%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU712^1 : 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 : n004.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 08:30:54 AM UTC 2026
% Result : Theorem 0.67s 0.45s
% Output : Refutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 29 unt; 0 typ; 10 def)
% Number of atoms : 4647 (1274 equ; 0 cnn)
% Maximal formula atoms : 230 ( 51 avg)
% Number of connectives : 2382 ( 98 ~; 85 |; 934 &; 324 @)
% ( 16 <=>; 925 =>; 0 <=; 0 <~>)
% Maximal formula depth : 236 ( 24 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 : 458 ( 455 usr; 267 con; 0-4 aty)
% Number of variables : 86 ( 0 sgn 68 !; 18 ?; 86 :)
% 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_269,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_270,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_271,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_272,type,
vOR: $o > $o > $o ).
thf(func_def_273,type,
vAND: $o > $o > $o ).
thf(func_def_274,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_275,type,
vNOT: $o > $o ).
thf(func_def_276,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_277,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_278,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_279,type,
vIMP: $o > $o > $o ).
thf(func_def_280,type,
sP0: $o ).
thf(func_def_281,type,
sP1: $i > $i > $o ).
thf(func_def_282,type,
sP2: $i > $o ).
thf(func_def_283,type,
sP3: $o ).
thf(func_def_312,type,
sK32: $i > $i > $o ).
thf(func_def_329,type,
sK49: $o ).
thf(func_def_337,type,
sK57: $o ).
thf(func_def_338,type,
sK58: $i > $o ).
thf(func_def_341,type,
sK61: $o ).
thf(func_def_349,type,
sK69: $i > ( $i > $o ) > $i ).
thf(func_def_350,type,
sK70: $i > $o ).
thf(func_def_357,type,
sK77: $o ).
thf(func_def_360,type,
sK80: $i > $i > $i ).
thf(func_def_361,type,
sK81: $i > ( $i > $i ) > $i > $i ).
thf(func_def_363,type,
sK83: $i > $i ).
thf(func_def_369,type,
sK89: $i > $i > $o ).
thf(func_def_371,type,
sK91: $i > $i ).
thf(func_def_372,type,
sK92: $i > $i ).
thf(func_def_373,type,
sK93: $i > ( $i > $i > $o ) > $i ).
thf(func_def_374,type,
sK94: $i > ( $i > $i > $o ) > $i ).
thf(func_def_375,type,
sK95: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_381,type,
sK101: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_382,type,
sK102: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_383,type,
sK103: $i > $o ).
thf(func_def_384,type,
sK104: $i > $o ).
thf(func_def_385,type,
sK105: $o ).
thf(func_def_392,type,
sK112: $i > ( $i > $i ) > $i > $i ).
thf(func_def_394,type,
sK114: $i > $i ).
thf(func_def_398,type,
sK118: $i > $i > $o ).
thf(func_def_413,type,
sK133: $i > $i > $o ).
thf(func_def_416,type,
sK136: $i > $i ).
thf(func_def_423,type,
sK143: $i > $o ).
thf(func_def_424,type,
sK144: ( $i > $o ) > $i ).
thf(func_def_428,type,
sK148: $i > $i > $i ).
thf(func_def_430,type,
sK150: $i > $i > $o ).
thf(func_def_438,type,
sK158: $i > $i > $i ).
thf(func_def_442,type,
sK162: ( $i > $o ) > $i ).
thf(func_def_443,type,
sK163: $i > $o ).
thf(func_def_444,type,
sK164: $i > $i ).
thf(func_def_450,type,
sK170: $i > $o ).
thf(func_def_453,type,
sK173: $i > $i > $i > $i > $i ).
thf(func_def_454,type,
sK174: $i > $i > $i > $i > $i ).
thf(func_def_461,type,
sK181: $i > $i > $o ).
thf(func_def_470,type,
sK190: $i > ( $i > $o ) > $i ).
thf(func_def_471,type,
sK191: $i > $o ).
thf(func_def_476,type,
sK196: $o ).
thf(func_def_483,type,
sK203: $o ).
thf(func_def_486,type,
sK206: $i > $o ).
thf(func_def_499,type,
sK219: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_500,type,
sK220: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_504,type,
sK224: $i > $o ).
thf(func_def_519,type,
sK239: $i > $i ).
thf(func_def_523,type,
sK243: $i > $i > ( $i > $i ) > $i ).
thf(func_def_525,type,
sK245: $i > $o ).
thf(func_def_534,type,
sK254: $i > $i > $i > $i > $i ).
thf(func_def_541,type,
sK261: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_542,type,
sK262: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_545,type,
sK265: $i > $o ).
thf(func_def_546,type,
sK266: $i > $o ).
thf(func_def_555,type,
sK275: $o ).
thf(func_def_559,type,
sK279: $i > $o ).
thf(func_def_578,type,
sK298: $i > $o ).
thf(func_def_584,type,
sK304: $o ).
thf(func_def_590,type,
sK310: $o ).
thf(func_def_594,type,
sK314: $o ).
thf(func_def_603,type,
sK323: $i > $i > $i ).
thf(func_def_613,type,
sK333: $i > $i > $i > $i > $i ).
thf(func_def_614,type,
sK334: $i > $i > $i > $i > $i ).
thf(func_def_615,type,
sK335: $i > $i > $i > $i > $i ).
thf(func_def_616,type,
sK336: $i > $i > $i > $i > $i ).
thf(func_def_623,type,
sK343: $i > $i > $o ).
thf(func_def_632,type,
sK352: $i > $i > $i ).
thf(func_def_640,type,
sK360: $i > $i ).
thf(func_def_641,type,
sK361: $i > $i > $i ).
thf(func_def_645,type,
sK365: $i > $o ).
thf(func_def_648,type,
sK368: $i > ( $i > $o ) > $i ).
thf(func_def_649,type,
sK369: $i > ( $i > $o ) > $i ).
thf(func_def_666,type,
sK386: $o ).
thf(func_def_667,type,
sK387: $i > $o ).
thf(func_def_668,type,
sK388: $i > $o ).
thf(func_def_669,type,
sK389: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_670,type,
sK390: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_676,type,
sK396: $i > $i ).
thf(func_def_678,type,
sK398: $i > $o ).
thf(func_def_686,type,
sK406: $i > $i ).
thf(func_def_687,type,
sK407: $i > $i ).
thf(func_def_688,type,
sK408: $i > $i ).
thf(func_def_689,type,
sK409: $i > $i ).
thf(func_def_690,type,
sK410: $i > $i ).
thf(func_def_691,type,
sK411: $i > $i > $i > $i ).
thf(func_def_692,type,
sK412: $i > $i ).
thf(func_def_693,type,
sK413: $i > $i ).
thf(func_def_694,type,
sK414: $i > $i ).
thf(func_def_695,type,
sK415: $i > $i ).
thf(func_def_696,type,
sK416: $i > $i > $i ).
thf(func_def_697,type,
sK417: $i > $i > $i ).
thf(func_def_698,type,
sK418: $i > $i > $i > $i ).
thf(func_def_699,type,
sK419: $i > $i > $i > $i ).
thf(func_def_700,type,
sK420: $i > $i > $i > $i ).
thf(func_def_701,type,
sK421: $i > $i > $i ).
thf(func_def_702,type,
sK422: $i > $i > $i ).
thf(func_def_703,type,
sK423: $i > $i > $i ).
thf(func_def_709,type,
sK429: $i > $i ).
thf(func_def_710,type,
sK430: ( $i > $i ) > $i > $i > $i ).
thf(func_def_718,type,
sK438: $i > $o ).
thf(func_def_724,type,
sK444: $i > $o ).
thf(func_def_726,type,
sK446: ( $i > $o ) > $i > $i ).
thf(func_def_729,type,
sK449: $i > $o ).
thf(func_def_730,type,
sK450: $o ).
thf(func_def_737,type,
sK457: ( $i > $o ) > $i > $i ).
thf(func_def_739,type,
sK459: $i > $o ).
thf(func_def_753,type,
sK473: $i > $i > $i > $i > $i ).
thf(func_def_761,type,
sK481: $i > ( $i > $o ) > $i ).
thf(func_def_762,type,
sK482: $i > $o ).
thf(func_def_766,type,
sK486: $i > $i ).
thf(func_def_767,type,
sK487: $i > $i ).
thf(func_def_773,type,
sK493: ( $i > $o ) > $i > $i ).
thf(func_def_775,type,
sK495: $i > $o ).
thf(func_def_782,type,
sK502: $i > $o ).
thf(func_def_784,type,
sK504: ( $i > $o ) > $i > $i ).
thf(func_def_789,type,
sK509: $o ).
thf(func_def_793,type,
sK513: $o ).
thf(func_def_797,type,
sK517: $i > $i ).
thf(func_def_799,type,
sK519: ( $i > $o ) > $i > $i ).
thf(func_def_800,type,
sK520: ( $i > $o ) > $i > $i ).
thf(func_def_802,type,
sK522: $i > $o ).
thf(func_def_862,type,
sK582: $i > $o ).
thf(func_def_865,type,
sK585: $i > $o ).
thf(func_def_867,type,
sK587: ( $i > $o ) > $i ).
thf(func_def_868,type,
sK588: ( $i > $o ) > $i ).
thf(func_def_871,type,
sK591: $i > $i > $i > $i ).
thf(func_def_872,type,
sK592: $i > $i > $i > $i ).
thf(func_def_886,type,
sK606: $i > $i > $i ).
thf(func_def_887,type,
sK607: $i > $i > $i ).
thf(func_def_888,type,
sK608: $i > ( $i > $o ) > $i ).
thf(func_def_889,type,
sK609: $i > $o ).
thf(func_def_896,type,
sK616: $i > $o ).
thf(func_def_898,type,
sK618: $i > $o ).
thf(func_def_900,type,
sK620: $i > ( $i > $o ) > $i ).
thf(func_def_905,type,
sK625: $i > $i > $i ).
thf(func_def_909,type,
sK629: $o ).
thf(func_def_914,type,
sK634: $o ).
thf(func_def_915,type,
sK635: $o > $i > $i > $i ).
thf(func_def_921,type,
sK641: $i > $i > ( $i > $i ) > $i ).
thf(func_def_922,type,
sK642: $i > $i ).
thf(func_def_938,type,
sK658: $i > $o ).
thf(func_def_939,type,
sK659: ( $i > $o ) > $i > $i > $i ).
thf(func_def_940,type,
sK660: ( $i > $o ) > $i ).
thf(func_def_941,type,
sK661: $i > $o ).
thf(func_def_942,type,
sK662: $i > $i ).
thf(func_def_945,type,
sK665: $i > $i > $o ).
thf(func_def_951,type,
sK671: $i > $o ).
thf(func_def_957,type,
sK677: $i > $i > $i ).
thf(func_def_958,type,
sK678: $i > $i ).
thf(func_def_961,type,
sK681: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_962,type,
sK682: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_966,type,
sK686: $i > $o ).
thf(func_def_976,type,
sK696: $i > $o ).
thf(func_def_983,type,
sK703: $i > $i > $i > $i > $i ).
thf(func_def_984,type,
sK704: ( $i > $i ) > $i > $i > $i ).
thf(func_def_987,type,
sK707: $i > $i ).
thf(f92,axiom,
( subset2powerset
= ( ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(f96,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(f98,axiom,
( powersetsubset
= ( ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(f233,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
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( powerset @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(f234,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
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( powerset @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f233]) ).
thf(f394,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
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( in @ ( powerset @ X0 ) @ ( powerset @ ( powerset @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f234]) ).
thf(f395,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 )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ( ( in @ ( powerset @ X0 ) @ ( powerset @ ( powerset @ X1 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f394]) ).
thf(f442,plain,
( subset2powerset
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[],[f92]) ).
thf(f443,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( subset2powerset = $true ) ),
inference(fool_elimination,[],[f442]) ).
thf(f456,plain,
( powersetsubset
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[],[f98]) ).
thf(f457,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetsubset = $true ) ),
inference(fool_elimination,[],[f456]) ).
thf(f588,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= powersetE1 ),
inference(rectify,[],[f96]) ).
thf(f589,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(fool_elimination,[],[f588]) ).
thf(f755,plain,
( ( powersetsubset = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f457]) ).
thf(f771,plain,
( ( subset2powerset = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f443]) ).
thf(f793,plain,
( ( powersetE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f589]) ).
thf(f843,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ ( powerset @ X0 ) @ ( powerset @ ( powerset @ X1 ) ) )
!= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $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,[],[f395]) ).
thf(f844,plain,
( ( omegaSAx = $true )
& ( upairequniteq = $true )
& ( dsetconstr__Cong = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetAx = $true )
& ( secondinupair = $true )
& ( setminusSubset2 = $true )
& ( funcGraphProp1 = $true )
& ( setext = $true )
& ( sepInPowerset = $true )
& ( binintersectER = $true )
& ( nonemptyI = $true )
& ( ex1E1 = $true )
& ( powersetAx = $true )
& ( setunionsingleton1 = $true )
& ( binunionRsub = $true )
& ( beta1 = $true )
& ( kpairiskpair = $true )
& ( cartprodfstpairEq = $true )
& ( notsubsetI = $true )
& ( symdiffIneg1 = $true )
& ( exu__Cong = $true )
& ( brelnall1 = $true )
& ( nonemptyI1 = $true )
& ( upairinpowunion = $true )
& ( setminusI = $true )
& ( symdiffE = $true )
& ( funcImageSingleton = $true )
& ( setunionsingleton = $true )
& ( emptyI = $true )
& ( kfstsingleton = $true )
& ( eta2 = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinAx = $true )
& ( cartprodmempair = $true )
& ( setadjoinE = $true )
& ( symdiffI2 = $true )
& ( binintersectSubset3 = $true )
& ( notdexE = $true )
& ( cartprodpairsurjEq = $true )
& ( brelnall2 = $true )
& ( eqbreln = $true )
& ( setukpairinjL = $true )
& ( setextAx = $true )
& ( subbreln = $true )
& ( bs114d = $true )
& ( emptysetsubset = $true )
& ( dpsetconstrSub = $true )
& ( iffalseProp2 = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectSubset4 = $true )
& ( setukpairinjR11 = $true )
& ( binunionEcases = $true )
& ( replAx = $true )
& ( ap2apEq1 = $true )
& ( powersetI1 = $true )
& ( powersetE = $true )
& ( emptysetE = $true )
& ( cartprodsndin = $true )
& ( iftrueProp2 = $true )
& ( sepSubset = $true )
& ( inPowerset = $true )
& ( upairsetE = $true )
& ( binintersectRsub = $true )
& ( binintersectSubset1 = $true )
& ( exuI1 = $true )
& ( kpairp = $true )
& ( cartprodpairin = $true )
& ( cartprodsndpairEq = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( lam2p = $true )
& ( upairsetIR = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( funcinfuncset = $true )
& ( setadjoinSub = $true )
& ( kpairsurjEq = $true )
& ( setukpairinjR2 = $true )
& ( singletonprop = $true )
& ( wellorderingAx = $true )
& ( cartprodpairmemER = $true )
& ( singletoninpowerset = $true )
& ( iffalse = $true )
& ( setunionE = $true )
& ( binintersectI = $true )
& ( binintersectSubset2 = $true )
& ( notinsingleton = $true )
& ( setadjoinSub2 = $true )
& ( eqinunit = $true )
& ( singletonsuniq = $true )
& ( notdallE = $true )
& ( beta2 = $true )
& ( emptyinunitempty = $true )
& ( emptyinPowerset = $true )
& ( emptyE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( omega0Ax = $true )
& ( binunionT_lem = $true )
& ( setukpairIR = $true )
& ( descrp = $true )
& ( nonemptyE1 = $true )
& ( ifp = $true )
& ( subsetTrans = $true )
& ( ap2p = $true )
& ( exuE3e = $true )
& ( upairset2E = $true )
& ( infuncsetfunc = $true )
& ( upairset2IR = $true )
& ( binunionLsub = $true )
& ( ksndsingleton = $true )
& ( setadjoin__Cong = $true )
& ( in__Cong = $true )
& ( subsetI1 = $true )
& ( ksndpairEq = $true )
& ( subsetemptysetimpeq = $true )
& ( uniqinunit = $true )
& ( exuE1 = $true )
& ( exuI3 = $true )
& ( upairsubunion = $true )
& ( exuE2 = $true )
& ( eqimpsubset2 = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL2 = $true )
& ( nonemptyImpWitness = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL1 = $true )
& ( symdiffIneg2 = $true )
& ( notequalI2 = $true )
& ( singletonsubset = $true )
& ( dpsetconstrERa = $true )
& ( disjointsetsI1 = $true )
& ( setunionE2 = $true )
& ( setminusILneg = $true )
& ( binintersectLsub = $true )
& ( subPowSU = $true )
& ( setunionsingleton2 = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ ( powerset @ X0 ) @ ( powerset @ ( powerset @ X1 ) ) )
!= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( iftrue = $true )
& ( dsetconstrEL = $true )
& ( iftrueorfalse = $true )
& ( setunionI = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( quantDeMorgan1 = $true )
& ( lamProp = $true )
& ( ex1I = $true )
& ( apProp = $true )
& ( cartprodpairmemEL = $true )
& ( app = $true )
& ( setminusEL = $true )
& ( eqimpsubset1 = $true )
& ( setadjoinIL = $true )
& ( funcGraphProp3 = $true )
& ( singletoninpowunion = $true )
& ( theeq = $true )
& ( subsetE2 = $true )
& ( notinemptyset = $true )
& ( ex1I2 = $true )
& ( ex1E2 = $true )
& ( prop2set2propI = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem1 = $true )
& ( kfstpairEq = $true )
& ( funcext2 = $true )
& ( powersetsubset = $true )
& ( setukpairinjL2 = $true )
& ( exuEu = $true )
& ( omegaIndAx = $true )
& ( setukpairIL = $true )
& ( inCongP = $true )
& ( setminusELneg = $true )
& ( subsetRefl = $true )
& ( lamp = $true )
& ( ifSingleton = $true )
& ( setminusIRneg = $true )
& ( powersetE1 = $true )
& ( setOfPairsIsBReln = $true )
& ( symdiffI1 = $true )
& ( binunionIL = $true )
& ( theprop = $true )
& ( exuI2 = $true )
& ( powersetI = $true )
& ( setadjoinIR = $true )
& ( dsetconstrER = $true )
& ( singletonsswitch = $true )
& ( eta1 = $true )
& ( setextsub = $true )
& ( emptysetimpfalse = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setukpairinjR12 = $true )
& ( omega__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( binunionE = $true )
& ( setukpairinjR1 = $true )
& ( iffalseProp1 = $true )
& ( ap2apEq2 = $true )
& ( subset2powerset = $true )
& ( descr__Cong = $true )
& ( vacuousDall = $true )
& ( lam2lamEq = $true )
& ( subsetI2 = $true )
& ( funcextLem = $true )
& ( upairsetIL = $true )
& ( ubforcartprodlem3 = $true )
& ( setukpairinjR = $true )
& ( setminusSubset1 = $true )
& ( funcext = $true )
& ( foundationAx = $true )
& ( funcGraphProp2 = $true )
& ( prop2setI = $true )
& ( funcGraphProp4 = $true )
& ( subsetE = $true )
& ( cartprodfstin = $true )
& ( setoftrueEq = $true )
& ( cartprodmempair1 = $true )
& ( setminusERneg = $true )
& ( binintersectEL = $true )
& ( setminusER = $true )
& ( setminusLsub = $true )
& ( binunionIR = $true )
& ( binintersectT_lem = $true )
& ( emptyset__Cong = $true )
& ( exuE3u = $true )
& ( setunionAx = $true )
& ( iftrueProp1 = $true ) ),
inference(flattening,[],[f843]) ).
thf(f997,plain,
( ( ( powersetE1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( powersetE1 != $true ) ) ),
inference(nnf_transformation,[],[f793]) ).
thf(f998,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) )
| ( powersetE1 != $true ) ) ),
inference(rectify,[],[f997]) ).
thf(f999,plain,
( ( ( powersetE1 = $true )
| ( ( $true
!= ( subset @ sK16 @ sK15 ) )
& ( ( in @ sK16 @ ( powerset @ sK15 ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) )
| ( powersetE1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X1,sK16)],[f998]) ).
thf(f1174,plain,
( ( ( subset2powerset = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( subset2powerset != $true ) ) ),
inference(nnf_transformation,[],[f771]) ).
thf(f1175,plain,
( ( ( subset2powerset = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ( subset2powerset != $true ) ) ),
inference(rectify,[],[f1174]) ).
thf(f1176,plain,
( ( ( subset2powerset = $true )
| ( ( $true
!= ( in @ sK205 @ ( powerset @ sK204 ) ) )
& ( ( subset @ sK205 @ sK204 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ( subset2powerset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204,sK205]),skolemize(X0,sK204),skolemize(X1,sK205)],[f1175]) ).
thf(f1213,plain,
( ( omegaSAx = $true )
& ( upairequniteq = $true )
& ( dsetconstr__Cong = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetAx = $true )
& ( secondinupair = $true )
& ( setminusSubset2 = $true )
& ( funcGraphProp1 = $true )
& ( setext = $true )
& ( sepInPowerset = $true )
& ( binintersectER = $true )
& ( nonemptyI = $true )
& ( ex1E1 = $true )
& ( powersetAx = $true )
& ( setunionsingleton1 = $true )
& ( binunionRsub = $true )
& ( beta1 = $true )
& ( kpairiskpair = $true )
& ( cartprodfstpairEq = $true )
& ( notsubsetI = $true )
& ( symdiffIneg1 = $true )
& ( exu__Cong = $true )
& ( brelnall1 = $true )
& ( nonemptyI1 = $true )
& ( upairinpowunion = $true )
& ( setminusI = $true )
& ( symdiffE = $true )
& ( funcImageSingleton = $true )
& ( setunionsingleton = $true )
& ( emptyI = $true )
& ( kfstsingleton = $true )
& ( eta2 = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinAx = $true )
& ( cartprodmempair = $true )
& ( setadjoinE = $true )
& ( symdiffI2 = $true )
& ( binintersectSubset3 = $true )
& ( notdexE = $true )
& ( cartprodpairsurjEq = $true )
& ( brelnall2 = $true )
& ( eqbreln = $true )
& ( setukpairinjL = $true )
& ( setextAx = $true )
& ( subbreln = $true )
& ( bs114d = $true )
& ( emptysetsubset = $true )
& ( dpsetconstrSub = $true )
& ( iffalseProp2 = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectSubset4 = $true )
& ( setukpairinjR11 = $true )
& ( binunionEcases = $true )
& ( replAx = $true )
& ( ap2apEq1 = $true )
& ( powersetI1 = $true )
& ( powersetE = $true )
& ( emptysetE = $true )
& ( cartprodsndin = $true )
& ( iftrueProp2 = $true )
& ( sepSubset = $true )
& ( inPowerset = $true )
& ( upairsetE = $true )
& ( binintersectRsub = $true )
& ( binintersectSubset1 = $true )
& ( exuI1 = $true )
& ( kpairp = $true )
& ( cartprodpairin = $true )
& ( cartprodsndpairEq = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( lam2p = $true )
& ( upairsetIR = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( funcinfuncset = $true )
& ( setadjoinSub = $true )
& ( kpairsurjEq = $true )
& ( setukpairinjR2 = $true )
& ( singletonprop = $true )
& ( wellorderingAx = $true )
& ( cartprodpairmemER = $true )
& ( singletoninpowerset = $true )
& ( iffalse = $true )
& ( setunionE = $true )
& ( binintersectI = $true )
& ( binintersectSubset2 = $true )
& ( notinsingleton = $true )
& ( setadjoinSub2 = $true )
& ( eqinunit = $true )
& ( singletonsuniq = $true )
& ( notdallE = $true )
& ( beta2 = $true )
& ( emptyinunitempty = $true )
& ( emptyinPowerset = $true )
& ( emptyE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( omega0Ax = $true )
& ( binunionT_lem = $true )
& ( setukpairIR = $true )
& ( descrp = $true )
& ( nonemptyE1 = $true )
& ( ifp = $true )
& ( subsetTrans = $true )
& ( ap2p = $true )
& ( exuE3e = $true )
& ( upairset2E = $true )
& ( infuncsetfunc = $true )
& ( upairset2IR = $true )
& ( binunionLsub = $true )
& ( ksndsingleton = $true )
& ( setadjoin__Cong = $true )
& ( in__Cong = $true )
& ( subsetI1 = $true )
& ( ksndpairEq = $true )
& ( subsetemptysetimpeq = $true )
& ( uniqinunit = $true )
& ( exuE1 = $true )
& ( exuI3 = $true )
& ( upairsubunion = $true )
& ( exuE2 = $true )
& ( eqimpsubset2 = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL2 = $true )
& ( nonemptyImpWitness = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL1 = $true )
& ( symdiffIneg2 = $true )
& ( notequalI2 = $true )
& ( singletonsubset = $true )
& ( dpsetconstrERa = $true )
& ( disjointsetsI1 = $true )
& ( setunionE2 = $true )
& ( setminusILneg = $true )
& ( binintersectLsub = $true )
& ( subPowSU = $true )
& ( setunionsingleton2 = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ ( powerset @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( iftrue = $true )
& ( dsetconstrEL = $true )
& ( iftrueorfalse = $true )
& ( setunionI = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( quantDeMorgan1 = $true )
& ( lamProp = $true )
& ( ex1I = $true )
& ( apProp = $true )
& ( cartprodpairmemEL = $true )
& ( app = $true )
& ( setminusEL = $true )
& ( eqimpsubset1 = $true )
& ( setadjoinIL = $true )
& ( funcGraphProp3 = $true )
& ( singletoninpowunion = $true )
& ( theeq = $true )
& ( subsetE2 = $true )
& ( notinemptyset = $true )
& ( ex1I2 = $true )
& ( ex1E2 = $true )
& ( prop2set2propI = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem1 = $true )
& ( kfstpairEq = $true )
& ( funcext2 = $true )
& ( powersetsubset = $true )
& ( setukpairinjL2 = $true )
& ( exuEu = $true )
& ( omegaIndAx = $true )
& ( setukpairIL = $true )
& ( inCongP = $true )
& ( setminusELneg = $true )
& ( subsetRefl = $true )
& ( lamp = $true )
& ( ifSingleton = $true )
& ( setminusIRneg = $true )
& ( powersetE1 = $true )
& ( setOfPairsIsBReln = $true )
& ( symdiffI1 = $true )
& ( binunionIL = $true )
& ( theprop = $true )
& ( exuI2 = $true )
& ( powersetI = $true )
& ( setadjoinIR = $true )
& ( dsetconstrER = $true )
& ( singletonsswitch = $true )
& ( eta1 = $true )
& ( setextsub = $true )
& ( emptysetimpfalse = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setukpairinjR12 = $true )
& ( omega__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( binunionE = $true )
& ( setukpairinjR1 = $true )
& ( iffalseProp1 = $true )
& ( ap2apEq2 = $true )
& ( subset2powerset = $true )
& ( descr__Cong = $true )
& ( vacuousDall = $true )
& ( lam2lamEq = $true )
& ( subsetI2 = $true )
& ( funcextLem = $true )
& ( upairsetIL = $true )
& ( ubforcartprodlem3 = $true )
& ( setukpairinjR = $true )
& ( setminusSubset1 = $true )
& ( funcext = $true )
& ( foundationAx = $true )
& ( funcGraphProp2 = $true )
& ( prop2setI = $true )
& ( funcGraphProp4 = $true )
& ( subsetE = $true )
& ( cartprodfstin = $true )
& ( setoftrueEq = $true )
& ( cartprodmempair1 = $true )
& ( setminusERneg = $true )
& ( binintersectEL = $true )
& ( setminusER = $true )
& ( setminusLsub = $true )
& ( binunionIR = $true )
& ( binintersectT_lem = $true )
& ( emptyset__Cong = $true )
& ( exuE3u = $true )
& ( setunionAx = $true )
& ( iftrueProp1 = $true ) ),
inference(rectify,[],[f844]) ).
thf(f1214,plain,
( ( omegaSAx = $true )
& ( upairequniteq = $true )
& ( dsetconstr__Cong = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetAx = $true )
& ( secondinupair = $true )
& ( setminusSubset2 = $true )
& ( funcGraphProp1 = $true )
& ( setext = $true )
& ( sepInPowerset = $true )
& ( binintersectER = $true )
& ( nonemptyI = $true )
& ( ex1E1 = $true )
& ( powersetAx = $true )
& ( setunionsingleton1 = $true )
& ( binunionRsub = $true )
& ( beta1 = $true )
& ( kpairiskpair = $true )
& ( cartprodfstpairEq = $true )
& ( notsubsetI = $true )
& ( symdiffIneg1 = $true )
& ( exu__Cong = $true )
& ( brelnall1 = $true )
& ( nonemptyI1 = $true )
& ( upairinpowunion = $true )
& ( setminusI = $true )
& ( symdiffE = $true )
& ( funcImageSingleton = $true )
& ( setunionsingleton = $true )
& ( emptyI = $true )
& ( kfstsingleton = $true )
& ( eta2 = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinAx = $true )
& ( cartprodmempair = $true )
& ( setadjoinE = $true )
& ( symdiffI2 = $true )
& ( binintersectSubset3 = $true )
& ( notdexE = $true )
& ( cartprodpairsurjEq = $true )
& ( brelnall2 = $true )
& ( eqbreln = $true )
& ( setukpairinjL = $true )
& ( setextAx = $true )
& ( subbreln = $true )
& ( bs114d = $true )
& ( emptysetsubset = $true )
& ( dpsetconstrSub = $true )
& ( iffalseProp2 = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectSubset4 = $true )
& ( setukpairinjR11 = $true )
& ( binunionEcases = $true )
& ( replAx = $true )
& ( ap2apEq1 = $true )
& ( powersetI1 = $true )
& ( powersetE = $true )
& ( emptysetE = $true )
& ( cartprodsndin = $true )
& ( iftrueProp2 = $true )
& ( sepSubset = $true )
& ( inPowerset = $true )
& ( upairsetE = $true )
& ( binintersectRsub = $true )
& ( binintersectSubset1 = $true )
& ( exuI1 = $true )
& ( kpairp = $true )
& ( cartprodpairin = $true )
& ( cartprodsndpairEq = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( lam2p = $true )
& ( upairsetIR = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( funcinfuncset = $true )
& ( setadjoinSub = $true )
& ( kpairsurjEq = $true )
& ( setukpairinjR2 = $true )
& ( singletonprop = $true )
& ( wellorderingAx = $true )
& ( cartprodpairmemER = $true )
& ( singletoninpowerset = $true )
& ( iffalse = $true )
& ( setunionE = $true )
& ( binintersectI = $true )
& ( binintersectSubset2 = $true )
& ( notinsingleton = $true )
& ( setadjoinSub2 = $true )
& ( eqinunit = $true )
& ( singletonsuniq = $true )
& ( notdallE = $true )
& ( beta2 = $true )
& ( emptyinunitempty = $true )
& ( emptyinPowerset = $true )
& ( emptyE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( omega0Ax = $true )
& ( binunionT_lem = $true )
& ( setukpairIR = $true )
& ( descrp = $true )
& ( nonemptyE1 = $true )
& ( ifp = $true )
& ( subsetTrans = $true )
& ( ap2p = $true )
& ( exuE3e = $true )
& ( upairset2E = $true )
& ( infuncsetfunc = $true )
& ( upairset2IR = $true )
& ( binunionLsub = $true )
& ( ksndsingleton = $true )
& ( setadjoin__Cong = $true )
& ( in__Cong = $true )
& ( subsetI1 = $true )
& ( ksndpairEq = $true )
& ( subsetemptysetimpeq = $true )
& ( uniqinunit = $true )
& ( exuE1 = $true )
& ( exuI3 = $true )
& ( upairsubunion = $true )
& ( exuE2 = $true )
& ( eqimpsubset2 = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL2 = $true )
& ( nonemptyImpWitness = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL1 = $true )
& ( symdiffIneg2 = $true )
& ( notequalI2 = $true )
& ( singletonsubset = $true )
& ( dpsetconstrERa = $true )
& ( disjointsetsI1 = $true )
& ( setunionE2 = $true )
& ( setminusILneg = $true )
& ( binintersectLsub = $true )
& ( subPowSU = $true )
& ( setunionsingleton2 = $true )
& ( $true
!= ( in @ ( powerset @ sK249 ) @ ( powerset @ ( powerset @ sK248 ) ) ) )
& ( ( in @ sK249 @ ( powerset @ sK248 ) )
= $true )
& ( iftrue = $true )
& ( dsetconstrEL = $true )
& ( iftrueorfalse = $true )
& ( setunionI = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( quantDeMorgan1 = $true )
& ( lamProp = $true )
& ( ex1I = $true )
& ( apProp = $true )
& ( cartprodpairmemEL = $true )
& ( app = $true )
& ( setminusEL = $true )
& ( eqimpsubset1 = $true )
& ( setadjoinIL = $true )
& ( funcGraphProp3 = $true )
& ( singletoninpowunion = $true )
& ( theeq = $true )
& ( subsetE2 = $true )
& ( notinemptyset = $true )
& ( ex1I2 = $true )
& ( ex1E2 = $true )
& ( prop2set2propI = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem1 = $true )
& ( kfstpairEq = $true )
& ( funcext2 = $true )
& ( powersetsubset = $true )
& ( setukpairinjL2 = $true )
& ( exuEu = $true )
& ( omegaIndAx = $true )
& ( setukpairIL = $true )
& ( inCongP = $true )
& ( setminusELneg = $true )
& ( subsetRefl = $true )
& ( lamp = $true )
& ( ifSingleton = $true )
& ( setminusIRneg = $true )
& ( powersetE1 = $true )
& ( setOfPairsIsBReln = $true )
& ( symdiffI1 = $true )
& ( binunionIL = $true )
& ( theprop = $true )
& ( exuI2 = $true )
& ( powersetI = $true )
& ( setadjoinIR = $true )
& ( dsetconstrER = $true )
& ( singletonsswitch = $true )
& ( eta1 = $true )
& ( setextsub = $true )
& ( emptysetimpfalse = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setukpairinjR12 = $true )
& ( omega__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( binunionE = $true )
& ( setukpairinjR1 = $true )
& ( iffalseProp1 = $true )
& ( ap2apEq2 = $true )
& ( subset2powerset = $true )
& ( descr__Cong = $true )
& ( vacuousDall = $true )
& ( lam2lamEq = $true )
& ( subsetI2 = $true )
& ( funcextLem = $true )
& ( upairsetIL = $true )
& ( ubforcartprodlem3 = $true )
& ( setukpairinjR = $true )
& ( setminusSubset1 = $true )
& ( funcext = $true )
& ( foundationAx = $true )
& ( funcGraphProp2 = $true )
& ( prop2setI = $true )
& ( funcGraphProp4 = $true )
& ( subsetE = $true )
& ( cartprodfstin = $true )
& ( setoftrueEq = $true )
& ( cartprodmempair1 = $true )
& ( setminusERneg = $true )
& ( binintersectEL = $true )
& ( setminusER = $true )
& ( setminusLsub = $true )
& ( binunionIR = $true )
& ( binintersectT_lem = $true )
& ( emptyset__Cong = $true )
& ( exuE3u = $true )
& ( setunionAx = $true )
& ( iftrueProp1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248,sK249]),skolemize(X0,sK248),skolemize(X1,sK249)],[f1213]) ).
thf(f1257,plain,
( ( ( powersetsubset = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( powersetsubset != $true ) ) ),
inference(nnf_transformation,[],[f755]) ).
thf(f1258,plain,
( ( ( powersetsubset = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ ( powerset @ X3 ) @ ( powerset @ X2 ) )
= $true )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ( powersetsubset != $true ) ) ),
inference(rectify,[],[f1257]) ).
thf(f1259,plain,
( ( ( powersetsubset = $true )
| ( ( ( subset @ ( powerset @ sK296 ) @ ( powerset @ sK295 ) )
!= $true )
& ( ( subset @ sK296 @ sK295 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ ( powerset @ X3 ) @ ( powerset @ X2 ) )
= $true )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ( powersetsubset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK295,sK296]),skolemize(X0,sK295),skolemize(X1,sK296)],[f1258]) ).
thf(f1684,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( powersetE1 != $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(cnf_transformation,[],[f999]) ).
thf(f1913,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
!= $true )
| ( subset2powerset != $true )
| ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(cnf_transformation,[],[f1176]) ).
thf(f1998,plain,
subset2powerset = $true,
inference(cnf_transformation,[],[f1214]) ).
thf(f2020,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f1214]) ).
thf(f2031,plain,
powersetsubset = $true,
inference(cnf_transformation,[],[f1214]) ).
thf(f2059,plain,
( ( in @ sK249 @ ( powerset @ sK248 ) )
= $true ),
inference(cnf_transformation,[],[f1214]) ).
thf(f2060,plain,
( $true
!= ( in @ ( powerset @ sK249 ) @ ( powerset @ ( powerset @ sK248 ) ) ) ),
inference(cnf_transformation,[],[f1214]) ).
thf(f2254,plain,
! [X2: $i,X3: $i] :
( ( powersetsubset != $true )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( ( subset @ ( powerset @ X3 ) @ ( powerset @ X2 ) )
= $true ) ),
inference(cnf_transformation,[],[f1259]) ).
thf(f3336,definition,
( spl711_64
<=> ( powersetE1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl711_64])],[avatar_definition]) ).
thf(f3339,plain,
spl711_64,
inference(avatar_split_clause,[],[f2020,f3336]) ).
thf(f3422,definition,
( spl711_84
<=> ( powersetsubset = $true ) ),
introduced(definition,[new_symbols(definition,[spl711_84])],[avatar_definition]) ).
thf(f3426,definition,
( spl711_85
<=> ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
!= $true )
| ( ( subset @ ( powerset @ X3 ) @ ( powerset @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl711_85])],[avatar_definition]) ).
thf(f3427,plain,
( ! [X2: $i,X3: $i] :
( ( ( subset @ ( powerset @ X3 ) @ ( powerset @ X2 ) )
= $true )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ~ spl711_85 ),
inference(avatar_component_clause,[],[f3426]) ).
thf(f3428,plain,
( ~ spl711_84
| spl711_85 ),
inference(avatar_split_clause,[],[f2254,f3426,f3422]) ).
thf(f5158,definition,
( spl711_467
<=> ( subset2powerset = $true ) ),
introduced(definition,[new_symbols(definition,[spl711_467])],[avatar_definition]) ).
thf(f5840,definition,
( spl711_612
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl711_612])],[avatar_definition]) ).
thf(f5841,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ~ spl711_612 ),
inference(avatar_component_clause,[],[f5840]) ).
thf(f6259,definition,
( spl711_700
<=> ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl711_700])],[avatar_definition]) ).
thf(f6260,plain,
( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( subset @ X3 @ X2 )
= $true ) )
| ~ spl711_700 ),
inference(avatar_component_clause,[],[f6259]) ).
thf(f6261,plain,
( spl711_700
| ~ spl711_64 ),
inference(avatar_split_clause,[],[f1684,f3336,f6259]) ).
thf(f6591,plain,
( spl711_612
| ~ spl711_467 ),
inference(avatar_split_clause,[],[f1913,f5158,f5840]) ).
thf(f7002,definition,
( spl711_857
<=> ( ( in @ sK249 @ ( powerset @ sK248 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl711_857])],[avatar_definition]) ).
thf(f7004,plain,
( ( ( in @ sK249 @ ( powerset @ sK248 ) )
= $true )
| ~ spl711_857 ),
inference(avatar_component_clause,[],[f7002]) ).
thf(f7005,plain,
spl711_857,
inference(avatar_split_clause,[],[f2059,f7002]) ).
thf(f7063,definition,
( spl711_869
<=> ( $true
= ( in @ ( powerset @ sK249 ) @ ( powerset @ ( powerset @ sK248 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl711_869])],[avatar_definition]) ).
thf(f7065,plain,
( ( $true
!= ( in @ ( powerset @ sK249 ) @ ( powerset @ ( powerset @ sK248 ) ) ) )
| spl711_869 ),
inference(avatar_component_clause,[],[f7063]) ).
thf(f7066,plain,
~ spl711_869,
inference(avatar_split_clause,[],[f2060,f7063]) ).
thf(f7100,plain,
spl711_467,
inference(avatar_split_clause,[],[f1998,f5158]) ).
thf(f8179,plain,
spl711_84,
inference(avatar_split_clause,[],[f2031,f3422]) ).
thf(f8658,plain,
( ( $true != $true )
| ( $true
!= ( subset @ ( powerset @ sK249 ) @ ( powerset @ sK248 ) ) )
| ~ spl711_612
| spl711_869 ),
inference(superposition,[],[f7065,f5841]) ).
thf(f8661,plain,
( ( $true
!= ( subset @ ( powerset @ sK249 ) @ ( powerset @ sK248 ) ) )
| ~ spl711_612
| spl711_869 ),
inference(trivial_inequality_removal,[],[f8658]) ).
thf(f8667,definition,
( spl711_1113
<=> ( $true
= ( subset @ ( powerset @ sK249 ) @ ( powerset @ sK248 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl711_1113])],[avatar_definition]) ).
thf(f8669,plain,
( ( $true
!= ( subset @ ( powerset @ sK249 ) @ ( powerset @ sK248 ) ) )
| spl711_1113 ),
inference(avatar_component_clause,[],[f8667]) ).
thf(f8670,plain,
( ~ spl711_1113
| ~ spl711_612
| spl711_869 ),
inference(avatar_split_clause,[],[f8661,f7063,f5840,f8667]) ).
thf(f8692,plain,
( ( $true
= ( subset @ sK249 @ sK248 ) )
| ( $true != $true )
| ~ spl711_700
| ~ spl711_857 ),
inference(superposition,[],[f6260,f7004]) ).
thf(f8703,plain,
( ( $true
= ( subset @ sK249 @ sK248 ) )
| ~ spl711_700
| ~ spl711_857 ),
inference(trivial_inequality_removal,[],[f8692]) ).
thf(f8710,definition,
( spl711_1117
<=> ( $true
= ( subset @ sK249 @ sK248 ) ) ),
introduced(definition,[new_symbols(definition,[spl711_1117])],[avatar_definition]) ).
thf(f8712,plain,
( ( $true
= ( subset @ sK249 @ sK248 ) )
| ~ spl711_1117 ),
inference(avatar_component_clause,[],[f8710]) ).
thf(f8713,plain,
( spl711_1117
| ~ spl711_700
| ~ spl711_857 ),
inference(avatar_split_clause,[],[f8703,f7002,f6259,f8710]) ).
thf(f8817,plain,
( ( $true != $true )
| ( $true
!= ( subset @ sK249 @ sK248 ) )
| ~ spl711_85
| spl711_1113 ),
inference(superposition,[],[f8669,f3427]) ).
thf(f8820,plain,
( ( $true
!= ( subset @ sK249 @ sK248 ) )
| ~ spl711_85
| spl711_1113 ),
inference(trivial_inequality_removal,[],[f8817]) ).
thf(f8821,plain,
( $false
| ~ spl711_85
| spl711_1113
| ~ spl711_1117 ),
inference(forward_subsumption_resolution,[],[f8820,f8712]) ).
thf(f8822,plain,
( ~ spl711_85
| spl711_1113
| ~ spl711_1117 ),
inference(avatar_contradiction_clause,[],[f8821]) ).
cnf(s40,plain,
spl711_64,
inference(sat_conversion,[],[f3339]) ).
cnf(s52,plain,
( ~ spl711_84
| spl711_85 ),
inference(sat_conversion,[],[f3428]) ).
cnf(s608,plain,
( ~ spl711_64
| spl711_700 ),
inference(sat_conversion,[],[f6261]) ).
cnf(s688,plain,
( ~ spl711_467
| spl711_612 ),
inference(sat_conversion,[],[f6591]) ).
cnf(s793,plain,
spl711_857,
inference(sat_conversion,[],[f7005]) ).
cnf(s810,plain,
~ spl711_869,
inference(sat_conversion,[],[f7066]) ).
cnf(s821,plain,
spl711_467,
inference(sat_conversion,[],[f7100]) ).
cnf(s1110,plain,
spl711_84,
inference(sat_conversion,[],[f8179]) ).
cnf(s1138,plain,
( ~ spl711_612
| spl711_869
| ~ spl711_1113 ),
inference(sat_conversion,[],[f8670]) ).
cnf(s1142,plain,
( ~ spl711_700
| ~ spl711_857
| spl711_1117 ),
inference(sat_conversion,[],[f8713]) ).
cnf(s1146,plain,
( ~ spl711_85
| spl711_1113
| ~ spl711_1117 ),
inference(sat_conversion,[],[f8822]) ).
cnf(s1190,plain,
spl711_612,
inference(rat,[],[s688,s821]) ).
cnf(s1191,plain,
~ spl711_1113,
inference(rat,[],[s1138,s810,s1190]) ).
cnf(s1418,plain,
spl711_85,
inference(rat,[],[s52,s1110]) ).
cnf(s1419,plain,
~ spl711_1117,
inference(rat,[],[s1146,s1191,s1418]) ).
cnf(s1420,plain,
~ spl711_700,
inference(rat,[],[s1142,s793,s1419]) ).
cnf(s1421,plain,
~ spl711_64,
inference(rat,[],[s608,s1420]) ).
cnf(s1430,plain,
$false,
inference(rat,[],[s40,s1421]) ).
thf(f8823,plain,
$false,
inference(avatar_sat_refutation,[],[s1430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU712^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:13:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.25/0.31 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
% 0.67/0.45 % (1346918)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.67/0.45 % (1346932)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=3476889048: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)
% 0.67/0.45 % (1346935)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.67/0.45 % (1346935)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
% 0.67/0.45 % (1346929)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2210185672:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.67/0.45 % (1346931)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1738683224:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.67/0.45 % (1346933)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=469106385:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.67/0.45 % (1346935)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=1063323768:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.67/0.45 % (1346934)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1010730433:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.67/0.45 % (1346931)Instruction limit reached!
% 0.67/0.45 % (1346931)------------------------------
% 0.67/0.45 % (1346931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346931)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346931)Termination reason: Instruction limit
% 0.67/0.45 % (1346931)Termination phase: shuffling
% 0.67/0.45 % (1346931)Time elapsed: 0.003 s
% 0.67/0.45 % (1346931)Peak memory usage: 10 MB
% 0.67/0.45 % (1346931)Instructions burned: 7 (million)
% 0.67/0.45 % (1346930)lrs+10_16_si=on:nwc=1.5:random_seed=838135531:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.67/0.45 % (1346933)Instruction limit reached!
% 0.67/0.45 % (1346933)------------------------------
% 0.67/0.45 % (1346933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346933)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346933)Termination reason: Instruction limit
% 0.67/0.45 % (1346933)Termination phase: Property scanning
% 0.67/0.45 % (1346933)Time elapsed: 0.012 s
% 0.67/0.45 % (1346933)Peak memory usage: 10 MB
% 0.67/0.45 % (1346933)Instructions burned: 26 (million)
% 0.67/0.45 % (1346930)Instruction limit reached!
% 0.67/0.45 % (1346930)------------------------------
% 0.67/0.45 % (1346930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346930)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346930)Termination reason: Instruction limit
% 0.67/0.45 % (1346930)Termination phase: shuffling
% 0.67/0.45 % (1346930)Time elapsed: 0.016 s
% 0.67/0.45 % (1346930)Peak memory usage: 10 MB
% 0.67/0.45 % (1346930)Instructions burned: 20 (million)
% 0.67/0.45 % (1346944)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2741543177:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.67/0.45 % (1346944)Instruction limit reached!
% 0.67/0.45 % (1346944)------------------------------
% 0.67/0.45 % (1346944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346944)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346944)Termination reason: Instruction limit
% 0.67/0.45 % (1346944)Termination phase: shuffling
% 0.67/0.45 % (1346944)Time elapsed: 0.003 s
% 0.67/0.45 % (1346944)Peak memory usage: 10 MB
% 0.67/0.45 % (1346944)Instructions burned: 5 (million)
% 0.67/0.45 % (1346934)Instruction limit reached!
% 0.67/0.45 % (1346934)------------------------------
% 0.67/0.45 % (1346934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346934)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346934)Termination reason: Instruction limit
% 0.67/0.45 % (1346934)Termination phase: Preprocessing 3
% 0.67/0.45 % (1346942)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3697981112:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.67/0.45 % (1346934)Time elapsed: 0.034 s
% 0.67/0.45 % (1346934)Peak memory usage: 12 MB
% 0.67/0.45 % (1346934)Instructions burned: 75 (million)
% 0.67/0.45 % (1346942)Instruction limit reached!
% 0.67/0.45 % (1346942)------------------------------
% 0.67/0.45 % (1346942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346942)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346942)Termination reason: Instruction limit
% 0.67/0.45 % (1346942)Termination phase: shuffling
% 0.67/0.45 % (1346942)Time elapsed: 0.002 s
% 0.67/0.45 % (1346942)Peak memory usage: 10 MB
% 0.67/0.45 % (1346942)Instructions burned: 3 (million)
% 0.67/0.45 % (1346929)Instruction limit reached!
% 0.67/0.45 % (1346929)------------------------------
% 0.67/0.45 % (1346929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346929)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346929)Termination reason: Instruction limit
% 0.67/0.45 % (1346929)Termination phase: Property scanning
% 0.67/0.45 % (1346929)Time elapsed: 0.041 s
% 0.67/0.45 % (1346929)Peak memory usage: 13 MB
% 0.67/0.45 % (1346929)Instructions burned: 89 (million)
% 0.67/0.45 % (1346949)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
% 0.67/0.45 % (1346949)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.45 % (1346945)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.45 % (1346949)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2935930523:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.67/0.45 % (1346950)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=2124249937:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.67/0.45 % (1346951)lrs+10_1_si=on:cs=on:random_seed=16821063:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.67/0.45 % (1346945)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1705658654:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.67/0.45 % (1346951)Instruction limit reached!
% 0.67/0.45 % (1346951)------------------------------
% 0.67/0.45 % (1346951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346951)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346951)Termination reason: Instruction limit
% 0.67/0.45 % (1346951)Termination phase: shuffling
% 0.67/0.45 % (1346951)Time elapsed: 0.004 s
% 0.67/0.45 % (1346951)Peak memory usage: 10 MB
% 0.67/0.45 % (1346951)Instructions burned: 8 (million)
% 0.67/0.45 % (1346935)Instruction limit reached!
% 0.67/0.45 % (1346935)------------------------------
% 0.67/0.45 % (1346935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346935)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346935)Termination reason: Instruction limit
% 0.67/0.45 % (1346935)Termination phase: Saturation
% 0.67/0.45 % (1346935)Time elapsed: 0.067 s
% 0.67/0.45 % (1346935)Peak memory usage: 14 MB
% 0.67/0.45 % (1346935)Instructions burned: 158 (million)
% 0.67/0.45 % (1346947)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=943420961:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.67/0.45 % (1346945)Instruction limit reached!
% 0.67/0.45 % (1346945)------------------------------
% 0.67/0.45 % (1346945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346945)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346945)Termination reason: Instruction limit
% 0.67/0.45 % (1346945)Termination phase: shuffling
% 0.67/0.45 % (1346945)Time elapsed: 0.007 s
% 0.67/0.45 % (1346945)Peak memory usage: 10 MB
% 0.67/0.45 % (1346945)Instructions burned: 8 (million)
% 0.67/0.45 % (1346949)Instruction limit reached!
% 0.67/0.45 % (1346949)------------------------------
% 0.67/0.45 % (1346949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346949)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346949)Termination reason: Instruction limit
% 0.67/0.45 % (1346949)Termination phase: shuffling
% 0.67/0.45 % (1346949)Time elapsed: 0.013 s
% 0.67/0.45 % (1346949)Peak memory usage: 10 MB
% 0.67/0.45 % (1346949)Instructions burned: 29 (million)
% 0.67/0.45 % (1346932) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1346918-1346932"...
% 0.67/0.45 % (1346947)Instruction limit reached!
% 0.67/0.45 % (1346947)------------------------------
% 0.67/0.45 % (1346947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346947)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346947)Termination reason: Instruction limit
% 0.67/0.45 % (1346947)Termination phase: shuffling
% 0.67/0.45 % (1346947)Time elapsed: 0.006 s
% 0.67/0.45 % (1346947)Peak memory usage: 10 MB
% 0.67/0.45 % (1346947)Instructions burned: 13 (million)
% 0.67/0.45 % (1346932)...printing done.
% 0.67/0.45 % (1346932)Refutation found. Thanks to Tanya!
% 0.67/0.45 % SZS status Theorem for theBenchmark
% 0.67/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.67/0.45 % (1346932)------------------------------
% 0.67/0.45 % (1346932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.45 % (1346932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.45 % (1346932)CaDiCaL version: 2.1.3
% 0.67/0.45 % (1346932)Termination reason: Refutation
% 0.67/0.45 % (1346932)Time elapsed: 0.085 s
% 0.67/0.45 % (1346932)Peak memory usage: 19 MB
% 0.67/0.45 % (1346932)Instructions burned: 320 (million)
% 0.67/0.45 % (1346918)Success in time 0.127 s
% 0.67/0.45 % Vampire exiting
%------------------------------------------------------------------------------