%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU693^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:30:48 AM UTC 2026
% Result : Theorem 0.54s 0.41s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 3829 (1064 equ; 0 cnn)
% Maximal formula atoms : 212 ( 382 avg)
% Number of connectives : 1816 ( 8 ~; 0 |; 844 &; 120 @)
% ( 0 <=>; 844 =>; 0 <=; 0 <~>)
% Maximal formula depth : 219 ( 173 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 408 ( 405 usr; 225 con; 0-4 aty)
% Number of variables : 28 ( 0 ^; 16 !; 12 ?; 28 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_248,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_251,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_252,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_253,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_254,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_255,type,
vAND: $o > $o > $o ).
thf(func_def_256,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_257,type,
vIMP: $o > $o > $o ).
thf(func_def_258,type,
vNOT: $o > $o ).
thf(func_def_259,type,
sP0: $o ).
thf(func_def_260,type,
sP1: $i > $i > $o ).
thf(func_def_261,type,
sP2: $i > $o ).
thf(func_def_262,type,
sP3: $o ).
thf(func_def_263,type,
sK4: $i > $o ).
thf(func_def_266,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_274,type,
sK15: $i > $i > $o ).
thf(func_def_291,type,
sK32: $i > $i > $i ).
thf(func_def_302,type,
sK43: $o ).
thf(func_def_303,type,
sK44: $o > $i > $i > $i ).
thf(func_def_304,type,
sK45: $i > $i > $i ).
thf(func_def_311,type,
sK52: $i > $o ).
thf(func_def_325,type,
sK66: $i > $i ).
thf(func_def_326,type,
sK67: $i > $i ).
thf(func_def_328,type,
sK69: $i > $i > $i ).
thf(func_def_340,type,
sK81: $i > $o ).
thf(func_def_343,type,
sK84: $i > $i > $o ).
thf(func_def_344,type,
sK85: $i > $i ).
thf(func_def_345,type,
sK86: $i > $i ).
thf(func_def_346,type,
sK87: ( $i > $i > $o ) > $i > $i ).
thf(func_def_347,type,
sK88: ( $i > $i > $o ) > $i > $i ).
thf(func_def_348,type,
sK89: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_354,type,
sK95: $i > $o ).
thf(func_def_360,type,
sK101: $i > $i > $i > $i > $i ).
thf(func_def_361,type,
sK102: $i > $i > $i > $i > $i ).
thf(func_def_362,type,
sK103: $i > $i > $i > $i > $i ).
thf(func_def_363,type,
sK104: $i > $i > $i > $i > $i ).
thf(func_def_381,type,
sK122: $i > $o ).
thf(func_def_388,type,
sK129: ( $i > $o ) > $i ).
thf(func_def_389,type,
sK130: $i > $o ).
thf(func_def_390,type,
sK131: $i > $i ).
thf(func_def_391,type,
sK132: ( $i > $o ) > $i > $i ).
thf(func_def_393,type,
sK134: $i > $o ).
thf(func_def_401,type,
sK142: $i > $o ).
thf(func_def_407,type,
sK148: $o ).
thf(func_def_417,type,
sK158: $i > $o ).
thf(func_def_425,type,
sK166: $i > $o ).
thf(func_def_433,type,
sK174: $i > $o ).
thf(func_def_435,type,
sK176: ( $i > $o ) > $i ).
thf(func_def_436,type,
sK177: ( $i > $o ) > $i ).
thf(func_def_439,type,
sK180: $i > $i ).
thf(func_def_443,type,
sK184: $i > $i > $i ).
thf(func_def_452,type,
sK193: $i > $i > $i > $i ).
thf(func_def_453,type,
sK194: $i > $i > $i > $i ).
thf(func_def_462,type,
sK203: $i > $i ).
thf(func_def_463,type,
sK204: ( $i > $i ) > $i > $i > $i ).
thf(func_def_464,type,
sK205: ( $i > $o ) > $i > $i > $i ).
thf(func_def_467,type,
sK208: $i > $o ).
thf(func_def_469,type,
sK210: $i > ( $i > $o ) > $i ).
thf(func_def_470,type,
sK211: $i > ( $i > $o ) > $i ).
thf(func_def_471,type,
sK212: $i > $o ).
thf(func_def_476,type,
sK217: $i > $i > $i ).
thf(func_def_477,type,
sK218: $i > $i > $i ).
thf(func_def_478,type,
sK219: $i > $i > $i ).
thf(func_def_484,type,
sK225: $i > $i ).
thf(func_def_485,type,
sK226: $i > $i ).
thf(func_def_486,type,
sK227: $i > $i ).
thf(func_def_487,type,
sK228: $i > $i ).
thf(func_def_488,type,
sK229: $i > $i ).
thf(func_def_489,type,
sK230: $i > $i > $i > $i ).
thf(func_def_490,type,
sK231: $i > $i ).
thf(func_def_491,type,
sK232: $i > $i ).
thf(func_def_492,type,
sK233: $i > $i ).
thf(func_def_493,type,
sK234: $i > $i ).
thf(func_def_494,type,
sK235: $i > $i > $i ).
thf(func_def_495,type,
sK236: $i > $i > $i > $i ).
thf(func_def_496,type,
sK237: $i > $i > $i > $i ).
thf(func_def_497,type,
sK238: $i > $i > $i > $i ).
thf(func_def_498,type,
sK239: $i > $i > $i ).
thf(func_def_499,type,
sK240: $i > $i > $i ).
thf(func_def_500,type,
sK241: $i > $i > $i ).
thf(func_def_501,type,
sK242: $i > $i > $i ).
thf(func_def_511,type,
sK252: $i > $i > $i ).
thf(func_def_515,type,
sK256: $i > $i ).
thf(func_def_517,type,
sK258: $i > ( $i > $i ) > $i > $i ).
thf(func_def_518,type,
sK259: $i > ( $i > $o ) > $i ).
thf(func_def_519,type,
sK260: $i > $o ).
thf(func_def_530,type,
sK271: $i > $i > $o ).
thf(func_def_533,type,
sK274: $i > $i > $o ).
thf(func_def_542,type,
sK283: $i > $o ).
thf(func_def_544,type,
sK285: $o ).
thf(func_def_546,type,
sK287: $i > $o ).
thf(func_def_558,type,
sK299: $i > $i ).
thf(func_def_581,type,
sK322: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_582,type,
sK323: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_583,type,
sK324: $i > $o ).
thf(func_def_584,type,
sK325: $i > $o ).
thf(func_def_585,type,
sK326: $i > $o ).
thf(func_def_586,type,
sK327: $i > $i ).
thf(func_def_587,type,
sK328: ( $i > $o ) > $i ).
thf(func_def_591,type,
sK332: $i > $o ).
thf(func_def_593,type,
sK334: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_594,type,
sK335: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_605,type,
sK346: $i > ( $i > $o ) > $i ).
thf(func_def_606,type,
sK347: $i > $o ).
thf(func_def_609,type,
sK350: $i > $i > $i > $i > $i ).
thf(func_def_616,type,
sK357: $i > $o ).
thf(func_def_617,type,
sK358: ( $i > $o ) > $i ).
thf(func_def_629,type,
sK370: $i > ( $i > $o ) > $i ).
thf(func_def_630,type,
sK371: $i > $o ).
thf(func_def_633,type,
sK374: $i > $o ).
thf(func_def_634,type,
sK375: $i > $o ).
thf(func_def_635,type,
sK376: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_636,type,
sK377: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_637,type,
sK378: $i > $o ).
thf(func_def_639,type,
sK380: $i > ( $i > $o ) > $i ).
thf(func_def_653,type,
sK394: $i > $i > $i ).
thf(func_def_662,type,
sK403: $i > $o ).
thf(func_def_664,type,
sK405: ( $i > $o ) > $i > $i ).
thf(func_def_669,type,
sK410: $i > $i > $o ).
thf(func_def_676,type,
sK417: $i > $i > $o ).
thf(func_def_680,type,
sK421: $i > $i ).
thf(func_def_692,type,
sK433: $i > $o ).
thf(func_def_715,type,
sK456: $o ).
thf(func_def_717,type,
sK458: $i > $o ).
thf(func_def_734,type,
sK475: $i > $o ).
thf(func_def_741,type,
sK482: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_742,type,
sK483: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_746,type,
sK487: $i > $o ).
thf(func_def_749,type,
sK490: $o ).
thf(func_def_754,type,
sK495: $o ).
thf(func_def_763,type,
sK504: $i > $i > $i > $i > $i ).
thf(func_def_768,type,
sK509: $i > $i > $i > $i > $i ).
thf(func_def_769,type,
sK510: $i > $i > $i > $i > $i ).
thf(func_def_788,type,
sK529: $i > $o ).
thf(func_def_790,type,
sK531: $i > ( $i > $o ) > $i ).
thf(func_def_813,type,
sK554: $i > $i > $i ).
thf(func_def_814,type,
sK555: $o ).
thf(func_def_825,type,
sK566: $i > $i > $i > $i > $i ).
thf(func_def_831,type,
sK572: $i > $i ).
thf(func_def_836,type,
sK577: $i > $i > $o ).
thf(func_def_838,type,
sK579: $i > $o ).
thf(func_def_840,type,
sK581: $i > ( $i > $o ) > $i ).
thf(func_def_844,type,
sK585: $i > $i ).
thf(func_def_847,type,
sK588: $i > $i > ( $i > $i ) > $i ).
thf(func_def_855,type,
sK596: $i > $i > $o ).
thf(func_def_857,type,
sK598: $o ).
thf(func_def_862,type,
sK603: $i > $o ).
thf(func_def_867,type,
sK608: $i > $o ).
thf(func_def_870,type,
sK611: $i > ( $i > $o ) > $i ).
thf(func_def_871,type,
sK612: $i > ( $i > $o ) > $i ).
thf(func_def_881,type,
sK622: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_882,type,
sK623: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_885,type,
sK626: $i > $o ).
thf(func_def_886,type,
sK627: $i > $o ).
thf(func_def_887,type,
sK628: $i > $i ).
thf(f216,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
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(f217,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
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f216]) ).
thf(f305,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X2 @ X1 @ X3 )
= ( ap @ X0 @ X2 @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f217]) ).
thf(f306,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 )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ap @ X0 @ X2 @ X1 @ X3 )
= ( ap @ X0 @ X2 @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f305]) ).
thf(f893,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ? [X3: $i] :
( ( ( ap @ X0 @ X2 @ X1 @ X3 )
!= ( ap @ X0 @ X2 @ X1 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $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,[],[f306]) ).
thf(f894,plain,
( ( emptysetE = $true )
& ( emptyset__Cong = $true )
& ( upairinpowunion = $true )
& ( setunionE = $true )
& ( symdiffI1 = $true )
& ( subsetI1 = $true )
& ( setunionsingleton1 = $true )
& ( setadjoin__Cong = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( emptysetAx = $true )
& ( upairequniteq = $true )
& ( dpsetconstrSub = $true )
& ( binunionRsub = $true )
& ( wellorderingAx = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI1 = $true )
& ( vacuousDall = $true )
& ( setminusI = $true )
& ( uniqinunit = $true )
& ( dsetconstr__Cong = $true )
& ( exu__Cong = $true )
& ( setminusER = $true )
& ( dsetconstrER = $true )
& ( setukpairinjR1 = $true )
& ( kpairsurjEq = $true )
& ( setunionE2 = $true )
& ( powersetI = $true )
& ( symdiffIneg1 = $true )
& ( subPowSU = $true )
& ( emptysetimpfalse = $true )
& ( kfstsingleton = $true )
& ( cartprodpairmemER = $true )
& ( funcGraphProp4 = $true )
& ( binintersectI = $true )
& ( emptyI = $true )
& ( upairsubunion = $true )
& ( singletoninpowerset = $true )
& ( setadjoinE = $true )
& ( binunionIL = $true )
& ( setminusLsub = $true )
& ( symdiffI2 = $true )
& ( sepInPowerset = $true )
& ( brelnall2 = $true )
& ( powersetE1 = $true )
& ( inCongP = $true )
& ( setunion__Cong = $true )
& ( cartprodpairin = $true )
& ( binunionIR = $true )
& ( omega__Cong = $true )
& ( setukpairinjR11 = $true )
& ( binintersectSubset3 = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset1 = $true )
& ( setminusILneg = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( setadjoinIL = $true )
& ( setukpairinjR12 = $true )
& ( notequalI2 = $true )
& ( inPowerset = $true )
& ( eqbreln = $true )
& ( setukpairinjL2 = $true )
& ( noeltsimpempty = $true )
& ( ap2p = $true )
& ( notdexE = $true )
& ( infuncsetfunc = $true )
& ( funcImageSingleton = $true )
& ( binintersectSubset5 = $true )
& ( binunionEcases = $true )
& ( setext = $true )
& ( dpsetconstrER = $true )
& ( subset2powerset = $true )
& ( exuI3 = $true )
& ( setunionAx = $true )
& ( upairsetIL = $true )
& ( quantDeMorgan1 = $true )
& ( notequalI1 = $true )
& ( cartprodmempaircEq = $true )
& ( binunionE = $true )
& ( nonemptyImpWitness = $true )
& ( singletonsubset = $true )
& ( eqimpsubset1 = $true )
& ( exuI2 = $true )
& ( emptyinunitempty = $true )
& ( setukpairinjR = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoinOr = $true )
& ( powersetAx = $true )
& ( subsetemptysetimpeq = $true )
& ( setbeta = $true )
& ( ex1I2 = $true )
& ( nonemptyI = $true )
& ( kpairp = $true )
& ( upairset2E = $true )
& ( omegaIndAx = $true )
& ( cartprodfstin = $true )
& ( exuE2 = $true )
& ( ex1E1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptyinPowerset = $true )
& ( powersetsubset = $true )
& ( ksndsingleton = $true )
& ( quantDeMorgan4 = $true )
& ( funcext2 = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjR2 = $true )
& ( binintersectRsub = $true )
& ( setadjoinAx = $true )
& ( upairset2IR = $true )
& ( setOfPairsIsBReln = $true )
& ( replAx = $true )
& ( eqimpsubset2 = $true )
& ( sepSubset = $true )
& ( lamp = $true )
& ( bs114d = $true )
& ( ubforcartprodlem3 = $true )
& ( descr__Cong = $true )
& ( omega0Ax = $true )
& ( powerset__Cong = $true )
& ( prop2setI = $true )
& ( exuE1 = $true )
& ( ex1I = $true )
& ( cartprodmempair1 = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinSub = $true )
& ( cartprodpairsurjEq = $true )
& ( dpsetconstrI = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( exuI1 = $true )
& ( subbreln = $true )
& ( setunionI = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ? [X3: $i] :
( ( ( ap @ X0 @ X2 @ X1 @ X3 )
!= ( ap @ X0 @ X2 @ X1 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( funcGraphProp2 = $true )
& ( upairsetIR = $true )
& ( theprop = $true )
& ( subsetI2 = $true )
& ( binintersectSubset2 = $true )
& ( funcGraphProp1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusIRneg = $true )
& ( quantDeMorgan3 = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjL = $true )
& ( cartprodfstpairEq = $true )
& ( funcextLem = $true )
& ( funcGraphProp3 = $true )
& ( ubforcartprodlem2 = $true )
& ( symdiffE = $true )
& ( powersetE = $true )
& ( setminusELneg = $true )
& ( app = $true )
& ( kpairiskpair = $true )
& ( apProp = $true )
& ( setukpairinjL1 = $true )
& ( lam2p = $true )
& ( subsetTrans = $true )
& ( in__Cong = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( setadjoinIR = $true )
& ( setminusSubset2 = $true )
& ( brelnall1 = $true )
& ( kfstpairEq = $true )
& ( singletoninpowunion = $true )
& ( setminusEL = $true )
& ( dsetconstrI = $true )
& ( exuE3u = $true )
& ( setadjoinSub2 = $true )
& ( secondinupair = $true )
& ( dpsetconstrERa = $true )
& ( binintersectLsub = $true )
& ( setminusERneg = $true )
& ( eqinunit = $true )
& ( powersetI1 = $true )
& ( cartprodsndin = $true )
& ( setextAx = $true )
& ( ksndpairEq = $true )
& ( cartprodpairmemEL = $true )
& ( subsetE2 = $true )
& ( setukpairIL = $true )
& ( notinsingleton = $true )
& ( emptyE1 = $true )
& ( singletonsuniq = $true )
& ( setukpairIR = $true )
& ( notdallE = $true )
& ( funcext = $true )
& ( cartprodsndpairEq = $true )
& ( disjointsetsI1 = $true )
& ( prop2setE = $true )
& ( binintersectSubset4 = $true )
& ( lamProp = $true )
& ( binintersectEL = $true )
& ( binintersectER = $true )
& ( notsubsetI = $true )
& ( setunionsingleton = $true )
& ( cartprodmempair = $true )
& ( ex1E2 = $true )
& ( upairsetE = $true )
& ( setminusSubset1 = $true )
& ( dpsetconstrEL1 = $true )
& ( funcinfuncset = $true )
& ( foundationAx = $true )
& ( singletonsswitch = $true )
& ( emptysetsubset = $true )
& ( singletonprop = $true )
& ( setextsub = $true ) ),
inference(flattening,[],[f893]) ).
thf(f1484,plain,
( ( emptysetE = $true )
& ( emptyset__Cong = $true )
& ( upairinpowunion = $true )
& ( setunionE = $true )
& ( symdiffI1 = $true )
& ( subsetI1 = $true )
& ( setunionsingleton1 = $true )
& ( setadjoin__Cong = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( emptysetAx = $true )
& ( upairequniteq = $true )
& ( dpsetconstrSub = $true )
& ( binunionRsub = $true )
& ( wellorderingAx = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI1 = $true )
& ( vacuousDall = $true )
& ( setminusI = $true )
& ( uniqinunit = $true )
& ( dsetconstr__Cong = $true )
& ( exu__Cong = $true )
& ( setminusER = $true )
& ( dsetconstrER = $true )
& ( setukpairinjR1 = $true )
& ( kpairsurjEq = $true )
& ( setunionE2 = $true )
& ( powersetI = $true )
& ( symdiffIneg1 = $true )
& ( subPowSU = $true )
& ( emptysetimpfalse = $true )
& ( kfstsingleton = $true )
& ( cartprodpairmemER = $true )
& ( funcGraphProp4 = $true )
& ( binintersectI = $true )
& ( emptyI = $true )
& ( upairsubunion = $true )
& ( singletoninpowerset = $true )
& ( setadjoinE = $true )
& ( binunionIL = $true )
& ( setminusLsub = $true )
& ( symdiffI2 = $true )
& ( sepInPowerset = $true )
& ( brelnall2 = $true )
& ( powersetE1 = $true )
& ( inCongP = $true )
& ( setunion__Cong = $true )
& ( cartprodpairin = $true )
& ( binunionIR = $true )
& ( omega__Cong = $true )
& ( setukpairinjR11 = $true )
& ( binintersectSubset3 = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset1 = $true )
& ( setminusILneg = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( setadjoinIL = $true )
& ( setukpairinjR12 = $true )
& ( notequalI2 = $true )
& ( inPowerset = $true )
& ( eqbreln = $true )
& ( setukpairinjL2 = $true )
& ( noeltsimpempty = $true )
& ( ap2p = $true )
& ( notdexE = $true )
& ( infuncsetfunc = $true )
& ( funcImageSingleton = $true )
& ( binintersectSubset5 = $true )
& ( binunionEcases = $true )
& ( setext = $true )
& ( dpsetconstrER = $true )
& ( subset2powerset = $true )
& ( exuI3 = $true )
& ( setunionAx = $true )
& ( upairsetIL = $true )
& ( quantDeMorgan1 = $true )
& ( notequalI1 = $true )
& ( cartprodmempaircEq = $true )
& ( binunionE = $true )
& ( nonemptyImpWitness = $true )
& ( singletonsubset = $true )
& ( eqimpsubset1 = $true )
& ( exuI2 = $true )
& ( emptyinunitempty = $true )
& ( setukpairinjR = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoinOr = $true )
& ( powersetAx = $true )
& ( subsetemptysetimpeq = $true )
& ( setbeta = $true )
& ( ex1I2 = $true )
& ( nonemptyI = $true )
& ( kpairp = $true )
& ( upairset2E = $true )
& ( omegaIndAx = $true )
& ( cartprodfstin = $true )
& ( exuE2 = $true )
& ( ex1E1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptyinPowerset = $true )
& ( powersetsubset = $true )
& ( ksndsingleton = $true )
& ( quantDeMorgan4 = $true )
& ( funcext2 = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjR2 = $true )
& ( binintersectRsub = $true )
& ( setadjoinAx = $true )
& ( upairset2IR = $true )
& ( setOfPairsIsBReln = $true )
& ( replAx = $true )
& ( eqimpsubset2 = $true )
& ( sepSubset = $true )
& ( lamp = $true )
& ( bs114d = $true )
& ( ubforcartprodlem3 = $true )
& ( descr__Cong = $true )
& ( omega0Ax = $true )
& ( powerset__Cong = $true )
& ( prop2setI = $true )
& ( exuE1 = $true )
& ( ex1I = $true )
& ( cartprodmempair1 = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinSub = $true )
& ( cartprodpairsurjEq = $true )
& ( dpsetconstrI = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( exuI1 = $true )
& ( subbreln = $true )
& ( setunionI = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
& ? [X3: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= ( ap @ X2 @ X0 @ X1 @ X3 ) )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( funcGraphProp2 = $true )
& ( upairsetIR = $true )
& ( theprop = $true )
& ( subsetI2 = $true )
& ( binintersectSubset2 = $true )
& ( funcGraphProp1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusIRneg = $true )
& ( quantDeMorgan3 = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjL = $true )
& ( cartprodfstpairEq = $true )
& ( funcextLem = $true )
& ( funcGraphProp3 = $true )
& ( ubforcartprodlem2 = $true )
& ( symdiffE = $true )
& ( powersetE = $true )
& ( setminusELneg = $true )
& ( app = $true )
& ( kpairiskpair = $true )
& ( apProp = $true )
& ( setukpairinjL1 = $true )
& ( lam2p = $true )
& ( subsetTrans = $true )
& ( in__Cong = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( setadjoinIR = $true )
& ( setminusSubset2 = $true )
& ( brelnall1 = $true )
& ( kfstpairEq = $true )
& ( singletoninpowunion = $true )
& ( setminusEL = $true )
& ( dsetconstrI = $true )
& ( exuE3u = $true )
& ( setadjoinSub2 = $true )
& ( secondinupair = $true )
& ( dpsetconstrERa = $true )
& ( binintersectLsub = $true )
& ( setminusERneg = $true )
& ( eqinunit = $true )
& ( powersetI1 = $true )
& ( cartprodsndin = $true )
& ( setextAx = $true )
& ( ksndpairEq = $true )
& ( cartprodpairmemEL = $true )
& ( subsetE2 = $true )
& ( setukpairIL = $true )
& ( notinsingleton = $true )
& ( emptyE1 = $true )
& ( singletonsuniq = $true )
& ( setukpairIR = $true )
& ( notdallE = $true )
& ( funcext = $true )
& ( cartprodsndpairEq = $true )
& ( disjointsetsI1 = $true )
& ( prop2setE = $true )
& ( binintersectSubset4 = $true )
& ( lamProp = $true )
& ( binintersectEL = $true )
& ( binintersectER = $true )
& ( notsubsetI = $true )
& ( setunionsingleton = $true )
& ( cartprodmempair = $true )
& ( ex1E2 = $true )
& ( upairsetE = $true )
& ( setminusSubset1 = $true )
& ( dpsetconstrEL1 = $true )
& ( funcinfuncset = $true )
& ( foundationAx = $true )
& ( singletonsswitch = $true )
& ( emptysetsubset = $true )
& ( singletonprop = $true )
& ( setextsub = $true ) ),
inference(rectify,[],[f894]) ).
thf(f1485,plain,
( ( emptysetE = $true )
& ( emptyset__Cong = $true )
& ( upairinpowunion = $true )
& ( setunionE = $true )
& ( symdiffI1 = $true )
& ( subsetI1 = $true )
& ( setunionsingleton1 = $true )
& ( setadjoin__Cong = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( emptysetAx = $true )
& ( upairequniteq = $true )
& ( dpsetconstrSub = $true )
& ( binunionRsub = $true )
& ( wellorderingAx = $true )
& ( dsetconstrEL = $true )
& ( nonemptyI1 = $true )
& ( vacuousDall = $true )
& ( setminusI = $true )
& ( uniqinunit = $true )
& ( dsetconstr__Cong = $true )
& ( exu__Cong = $true )
& ( setminusER = $true )
& ( dsetconstrER = $true )
& ( setukpairinjR1 = $true )
& ( kpairsurjEq = $true )
& ( setunionE2 = $true )
& ( powersetI = $true )
& ( symdiffIneg1 = $true )
& ( subPowSU = $true )
& ( emptysetimpfalse = $true )
& ( kfstsingleton = $true )
& ( cartprodpairmemER = $true )
& ( funcGraphProp4 = $true )
& ( binintersectI = $true )
& ( emptyI = $true )
& ( upairsubunion = $true )
& ( singletoninpowerset = $true )
& ( setadjoinE = $true )
& ( binunionIL = $true )
& ( setminusLsub = $true )
& ( symdiffI2 = $true )
& ( sepInPowerset = $true )
& ( brelnall2 = $true )
& ( powersetE1 = $true )
& ( inCongP = $true )
& ( setunion__Cong = $true )
& ( cartprodpairin = $true )
& ( binunionIR = $true )
& ( omega__Cong = $true )
& ( setukpairinjR11 = $true )
& ( binintersectSubset3 = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset1 = $true )
& ( setminusILneg = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( setadjoinIL = $true )
& ( setukpairinjR12 = $true )
& ( notequalI2 = $true )
& ( inPowerset = $true )
& ( eqbreln = $true )
& ( setukpairinjL2 = $true )
& ( noeltsimpempty = $true )
& ( ap2p = $true )
& ( notdexE = $true )
& ( infuncsetfunc = $true )
& ( funcImageSingleton = $true )
& ( binintersectSubset5 = $true )
& ( binunionEcases = $true )
& ( setext = $true )
& ( dpsetconstrER = $true )
& ( subset2powerset = $true )
& ( exuI3 = $true )
& ( setunionAx = $true )
& ( upairsetIL = $true )
& ( quantDeMorgan1 = $true )
& ( notequalI1 = $true )
& ( cartprodmempaircEq = $true )
& ( binunionE = $true )
& ( nonemptyImpWitness = $true )
& ( singletonsubset = $true )
& ( eqimpsubset1 = $true )
& ( exuI2 = $true )
& ( emptyinunitempty = $true )
& ( setukpairinjR = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoinOr = $true )
& ( powersetAx = $true )
& ( subsetemptysetimpeq = $true )
& ( setbeta = $true )
& ( ex1I2 = $true )
& ( nonemptyI = $true )
& ( kpairp = $true )
& ( upairset2E = $true )
& ( omegaIndAx = $true )
& ( cartprodfstin = $true )
& ( exuE2 = $true )
& ( ex1E1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptyinPowerset = $true )
& ( powersetsubset = $true )
& ( ksndsingleton = $true )
& ( quantDeMorgan4 = $true )
& ( funcext2 = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjR2 = $true )
& ( binintersectRsub = $true )
& ( setadjoinAx = $true )
& ( upairset2IR = $true )
& ( setOfPairsIsBReln = $true )
& ( replAx = $true )
& ( eqimpsubset2 = $true )
& ( sepSubset = $true )
& ( lamp = $true )
& ( bs114d = $true )
& ( ubforcartprodlem3 = $true )
& ( descr__Cong = $true )
& ( omega0Ax = $true )
& ( powerset__Cong = $true )
& ( prop2setI = $true )
& ( exuE1 = $true )
& ( ex1I = $true )
& ( cartprodmempair1 = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinSub = $true )
& ( cartprodpairsurjEq = $true )
& ( dpsetconstrI = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( exuI1 = $true )
& ( subbreln = $true )
& ( setunionI = $true )
& ( $true
= ( in @ sK590 @ ( funcSet @ sK591 @ sK589 ) ) )
& ( ( ap @ sK591 @ sK589 @ sK590 @ sK592 )
!= ( ap @ sK591 @ sK589 @ sK590 @ sK592 ) )
& ( $true
= ( in @ sK592 @ sK591 ) )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( funcGraphProp2 = $true )
& ( upairsetIR = $true )
& ( theprop = $true )
& ( subsetI2 = $true )
& ( binintersectSubset2 = $true )
& ( funcGraphProp1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusIRneg = $true )
& ( quantDeMorgan3 = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjL = $true )
& ( cartprodfstpairEq = $true )
& ( funcextLem = $true )
& ( funcGraphProp3 = $true )
& ( ubforcartprodlem2 = $true )
& ( symdiffE = $true )
& ( powersetE = $true )
& ( setminusELneg = $true )
& ( app = $true )
& ( kpairiskpair = $true )
& ( apProp = $true )
& ( setukpairinjL1 = $true )
& ( lam2p = $true )
& ( subsetTrans = $true )
& ( in__Cong = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( setadjoinIR = $true )
& ( setminusSubset2 = $true )
& ( brelnall1 = $true )
& ( kfstpairEq = $true )
& ( singletoninpowunion = $true )
& ( setminusEL = $true )
& ( dsetconstrI = $true )
& ( exuE3u = $true )
& ( setadjoinSub2 = $true )
& ( secondinupair = $true )
& ( dpsetconstrERa = $true )
& ( binintersectLsub = $true )
& ( setminusERneg = $true )
& ( eqinunit = $true )
& ( powersetI1 = $true )
& ( cartprodsndin = $true )
& ( setextAx = $true )
& ( ksndpairEq = $true )
& ( cartprodpairmemEL = $true )
& ( subsetE2 = $true )
& ( setukpairIL = $true )
& ( notinsingleton = $true )
& ( emptyE1 = $true )
& ( singletonsuniq = $true )
& ( setukpairIR = $true )
& ( notdallE = $true )
& ( funcext = $true )
& ( cartprodsndpairEq = $true )
& ( disjointsetsI1 = $true )
& ( prop2setE = $true )
& ( binintersectSubset4 = $true )
& ( lamProp = $true )
& ( binintersectEL = $true )
& ( binintersectER = $true )
& ( notsubsetI = $true )
& ( setunionsingleton = $true )
& ( cartprodmempair = $true )
& ( ex1E2 = $true )
& ( upairsetE = $true )
& ( setminusSubset1 = $true )
& ( dpsetconstrEL1 = $true )
& ( funcinfuncset = $true )
& ( foundationAx = $true )
& ( singletonsswitch = $true )
& ( emptysetsubset = $true )
& ( singletonprop = $true )
& ( setextsub = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK589,sK590,sK591,sK592]),skolemize(X0,sK589),skolemize(X1,sK590),skolemize(X2,sK591),skolemize(X3,sK592)],[f1484]) ).
thf(f2393,plain,
( ( ap @ sK591 @ sK589 @ sK590 @ sK592 )
!= ( ap @ sK591 @ sK589 @ sK590 @ sK592 ) ),
inference(cnf_transformation,[],[f1485]) ).
thf(f2748,plain,
$false,
inference(trivial_inequality_removal,[],[f2393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU693^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:11:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.23/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.40 % (2722586)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.40 % (2722591)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1339813436:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.40 % (2722597)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.40 % (2722597)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
% 0.54/0.40 % (2722592)lrs+10_16_si=on:nwc=1.5:random_seed=1268622477:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.40 % (2722593)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1604023553:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.40 % (2722597)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=3147544310:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.40 % (2722595)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3194969000:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.40 % (2722594)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=3017518868: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)
% 0.54/0.40 % (2722596)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1661969675:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.40 % (2722593)Instruction limit reached!
% 0.54/0.40 % (2722593)------------------------------
% 0.54/0.40 % (2722593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.40 % (2722593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.40 % (2722593)CaDiCaL version: 2.1.3
% 0.54/0.40 % (2722593)Termination reason: Instruction limit
% 0.54/0.40 % (2722593)Termination phase: shuffling
% 0.54/0.40 % (2722593)Time elapsed: 0.002 s
% 0.54/0.40 % (2722593)Peak memory usage: 10 MB
% 0.54/0.40 % (2722593)Instructions burned: 3 (million)
% 0.54/0.40 % (2722592)Instruction limit reached!
% 0.54/0.40 % (2722592)------------------------------
% 0.54/0.40 % (2722592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.40 % (2722592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.40 % (2722592)CaDiCaL version: 2.1.3
% 0.54/0.40 % (2722592)Termination reason: Instruction limit
% 0.54/0.40 % (2722592)Termination phase: shuffling
% 0.54/0.40 % (2722592)Time elapsed: 0.009 s
% 0.54/0.40 % (2722592)Peak memory usage: 10 MB
% 0.54/0.40 % (2722592)Instructions burned: 18 (million)
% 0.54/0.40 % (2722595)Instruction limit reached!
% 0.54/0.40 % (2722595)------------------------------
% 0.54/0.40 % (2722595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.40 % (2722595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.40 % (2722595)CaDiCaL version: 2.1.3
% 0.54/0.40 % (2722595)Termination reason: Instruction limit
% 0.54/0.40 % (2722595)Termination phase: Property scanning
% 0.54/0.40 % (2722595)Time elapsed: 0.011 s
% 0.54/0.40 % (2722595)Peak memory usage: 10 MB
% 0.54/0.40 % (2722595)Instructions burned: 25 (million)
% 0.54/0.40 % (2722591)Instruction limit reached!
% 0.54/0.40 % (2722591)------------------------------
% 0.54/0.40 % (2722591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.40 % (2722591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.40 % (2722591)CaDiCaL version: 2.1.3
% 0.54/0.40 % (2722591)Termination reason: Instruction limit
% 0.54/0.40 % (2722591)Termination phase: Property scanning
% 0.54/0.40 % (2722591)Time elapsed: 0.022 s
% 0.54/0.40 % (2722591)Peak memory usage: 13 MB
% 0.54/0.40 % (2722591)Instructions burned: 90 (million)
% 0.54/0.40 % (2722605)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2404807435:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.40 % (2722608)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1410462741:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.41 % (2722605)Instruction limit reached!
% 0.54/0.41 % (2722605)------------------------------
% 0.54/0.41 % (2722605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722605)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722605)Termination reason: Instruction limit
% 0.54/0.41 % (2722605)Termination phase: shuffling
% 0.54/0.41 % (2722605)Time elapsed: 0.003 s
% 0.54/0.41 % (2722605)Peak memory usage: 10 MB
% 0.54/0.41 % (2722605)Instructions burned: 5 (million)
% 0.54/0.41 % (2722607)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.41 % (2722608)Instruction limit reached!
% 0.54/0.41 % (2722608)------------------------------
% 0.54/0.41 % (2722608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722608)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722608)Termination reason: Instruction limit
% 0.54/0.41 % (2722608)Termination phase: shuffling
% 0.54/0.41 % (2722608)Time elapsed: 0.004 s
% 0.54/0.41 % (2722608)Peak memory usage: 10 MB
% 0.54/0.41 % (2722608)Instructions burned: 18 (million)
% 0.54/0.41 % (2722607)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3694279903:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.41 % (2722606)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2260880898:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.41 % (2722606)Instruction limit reached!
% 0.54/0.41 % (2722606)------------------------------
% 0.54/0.41 % (2722606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722606)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722606)Termination reason: Instruction limit
% 0.54/0.41 % (2722606)Termination phase: shuffling
% 0.54/0.41 % (2722606)Time elapsed: 0.003 s
% 0.54/0.41 % (2722607)Instruction limit reached!
% 0.54/0.41 % (2722607)------------------------------
% 0.54/0.41 % (2722607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722606)Peak memory usage: 10 MB
% 0.54/0.41 % (2722606)Instructions burned: 6 (million)
% 0.54/0.41 % (2722607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722607)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722607)Termination reason: Instruction limit
% 0.54/0.41 % (2722607)Termination phase: shuffling
% 0.54/0.41 % (2722607)Time elapsed: 0.004 s
% 0.54/0.41 % (2722607)Peak memory usage: 10 MB
% 0.54/0.41 % (2722607)Instructions burned: 8 (million)
% 0.54/0.41 % (2722596)Instruction limit reached!
% 0.54/0.41 % (2722596)------------------------------
% 0.54/0.41 % (2722596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722596)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722596)Termination reason: Instruction limit
% 0.54/0.41 % (2722596)Termination phase: Preprocessing 3
% 0.54/0.41 % (2722596)Time elapsed: 0.035 s
% 0.54/0.41 % (2722596)Peak memory usage: 12 MB
% 0.54/0.41 % (2722596)Instructions burned: 75 (million)
% 0.54/0.41 % (2722612)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=55653287:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.41 % (2722611)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
% 0.54/0.41 % (2722611)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.41 % (2722611)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1522914578:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.41 % (2722616)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.54/0.41 % (2722615)lrs+10_1_si=on:cs=on:random_seed=1808717377:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.54/0.41 % (2722617)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=60133086:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.54/0.41 % (2722616)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=3369744039:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.41 % (2722616)Instruction limit reached!
% 0.54/0.41 % (2722616)------------------------------
% 0.54/0.41 % (2722616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722616)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722616)Termination reason: Instruction limit
% 0.54/0.41 % (2722616)Termination phase: shuffling
% 0.54/0.41 % (2722616)Time elapsed: 0.002 s
% 0.54/0.41 % (2722616)Peak memory usage: 10 MB
% 0.54/0.41 % (2722616)Instructions burned: 3 (million)
% 0.54/0.41 % (2722611)Instruction limit reached!
% 0.54/0.41 % (2722611)------------------------------
% 0.54/0.41 % (2722611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722611)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722611)Termination reason: Instruction limit
% 0.54/0.41 % (2722611)Termination phase: Property scanning
% 0.54/0.41 % (2722611)Time elapsed: 0.013 s
% 0.54/0.41 % (2722611)Peak memory usage: 10 MB
% 0.54/0.41 % (2722611)Instructions burned: 29 (million)
% 0.54/0.41 % (2722615)Instruction limit reached!
% 0.54/0.41 % (2722615)------------------------------
% 0.54/0.41 % (2722615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722615)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722615)Termination reason: Instruction limit
% 0.54/0.41 % (2722615)Termination phase: shuffling
% 0.54/0.41 % (2722615)Time elapsed: 0.004 s
% 0.54/0.41 % (2722615)Peak memory usage: 10 MB
% 0.54/0.41 % (2722615)Instructions burned: 8 (million)
% 0.54/0.41 % (2722612)Instruction limit reached!
% 0.54/0.41 % (2722612)------------------------------
% 0.54/0.41 % (2722612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722612)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722612)Termination reason: Instruction limit
% 0.54/0.41 % (2722612)Termination phase: Property scanning
% 0.54/0.41 % (2722612)Time elapsed: 0.019 s
% 0.54/0.41 % (2722612)Peak memory usage: 11 MB
% 0.54/0.41 % (2722612)Instructions burned: 88 (million)
% 0.54/0.41 % (2722597)Instruction limit reached!
% 0.54/0.41 % (2722597)------------------------------
% 0.54/0.41 % (2722597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722597)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722597)Termination reason: Instruction limit
% 0.54/0.41 % (2722597)Termination phase: Saturation
% 0.54/0.41 % (2722597)Time elapsed: 0.066 s
% 0.54/0.41 % (2722597)Peak memory usage: 14 MB
% 0.54/0.41 % (2722597)Instructions burned: 158 (million)
% 0.54/0.41 % (2722626)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2630164221:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.54/0.41 % (2722617)Instruction limit reached!
% 0.54/0.41 % (2722617)------------------------------
% 0.54/0.41 % (2722617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722617)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722617)Termination reason: Instruction limit
% 0.54/0.41 % (2722617)Termination phase: Preprocessing 2
% 0.54/0.41 % (2722617)Time elapsed: 0.017 s
% 0.54/0.41 % (2722617)Peak memory usage: 11 MB
% 0.54/0.41 % (2722617)Instructions burned: 40 (million)
% 0.54/0.41 % (2722594) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2722586-2722594"...
% 0.54/0.41 % (2722623)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1211815516:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.54/0.41 % (2722624)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=313666761:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.54/0.41 % (2722625)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3142990150:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.54/0.41 % (2722594)...printing done.
% 0.54/0.41 % (2722594)Refutation found. Thanks to Tanya!
% 0.54/0.41 % SZS status Theorem for theBenchmark
% 0.54/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.54/0.41 % (2722594)------------------------------
% 0.54/0.41 % (2722594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (2722594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (2722594)CaDiCaL version: 2.1.3
% 0.54/0.41 % (2722594)Termination reason: Refutation
% 0.54/0.41 % (2722594)Time elapsed: 0.079 s
% 0.54/0.41 % (2722594)Peak memory usage: 14 MB
% 0.54/0.41 % (2722594)Instructions burned: 178 (million)
% 0.54/0.41 % (2722586)Success in time 0.126 s
% 0.54/0.41 % Vampire exiting
%------------------------------------------------------------------------------