = $true )
& ( singletonsubset = $true )
& ( binintersectSubset3 = $true )
& ( doubleComplementEq = $true )
& ( eta2 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( upairinpowunion = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( subset2powerset = $true )
& ( cartprodfstpairEq = $true )
& ( singletoninpowerset = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( setunionsingleton2 = $true )
& ( prop2setE = $true )
& ( exuI2 = $true )
& ( subsetE2 = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true ) ),
inference(rectify,[],[f962]) ).
thf(f1757,plain,
( ( dsetconstr__Cong = $true )
& ( setukpairIR = $true )
& ( eta1 = $true )
& ( dpsetconstrERa = $true )
& ( setbeta = $true )
& ( inCongP = $true )
& ( setukpairinjR1 = $true )
& ( lam2p = $true )
& ( notdallE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( subPowSU = $true )
& ( upairset2E = $true )
& ( powersetI = $true )
& ( setminusI = $true )
& ( ubforcartprodlem1 = $true )
& ( setextT = $true )
& ( cartprodmempair = $true )
& ( cartprodmempaircEq = $true )
& ( binunionRsub = $true )
& ( setextAx = $true )
& ( eqbreln = $true )
& ( omegaSAx = $true )
& ( complementTI1 = $true )
& ( powersetAx = $true )
& ( exuE3e = $true )
& ( cartprodpairsurjEq = $true )
& ( binunionE = $true )
& ( quantDeMorgan1 = $true )
& ( binunionTILcontra = $true )
& ( singletonsswitch = $true )
& ( $true
= ( in @ sK670 @ sK669 ) )
& ( ( in @ sK670 @ ( binunion @ sK668 @ sK669 ) )
!= $true )
& ( ( in @ sK670 @ sK667 )
= $true )
& ( ( in @ sK669 @ ( powerset @ sK667 ) )
= $true )
& ( ( in @ sK668 @ ( powerset @ sK667 ) )
= $true )
& ( exuE2 = $true )
& ( setukpairinjL2 = $true )
& ( setunionsingleton = $true )
& ( upairsetE = $true )
& ( setukpairinjR2 = $true )
& ( setunionE = $true )
& ( subsetE = $true )
& ( omegaIndAx = $true )
& ( funcGraphProp4 = $true )
& ( exuI1 = $true )
& ( contrasubsetT3 = $true )
& ( iftrueorfalse = $true )
& ( ap2apEq1 = $true )
& ( doubleComplementSub2 = $true )
& ( iffalseProp2 = $true )
& ( upairsubunion = $true )
& ( binintersectSubset5 = $true )
& ( ex1I = $true )
& ( funcextLem = $true )
& ( complementTcontraSubset = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( binintersectER = $true )
& ( setOfPairsIsBReln = $true )
& ( descr__Cong = $true )
& ( complementT_lem = $true )
& ( setunionsingleton1 = $true )
& ( kpairiskpair = $true )
& ( kpairsurjEq = $true )
& ( beta2 = $true )
& ( binintersectSubset4 = $true )
& ( cartprodpairmemEL = $true )
& ( binintersectSubset2 = $true )
& ( setminusSubset2 = $true )
& ( setminusERneg = $true )
& ( secondinupair = $true )
& ( emptysetsubset = $true )
& ( powersetsubset = $true )
& ( setminusLsub = $true )
& ( inPowerset = $true )
& ( ifp = $true )
& ( emptysetimpfalse = $true )
& ( lam2lamEq = $true )
& ( subsetI2 = $true )
& ( setoftrueEq = $true )
& ( setunionI = $true )
& ( binintersectTELcontra = $true )
& ( contraSubsetComplement = $true )
& ( powersetE1 = $true )
& ( singletonsuniq = $true )
& ( setadjoinAx = $true )
& ( doubleComplementI1 = $true )
& ( ap2apEq2 = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( notinsingleton = $true )
& ( singletonprop = $true )
& ( theeq = $true )
& ( lamProp = $true )
& ( doubleComplementSub1 = $true )
& ( sepSubset = $true )
& ( notsubsetI = $true )
& ( binintersectSubset1 = $true )
& ( cartprodpairin = $true )
& ( setukpairIL = $true )
& ( setadjoinOr = $true )
& ( iftrueProp1 = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjL1 = $true )
& ( funcext2 = $true )
& ( setukpairinjR11 = $true )
& ( setadjoinE = $true )
& ( powersetE = $true )
& ( symdiffE = $true )
& ( foundationAx = $true )
& ( notequalI1 = $true )
& ( infuncsetfunc = $true )
& ( exuI3 = $true )
& ( ksndsingleton = $true )
& ( binintersectI = $true )
& ( powersetTE1 = $true )
& ( setadjoinIL = $true )
& ( complementTnotintersectT = $true )
& ( setminusSubset1 = $true )
& ( nonemptyE1 = $true )
& ( ifSingleton = $true )
& ( vacuousDall = $true )
& ( binintersectEL = $true )
& ( funcGraphProp3 = $true )
& ( symdiffIneg1 = $true )
& ( complementImpComplementIntersect = $true )
& ( setadjoinSub2 = $true )
& ( brelnall1 = $true )
& ( nonemptyI1 = $true )
& ( cartprodpairmemER = $true )
& ( binunionEcases = $true )
& ( notequalI2 = $true )
& ( setminusELneg = $true )
& ( sepInPowerset = $true )
& ( kfstpairEq = $true )
& ( upairequniteq = $true )
& ( lamp = $true )
& ( setukpairinjR12 = $true )
& ( kfstsingleton = $true )
& ( disjointsetsI1 = $true )
& ( powersetTI1 = $true )
& ( powersetI1 = $true )
& ( dpsetconstrER = $true )
& ( funcGraphProp2 = $true )
& ( ap2p = $true )
& ( ex1I2 = $true )
& ( dsetconstrEL = $true )
& ( setunion__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( brelnall2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setunionE2 = $true )
& ( funcImageSingleton = $true )
& ( setadjoinIR = $true )
& ( subsetRefl = $true )
& ( setukpairinjR = $true )
& ( quantDeMorgan2 = $true )
& ( iftrue = $true )
& ( nonemptyI = $true )
& ( ex1E1 = $true )
& ( iffalseProp1 = $true )
& ( emptysetAx = $true )
& ( wellorderingAx = $true )
& ( binintersectTERcontra = $true )
& ( binunionIL = $true )
& ( ex1E2 = $true )
& ( setukpairinjL = $true )
& ( funcext = $true )
& ( emptyset__Cong = $true )
& ( subsetTI = $true )
& ( setadjoinSub = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( setextsub = $true )
& ( upairsetIL = $true )
& ( contrasubsetT1 = $true )
& ( binunionLsub = $true )
& ( dsetconstrER = $true )
& ( subbreln = $true )
& ( kpairp = $true )
& ( setminusEL = $true )
& ( contrasubsetT2 = $true )
& ( noeltsimpempty = $true )
& ( apProp = $true )
& ( eqimpsubset2 = $true )
& ( emptysetE = $true )
& ( cartprodmempair1 = $true )
& ( contrasubsetT = $true )
& ( setminusER = $true )
& ( setminusILneg = $true )
& ( exuE1 = $true )
& ( beta1 = $true )
& ( setadjoin__Cong = $true )
& ( ksndpairEq = $true )
& ( doubleComplementE1 = $true )
& ( cartprodsndpairEq = $true )
& ( funcinfuncset = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( subsetI1 = $true )
& ( theprop = $true )
& ( cartprodfstin = $true )
& ( cartprodsndin = $true )
& ( omega0Ax = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectT_lem = $true )
& ( singletoninpowunion = $true )
& ( subsetTrans = $true )
& ( setminusIRneg = $true )
& ( upairsetIR = $true )
& ( dpsetconstrEL2 = $true )
& ( notdexE = $true )
& ( symdiffI2 = $true )
& ( exuE3u = $true )
& ( prop2set2propI = $true )
& ( emptyE1 = $true )
& ( replAx = $true )
& ( iffalse = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( notinemptyset = $true )
& ( app = $true )
& ( emptyinunitempty = $true )
& ( exuEu = $true )
& ( complementTE1 = $true )
& ( dpsetconstrEL1 = $true )
& ( exu__Cong = $true )
& ( omega__Cong = $true )
& ( upairset2IR = $true )
& ( setminusT_lem = $true )
& ( iftrueProp2 = $true )
& ( bs114d = $true )
& ( ubforcartprodlem3 = $true )
& ( dpsetconstrSub = $true )
& ( singletonsubset = $true )
& ( binintersectSubset3 = $true )
& ( doubleComplementEq = $true )
& ( eta2 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( upairinpowunion = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( subset2powerset = $true )
& ( cartprodfstpairEq = $true )
& ( singletoninpowerset = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( setunionsingleton2 = $true )
& ( prop2setE = $true )
& ( exuI2 = $true )
& ( subsetE2 = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK667,sK668,sK669,sK670]),skolemize(X0,sK667),skolemize(X1,sK668),skolemize(X2,sK669),skolemize(X3,sK670)],[f1756]) ).
thf(f2583,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( binunionIR != $true )
| ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f1608]) ).
thf(f2838,plain,
binunionIR = $true,
inference(cnf_transformation,[],[f1757]) ).
thf(f3004,plain,
( ( in @ sK670 @ ( binunion @ sK668 @ sK669 ) )
!= $true ),
inference(cnf_transformation,[],[f1757]) ).
thf(f3005,plain,
( $true
= ( in @ sK670 @ sK669 ) ),
inference(cnf_transformation,[],[f1757]) ).
thf(f5965,definition,
( spl802_554
<=> ( binunionIR = $true ) ),
introduced(definition,[new_symbols(definition,[spl802_554])],[avatar_definition]) ).
thf(f5968,plain,
spl802_554,
inference(avatar_split_clause,[],[f2838,f5965]) ).
thf(f7568,definition,
( spl802_889
<=> ( $true
= ( in @ sK670 @ sK669 ) ) ),
introduced(definition,[new_symbols(definition,[spl802_889])],[avatar_definition]) ).
thf(f7570,plain,
( ( $true
= ( in @ sK670 @ sK669 ) )
| ~ spl802_889 ),
inference(avatar_component_clause,[],[f7568]) ).
thf(f7571,plain,
spl802_889,
inference(avatar_split_clause,[],[f3005,f7568]) ).
thf(f8888,definition,
( spl802_1164
<=> ( ( in @ sK670 @ ( binunion @ sK668 @ sK669 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl802_1164])],[avatar_definition]) ).
thf(f8890,plain,
( ( ( in @ sK670 @ ( binunion @ sK668 @ sK669 ) )
!= $true )
| spl802_1164 ),
inference(avatar_component_clause,[],[f8888]) ).
thf(f8891,plain,
~ spl802_1164,
inference(avatar_split_clause,[],[f3004,f8888]) ).
thf(f9365,definition,
( spl802_1260
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl802_1260])],[avatar_definition]) ).
thf(f9366,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ~ spl802_1260 ),
inference(avatar_component_clause,[],[f9365]) ).
thf(f9367,plain,
( spl802_1260
| ~ spl802_554 ),
inference(avatar_split_clause,[],[f2583,f5965,f9365]) ).
thf(f10495,plain,
( ( $true
!= ( in @ sK670 @ sK669 ) )
| ( $true != $true )
| spl802_1164
| ~ spl802_1260 ),
inference(superposition,[],[f8890,f9366]) ).
thf(f10498,plain,
( ( $true
!= ( in @ sK670 @ sK669 ) )
| spl802_1164
| ~ spl802_1260 ),
inference(trivial_inequality_removal,[],[f10495]) ).
thf(f10506,plain,
( $false
| ~ spl802_889
| spl802_1164
| ~ spl802_1260 ),
inference(forward_subsumption_resolution,[],[f10498,f7570]) ).
thf(f10507,plain,
( ~ spl802_889
| spl802_1164
| ~ spl802_1260 ),
inference(avatar_contradiction_clause,[],[f10506]) ).
cnf(s439,plain,
spl802_554,
inference(sat_conversion,[],[f5968]) ).
cnf(s813,plain,
spl802_889,
inference(sat_conversion,[],[f7571]) ).
cnf(s1147,plain,
~ spl802_1164,
inference(sat_conversion,[],[f8891]) ).
cnf(s1279,plain,
( ~ spl802_554
| spl802_1260 ),
inference(sat_conversion,[],[f9367]) ).
cnf(s1339,plain,
( ~ spl802_889
| spl802_1164
| ~ spl802_1260 ),
inference(sat_conversion,[],[f10507]) ).
cnf(s1389,plain,
~ spl802_1260,
inference(rat,[],[s1339,s1147,s813]) ).
cnf(s1391,plain,
~ spl802_554,
inference(rat,[],[s1279,s1389]) ).
cnf(s1512,plain,
$false,
inference(rat,[],[s439,s1391]) ).
thf(f10508,plain,
$false,
inference(avatar_sat_refutation,[],[s1512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU739^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n003.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 14:20:43 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.23/0.27 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
% 0.47/0.43 % (2572111)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.47/0.43 % (2572120)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=1196748248: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)
% 0.47/0.43 % (2572117)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2949707625:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.47/0.43 % (2572119)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=895772109:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.47/0.43 % (2572118)lrs+10_16_si=on:nwc=1.5:random_seed=818777718:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.47/0.43 % (2572119)Instruction limit reached!
% 0.47/0.43 % (2572119)------------------------------
% 0.47/0.43 % (2572119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (2572119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (2572119)CaDiCaL version: 2.1.3
% 0.47/0.43 % (2572119)Termination reason: Instruction limit
% 0.47/0.43 % (2572119)Termination phase: shuffling
% 0.47/0.43 % (2572119)Time elapsed: 0.002 s
% 0.47/0.43 % (2572119)Peak memory usage: 10 MB
% 0.47/0.43 % (2572119)Instructions burned: 4 (million)
% 0.47/0.43 % (2572122)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=500707329:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.47/0.43 % (2572118)Instruction limit reached!
% 0.47/0.43 % (2572118)------------------------------
% 0.47/0.43 % (2572118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (2572118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (2572118)CaDiCaL version: 2.1.3
% 0.47/0.43 % (2572118)Termination reason: Instruction limit
% 0.47/0.43 % (2572118)Termination phase: shuffling
% 0.47/0.43 % (2572118)Time elapsed: 0.009 s
% 0.47/0.43 % (2572118)Peak memory usage: 10 MB
% 0.47/0.43 % (2572118)Instructions burned: 18 (million)
% 0.47/0.43 % (2572123)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.47/0.43 % (2572123)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
% 0.47/0.43 % (2572121)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1473391059:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.47/0.43 % (2572128)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=450325546:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.47/0.43 % (2572123)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=660660466:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.47/0.43 % (2572128)Instruction limit reached!
% 0.47/0.43 % (2572128)------------------------------
% 0.47/0.43 % (2572128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (2572128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (2572128)CaDiCaL version: 2.1.3
% 0.47/0.43 % (2572128)Termination reason: Instruction limit
% 0.47/0.43 % (2572128)Termination phase: shuffling
% 0.47/0.43 % (2572128)Time elapsed: 0.002 s
% 0.47/0.43 % (2572128)Peak memory usage: 10 MB
% 0.47/0.43 % (2572128)Instructions burned: 3 (million)
% 0.47/0.43 % (2572130)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=653301416:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.47/0.43 % (2572130)Instruction limit reached!
% 0.47/0.43 % (2572130)------------------------------
% 0.47/0.43 % (2572130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (2572130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (2572130)CaDiCaL version: 2.1.3
% 0.47/0.43 % (2572130)Termination reason: Instruction limit
% 0.47/0.43 % (2572130)Termination phase: shuffling
% 0.47/0.43 % (2572130)Time elapsed: 0.003 s
% 0.47/0.43 % (2572130)Peak memory usage: 10 MB
% 0.47/0.43 % (2572130)Instructions burned: 5 (million)
% 0.47/0.46 % (2572121)Instruction limit reached!
% 0.47/0.46 % (2572121)------------------------------
% 0.47/0.46 % (2572121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572121)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572121)Termination reason: Instruction limit
% 0.47/0.46 % (2572121)Termination phase: Property scanning
% 0.47/0.46 % (2572121)Time elapsed: 0.012 s
% 0.47/0.46 % (2572121)Peak memory usage: 11 MB
% 0.47/0.46 % (2572121)Instructions burned: 25 (million)
% 0.47/0.46 % (2572122)Instruction limit reached!
% 0.47/0.46 % (2572122)------------------------------
% 0.47/0.46 % (2572122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572122)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572122)Termination reason: Instruction limit
% 0.47/0.46 % (2572122)Termination phase: Preprocessing 3
% 0.47/0.46 % (2572122)Time elapsed: 0.036 s
% 0.47/0.46 % (2572122)Peak memory usage: 12 MB
% 0.47/0.46 % (2572122)Instructions burned: 76 (million)
% 0.47/0.46 % (2572117)Instruction limit reached!
% 0.47/0.46 % (2572117)------------------------------
% 0.47/0.46 % (2572117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572117)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572117)Termination reason: Instruction limit
% 0.47/0.46 % (2572117)Termination phase: Preprocessing 3
% 0.47/0.46 % (2572117)Time elapsed: 0.042 s
% 0.47/0.46 % (2572117)Peak memory usage: 13 MB
% 0.47/0.46 % (2572117)Instructions burned: 89 (million)
% 0.47/0.46 % (2572134)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.47/0.46 % (2572134)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1906256604:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.47/0.46 % (2572137)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
% 0.47/0.46 % (2572137)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.47/0.46 % (2572134)Instruction limit reached!
% 0.47/0.46 % (2572134)------------------------------
% 0.47/0.46 % (2572134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572134)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572134)Termination reason: Instruction limit
% 0.47/0.46 % (2572134)Termination phase: shuffling
% 0.47/0.46 % (2572134)Time elapsed: 0.004 s
% 0.47/0.46 % (2572134)Peak memory usage: 10 MB
% 0.47/0.46 % (2572134)Instructions burned: 8 (million)
% 0.47/0.46 % (2572136)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2843023514:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.47/0.46 % (2572137)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3944197378:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.47/0.46 % (2572136)Instruction limit reached!
% 0.47/0.46 % (2572136)------------------------------
% 0.47/0.46 % (2572136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572136)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572136)Termination reason: Instruction limit
% 0.47/0.46 % (2572136)Termination phase: shuffling
% 0.47/0.46 % (2572136)Time elapsed: 0.006 s
% 0.47/0.46 % (2572136)Peak memory usage: 10 MB
% 0.47/0.46 % (2572136)Instructions burned: 13 (million)
% 0.47/0.46 % (2572138)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=3598864939:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.47/0.46 % (2572139)lrs+10_1_si=on:cs=on:random_seed=2457108195:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.47/0.46 % (2572139)Instruction limit reached!
% 0.47/0.46 % (2572139)------------------------------
% 0.47/0.46 % (2572139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572139)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572139)Termination reason: Instruction limit
% 0.47/0.46 % (2572139)Termination phase: shuffling
% 0.47/0.46 % (2572139)Time elapsed: 0.005 s
% 0.47/0.46 % (2572139)Peak memory usage: 10 MB
% 0.47/0.46 % (2572139)Instructions burned: 10 (million)
% 0.47/0.46 % (2572141)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.47/0.46 % (2572137)Instruction limit reached!
% 0.47/0.46 % (2572137)------------------------------
% 0.47/0.46 % (2572137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572137)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572137)Termination reason: Instruction limit
% 0.47/0.46 % (2572137)Termination phase: shuffling
% 0.47/0.46 % (2572137)Time elapsed: 0.013 s
% 0.47/0.46 % (2572137)Peak memory usage: 10 MB
% 0.47/0.46 % (2572137)Instructions burned: 29 (million)
% 0.47/0.46 % (2572141)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=1682386029:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.47/0.46 % (2572141)Instruction limit reached!
% 0.47/0.46 % (2572141)------------------------------
% 0.47/0.46 % (2572141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572141)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572141)Termination reason: Instruction limit
% 0.47/0.46 % (2572141)Termination phase: shuffling
% 0.47/0.46 % (2572141)Time elapsed: 0.002 s
% 0.47/0.46 % (2572141)Peak memory usage: 10 MB
% 0.47/0.46 % (2572141)Instructions burned: 4 (million)
% 0.47/0.46 % (2572144)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1051948816:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.47/0.46 % (2572147)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2330649049:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.47/0.46 % (2572148)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1575122274:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.47/0.46 % (2572150)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3373902256:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.47/0.46 % (2572144)Instruction limit reached!
% 0.47/0.46 % (2572144)------------------------------
% 0.47/0.46 % (2572144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572144)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572144)Termination reason: Instruction limit
% 0.47/0.46 % (2572144)Termination phase: Property scanning
% 0.47/0.46 % (2572144)Time elapsed: 0.017 s
% 0.47/0.46 % (2572144)Peak memory usage: 11 MB
% 0.47/0.46 % (2572144)Instructions burned: 39 (million)
% 0.47/0.46 % (2572150)Instruction limit reached!
% 0.47/0.46 % (2572150)------------------------------
% 0.47/0.46 % (2572150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572148)Instruction limit reached!
% 0.47/0.46 % (2572148)------------------------------
% 0.47/0.46 % (2572148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572150)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572150)Termination reason: Instruction limit
% 0.47/0.46 % (2572150)Termination phase: shuffling
% 0.47/0.46 % (2572148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572150)Time elapsed: 0.007 s
% 0.47/0.46 % (2572150)Peak memory usage: 10 MB
% 0.47/0.46 % (2572148)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572150)Instructions burned: 15 (million)
% 0.47/0.46 % (2572148)Termination reason: Instruction limit
% 0.47/0.46 % (2572148)Termination phase: Property scanning
% 0.47/0.46 % (2572148)Time elapsed: 0.013 s
% 0.47/0.46 % (2572148)Peak memory usage: 11 MB
% 0.47/0.46 % (2572148)Instructions burned: 30 (million)
% 0.47/0.46 % (2572138)Instruction limit reached!
% 0.47/0.46 % (2572138)------------------------------
% 0.47/0.46 % (2572138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572138)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572138)Termination reason: Instruction limit
% 0.47/0.46 % (2572138)Termination phase: Property scanning
% 0.47/0.46 % (2572138)Time elapsed: 0.040 s
% 0.47/0.46 % (2572138)Peak memory usage: 11 MB
% 0.47/0.46 % (2572138)Instructions burned: 96 (million)
% 0.47/0.46 % (2572155)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2464871034:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.47/0.46 % (2572120) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2572111-2572120"...
% 0.47/0.46 % (2572120)...printing done.
% 0.47/0.46 % (2572156)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1383507465:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.47/0.46 % (2572158)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4290191357:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.47/0.46 % (2572157)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=869608168:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.47/0.46 % (2572157)Instruction limit reached!
% 0.47/0.46 % (2572157)------------------------------
% 0.47/0.46 % (2572157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (2572157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (2572157)CaDiCaL version: 2.1.3
% 0.47/0.46 % (2572157)Termination reason: Instruction limit
% 0.47/0.46 % (2572157)Termination phase: shuffling
% 0.47/0.46 % (2572157)Time elapsed: 0.002 s
% 0.47/0.46 % (2572157)Peak memory usage: 10 MB
% 0.47/0.46 % (2572157)Instructions burned: 3 (million)
% 0.47/0.46 % (2572120)Refutation found. Thanks to Tanya!
% 0.47/0.46 % SZS status Theorem for theBenchmark
% 0.47/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 1.26/0.46 % (2572120)------------------------------
% 1.26/0.46 % (2572120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.46 % (2572120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.46 % (2572120)CaDiCaL version: 2.1.3
% 1.26/0.46 % (2572120)Termination reason: Refutation
% 1.26/0.46 % (2572120)Time elapsed: 0.126 s
% 1.26/0.46 % (2572120)Peak memory usage: 20 MB
% 1.26/0.46 % (2572120)Instructions burned: 407 (million)
% 1.26/0.46 % (2572111)Success in time 0.18 s
% 1.26/0.46 % Vampire exiting
%------------------------------------------------------------------------------