%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU719^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:30:56 AM UTC 2026
% Result : Theorem 0.74s 0.44s
% Output : Refutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 4513 (1242 equ; 0 cnn)
% Maximal formula atoms : 239 ( 102 avg)
% Number of connectives : 2199 ( 53 ~; 31 |; 720 &; 194 @)
% ( 7 <=>;1194 =>; 0 <=; 0 <~>)
% Maximal formula depth : 247 ( 47 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 : 461 ( 458 usr; 266 con; 0-4 aty)
% Number of variables : 60 ( 0 sgn 48 !; 12 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_276,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_277,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_278,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_279,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_280,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_281,type,
vOR: $o > $o > $o ).
thf(func_def_282,type,
vAND: $o > $o > $o ).
thf(func_def_283,type,
vNOT: $o > $o ).
thf(func_def_284,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_285,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_286,type,
vIMP: $o > $o > $o ).
thf(func_def_287,type,
sP0: $o ).
thf(func_def_288,type,
sP1: $i > $i > $o ).
thf(func_def_289,type,
sP2: $i > $o ).
thf(func_def_290,type,
sP3: $o ).
thf(func_def_304,type,
sK17: $i > $i > $i ).
thf(func_def_305,type,
sK18: $i > $i > $i ).
thf(func_def_308,type,
sK21: $i > $i > $i > $i ).
thf(func_def_312,type,
sK25: $i > $i > $i > $i > $i ).
thf(func_def_327,type,
sK40: ( $i > $i ) > $i > $i > $i ).
thf(func_def_330,type,
sK43: $i > $i ).
thf(func_def_331,type,
sK44: $i > $i > $i ).
thf(func_def_339,type,
sK52: $i > $i > $i > $i ).
thf(func_def_343,type,
sK56: $i > $i > $i > $i ).
thf(func_def_344,type,
sK57: $i > $i > $i > $i ).
thf(func_def_349,type,
sK62: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_350,type,
sK63: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_354,type,
sK67: $i > $o ).
thf(func_def_356,type,
sK69: $i > $i > $i ).
thf(func_def_362,type,
sK75: $i > $i > ( $i > $i ) > $i ).
thf(func_def_363,type,
sK76: $i > $i ).
thf(func_def_370,type,
sK83: $i > $i > $i > $i > $i ).
thf(func_def_371,type,
sK84: $i > $i > $i > $i > $i ).
thf(func_def_372,type,
sK85: $i > $i > $i > $i > $i ).
thf(func_def_373,type,
sK86: $i > $i > $i > $i > $i ).
thf(func_def_377,type,
sK90: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_378,type,
sK91: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_379,type,
sK92: $i > $o ).
thf(func_def_380,type,
sK93: $i > $o ).
thf(func_def_391,type,
sK104: $i > $o ).
thf(func_def_400,type,
sK113: $i > ( $i > $o ) > $i ).
thf(func_def_401,type,
sK114: $i > $o ).
thf(func_def_413,type,
sK126: $i > $o ).
thf(func_def_414,type,
sK127: ( $i > $o ) > $i > $i ).
thf(func_def_415,type,
sK128: $i > $i > $i ).
thf(func_def_419,type,
sK132: $i > $o ).
thf(func_def_422,type,
sK135: $o ).
thf(func_def_430,type,
sK143: $o ).
thf(func_def_449,type,
sK162: $i > $i ).
thf(func_def_451,type,
sK164: $i > $i ).
thf(func_def_462,type,
sK175: $o ).
thf(func_def_492,type,
sK205: $i > $i ).
thf(func_def_506,type,
sK219: $i > $o ).
thf(func_def_507,type,
sK220: ( $i > $o ) > $i ).
thf(func_def_508,type,
sK221: $i > $o ).
thf(func_def_516,type,
sK229: $o ).
thf(func_def_528,type,
sK241: $o ).
thf(func_def_532,type,
sK245: $i > $i > $o ).
thf(func_def_543,type,
sK256: $i > $o ).
thf(func_def_545,type,
sK258: $i > ( $i > $o ) > $i ).
thf(func_def_546,type,
sK259: $i > $i ).
thf(func_def_554,type,
sK267: $i > ( $i > $o ) > $i ).
thf(func_def_555,type,
sK268: $i > $o ).
thf(func_def_559,type,
sK272: $o ).
thf(func_def_565,type,
sK278: $i > $i > $i > $i > $i ).
thf(func_def_570,type,
sK283: $i > ( $i > $o ) > $i ).
thf(func_def_571,type,
sK284: $i > ( $i > $o ) > $i ).
thf(func_def_572,type,
sK285: $i > $o ).
thf(func_def_576,type,
sK289: $i > $i > $o ).
thf(func_def_590,type,
sK303: $o ).
thf(func_def_591,type,
sK304: $i > ( $i > $i ) > $i > $i ).
thf(func_def_593,type,
sK306: $i > $i ).
thf(func_def_596,type,
sK309: ( $i > $i ) > $i > $i > $i ).
thf(func_def_599,type,
sK312: $i > $i ).
thf(func_def_601,type,
sK314: $i > $i > ( $i > $o ) > $i ).
thf(func_def_602,type,
sK315: $i > $o ).
thf(func_def_611,type,
sK324: $i > $i > $i > $i > $i ).
thf(func_def_612,type,
sK325: $i > $i > $i ).
thf(func_def_618,type,
sK331: $i > $i > $i ).
thf(func_def_623,type,
sK336: $i > $i > $o ).
thf(func_def_629,type,
sK342: $i > $i > $i ).
thf(func_def_630,type,
sK343: $i > $i > $i ).
thf(func_def_633,type,
sK346: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_634,type,
sK347: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_638,type,
sK351: $i > $o ).
thf(func_def_647,type,
sK360: $i > $i ).
thf(func_def_658,type,
sK371: $o ).
thf(func_def_662,type,
sK375: $i > $o ).
thf(func_def_665,type,
sK378: $i > ( $i > $o ) > $i ).
thf(func_def_670,type,
sK383: $o ).
thf(func_def_671,type,
sK384: $i > $o ).
thf(func_def_674,type,
sK387: $i > ( $i > $o ) > $i ).
thf(func_def_675,type,
sK388: $i > ( $i > $o ) > $i ).
thf(func_def_676,type,
sK389: $i > $i > $i ).
thf(func_def_683,type,
sK396: $i > $i > $o ).
thf(func_def_686,type,
sK399: $i > $o ).
thf(func_def_690,type,
sK403: $o ).
thf(func_def_691,type,
sK404: ( $i > $i ) > $i > $i > $i ).
thf(func_def_694,type,
sK407: $i > $i ).
thf(func_def_740,type,
sK453: $o ).
thf(func_def_749,type,
sK462: $i > $o ).
thf(func_def_756,type,
sK469: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_757,type,
sK470: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_758,type,
sK471: $i > $o ).
thf(func_def_759,type,
sK472: $i > $o ).
thf(func_def_761,type,
sK474: $i > $o ).
thf(func_def_763,type,
sK476: ( $i > $o ) > $i > $i ).
thf(func_def_766,type,
sK479: $i > $i ).
thf(func_def_778,type,
sK491: $i > $i ).
thf(func_def_779,type,
sK492: $i > ( $i > $i > $o ) > $i ).
thf(func_def_780,type,
sK493: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_781,type,
sK494: $i > ( $i > $i > $o ) > $i ).
thf(func_def_782,type,
sK495: $i > $i > $o ).
thf(func_def_784,type,
sK497: $i > $i ).
thf(func_def_785,type,
sK498: $i > $i ).
thf(func_def_792,type,
sK505: $i > $o ).
thf(func_def_794,type,
sK507: $i > $o ).
thf(func_def_797,type,
sK510: $i > $i > $i > $i > $i ).
thf(func_def_798,type,
sK511: $i > $i > $i > $i > $i ).
thf(func_def_803,type,
sK516: $i > $o ).
thf(func_def_810,type,
sK523: $i > $o ).
thf(func_def_830,type,
sK543: ( $i > $o ) > $i ).
thf(func_def_831,type,
sK544: $i > $o ).
thf(func_def_832,type,
sK545: $i > $i ).
thf(func_def_833,type,
sK546: $i > $o ).
thf(func_def_835,type,
sK548: ( $i > $o ) > $i ).
thf(func_def_836,type,
sK549: ( $i > $o ) > $i ).
thf(func_def_841,type,
sK554: $i > $i > $o ).
thf(func_def_845,type,
sK558: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_846,type,
sK559: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_849,type,
sK562: $i > $o ).
thf(func_def_850,type,
sK563: $i > $o ).
thf(func_def_853,type,
sK566: $o ).
thf(func_def_862,type,
sK575: $i > $o ).
thf(func_def_864,type,
sK577: ( $i > $o ) > $i > $i ).
thf(func_def_866,type,
sK579: $i > $i ).
thf(func_def_867,type,
sK580: $i > $i ).
thf(func_def_868,type,
sK581: $i > $i ).
thf(func_def_869,type,
sK582: $i > $i ).
thf(func_def_870,type,
sK583: $i > $i ).
thf(func_def_871,type,
sK584: $i > $i > $i > $i ).
thf(func_def_872,type,
sK585: $i > $i ).
thf(func_def_873,type,
sK586: $i > $i ).
thf(func_def_874,type,
sK587: $i > $i ).
thf(func_def_875,type,
sK588: $i > $i ).
thf(func_def_876,type,
sK589: $i > $i > $i ).
thf(func_def_877,type,
sK590: $i > $i > $i ).
thf(func_def_878,type,
sK591: $i > $i > $i > $i ).
thf(func_def_879,type,
sK592: $i > $i > $i > $i ).
thf(func_def_880,type,
sK593: $i > $i > $i > $i ).
thf(func_def_881,type,
sK594: $i > $i > $i ).
thf(func_def_882,type,
sK595: $i > $i > $i ).
thf(func_def_883,type,
sK596: $i > $i > $i ).
thf(func_def_887,type,
sK600: $i > $i ).
thf(func_def_890,type,
sK603: $i > $i > ( $i > $i ) > $i ).
thf(func_def_899,type,
sK612: $o ).
thf(func_def_904,type,
sK617: $i > $i > $o ).
thf(func_def_916,type,
sK629: $i > $i > $i > $i ).
thf(func_def_917,type,
sK630: $i > $i > $i > $i ).
thf(func_def_921,type,
sK634: $i > $o ).
thf(func_def_930,type,
sK643: $i > $i > $o ).
thf(func_def_939,type,
sK652: $i > $o ).
thf(func_def_955,type,
sK668: $i > $o ).
thf(func_def_957,type,
sK670: ( $i > $o ) > $i > $i ).
thf(func_def_964,type,
sK677: $o > $i > $i > $i ).
thf(func_def_967,type,
sK680: $o ).
thf(func_def_971,type,
sK684: $i > $o ).
thf(func_def_976,type,
sK689: $i > $o ).
thf(func_def_979,type,
sK692: $i > ( $i > $o ) > $i ).
thf(func_def_995,type,
sK708: $i > $o ).
thf(func_def_998,type,
sK711: $o ).
thf(func_def_1011,type,
sK724: ( $i > $o ) > $i ).
thf(func_def_1012,type,
sK725: $i > $o ).
thf(func_def_1013,type,
sK726: $i > $i ).
thf(func_def_1017,type,
sK730: $o ).
thf(func_def_1019,type,
sK732: $o ).
thf(f127,axiom,
( setminusIRneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(f240,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTI1) ).
thf(f241,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f240]) ).
thf(f287,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f241]) ).
thf(f288,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f287]) ).
thf(f369,plain,
( setminusIRneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f127]) ).
thf(f370,plain,
( ( setminusIRneg = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ),
inference(fool_elimination,[],[f369]) ).
thf(f713,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f288]) ).
thf(f723,plain,
( ( setminusIRneg = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ),
inference(flattening,[],[f370]) ).
thf(f943,plain,
( ( setminusIRneg = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f723]) ).
thf(f976,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f713]) ).
thf(f977,plain,
( ( setukpairinjR = $true )
& ( upairsetIL = $true )
& ( binunionIR = $true )
& ( apProp = $true )
& ( setminusERneg = $true )
& ( exuI3 = $true )
& ( ubforcartprodlem3 = $true )
& ( binintersectSubset1 = $true )
& ( funcImageSingleton = $true )
& ( kpairiskpair = $true )
& ( omegaSAx = $true )
& ( ubforcartprodlem1 = $true )
& ( theeq = $true )
& ( binintersectLsub = $true )
& ( emptyE1 = $true )
& ( setminusELneg = $true )
& ( setunionI = $true )
& ( nonemptyImpWitness = $true )
& ( subset2powerset = $true )
& ( setadjoinIR = $true )
& ( subPowSU = $true )
& ( setunionsingleton2 = $true )
& ( ap2apEq2 = $true )
& ( upairsetIR = $true )
& ( dpsetconstrER = $true )
& ( funcinfuncset = $true )
& ( setukpairinjR11 = $true )
& ( upairsubunion = $true )
& ( cartprodmempair = $true )
& ( setukpairinjL1 = $true )
& ( funcext2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( funcGraphProp2 = $true )
& ( setextAx = $true )
& ( binunionEcases = $true )
& ( binintersectT_lem = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( kfstsingleton = $true )
& ( brelnall2 = $true )
& ( omega__Cong = $true )
& ( exuE1 = $true )
& ( setoftrueEq = $true )
& ( emptysetAx = $true )
& ( setadjoinIL = $true )
& ( subsetRefl = $true )
& ( funcextLem = $true )
& ( dpsetconstrERa = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( iftrueProp2 = $true )
& ( eqimpsubset1 = $true )
& ( singletonsswitch = $true )
& ( nonemptyI1 = $true )
& ( binunionE = $true )
& ( ifp = $true )
& ( setukpairinjL = $true )
& ( emptysetimpfalse = $true )
& ( binintersectSubset2 = $true )
& ( upairset2E = $true )
& ( inPowerset = $true )
& ( binintersectER = $true )
& ( kfstpairEq = $true )
& ( emptyInPowerset = $true )
& ( setadjoinSub = $true )
& ( notdallE = $true )
& ( vacuousDall = $true )
& ( emptysetE = $true )
& ( ap2apEq1 = $true )
& ( setadjoinSub2 = $true )
& ( setunionsingleton = $true )
& ( lamp = $true )
& ( symdiffIneg1 = $true )
& ( powerset__Cong = $true )
& ( emptyI = $true )
& ( exuEu = $true )
& ( setminusLsub = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( foundationAx = $true )
& ( disjointsetsI1 = $true )
& ( prop2set2propI = $true )
& ( exuI2 = $true )
& ( setminusER = $true )
& ( iftrueProp1 = $true )
& ( kpairsurjEq = $true )
& ( dpsetconstrSub = $true )
& ( singletonprop = $true )
& ( eqimpsubset2 = $true )
& ( dpsetconstrI = $true )
& ( setunionE = $true )
& ( setminusIRneg = $true )
& ( emptyset__Cong = $true )
& ( binintersectRsub = $true )
& ( beta1 = $true )
& ( setadjoin__Cong = $true )
& ( cartprodfstin = $true )
& ( setukpairinjR1 = $true )
& ( binunionIL = $true )
& ( powersetsubset = $true )
& ( dsetconstrI = $true )
& ( subsetTI = $true )
& ( exuE2 = $true )
& ( funcext = $true )
& ( ifSingleton = $true )
& ( in__Cong = $true )
& ( cartprodmempair1 = $true )
& ( notequalI2 = $true )
& ( subsetE = $true )
& ( powersetTE1 = $true )
& ( omegaIndAx = $true )
& ( eta1 = $true )
& ( ex1E2 = $true )
& ( setminusT_lem = $true )
& ( binintersectSubset4 = $true )
& ( setminusEL = $true )
& ( descrp = $true )
& ( bs114d = $true )
& ( kpairp = $true )
& ( setminusILneg = $true )
& ( subsetTrans = $true )
& ( funcGraphProp3 = $true )
& ( uniqinunit = $true )
& ( setextsub = $true )
& ( emptysetsubset = $true )
& ( setadjoinOr = $true )
& ( powersetTI1 = $true )
& ( setbeta = $true )
& ( ubforcartprodlem2 = $true )
& ( binunionLsub = $true )
& ( setminusSubset2 = $true )
& ( lamProp = $true )
& ( app = $true )
& ( binunionRsub = $true )
& ( exuE3u = $true )
& ( subsetI2 = $true )
& ( infuncsetfunc = $true )
& ( prop2setE = $true )
& ( cartprodpairmemEL = $true )
& ( descr__Cong = $true )
& ( setminusI = $true )
& ( beta2 = $true )
& ( setukpairinjR2 = $true )
& ( ksndsingleton = $true )
& ( ap2p = $true )
& ( powersetE1 = $true )
& ( notequalI1 = $true )
& ( replAx = $true )
& ( upairsetE = $true )
& ( prop2setI = $true )
& ( powersetT_lem = $true )
& ( ksndpairEq = $true )
& ( upairinpowunion = $true )
& ( singletonsubset = $true )
& ( cartprodpairsurjEq = $true )
& ( iftrueorfalse = $true )
& ( theprop = $true )
& ( upairset2IR = $true )
& ( complementT_lem = $true )
& ( emptyinPowerset = $true )
& ( cartprodpairin = $true )
& ( dpsetconstrEL2 = $true )
& ( iffalseProp2 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan4 = $true )
& ( setunionAx = $true )
& ( iffalseProp1 = $true )
& ( secondinupair = $true )
& ( funcGraphProp1 = $true )
& ( setukpairinjL2 = $true )
& ( singletonsuniq = $true )
& ( binintersectSubset5 = $true )
& ( subsetI1 = $true )
& ( notsubsetI = $true )
& ( dsetconstrEL = $true )
& ( dpsetconstrEL1 = $true )
& ( setadjoinE = $true )
& ( cartprodmempaircEq = $true )
& ( singletoninpowunion = $true )
& ( subbreln = $true )
& ( exu__Cong = $true )
& ( setunion__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairIR = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR12 = $true )
& ( ex1I2 = $true )
& ( eta2 = $true )
& ( exuE3e = $true )
& ( binintersectEL = $true )
& ( symdiffI2 = $true )
& ( exuI1 = $true )
& ( binintersectI = $true )
& ( setminusSubset1 = $true )
& ( noeltsimpempty = $true )
& ( setOfPairsIsBReln = $true )
& ( quantDeMorgan2 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodsndin = $true )
& ( singletoninpowerset = $true )
& ( eqbreln = $true )
& ( cartprodpairmemER = $true )
& ( notdexE = $true )
& ( symdiffIneg2 = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodfstpairEq = $true )
& ( powersetI1 = $true )
& ( setunionE2 = $true )
& ( subsetE2 = $true )
& ( eqinunit = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairIL = $true )
& ( nonemptyE1 = $true )
& ( setextT = $true )
& ( sepSubset = $true )
& ( setadjoinAx = $true )
& ( iftrue = $true )
& ( omega0Ax = $true )
& ( binintersectSubset3 = $true )
& ( binunionT_lem = $true )
& ( wellorderingAx = $true )
& ( iffalse = $true )
& ( upairequniteq = $true )
& ( inCongP = $true )
& ( setext = $true )
& ( symdiffE = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrER = $true )
& ( notinsingleton = $true )
& ( notinemptyset = $true )
& ( sepInPowerset = $true )
& ( nonemptyI = $true )
& ( lam2lamEq = $true )
& ( powersetE = $true )
& ( symdiffI1 = $true ) ),
inference(flattening,[],[f976]) ).
thf(f1046,plain,
( ( setukpairinjR = $true )
& ( upairsetIL = $true )
& ( binunionIR = $true )
& ( apProp = $true )
& ( setminusERneg = $true )
& ( exuI3 = $true )
& ( ubforcartprodlem3 = $true )
& ( binintersectSubset1 = $true )
& ( funcImageSingleton = $true )
& ( kpairiskpair = $true )
& ( omegaSAx = $true )
& ( ubforcartprodlem1 = $true )
& ( theeq = $true )
& ( binintersectLsub = $true )
& ( emptyE1 = $true )
& ( setminusELneg = $true )
& ( setunionI = $true )
& ( nonemptyImpWitness = $true )
& ( subset2powerset = $true )
& ( setadjoinIR = $true )
& ( subPowSU = $true )
& ( setunionsingleton2 = $true )
& ( ap2apEq2 = $true )
& ( upairsetIR = $true )
& ( dpsetconstrER = $true )
& ( funcinfuncset = $true )
& ( setukpairinjR11 = $true )
& ( upairsubunion = $true )
& ( cartprodmempair = $true )
& ( setukpairinjL1 = $true )
& ( funcext2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( funcGraphProp2 = $true )
& ( setextAx = $true )
& ( binunionEcases = $true )
& ( binintersectT_lem = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( kfstsingleton = $true )
& ( brelnall2 = $true )
& ( omega__Cong = $true )
& ( exuE1 = $true )
& ( setoftrueEq = $true )
& ( emptysetAx = $true )
& ( setadjoinIL = $true )
& ( subsetRefl = $true )
& ( funcextLem = $true )
& ( dpsetconstrERa = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( iftrueProp2 = $true )
& ( eqimpsubset1 = $true )
& ( singletonsswitch = $true )
& ( nonemptyI1 = $true )
& ( binunionE = $true )
& ( ifp = $true )
& ( setukpairinjL = $true )
& ( emptysetimpfalse = $true )
& ( binintersectSubset2 = $true )
& ( upairset2E = $true )
& ( inPowerset = $true )
& ( binintersectER = $true )
& ( kfstpairEq = $true )
& ( emptyInPowerset = $true )
& ( setadjoinSub = $true )
& ( notdallE = $true )
& ( vacuousDall = $true )
& ( emptysetE = $true )
& ( ap2apEq1 = $true )
& ( setadjoinSub2 = $true )
& ( setunionsingleton = $true )
& ( lamp = $true )
& ( symdiffIneg1 = $true )
& ( powerset__Cong = $true )
& ( emptyI = $true )
& ( exuEu = $true )
& ( setminusLsub = $true )
& ( ( in @ sK38 @ ( powerset @ sK37 ) )
= $true )
& ( $true
= ( in @ sK39 @ ( setminus @ sK37 @ sK38 ) ) )
& ( ( in @ sK39 @ sK38 )
= $true )
& ( ( in @ sK39 @ sK37 )
= $true )
& ( foundationAx = $true )
& ( disjointsetsI1 = $true )
& ( prop2set2propI = $true )
& ( exuI2 = $true )
& ( setminusER = $true )
& ( iftrueProp1 = $true )
& ( kpairsurjEq = $true )
& ( dpsetconstrSub = $true )
& ( singletonprop = $true )
& ( eqimpsubset2 = $true )
& ( dpsetconstrI = $true )
& ( setunionE = $true )
& ( setminusIRneg = $true )
& ( emptyset__Cong = $true )
& ( binintersectRsub = $true )
& ( beta1 = $true )
& ( setadjoin__Cong = $true )
& ( cartprodfstin = $true )
& ( setukpairinjR1 = $true )
& ( binunionIL = $true )
& ( powersetsubset = $true )
& ( dsetconstrI = $true )
& ( subsetTI = $true )
& ( exuE2 = $true )
& ( funcext = $true )
& ( ifSingleton = $true )
& ( in__Cong = $true )
& ( cartprodmempair1 = $true )
& ( notequalI2 = $true )
& ( subsetE = $true )
& ( powersetTE1 = $true )
& ( omegaIndAx = $true )
& ( eta1 = $true )
& ( ex1E2 = $true )
& ( setminusT_lem = $true )
& ( binintersectSubset4 = $true )
& ( setminusEL = $true )
& ( descrp = $true )
& ( bs114d = $true )
& ( kpairp = $true )
& ( setminusILneg = $true )
& ( subsetTrans = $true )
& ( funcGraphProp3 = $true )
& ( uniqinunit = $true )
& ( setextsub = $true )
& ( emptysetsubset = $true )
& ( setadjoinOr = $true )
& ( powersetTI1 = $true )
& ( setbeta = $true )
& ( ubforcartprodlem2 = $true )
& ( binunionLsub = $true )
& ( setminusSubset2 = $true )
& ( lamProp = $true )
& ( app = $true )
& ( binunionRsub = $true )
& ( exuE3u = $true )
& ( subsetI2 = $true )
& ( infuncsetfunc = $true )
& ( prop2setE = $true )
& ( cartprodpairmemEL = $true )
& ( descr__Cong = $true )
& ( setminusI = $true )
& ( beta2 = $true )
& ( setukpairinjR2 = $true )
& ( ksndsingleton = $true )
& ( ap2p = $true )
& ( powersetE1 = $true )
& ( notequalI1 = $true )
& ( replAx = $true )
& ( upairsetE = $true )
& ( prop2setI = $true )
& ( powersetT_lem = $true )
& ( ksndpairEq = $true )
& ( upairinpowunion = $true )
& ( singletonsubset = $true )
& ( cartprodpairsurjEq = $true )
& ( iftrueorfalse = $true )
& ( theprop = $true )
& ( upairset2IR = $true )
& ( complementT_lem = $true )
& ( emptyinPowerset = $true )
& ( cartprodpairin = $true )
& ( dpsetconstrEL2 = $true )
& ( iffalseProp2 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan4 = $true )
& ( setunionAx = $true )
& ( iffalseProp1 = $true )
& ( secondinupair = $true )
& ( funcGraphProp1 = $true )
& ( setukpairinjL2 = $true )
& ( singletonsuniq = $true )
& ( binintersectSubset5 = $true )
& ( subsetI1 = $true )
& ( notsubsetI = $true )
& ( dsetconstrEL = $true )
& ( dpsetconstrEL1 = $true )
& ( setadjoinE = $true )
& ( cartprodmempaircEq = $true )
& ( singletoninpowunion = $true )
& ( subbreln = $true )
& ( exu__Cong = $true )
& ( setunion__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairIR = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR12 = $true )
& ( ex1I2 = $true )
& ( eta2 = $true )
& ( exuE3e = $true )
& ( binintersectEL = $true )
& ( symdiffI2 = $true )
& ( exuI1 = $true )
& ( binintersectI = $true )
& ( setminusSubset1 = $true )
& ( noeltsimpempty = $true )
& ( setOfPairsIsBReln = $true )
& ( quantDeMorgan2 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodsndin = $true )
& ( singletoninpowerset = $true )
& ( eqbreln = $true )
& ( cartprodpairmemER = $true )
& ( notdexE = $true )
& ( symdiffIneg2 = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodfstpairEq = $true )
& ( powersetI1 = $true )
& ( setunionE2 = $true )
& ( subsetE2 = $true )
& ( eqinunit = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairIL = $true )
& ( nonemptyE1 = $true )
& ( setextT = $true )
& ( sepSubset = $true )
& ( setadjoinAx = $true )
& ( iftrue = $true )
& ( omega0Ax = $true )
& ( binintersectSubset3 = $true )
& ( binunionT_lem = $true )
& ( wellorderingAx = $true )
& ( iffalse = $true )
& ( upairequniteq = $true )
& ( inCongP = $true )
& ( setext = $true )
& ( symdiffE = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrER = $true )
& ( notinsingleton = $true )
& ( notinemptyset = $true )
& ( sepInPowerset = $true )
& ( nonemptyI = $true )
& ( lam2lamEq = $true )
& ( powersetE = $true )
& ( symdiffI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38,sK39]),skolemize(X0,sK37),skolemize(X1,sK38),skolemize(X2,sK39)],[f977]) ).
thf(f1586,plain,
( ( ( setminusIRneg = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
| ( setminusIRneg != $true ) ) ),
inference(nnf_transformation,[],[f943]) ).
thf(f1587,plain,
( ( ( setminusIRneg = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( $true
!= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) ) )
| ( setminusIRneg != $true ) ) ),
inference(rectify,[],[f1586]) ).
thf(f1588,plain,
( ( ( setminusIRneg = $true )
| ( ( ( in @ sK609 @ sK608 )
= $true )
& ( ( in @ sK609 @ ( setminus @ sK610 @ sK608 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( $true
!= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) ) )
| ( setminusIRneg != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK608,sK609,sK610]),skolemize(X0,sK608),skolemize(X1,sK609),skolemize(X2,sK610)],[f1587]) ).
thf(f1913,plain,
setminusIRneg = $true,
inference(cnf_transformation,[],[f1046]) ).
thf(f1927,plain,
( ( in @ sK39 @ sK38 )
= $true ),
inference(cnf_transformation,[],[f1046]) ).
thf(f1928,plain,
( $true
= ( in @ sK39 @ ( setminus @ sK37 @ sK38 ) ) ),
inference(cnf_transformation,[],[f1046]) ).
thf(f2781,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( setminusIRneg != $true )
| ( $true
!= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( ( in @ X4 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f1588]) ).
thf(f4484,definition,
( spl736_300
<=> ( setminusIRneg = $true ) ),
introduced(definition,[new_symbols(definition,[spl736_300])],[avatar_definition]) ).
thf(f4526,definition,
( spl736_309
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl736_309])],[avatar_definition]) ).
thf(f4527,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ~ spl736_309 ),
inference(avatar_component_clause,[],[f4526]) ).
thf(f4808,definition,
( spl736_371
<=> ( $true
= ( in @ sK39 @ ( setminus @ sK37 @ sK38 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl736_371])],[avatar_definition]) ).
thf(f4810,plain,
( ( $true
= ( in @ sK39 @ ( setminus @ sK37 @ sK38 ) ) )
| ~ spl736_371 ),
inference(avatar_component_clause,[],[f4808]) ).
thf(f4811,plain,
spl736_371,
inference(avatar_split_clause,[],[f1928,f4808]) ).
thf(f7425,plain,
spl736_300,
inference(avatar_split_clause,[],[f1913,f4484]) ).
thf(f7445,plain,
( spl736_309
| ~ spl736_300 ),
inference(avatar_split_clause,[],[f2781,f4484,f4526]) ).
thf(f8440,definition,
( spl736_1129
<=> ( ( in @ sK39 @ sK38 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl736_1129])],[avatar_definition]) ).
thf(f8442,plain,
( ( ( in @ sK39 @ sK38 )
= $true )
| ~ spl736_1129 ),
inference(avatar_component_clause,[],[f8440]) ).
thf(f8443,plain,
spl736_1129,
inference(avatar_split_clause,[],[f1927,f8440]) ).
thf(f8649,plain,
( ( $true != $true )
| ( ( in @ sK39 @ sK38 )
!= $true )
| ~ spl736_309
| ~ spl736_371 ),
inference(superposition,[],[f4527,f4810]) ).
thf(f8650,plain,
( ( ( in @ sK39 @ sK38 )
!= $true )
| ~ spl736_309
| ~ spl736_371 ),
inference(trivial_inequality_removal,[],[f8649]) ).
thf(f8651,plain,
( $false
| ~ spl736_309
| ~ spl736_371
| ~ spl736_1129 ),
inference(forward_subsumption_resolution,[],[f8650,f8442]) ).
thf(f8652,plain,
( ~ spl736_309
| ~ spl736_371
| ~ spl736_1129 ),
inference(avatar_contradiction_clause,[],[f8651]) ).
cnf(s260,plain,
spl736_371,
inference(sat_conversion,[],[f4811]) ).
cnf(s864,plain,
spl736_300,
inference(sat_conversion,[],[f7425]) ).
cnf(s870,plain,
( ~ spl736_300
| spl736_309 ),
inference(sat_conversion,[],[f7445]) ).
cnf(s1143,plain,
spl736_1129,
inference(sat_conversion,[],[f8443]) ).
cnf(s1184,plain,
( ~ spl736_309
| ~ spl736_371
| ~ spl736_1129 ),
inference(sat_conversion,[],[f8652]) ).
cnf(s1211,plain,
spl736_309,
inference(rat,[],[s870,s864]) ).
cnf(s1212,plain,
~ spl736_371,
inference(rat,[],[s1184,s1143,s1211]) ).
cnf(s1355,plain,
$false,
inference(rat,[],[s260,s1212]) ).
thf(f8653,plain,
$false,
inference(avatar_sat_refutation,[],[s1355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU719^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n005.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 14:14:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.74/0.38 % (1728681)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.38 % (1728692)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.38 % (1728692)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
% 0.74/0.38 % (1728692)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=3207202594:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.38 % (1728686)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=963853550:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.38 % (1728687)lrs+10_16_si=on:nwc=1.5:random_seed=295544773:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.38 % (1728688)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=906342258:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.38 % (1728690)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3540485092:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.38 % (1728689)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=102064964: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)
% 0.74/0.38 % (1728691)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1982812169:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.38 % (1728688)Instruction limit reached!
% 0.74/0.38 % (1728688)------------------------------
% 0.74/0.38 % (1728688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (1728688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (1728688)CaDiCaL version: 2.1.3
% 0.74/0.38 % (1728688)Termination reason: Instruction limit
% 0.74/0.38 % (1728688)Termination phase: shuffling
% 0.74/0.38 % (1728688)Time elapsed: 0.002 s
% 0.74/0.38 % (1728688)Peak memory usage: 10 MB
% 0.74/0.38 % (1728688)Instructions burned: 3 (million)
% 0.74/0.38 % (1728687)Instruction limit reached!
% 0.74/0.38 % (1728687)------------------------------
% 0.74/0.38 % (1728687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (1728687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (1728687)CaDiCaL version: 2.1.3
% 0.74/0.38 % (1728687)Termination reason: Instruction limit
% 0.74/0.38 % (1728687)Termination phase: shuffling
% 0.74/0.38 % (1728687)Time elapsed: 0.008 s
% 0.74/0.38 % (1728687)Peak memory usage: 10 MB
% 0.74/0.38 % (1728687)Instructions burned: 18 (million)
% 0.74/0.38 % (1728690)Instruction limit reached!
% 0.74/0.38 % (1728690)------------------------------
% 0.74/0.38 % (1728690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (1728690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (1728690)CaDiCaL version: 2.1.3
% 0.74/0.38 % (1728690)Termination reason: Instruction limit
% 0.74/0.38 % (1728690)Termination phase: Property scanning
% 0.74/0.38 % (1728690)Time elapsed: 0.011 s
% 0.74/0.38 % (1728690)Peak memory usage: 10 MB
% 0.74/0.38 % (1728690)Instructions burned: 26 (million)
% 0.74/0.38 % (1728700)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1090119392:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.38 % (1728700)Instruction limit reached!
% 0.74/0.38 % (1728700)------------------------------
% 0.74/0.38 % (1728700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (1728700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (1728700)CaDiCaL version: 2.1.3
% 0.74/0.38 % (1728700)Termination reason: Instruction limit
% 0.74/0.38 % (1728700)Termination phase: shuffling
% 0.74/0.38 % (1728700)Time elapsed: 0.002 s
% 0.74/0.38 % (1728700)Peak memory usage: 10 MB
% 0.74/0.38 % (1728700)Instructions burned: 3 (million)
% 0.74/0.38 % (1728702)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.41 % (1728692)Instruction limit reached!
% 0.74/0.41 % (1728692)------------------------------
% 0.74/0.41 % (1728692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (1728692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (1728692)CaDiCaL version: 2.1.3
% 0.74/0.41 % (1728692)Termination reason: Instruction limit
% 0.74/0.41 % (1728692)Termination phase: Saturation
% 0.74/0.41 % (1728692)Time elapsed: 0.035 s
% 0.74/0.41 % (1728692)Peak memory usage: 13 MB
% 0.74/0.41 % (1728692)Instructions burned: 158 (million)
% 0.74/0.41 % (1728701)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2696315740:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.41 % (1728701)Instruction limit reached!
% 0.74/0.41 % (1728701)------------------------------
% 0.74/0.41 % (1728701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (1728701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (1728701)CaDiCaL version: 2.1.3
% 0.74/0.41 % (1728701)Termination reason: Instruction limit
% 0.74/0.41 % (1728701)Termination phase: shuffling
% 0.74/0.41 % (1728701)Time elapsed: 0.003 s
% 0.74/0.41 % (1728701)Peak memory usage: 10 MB
% 0.74/0.41 % (1728701)Instructions burned: 6 (million)
% 0.74/0.41 % (1728702)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3869443335:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.41 % (1728691)Instruction limit reached!
% 0.74/0.41 % (1728691)------------------------------
% 0.74/0.41 % (1728691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (1728691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (1728691)CaDiCaL version: 2.1.3
% 0.74/0.41 % (1728691)Termination reason: Instruction limit
% 0.74/0.41 % (1728691)Termination phase: Preprocessing 3
% 0.74/0.41 % (1728691)Time elapsed: 0.034 s
% 0.74/0.41 % (1728691)Peak memory usage: 12 MB
% 0.74/0.41 % (1728691)Instructions burned: 76 (million)
% 0.74/0.41 % (1728702)Instruction limit reached!
% 0.74/0.41 % (1728702)------------------------------
% 0.74/0.41 % (1728702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (1728702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (1728702)CaDiCaL version: 2.1.3
% 0.74/0.41 % (1728702)Termination reason: Instruction limit
% 0.74/0.41 % (1728702)Termination phase: shuffling
% 0.74/0.41 % (1728702)Time elapsed: 0.004 s
% 0.74/0.41 % (1728702)Peak memory usage: 10 MB
% 0.74/0.41 % (1728702)Instructions burned: 9 (million)
% 0.74/0.41 % (1728706)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
% 0.74/0.41 % (1728706)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.41 % (1728706)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2949260312:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.41 % (1728686)Instruction limit reached!
% 0.74/0.41 % (1728686)------------------------------
% 0.74/0.41 % (1728686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (1728686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (1728686)CaDiCaL version: 2.1.3
% 0.74/0.41 % (1728686)Termination reason: Instruction limit
% 0.74/0.41 % (1728686)Termination phase: Preprocessing 3
% 0.74/0.41 % (1728686)Time elapsed: 0.041 s
% 0.74/0.41 % (1728686)Peak memory usage: 13 MB
% 0.74/0.41 % (1728686)Instructions burned: 87 (million)
% 0.74/0.41 % (1728706)Instruction limit reached!
% 0.74/0.41 % (1728706)------------------------------
% 0.74/0.41 % (1728706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (1728706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (1728706)CaDiCaL version: 2.1.3
% 0.74/0.41 % (1728706)Termination reason: Instruction limit
% 0.74/0.41 % (1728706)Termination phase: shuffling
% 0.74/0.41 % (1728706)Time elapsed: 0.007 s
% 0.74/0.41 % (1728706)Peak memory usage: 10 MB
% 0.74/0.41 % (1728706)Instructions burned: 28 (million)
% 0.74/0.41 % (1728704)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2774096261:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.44 % (1728708)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=461820455:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.44 % (1728710)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.44 % (1728709)lrs+10_1_si=on:cs=on:random_seed=3538917763:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.44 % (1728710)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1139713652:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.44 % (1728713)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=591734735:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.74/0.44 % (1728704)Instruction limit reached!
% 0.74/0.44 % (1728704)------------------------------
% 0.74/0.44 % (1728704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728704)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728704)Termination reason: Instruction limit
% 0.74/0.44 % (1728704)Termination phase: shuffling
% 0.74/0.44 % (1728704)Time elapsed: 0.007 s
% 0.74/0.44 % (1728704)Peak memory usage: 10 MB
% 0.74/0.44 % (1728704)Instructions burned: 14 (million)
% 0.74/0.44 % (1728710)Instruction limit reached!
% 0.74/0.44 % (1728710)------------------------------
% 0.74/0.44 % (1728710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728710)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728710)Termination reason: Instruction limit
% 0.74/0.44 % (1728710)Termination phase: shuffling
% 0.74/0.44 % (1728710)Time elapsed: 0.002 s
% 0.74/0.44 % (1728710)Peak memory usage: 10 MB
% 0.74/0.44 % (1728710)Instructions burned: 3 (million)
% 0.74/0.44 % (1728712)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4245918411:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.44 % (1728709)Instruction limit reached!
% 0.74/0.44 % (1728709)------------------------------
% 0.74/0.44 % (1728709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728709)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728709)Termination reason: Instruction limit
% 0.74/0.44 % (1728709)Termination phase: shuffling
% 0.74/0.44 % (1728709)Time elapsed: 0.007 s
% 0.74/0.44 % (1728709)Peak memory usage: 10 MB
% 0.74/0.44 % (1728709)Instructions burned: 16 (million)
% 0.74/0.44 % (1728719)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2604843101:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.74/0.44 % (1728720)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1255073560:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.44 % (1728712)Instruction limit reached!
% 0.74/0.44 % (1728712)------------------------------
% 0.74/0.44 % (1728712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728712)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728712)Termination reason: Instruction limit
% 0.74/0.44 % (1728712)Termination phase: SInE selection
% 0.74/0.44 % (1728712)Time elapsed: 0.017 s
% 0.74/0.44 % (1728712)Peak memory usage: 11 MB
% 0.74/0.44 % (1728712)Instructions burned: 39 (million)
% 0.74/0.44 % (1728722)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1118398732:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.74/0.44 % (1728720)Instruction limit reached!
% 0.74/0.44 % (1728720)------------------------------
% 0.74/0.44 % (1728720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728720)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728720)Termination reason: Instruction limit
% 0.74/0.44 % (1728720)Termination phase: shuffling
% 0.74/0.44 % (1728720)Time elapsed: 0.007 s
% 0.74/0.44 % (1728720)Peak memory usage: 11 MB
% 0.74/0.44 % (1728720)Instructions burned: 16 (million)
% 0.74/0.44 % (1728708)Instruction limit reached!
% 0.74/0.44 % (1728708)------------------------------
% 0.74/0.44 % (1728708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728708)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728708)Termination reason: Instruction limit
% 0.74/0.44 % (1728708)Termination phase: Property scanning
% 0.74/0.44 % (1728708)Time elapsed: 0.036 s
% 0.74/0.44 % (1728708)Peak memory usage: 11 MB
% 0.74/0.44 % (1728708)Instructions burned: 88 (million)
% 0.74/0.44 % (1728719)Instruction limit reached!
% 0.74/0.44 % (1728719)------------------------------
% 0.74/0.44 % (1728719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728719)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728719)Termination reason: Instruction limit
% 0.74/0.44 % (1728719)Termination phase: Property scanning
% 0.74/0.44 % (1728719)Time elapsed: 0.012 s
% 0.74/0.44 % (1728719)Peak memory usage: 11 MB
% 0.74/0.44 % (1728719)Instructions burned: 26 (million)
% 0.74/0.44 % (1728725)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=698031109:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.44 % (1728727)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3947992657:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.74/0.44 % (1728725)Instruction limit reached!
% 0.74/0.44 % (1728725)------------------------------
% 0.74/0.44 % (1728725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728725)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728725)Termination reason: Instruction limit
% 0.74/0.44 % (1728725)Termination phase: shuffling
% 0.74/0.44 % (1728725)Time elapsed: 0.007 s
% 0.74/0.44 % (1728725)Peak memory usage: 10 MB
% 0.74/0.44 % (1728725)Instructions burned: 16 (million)
% 0.74/0.44 % (1728727)Instruction limit reached!
% 0.74/0.44 % (1728727)------------------------------
% 0.74/0.44 % (1728727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728727)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728727)Termination reason: Instruction limit
% 0.74/0.44 % (1728727)Termination phase: shuffling
% 0.74/0.44 % (1728727)Time elapsed: 0.002 s
% 0.74/0.44 % (1728727)Peak memory usage: 10 MB
% 0.74/0.44 % (1728727)Instructions burned: 3 (million)
% 0.74/0.44 % (1728728)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=513830398:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.74/0.44 % (1728729)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2325225519:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.74/0.44 % (1728713)Instruction limit reached!
% 0.74/0.44 % (1728713)------------------------------
% 0.74/0.44 % (1728713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728713)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728713)Termination reason: Instruction limit
% 0.74/0.44 % (1728713)Termination phase: Saturation
% 0.74/0.44 % (1728713)Time elapsed: 0.060 s
% 0.74/0.44 % (1728713)Peak memory usage: 15 MB
% 0.74/0.44 % (1728713)Instructions burned: 251 (million)
% 0.74/0.44 % (1728729)Instruction limit reached!
% 0.74/0.44 % (1728729)------------------------------
% 0.74/0.44 % (1728729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728729)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728729)Termination reason: Instruction limit
% 0.74/0.44 % (1728729)Termination phase: shuffling
% 0.74/0.44 % (1728729)Time elapsed: 0.010 s
% 0.74/0.44 % (1728729)Peak memory usage: 10 MB
% 0.74/0.44 % (1728729)Instructions burned: 23 (million)
% 0.74/0.44 % (1728728)Instruction limit reached!
% 0.74/0.44 % (1728728)------------------------------
% 0.74/0.44 % (1728728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728728)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728728)Termination reason: Instruction limit
% 0.74/0.44 % (1728728)Termination phase: shuffling
% 0.74/0.44 % (1728728)Time elapsed: 0.012 s
% 0.74/0.44 % (1728728)Peak memory usage: 10 MB
% 0.74/0.44 % (1728728)Instructions burned: 26 (million)
% 0.74/0.44 % (1728734)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.74/0.44 % (1728734)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.74/0.44 % (1728732)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1749281551:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.74/0.44 % (1728736)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.74/0.44 % (1728734)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3155421052:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.44 % (1728736)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=722894547:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.74/0.44 % (1728736)Instruction limit reached!
% 0.74/0.44 % (1728736)------------------------------
% 0.74/0.44 % (1728736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728736)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728736)Termination reason: Instruction limit
% 0.74/0.44 % (1728736)Termination phase: shuffling
% 0.74/0.44 % (1728736)Time elapsed: 0.003 s
% 0.74/0.44 % (1728736)Peak memory usage: 10 MB
% 0.74/0.44 % (1728736)Instructions burned: 12 (million)
% 0.74/0.44 % (1728689) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1728681-1728689"...
% 0.74/0.44 % (1728734)Instruction limit reached!
% 0.74/0.44 % (1728734)------------------------------
% 0.74/0.44 % (1728734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728734)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728734)Termination reason: Instruction limit
% 0.74/0.44 % (1728734)Termination phase: shuffling
% 0.74/0.44 % (1728734)Time elapsed: 0.006 s
% 0.74/0.44 % (1728734)Peak memory usage: 10 MB
% 0.74/0.44 % (1728734)Instructions burned: 14 (million)
% 0.74/0.44 % (1728737)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3578602356:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.74/0.44 % (1728738)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2876352639:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.74/0.44 % (1728689)...printing done.
% 0.74/0.44 % (1728742)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1020452961:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.74/0.44 % (1728689)Refutation found. Thanks to Tanya!
% 0.74/0.44 % SZS status Theorem for theBenchmark
% 0.74/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.74/0.44 % (1728689)------------------------------
% 0.74/0.44 % (1728689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (1728689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (1728689)CaDiCaL version: 2.1.3
% 0.74/0.44 % (1728689)Termination reason: Refutation
% 0.74/0.44 % (1728689)Time elapsed: 0.138 s
% 0.74/0.44 % (1728689)Peak memory usage: 19 MB
% 0.74/0.44 % (1728689)Instructions burned: 289 (million)
% 0.74/0.44 % (1728681)Success in time 0.186 s
% 0.74/0.44 % Vampire exiting
%------------------------------------------------------------------------------