%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU709^1 : 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 : n009.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 08:30:53 AM UTC 2026
% Result : Theorem 2.65s 0.78s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 118 ( 37 unt; 0 typ; 13 def)
% Number of atoms : 4934 (1351 equ; 0 cnn)
% Maximal formula atoms : 229 ( 41 avg)
% Number of connectives : 2807 ( 167 ~; 167 |; 938 &; 584 @)
% ( 22 <=>; 929 =>; 0 <=; 0 <~>)
% Maximal formula depth : 239 ( 20 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 : 464 ( 461 usr; 273 con; 0-4 aty)
% Number of variables : 181 ( 0 sgn 145 !; 36 ?; 181 :)
% 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_266,type,
vOR: $o > $o > $o ).
thf(func_def_267,type,
vAND: $o > $o > $o ).
thf(func_def_268,type,
vNOT: $o > $o ).
thf(func_def_269,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_270,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_271,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_272,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_273,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_274,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_275,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_276,type,
vIMP: $o > $o > $o ).
thf(func_def_277,type,
sP0: $o ).
thf(func_def_278,type,
sP1: $i > $i > $o ).
thf(func_def_279,type,
sP2: $i > $o ).
thf(func_def_280,type,
sP3: $o ).
thf(func_def_281,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_283,type,
sK6: $i > $o ).
thf(func_def_297,type,
sK20: $i > $i ).
thf(func_def_306,type,
sK29: $i > $i > $o ).
thf(func_def_307,type,
sK30: $i > $i ).
thf(func_def_308,type,
sK31: $i > $i ).
thf(func_def_309,type,
sK32: ( $i > $i > $o ) > $i > $i ).
thf(func_def_310,type,
sK33: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_311,type,
sK34: ( $i > $i > $o ) > $i > $i ).
thf(func_def_318,type,
sK41: $i > $i ).
thf(func_def_321,type,
sK44: $i > $i > ( $i > $i ) > $i ).
thf(func_def_322,type,
sK45: $i > $i > $i ).
thf(func_def_325,type,
sK48: $i > $i > $i > $i > $i ).
thf(func_def_326,type,
sK49: $i > $i > $i > $i > $i ).
thf(func_def_331,type,
sK54: $i > $i > $i ).
thf(func_def_335,type,
sK58: $i > $i ).
thf(func_def_338,type,
sK61: $i > $i > $o ).
thf(func_def_340,type,
sK63: $i > $o ).
thf(func_def_346,type,
sK69: $i > $o ).
thf(func_def_349,type,
sK72: $i > ( $i > $o ) > $i ).
thf(func_def_352,type,
sK75: $i > $i ).
thf(func_def_353,type,
sK76: ( $i > $i ) > $i > $i > $i ).
thf(func_def_359,type,
sK82: $o ).
thf(func_def_365,type,
sK88: ( $i > $i ) > $i > $i > $i ).
thf(func_def_368,type,
sK91: $i > $i ).
thf(func_def_371,type,
sK94: $o ).
thf(func_def_375,type,
sK98: $i > $o ).
thf(func_def_382,type,
sK105: $i > $o ).
thf(func_def_383,type,
sK106: $i > $o ).
thf(func_def_384,type,
sK107: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_385,type,
sK108: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_391,type,
sK114: $i > $o ).
thf(func_def_402,type,
sK125: $i > $o ).
thf(func_def_404,type,
sK127: $i > ( $i > $o ) > $i ).
thf(func_def_405,type,
sK128: $o ).
thf(func_def_406,type,
sK129: $i > ( $i > $o ) > $i ).
thf(func_def_407,type,
sK130: $i > $o ).
thf(func_def_415,type,
sK138: $o ).
thf(func_def_419,type,
sK142: $o ).
thf(func_def_430,type,
sK153: $i > $o ).
thf(func_def_431,type,
sK154: $i > $o ).
thf(func_def_432,type,
sK155: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_433,type,
sK156: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_439,type,
sK162: $i > $i > $i > $i > $i ).
thf(func_def_440,type,
sK163: $i > $i > $i > $i > $i ).
thf(func_def_441,type,
sK164: $i > $i > $i > $i > $i ).
thf(func_def_442,type,
sK165: $i > $i > $i > $i > $i ).
thf(func_def_455,type,
sK178: $i > $i ).
thf(func_def_456,type,
sK179: $i > $i ).
thf(func_def_457,type,
sK180: $i > $o ).
thf(func_def_459,type,
sK182: $i > ( $i > $o ) > $i ).
thf(func_def_465,type,
sK188: ( $i > $o ) > $i ).
thf(func_def_466,type,
sK189: ( $i > $o ) > $i ).
thf(func_def_467,type,
sK190: $i > $o ).
thf(func_def_475,type,
sK198: $i > $i ).
thf(func_def_476,type,
sK199: ( $i > $i ) > $i > $i > $i ).
thf(func_def_479,type,
sK202: $i > $o ).
thf(func_def_480,type,
sK203: $i > ( $i > $i ) > $i > $i ).
thf(func_def_482,type,
sK205: $i > $i ).
thf(func_def_488,type,
sK211: $o ).
thf(func_def_495,type,
sK218: $i > $o ).
thf(func_def_508,type,
sK231: $i > $i ).
thf(func_def_534,type,
sK257: $o ).
thf(func_def_541,type,
sK264: $i > $i > $i > $i > $i ).
thf(func_def_545,type,
sK268: $i > $i > $i > $i ).
thf(func_def_546,type,
sK269: $i > $i > $i > $i ).
thf(func_def_547,type,
sK270: $i > $i > $i ).
thf(func_def_553,type,
sK276: $o ).
thf(func_def_571,type,
sK294: $i > ( $i > $o ) > $i ).
thf(func_def_572,type,
sK295: $i > $o ).
thf(func_def_576,type,
sK299: $i > $o ).
thf(func_def_578,type,
sK301: ( $i > $o ) > $i > $i ).
thf(func_def_579,type,
sK302: $o > $i > $i > $i ).
thf(func_def_582,type,
sK305: $o ).
thf(func_def_593,type,
sK316: $o ).
thf(func_def_597,type,
sK320: $i > $i > $o ).
thf(func_def_604,type,
sK327: $i > $i > $i ).
thf(func_def_609,type,
sK332: $i > $i > $i ).
thf(func_def_610,type,
sK333: $i > $i > $i ).
thf(func_def_621,type,
sK344: $o ).
thf(func_def_636,type,
sK359: $i > $i > $o ).
thf(func_def_649,type,
sK372: $i > $i > $i ).
thf(func_def_655,type,
sK378: $i > $i ).
thf(func_def_656,type,
sK379: $i > $i ).
thf(func_def_657,type,
sK380: $i > $i ).
thf(func_def_658,type,
sK381: $i > $i ).
thf(func_def_659,type,
sK382: $i > $i ).
thf(func_def_660,type,
sK383: $i > $i > $i > $i ).
thf(func_def_661,type,
sK384: $i > $i ).
thf(func_def_662,type,
sK385: $i > $i ).
thf(func_def_663,type,
sK386: $i > $i ).
thf(func_def_664,type,
sK387: $i > $i ).
thf(func_def_665,type,
sK388: $i > $i > $i ).
thf(func_def_666,type,
sK389: $i > $i > $i > $i ).
thf(func_def_667,type,
sK390: $i > $i > $i > $i ).
thf(func_def_668,type,
sK391: $i > $i > $i > $i ).
thf(func_def_669,type,
sK392: $i > $i > $i ).
thf(func_def_670,type,
sK393: $i > $i > $i ).
thf(func_def_671,type,
sK394: $i > $i > $i ).
thf(func_def_672,type,
sK395: $i > $i > $i ).
thf(func_def_687,type,
sK410: $i > $o ).
thf(func_def_695,type,
sK418: $o ).
thf(func_def_698,type,
sK421: $i > $i > $o ).
thf(func_def_718,type,
sK441: $i > $i > $i > $i > $i ).
thf(func_def_730,type,
sK453: $i > $o ).
thf(func_def_736,type,
sK459: $o ).
thf(func_def_742,type,
sK465: $o ).
thf(func_def_763,type,
sK486: $i > $o ).
thf(func_def_765,type,
sK488: $i > ( $i > $o ) > $i > $i ).
thf(func_def_766,type,
sK489: $i > $i ).
thf(func_def_771,type,
sK494: $i > $i > $o ).
thf(func_def_777,type,
sK500: $i > $o ).
thf(func_def_781,type,
sK504: $i > $o ).
thf(func_def_782,type,
sK505: $i > $o ).
thf(func_def_785,type,
sK508: $i > $i ).
thf(func_def_787,type,
sK510: $i > ( $i > $i ) > $i > $i ).
thf(func_def_788,type,
sK511: $i > $o ).
thf(func_def_789,type,
sK512: ( $i > $o ) > $i ).
thf(func_def_793,type,
sK516: $i > $i > $i ).
thf(func_def_794,type,
sK517: $i > $o ).
thf(func_def_806,type,
sK529: $i > $i > $i ).
thf(func_def_813,type,
sK536: $i > ( $i > $o ) > $i ).
thf(func_def_814,type,
sK537: $i > ( $i > $o ) > $i ).
thf(func_def_815,type,
sK538: $i > $o ).
thf(func_def_826,type,
sK549: $i > $o ).
thf(func_def_828,type,
sK551: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_829,type,
sK552: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_839,type,
sK562: $i > $o ).
thf(func_def_840,type,
sK563: $i > $i ).
thf(func_def_841,type,
sK564: ( $i > $o ) > $i ).
thf(func_def_848,type,
sK571: $i > $o ).
thf(func_def_850,type,
sK573: ( $i > $o ) > $i > $i ).
thf(func_def_851,type,
sK574: ( $i > $o ) > $i > $i ).
thf(func_def_853,type,
sK576: $i > $o ).
thf(func_def_874,type,
sK597: $i > $i > $i ).
thf(func_def_884,type,
sK607: $i > $i ).
thf(func_def_889,type,
sK612: $i > $o ).
thf(func_def_890,type,
sK613: $i > $i ).
thf(func_def_891,type,
sK614: ( $i > $o ) > $i ).
thf(func_def_899,type,
sK622: $o ).
thf(func_def_901,type,
sK624: $o ).
thf(func_def_913,type,
sK636: $i > $o ).
thf(func_def_915,type,
sK638: ( $i > $o ) > $i > $i ).
thf(func_def_916,type,
sK639: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_917,type,
sK640: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_920,type,
sK643: $i > $o ).
thf(func_def_921,type,
sK644: $i > $o ).
thf(func_def_928,type,
sK651: $i > $i > $i > $i > $i ).
thf(func_def_940,type,
sK663: $i > $i > $o ).
thf(func_def_941,type,
sK664: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_942,type,
sK665: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_946,type,
sK669: $i > $o ).
thf(func_def_962,type,
sK685: $i > $i > $o ).
thf(func_def_967,type,
sK690: ( $i > $o ) > $i > $i ).
thf(func_def_969,type,
sK692: $i > $o ).
thf(func_def_971,type,
sK694: $i > $o ).
thf(func_def_975,type,
sK698: $o ).
thf(f31,axiom,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f52,axiom,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairsetIR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(f228,axiom,
! [X1: $o,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X2 ) ) ) )
= iftrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).
thf(f229,axiom,
( iffalse
= ( ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).
thf(f230,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
=> ! [X1: $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(f231,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
=> ! [X1: $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f230]) ).
thf(f352,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( X0
=> ( ( if @ X1 @ X0 @ X2 @ X3 )
= X2 ) ) ) )
= iftrue ),
inference(rectify,[],[f228]) ).
thf(f353,plain,
( ! [X0: $o,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true = X0 )
=> ( ( if @ X1 @ X0 @ X2 @ X3 )
= X2 ) ) ) )
<=> ( iftrue = $true ) ),
inference(fool_elimination,[],[f352]) ).
thf(f563,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
=> ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( if @ X1 @ X0 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f231]) ).
thf(f564,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 )
=> ! [X1: $i,X0: $o,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( $true
= ( in @ ( if @ X1 @ X0 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f563]) ).
thf(f605,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
inference(rectify,[],[f31]) ).
thf(f606,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[],[f605]) ).
thf(f611,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairsetIR ),
inference(rectify,[],[f52]) ).
thf(f612,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
<=> ( upairsetIR = $true ) ),
inference(fool_elimination,[],[f611]) ).
thf(f677,plain,
( iffalse
= ( ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ~ X0
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) ) ) ),
inference(rectify,[],[f229]) ).
thf(f678,plain,
( ( iffalse = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true != X0 )
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) ) ),
inference(fool_elimination,[],[f677]) ).
thf(f722,plain,
( ! [X1: $i,X2: $i,X0: $o] :
( ( ( in @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true != X0 )
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) )
<=> ( iffalse = $true ) ),
inference(flattening,[],[f678]) ).
thf(f774,plain,
( ! [X0: $o,X2: $i,X1: $i] :
( ! [X3: $i] :
( ( ( if @ X1 @ X0 @ X2 @ X3 )
= X2 )
| ( $true != X0 )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( iftrue = $true ) ),
inference(ennf_transformation,[],[f353]) ).
thf(f775,plain,
( ( iftrue = $true )
<=> ! [X1: $i,X2: $i,X0: $o] :
( ! [X3: $i] :
( ( $true != X0 )
| ( ( if @ X1 @ X0 @ X2 @ X3 )
= X2 )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f774]) ).
thf(f885,plain,
( ! [X1: $i,X2: $i,X0: $o] :
( ! [X3: $i] :
( ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 )
| ( $true = X0 )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( iffalse = $true ) ),
inference(ennf_transformation,[],[f722]) ).
thf(f886,plain,
( ( iffalse = $true )
<=> ! [X1: $i,X2: $i,X0: $o] :
( ( ( in @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( $true = X0 )
| ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 )
| ( ( in @ X3 @ X2 )
!= $true ) ) ) ),
inference(flattening,[],[f885]) ).
thf(f939,plain,
( ? [X1: $i,X0: $o,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( $true
!= ( in @ ( if @ X1 @ X0 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
& ( ( in @ X3 @ X1 )
= $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,[],[f564]) ).
thf(f940,plain,
( ( eqimpsubset2 = $true )
& ( brelnall1 = $true )
& ( binintersectER = $true )
& ( cartprodfstin = $true )
& ( emptyset__Cong = $true )
& ( uniqinunit = $true )
& ( cartprodpairsurjEq = $true )
& ( quantDeMorgan3 = $true )
& ( noeltsimpempty = $true )
& ( binunionIL = $true )
& ( ex1E2 = $true )
& ( prop2setI = $true )
& ( prop2set2propI = $true )
& ( exuE2 = $true )
& ( omega0Ax = $true )
& ( lamp = $true )
& ( foundationAx = $true )
& ( cartprodfstpairEq = $true )
& ( emptyinPowerset = $true )
& ( setunionsingleton = $true )
& ( ex1I = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( descr__Cong = $true )
& ( setukpairinjR12 = $true )
& ( emptyE1 = $true )
& ( notdallE = $true )
& ( binintersectSubset1 = $true )
& ( setukpairinjR1 = $true )
& ( setminusI = $true )
& ( dpsetconstrER = $true )
& ( ksndsingleton = $true )
& ( dpsetconstrSub = $true )
& ( powerset__Cong = $true )
& ( descrp = $true )
& ( upairset2IR = $true )
& ( funcGraphProp3 = $true )
& ( setextsub = $true )
& ( ifp = $true )
& ( ap2apEq1 = $true )
& ( setadjoinIL = $true )
& ( dpsetconstrI = $true )
& ( setadjoin__Cong = $true )
& ( wellorderingAx = $true )
& ( cartprodsndin = $true )
& ( exuI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( setminusSubset2 = $true )
& ( upairset2E = $true )
& ( iffalseProp1 = $true )
& ( subbreln = $true )
& ( dpsetconstrEL1 = $true )
& ( kpairp = $true )
& ( notdexE = $true )
& ( binintersectEL = $true )
& ( setminusELneg = $true )
& ? [X1: $i,X0: $o,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( $true
!= ( in @ ( if @ X1 @ X0 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( upairsetE = $true )
& ( in__Cong = $true )
& ( vacuousDall = $true )
& ( eta1 = $true )
& ( notsubsetI = $true )
& ( kfstpairEq = $true )
& ( setunionE = $true )
& ( subsetI1 = $true )
& ( setoftrueEq = $true )
& ( exuI2 = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( subsetE2 = $true )
& ( subsetRefl = $true )
& ( binintersectSubset3 = $true )
& ( omegaIndAx = $true )
& ( setunionE2 = $true )
& ( app = $true )
& ( setminusERneg = $true )
& ( nonemptyE1 = $true )
& ( cartprodmempaircEq = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( upairsubunion = $true )
& ( quantDeMorgan4 = $true )
& ( setminusSubset1 = $true )
& ( funcext2 = $true )
& ( symdiffIneg2 = $true )
& ( lam2lamEq = $true )
& ( singletoninpowunion = $true )
& ( ksndpairEq = $true )
& ( emptysetsubset = $true )
& ( notinemptyset = $true )
& ( exuE3u = $true )
& ( subset2powerset = $true )
& ( upairinpowunion = $true )
& ( symdiffI2 = $true )
& ( symdiffIneg1 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL2 = $true )
& ( setunionAx = $true )
& ( powersetI1 = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinSub2 = $true )
& ( sepInPowerset = $true )
& ( ex1I2 = $true )
& ( binintersectLsub = $true )
& ( omegaSAx = $true )
& ( binunionRsub = $true )
& ( lam2p = $true )
& ( setukpairinjL1 = $true )
& ( subPowSU = $true )
& ( omega__Cong = $true )
& ( inPowerset = $true )
& ( symdiffE = $true )
& ( brelnall2 = $true )
& ( inCongP = $true )
& ( funcext = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( replAx = $true )
& ( dsetconstrER = $true )
& ( binintersectSubset2 = $true )
& ( setukpairinjL = $true )
& ( singletonsswitch = $true )
& ( eta2 = $true )
& ( iffalse = $true )
& ( funcGraphProp4 = $true )
& ( setukpairIL = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( kpairsurjEq = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( cartprodsndpairEq = $true )
& ( setadjoinIR = $true )
& ( symdiffI1 = $true )
& ( singletoninpowerset = $true )
& ( disjointsetsI1 = $true )
& ( ex1E1 = $true )
& ( beta1 = $true )
& ( dsetconstrEL = $true )
& ( subsetE = $true )
& ( emptyinunitempty = $true )
& ( exuI3 = $true )
& ( setadjoinSub = $true )
& ( bs114d = $true )
& ( binunionE = $true )
& ( setukpairinjR = $true )
& ( subsetTrans = $true )
& ( powersetAx = $true )
& ( singletonprop = $true )
& ( cartprodmempair = $true )
& ( notequalI2 = $true )
& ( funcinfuncset = $true )
& ( setbeta = $true )
& ( cartprodpairmemEL = $true )
& ( subsetI2 = $true )
& ( setadjoinE = $true )
& ( upairsetIL = $true )
& ( theeq = $true )
& ( iffalseProp2 = $true )
& ( powersetI = $true )
& ( iftrue = $true )
& ( setminusER = $true )
& ( binunionEcases = $true )
& ( cartprodpairin = $true )
& ( funcGraphProp1 = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusLsub = $true )
& ( setukpairinjR2 = $true )
& ( upairsetIR = $true )
& ( apProp = $true )
& ( prop2setE = $true )
& ( iftrueProp2 = $true )
& ( setminusIRneg = $true )
& ( notinsingleton = $true )
& ( setext = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodmempair1 = $true )
& ( emptysetAx = $true )
& ( ubforcartprodlem3 = $true )
& ( setunionsingleton1 = $true )
& ( sepSubset = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setukpairinjR11 = $true )
& ( beta2 = $true )
& ( funcGraphProp2 = $true )
& ( eqbreln = $true )
& ( powersetE1 = $true )
& ( nonemptyI = $true )
& ( iftrueProp1 = $true )
& ( subsetemptysetimpeq = $true )
& ( eqinunit = $true )
& ( emptysetimpfalse = $true )
& ( singletonsuniq = $true )
& ( exu__Cong = $true )
& ( theprop = $true )
& ( dpsetconstrERa = $true )
& ( lamProp = $true )
& ( binintersectRsub = $true )
& ( singletonsubset = $true )
& ( ubforcartprodlem1 = $true )
& ( ifSingleton = $true )
& ( eqimpsubset1 = $true )
& ( funcImageSingleton = $true )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinAx = $true )
& ( exuE3e = $true )
& ( ap2apEq2 = $true )
& ( setunionI = $true )
& ( binunionLsub = $true )
& ( exuEu = $true )
& ( emptysetE = $true )
& ( binintersectI = $true )
& ( setextAx = $true )
& ( binunionIR = $true )
& ( dsetconstr__Cong = $true )
& ( setminusEL = $true )
& ( secondinupair = $true )
& ( nonemptyI1 = $true )
& ( binintersectSubset4 = $true )
& ( kfstsingleton = $true )
& ( exuE1 = $true )
& ( funcextLem = $true )
& ( setunionsingleton2 = $true ) ),
inference(flattening,[],[f939]) ).
thf(f1112,plain,
( ( ( iffalse = $true )
| ? [X1: $i,X2: $i,X0: $o] :
( ( ( in @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( $true != X0 )
& ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X3 )
& ( ( in @ X3 @ X2 )
= $true ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $o] :
( ( ( in @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( $true = X0 )
| ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
| ( iffalse != $true ) ) ),
inference(nnf_transformation,[],[f886]) ).
thf(f1113,plain,
( ( ( iffalse = $true )
| ? [X0: $i,X1: $i,X2: $o] :
( ( $true
= ( in @ X0 @ X1 ) )
& ? [X3: $i] :
( ( $true != X2 )
& ( ( if @ X1 @ X2 @ X0 @ X3 )
!= X3 )
& ( ( in @ X3 @ X1 )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $o] :
( ( ( in @ X4 @ X5 )
!= $true )
| ! [X7: $i] :
( ( $true = X6 )
| ( ( if @ X5 @ X6 @ X4 @ X7 )
= X7 )
| ( $true
!= ( in @ X7 @ X5 ) ) ) )
| ( iffalse != $true ) ) ),
inference(rectify,[],[f1112]) ).
thf(f1114,plain,
( ( ( iffalse = $true )
| ( ( $true
= ( in @ sK140 @ sK141 ) )
& ( $true != sK142 )
& ( ( if @ sK141 @ sK142 @ sK140 @ sK143 )
!= sK143 )
& ( $true
= ( in @ sK143 @ sK141 ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $o] :
( ( ( in @ X4 @ X5 )
!= $true )
| ! [X7: $i] :
( ( $true = X6 )
| ( ( if @ X5 @ X6 @ X4 @ X7 )
= X7 )
| ( $true
!= ( in @ X7 @ X5 ) ) ) )
| ( iffalse != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140,sK141,sK142,sK143]),skolemize(X0,sK140),skolemize(X1,sK141),skolemize(X2,sK142),skolemize(X3,sK143)],[f1113]) ).
thf(f1362,plain,
( ( ( iftrue = $true )
| ? [X1: $i,X2: $i,X0: $o] :
( ? [X3: $i] :
( ( $true = X0 )
& ( ( if @ X1 @ X0 @ X2 @ X3 )
!= X2 )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $o] :
( ! [X3: $i] :
( ( $true != X0 )
| ( ( if @ X1 @ X0 @ X2 @ X3 )
= X2 )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( iftrue != $true ) ) ),
inference(nnf_transformation,[],[f775]) ).
thf(f1363,plain,
( ( ( iftrue = $true )
| ? [X0: $i,X1: $i,X2: $o] :
( ? [X3: $i] :
( ( $true = X2 )
& ( ( if @ X0 @ X2 @ X1 @ X3 )
!= X1 )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $o] :
( ! [X7: $i] :
( ( $true != X6 )
| ( ( if @ X4 @ X6 @ X5 @ X7 )
= X5 )
| ( $true
!= ( in @ X7 @ X4 ) ) )
| ( $true
!= ( in @ X5 @ X4 ) ) )
| ( iftrue != $true ) ) ),
inference(rectify,[],[f1362]) ).
thf(f1364,plain,
( ( ( iftrue = $true )
| ( ( $true = sK418 )
& ( ( if @ sK416 @ sK418 @ sK417 @ sK419 )
!= sK417 )
& ( $true
= ( in @ sK419 @ sK416 ) )
& ( $true
= ( in @ sK417 @ sK416 ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $o] :
( ! [X7: $i] :
( ( $true != X6 )
| ( ( if @ X4 @ X6 @ X5 @ X7 )
= X5 )
| ( $true
!= ( in @ X7 @ X4 ) ) )
| ( $true
!= ( in @ X5 @ X4 ) ) )
| ( iftrue != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK416,sK417,sK418,sK419]),skolemize(X0,sK416),skolemize(X1,sK417),skolemize(X2,sK418),skolemize(X3,sK419)],[f1363]) ).
thf(f1389,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f606]) ).
thf(f1390,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ) ) ),
inference(rectify,[],[f1389]) ).
thf(f1391,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK446 @ ( setadjoin @ sK446 @ sK447 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK446,sK447]),skolemize(X2,sK446),skolemize(X3,sK447)],[f1390]) ).
thf(f1443,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairsetIR != $true ) )
& ( ( upairsetIR = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f612]) ).
thf(f1444,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairsetIR != $true ) )
& ( ( upairsetIR = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f1443]) ).
thf(f1445,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairsetIR != $true ) )
& ( ( upairsetIR = $true )
| ( $true
!= ( in @ sK492 @ ( setadjoin @ sK491 @ ( setadjoin @ sK492 @ emptyset ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK491,sK492]),skolemize(X2,sK491),skolemize(X3,sK492)],[f1444]) ).
thf(f1645,plain,
( ( eqimpsubset2 = $true )
& ( brelnall1 = $true )
& ( binintersectER = $true )
& ( cartprodfstin = $true )
& ( emptyset__Cong = $true )
& ( uniqinunit = $true )
& ( cartprodpairsurjEq = $true )
& ( quantDeMorgan3 = $true )
& ( noeltsimpempty = $true )
& ( binunionIL = $true )
& ( ex1E2 = $true )
& ( prop2setI = $true )
& ( prop2set2propI = $true )
& ( exuE2 = $true )
& ( omega0Ax = $true )
& ( lamp = $true )
& ( foundationAx = $true )
& ( cartprodfstpairEq = $true )
& ( emptyinPowerset = $true )
& ( setunionsingleton = $true )
& ( ex1I = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( descr__Cong = $true )
& ( setukpairinjR12 = $true )
& ( emptyE1 = $true )
& ( notdallE = $true )
& ( binintersectSubset1 = $true )
& ( setukpairinjR1 = $true )
& ( setminusI = $true )
& ( dpsetconstrER = $true )
& ( ksndsingleton = $true )
& ( dpsetconstrSub = $true )
& ( powerset__Cong = $true )
& ( descrp = $true )
& ( upairset2IR = $true )
& ( funcGraphProp3 = $true )
& ( setextsub = $true )
& ( ifp = $true )
& ( ap2apEq1 = $true )
& ( setadjoinIL = $true )
& ( dpsetconstrI = $true )
& ( setadjoin__Cong = $true )
& ( wellorderingAx = $true )
& ( cartprodsndin = $true )
& ( exuI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( setminusSubset2 = $true )
& ( upairset2E = $true )
& ( iffalseProp1 = $true )
& ( subbreln = $true )
& ( dpsetconstrEL1 = $true )
& ( kpairp = $true )
& ( notdexE = $true )
& ( binintersectEL = $true )
& ( setminusELneg = $true )
& ? [X0: $i,X1: $o,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( upairsetE = $true )
& ( in__Cong = $true )
& ( vacuousDall = $true )
& ( eta1 = $true )
& ( notsubsetI = $true )
& ( kfstpairEq = $true )
& ( setunionE = $true )
& ( subsetI1 = $true )
& ( setoftrueEq = $true )
& ( exuI2 = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( subsetE2 = $true )
& ( subsetRefl = $true )
& ( binintersectSubset3 = $true )
& ( omegaIndAx = $true )
& ( setunionE2 = $true )
& ( app = $true )
& ( setminusERneg = $true )
& ( nonemptyE1 = $true )
& ( cartprodmempaircEq = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( upairsubunion = $true )
& ( quantDeMorgan4 = $true )
& ( setminusSubset1 = $true )
& ( funcext2 = $true )
& ( symdiffIneg2 = $true )
& ( lam2lamEq = $true )
& ( singletoninpowunion = $true )
& ( ksndpairEq = $true )
& ( emptysetsubset = $true )
& ( notinemptyset = $true )
& ( exuE3u = $true )
& ( subset2powerset = $true )
& ( upairinpowunion = $true )
& ( symdiffI2 = $true )
& ( symdiffIneg1 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL2 = $true )
& ( setunionAx = $true )
& ( powersetI1 = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinSub2 = $true )
& ( sepInPowerset = $true )
& ( ex1I2 = $true )
& ( binintersectLsub = $true )
& ( omegaSAx = $true )
& ( binunionRsub = $true )
& ( lam2p = $true )
& ( setukpairinjL1 = $true )
& ( subPowSU = $true )
& ( omega__Cong = $true )
& ( inPowerset = $true )
& ( symdiffE = $true )
& ( brelnall2 = $true )
& ( inCongP = $true )
& ( funcext = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( replAx = $true )
& ( dsetconstrER = $true )
& ( binintersectSubset2 = $true )
& ( setukpairinjL = $true )
& ( singletonsswitch = $true )
& ( eta2 = $true )
& ( iffalse = $true )
& ( funcGraphProp4 = $true )
& ( setukpairIL = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( kpairsurjEq = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( cartprodsndpairEq = $true )
& ( setadjoinIR = $true )
& ( symdiffI1 = $true )
& ( singletoninpowerset = $true )
& ( disjointsetsI1 = $true )
& ( ex1E1 = $true )
& ( beta1 = $true )
& ( dsetconstrEL = $true )
& ( subsetE = $true )
& ( emptyinunitempty = $true )
& ( exuI3 = $true )
& ( setadjoinSub = $true )
& ( bs114d = $true )
& ( binunionE = $true )
& ( setukpairinjR = $true )
& ( subsetTrans = $true )
& ( powersetAx = $true )
& ( singletonprop = $true )
& ( cartprodmempair = $true )
& ( notequalI2 = $true )
& ( funcinfuncset = $true )
& ( setbeta = $true )
& ( cartprodpairmemEL = $true )
& ( subsetI2 = $true )
& ( setadjoinE = $true )
& ( upairsetIL = $true )
& ( theeq = $true )
& ( iffalseProp2 = $true )
& ( powersetI = $true )
& ( iftrue = $true )
& ( setminusER = $true )
& ( binunionEcases = $true )
& ( cartprodpairin = $true )
& ( funcGraphProp1 = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusLsub = $true )
& ( setukpairinjR2 = $true )
& ( upairsetIR = $true )
& ( apProp = $true )
& ( prop2setE = $true )
& ( iftrueProp2 = $true )
& ( setminusIRneg = $true )
& ( notinsingleton = $true )
& ( setext = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodmempair1 = $true )
& ( emptysetAx = $true )
& ( ubforcartprodlem3 = $true )
& ( setunionsingleton1 = $true )
& ( sepSubset = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setukpairinjR11 = $true )
& ( beta2 = $true )
& ( funcGraphProp2 = $true )
& ( eqbreln = $true )
& ( powersetE1 = $true )
& ( nonemptyI = $true )
& ( iftrueProp1 = $true )
& ( subsetemptysetimpeq = $true )
& ( eqinunit = $true )
& ( emptysetimpfalse = $true )
& ( singletonsuniq = $true )
& ( exu__Cong = $true )
& ( theprop = $true )
& ( dpsetconstrERa = $true )
& ( lamProp = $true )
& ( binintersectRsub = $true )
& ( singletonsubset = $true )
& ( ubforcartprodlem1 = $true )
& ( ifSingleton = $true )
& ( eqimpsubset1 = $true )
& ( funcImageSingleton = $true )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinAx = $true )
& ( exuE3e = $true )
& ( ap2apEq2 = $true )
& ( setunionI = $true )
& ( binunionLsub = $true )
& ( exuEu = $true )
& ( emptysetE = $true )
& ( binintersectI = $true )
& ( setextAx = $true )
& ( binunionIR = $true )
& ( dsetconstr__Cong = $true )
& ( setminusEL = $true )
& ( secondinupair = $true )
& ( nonemptyI1 = $true )
& ( binintersectSubset4 = $true )
& ( kfstsingleton = $true )
& ( exuE1 = $true )
& ( funcextLem = $true )
& ( setunionsingleton2 = $true ) ),
inference(rectify,[],[f940]) ).
thf(f1646,plain,
( ( eqimpsubset2 = $true )
& ( brelnall1 = $true )
& ( binintersectER = $true )
& ( cartprodfstin = $true )
& ( emptyset__Cong = $true )
& ( uniqinunit = $true )
& ( cartprodpairsurjEq = $true )
& ( quantDeMorgan3 = $true )
& ( noeltsimpempty = $true )
& ( binunionIL = $true )
& ( ex1E2 = $true )
& ( prop2setI = $true )
& ( prop2set2propI = $true )
& ( exuE2 = $true )
& ( omega0Ax = $true )
& ( lamp = $true )
& ( foundationAx = $true )
& ( cartprodfstpairEq = $true )
& ( emptyinPowerset = $true )
& ( setunionsingleton = $true )
& ( ex1I = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( descr__Cong = $true )
& ( setukpairinjR12 = $true )
& ( emptyE1 = $true )
& ( notdallE = $true )
& ( binintersectSubset1 = $true )
& ( setukpairinjR1 = $true )
& ( setminusI = $true )
& ( dpsetconstrER = $true )
& ( ksndsingleton = $true )
& ( dpsetconstrSub = $true )
& ( powerset__Cong = $true )
& ( descrp = $true )
& ( upairset2IR = $true )
& ( funcGraphProp3 = $true )
& ( setextsub = $true )
& ( ifp = $true )
& ( ap2apEq1 = $true )
& ( setadjoinIL = $true )
& ( dpsetconstrI = $true )
& ( setadjoin__Cong = $true )
& ( wellorderingAx = $true )
& ( cartprodsndin = $true )
& ( exuI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( setminusSubset2 = $true )
& ( upairset2E = $true )
& ( iffalseProp1 = $true )
& ( subbreln = $true )
& ( dpsetconstrEL1 = $true )
& ( kpairp = $true )
& ( notdexE = $true )
& ( binintersectEL = $true )
& ( setminusELneg = $true )
& ( $true
= ( in @ sK699 @ sK697 ) )
& ( $true
!= ( in @ ( if @ sK697 @ sK698 @ sK699 @ sK700 ) @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) )
& ( $true
= ( in @ sK700 @ sK697 ) )
& ( upairsetE = $true )
& ( in__Cong = $true )
& ( vacuousDall = $true )
& ( eta1 = $true )
& ( notsubsetI = $true )
& ( kfstpairEq = $true )
& ( setunionE = $true )
& ( subsetI1 = $true )
& ( setoftrueEq = $true )
& ( exuI2 = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( subsetE2 = $true )
& ( subsetRefl = $true )
& ( binintersectSubset3 = $true )
& ( omegaIndAx = $true )
& ( setunionE2 = $true )
& ( app = $true )
& ( setminusERneg = $true )
& ( nonemptyE1 = $true )
& ( cartprodmempaircEq = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( upairsubunion = $true )
& ( quantDeMorgan4 = $true )
& ( setminusSubset1 = $true )
& ( funcext2 = $true )
& ( symdiffIneg2 = $true )
& ( lam2lamEq = $true )
& ( singletoninpowunion = $true )
& ( ksndpairEq = $true )
& ( emptysetsubset = $true )
& ( notinemptyset = $true )
& ( exuE3u = $true )
& ( subset2powerset = $true )
& ( upairinpowunion = $true )
& ( symdiffI2 = $true )
& ( symdiffIneg1 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL2 = $true )
& ( setunionAx = $true )
& ( powersetI1 = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinSub2 = $true )
& ( sepInPowerset = $true )
& ( ex1I2 = $true )
& ( binintersectLsub = $true )
& ( omegaSAx = $true )
& ( binunionRsub = $true )
& ( lam2p = $true )
& ( setukpairinjL1 = $true )
& ( subPowSU = $true )
& ( omega__Cong = $true )
& ( inPowerset = $true )
& ( symdiffE = $true )
& ( brelnall2 = $true )
& ( inCongP = $true )
& ( funcext = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( replAx = $true )
& ( dsetconstrER = $true )
& ( binintersectSubset2 = $true )
& ( setukpairinjL = $true )
& ( singletonsswitch = $true )
& ( eta2 = $true )
& ( iffalse = $true )
& ( funcGraphProp4 = $true )
& ( setukpairIL = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( kpairsurjEq = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( cartprodsndpairEq = $true )
& ( setadjoinIR = $true )
& ( symdiffI1 = $true )
& ( singletoninpowerset = $true )
& ( disjointsetsI1 = $true )
& ( ex1E1 = $true )
& ( beta1 = $true )
& ( dsetconstrEL = $true )
& ( subsetE = $true )
& ( emptyinunitempty = $true )
& ( exuI3 = $true )
& ( setadjoinSub = $true )
& ( bs114d = $true )
& ( binunionE = $true )
& ( setukpairinjR = $true )
& ( subsetTrans = $true )
& ( powersetAx = $true )
& ( singletonprop = $true )
& ( cartprodmempair = $true )
& ( notequalI2 = $true )
& ( funcinfuncset = $true )
& ( setbeta = $true )
& ( cartprodpairmemEL = $true )
& ( subsetI2 = $true )
& ( setadjoinE = $true )
& ( upairsetIL = $true )
& ( theeq = $true )
& ( iffalseProp2 = $true )
& ( powersetI = $true )
& ( iftrue = $true )
& ( setminusER = $true )
& ( binunionEcases = $true )
& ( cartprodpairin = $true )
& ( funcGraphProp1 = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusLsub = $true )
& ( setukpairinjR2 = $true )
& ( upairsetIR = $true )
& ( apProp = $true )
& ( prop2setE = $true )
& ( iftrueProp2 = $true )
& ( setminusIRneg = $true )
& ( notinsingleton = $true )
& ( setext = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodmempair1 = $true )
& ( emptysetAx = $true )
& ( ubforcartprodlem3 = $true )
& ( setunionsingleton1 = $true )
& ( sepSubset = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setukpairinjR11 = $true )
& ( beta2 = $true )
& ( funcGraphProp2 = $true )
& ( eqbreln = $true )
& ( powersetE1 = $true )
& ( nonemptyI = $true )
& ( iftrueProp1 = $true )
& ( subsetemptysetimpeq = $true )
& ( eqinunit = $true )
& ( emptysetimpfalse = $true )
& ( singletonsuniq = $true )
& ( exu__Cong = $true )
& ( theprop = $true )
& ( dpsetconstrERa = $true )
& ( lamProp = $true )
& ( binintersectRsub = $true )
& ( singletonsubset = $true )
& ( ubforcartprodlem1 = $true )
& ( ifSingleton = $true )
& ( eqimpsubset1 = $true )
& ( funcImageSingleton = $true )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinAx = $true )
& ( exuE3e = $true )
& ( ap2apEq2 = $true )
& ( setunionI = $true )
& ( binunionLsub = $true )
& ( exuEu = $true )
& ( emptysetE = $true )
& ( binintersectI = $true )
& ( setextAx = $true )
& ( binunionIR = $true )
& ( dsetconstr__Cong = $true )
& ( setminusEL = $true )
& ( secondinupair = $true )
& ( nonemptyI1 = $true )
& ( binintersectSubset4 = $true )
& ( kfstsingleton = $true )
& ( exuE1 = $true )
& ( funcextLem = $true )
& ( setunionsingleton2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK697,sK698,sK699,sK700]),skolemize(X0,sK697),skolemize(X1,sK698),skolemize(X2,sK699),skolemize(X3,sK700)],[f1645]) ).
thf(f1826,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( iffalse != $true )
| ( $true = X6 )
| ( ( if @ X5 @ X6 @ X4 @ X7 )
= X7 )
| ( ( in @ X4 @ X5 )
!= $true )
| ( $true
!= ( in @ X7 @ X5 ) ) ),
inference(cnf_transformation,[],[f1114]) ).
thf(f2210,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( $true != X6 )
| ( ( if @ X4 @ X6 @ X5 @ X7 )
= X5 )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X5 @ X4 ) )
| ( iftrue != $true ) ),
inference(cnf_transformation,[],[f1364]) ).
thf(f2245,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[],[f1391]) ).
thf(f2305,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairsetIR != $true ) ),
inference(cnf_transformation,[],[f1445]) ).
thf(f2621,plain,
upairsetIR = $true,
inference(cnf_transformation,[],[f1646]) ).
thf(f2629,plain,
iftrue = $true,
inference(cnf_transformation,[],[f1646]) ).
thf(f2666,plain,
iffalse = $true,
inference(cnf_transformation,[],[f1646]) ).
thf(f2734,plain,
( $true
= ( in @ sK700 @ sK697 ) ),
inference(cnf_transformation,[],[f1646]) ).
thf(f2735,plain,
( $true
!= ( in @ ( if @ sK697 @ sK698 @ sK699 @ sK700 ) @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f1646]) ).
thf(f2736,plain,
( $true
= ( in @ sK699 @ sK697 ) ),
inference(cnf_transformation,[],[f1646]) ).
thf(f2752,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f1646]) ).
thf(f2823,plain,
! [X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( iftrue != $true )
| ( $true
!= ( in @ X5 @ X4 ) )
| ( ( if @ X4 @ $true @ X5 @ X7 )
= X5 ) ),
inference(equality_resolution,[],[f2210]) ).
thf(f3708,definition,
( spl703_155
<=> ! [X5: $i,X4: $i,X7: $i,X6: $o] :
( ( $true = X6 )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( if @ X5 @ X6 @ X4 @ X7 )
= X7 ) ) ),
introduced(definition,[new_symbols(definition,[spl703_155])],[avatar_definition]) ).
thf(f3709,plain,
( ! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( ( if @ X5 @ X6 @ X4 @ X7 )
= X7 )
| ( $true = X6 )
| ( ( in @ X4 @ X5 )
!= $true )
| ( $true
!= ( in @ X7 @ X5 ) ) )
| ~ spl703_155 ),
inference(avatar_component_clause,[],[f3708]) ).
thf(f3711,definition,
( spl703_156
<=> ( iffalse = $true ) ),
introduced(definition,[new_symbols(definition,[spl703_156])],[avatar_definition]) ).
thf(f3714,plain,
( spl703_155
| ~ spl703_156 ),
inference(avatar_split_clause,[],[f1826,f3711,f3708]) ).
thf(f4407,definition,
( spl703_313
<=> ( $true
= ( in @ ( if @ sK697 @ sK698 @ sK699 @ sK700 ) @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl703_313])],[avatar_definition]) ).
thf(f4409,plain,
( ( $true
!= ( in @ ( if @ sK697 @ sK698 @ sK699 @ sK700 ) @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) )
| spl703_313 ),
inference(avatar_component_clause,[],[f4407]) ).
thf(f4410,plain,
~ spl703_313,
inference(avatar_split_clause,[],[f2735,f4407]) ).
thf(f4493,definition,
( spl703_333
<=> ( upairsetIR = $true ) ),
introduced(definition,[new_symbols(definition,[spl703_333])],[avatar_definition]) ).
thf(f5177,definition,
( spl703_483
<=> ( setadjoinIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl703_483])],[avatar_definition]) ).
thf(f5180,plain,
spl703_483,
inference(avatar_split_clause,[],[f2752,f5177]) ).
thf(f5377,definition,
( spl703_524
<=> ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl703_524])],[avatar_definition]) ).
thf(f5378,plain,
( ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ~ spl703_524 ),
inference(avatar_component_clause,[],[f5377]) ).
thf(f5438,definition,
( spl703_538
<=> ( iftrue = $true ) ),
introduced(definition,[new_symbols(definition,[spl703_538])],[avatar_definition]) ).
thf(f5716,plain,
spl703_156,
inference(avatar_split_clause,[],[f2666,f3711]) ).
thf(f5785,definition,
( spl703_609
<=> ! [X4: $i,X5: $i] :
( $true
= ( in @ X5 @ ( setadjoin @ X5 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl703_609])],[avatar_definition]) ).
thf(f5786,plain,
( ! [X4: $i,X5: $i] :
( $true
= ( in @ X5 @ ( setadjoin @ X5 @ X4 ) ) )
| ~ spl703_609 ),
inference(avatar_component_clause,[],[f5785]) ).
thf(f5797,plain,
( spl703_524
| ~ spl703_333 ),
inference(avatar_split_clause,[],[f2305,f4493,f5377]) ).
thf(f5811,definition,
( spl703_614
<=> ( $true
= ( in @ sK700 @ sK697 ) ) ),
introduced(definition,[new_symbols(definition,[spl703_614])],[avatar_definition]) ).
thf(f5813,plain,
( ( $true
= ( in @ sK700 @ sK697 ) )
| ~ spl703_614 ),
inference(avatar_component_clause,[],[f5811]) ).
thf(f5814,plain,
spl703_614,
inference(avatar_split_clause,[],[f2734,f5811]) ).
thf(f6008,definition,
( spl703_654
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( ( if @ X4 @ $true @ X5 @ X7 )
= X5 )
| ( $true
!= ( in @ X5 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl703_654])],[avatar_definition]) ).
thf(f6009,plain,
( ! [X7: $i,X4: $i,X5: $i] :
( ( ( if @ X4 @ $true @ X5 @ X7 )
= X5 )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X5 @ X4 ) ) )
| ~ spl703_654 ),
inference(avatar_component_clause,[],[f6008]) ).
thf(f6010,plain,
( spl703_654
| ~ spl703_538 ),
inference(avatar_split_clause,[],[f2823,f5438,f6008]) ).
thf(f6011,plain,
spl703_538,
inference(avatar_split_clause,[],[f2629,f5438]) ).
thf(f6496,plain,
( ~ spl703_483
| spl703_609 ),
inference(avatar_split_clause,[],[f2245,f5785,f5177]) ).
thf(f7717,definition,
( spl703_1008
<=> ( $true
= ( in @ sK699 @ sK697 ) ) ),
introduced(definition,[new_symbols(definition,[spl703_1008])],[avatar_definition]) ).
thf(f7719,plain,
( ( $true
= ( in @ sK699 @ sK697 ) )
| ~ spl703_1008 ),
inference(avatar_component_clause,[],[f7717]) ).
thf(f7720,plain,
spl703_1008,
inference(avatar_split_clause,[],[f2736,f7717]) ).
thf(f8079,plain,
spl703_333,
inference(avatar_split_clause,[],[f2621,f4493]) ).
thf(f8135,plain,
( ( $false = sK698 )
| ( $true
!= ( in @ ( if @ sK697 @ $true @ sK699 @ sK700 ) @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) )
| spl703_313 ),
inference(fool_paramodulation,[],[f4409]) ).
thf(f8137,definition,
( spl703_1091
<=> ( $true
= ( in @ ( if @ sK697 @ $true @ sK699 @ sK700 ) @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl703_1091])],[avatar_definition]) ).
thf(f8139,plain,
( ( $true
!= ( in @ ( if @ sK697 @ $true @ sK699 @ sK700 ) @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) )
| spl703_1091 ),
inference(avatar_component_clause,[],[f8137]) ).
thf(f8141,definition,
( spl703_1092
<=> ( $false = sK698 ) ),
introduced(definition,[new_symbols(definition,[spl703_1092])],[avatar_definition]) ).
thf(f8143,plain,
( ( $false = sK698 )
| ~ spl703_1092 ),
inference(avatar_component_clause,[],[f8141]) ).
thf(f8145,plain,
( ~ spl703_1091
| spl703_1092
| spl703_313 ),
inference(avatar_split_clause,[],[f8135,f4407,f8141,f8137]) ).
thf(f11091,plain,
( ( $true
!= ( in @ sK700 @ sK697 ) )
| ( $true
!= ( in @ sK699 @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) )
| ( $true
!= ( in @ sK699 @ sK697 ) )
| ~ spl703_654
| spl703_1091 ),
inference(superposition,[],[f8139,f6009]) ).
thf(f11095,plain,
( ( $true
!= ( in @ sK699 @ sK697 ) )
| ( $true
!= ( in @ sK699 @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) )
| ~ spl703_614
| ~ spl703_654
| spl703_1091 ),
inference(forward_subsumption_resolution,[],[f11091,f5813]) ).
thf(f11098,plain,
( ( $true
!= ( in @ sK699 @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) )
| ~ spl703_614
| ~ spl703_654
| ~ spl703_1008
| spl703_1091 ),
inference(forward_subsumption_resolution,[],[f11095,f7719]) ).
thf(f11109,plain,
( $false
| ~ spl703_609
| ~ spl703_614
| ~ spl703_654
| ~ spl703_1008
| spl703_1091 ),
inference(forward_subsumption_resolution,[],[f11098,f5786]) ).
thf(f11110,plain,
( ~ spl703_609
| ~ spl703_614
| ~ spl703_654
| ~ spl703_1008
| spl703_1091 ),
inference(avatar_contradiction_clause,[],[f11109]) ).
thf(f11150,plain,
( ( $true
!= ( in @ sK700 @ ( setadjoin @ sK699 @ ( setadjoin @ sK700 @ emptyset ) ) ) )
| ( $true = sK698 )
| ( $true
!= ( in @ sK699 @ sK697 ) )
| ( $true
!= ( in @ sK700 @ sK697 ) )
| ~ spl703_155
| spl703_313 ),
inference(superposition,[],[f4409,f3709]) ).
thf(f11154,plain,
( ( $true
!= ( in @ sK699 @ sK697 ) )
| ( $true
!= ( in @ sK700 @ sK697 ) )
| ( $true = sK698 )
| ~ spl703_155
| spl703_313
| ~ spl703_524 ),
inference(forward_subsumption_resolution,[],[f11150,f5378]) ).
thf(f11158,plain,
( ( $true = sK698 )
| ( $true
!= ( in @ sK700 @ sK697 ) )
| ~ spl703_155
| spl703_313
| ~ spl703_524
| ~ spl703_1008 ),
inference(forward_subsumption_resolution,[],[f11154,f7719]) ).
thf(f11164,plain,
( ( $true = sK698 )
| ~ spl703_155
| spl703_313
| ~ spl703_524
| ~ spl703_614
| ~ spl703_1008 ),
inference(forward_subsumption_resolution,[],[f11158,f5813]) ).
thf(f11168,plain,
( ( $true = $false )
| ~ spl703_155
| spl703_313
| ~ spl703_524
| ~ spl703_614
| ~ spl703_1008
| ~ spl703_1092 ),
inference(forward_demodulation,[],[f11164,f8143]) ).
thf(f11169,plain,
( $false
| ~ spl703_155
| spl703_313
| ~ spl703_524
| ~ spl703_614
| ~ spl703_1008
| ~ spl703_1092 ),
inference(trivial_inequality_removal,[],[f11168]) ).
thf(f11170,plain,
( ~ spl703_155
| spl703_313
| ~ spl703_524
| ~ spl703_614
| ~ spl703_1008
| ~ spl703_1092 ),
inference(avatar_contradiction_clause,[],[f11169]) ).
cnf(s99,plain,
( spl703_155
| ~ spl703_156 ),
inference(sat_conversion,[],[f3714]) ).
cnf(s212,plain,
~ spl703_313,
inference(sat_conversion,[],[f4410]) ).
cnf(s358,plain,
spl703_483,
inference(sat_conversion,[],[f5180]) ).
cnf(s488,plain,
spl703_156,
inference(sat_conversion,[],[f5716]) ).
cnf(s510,plain,
( ~ spl703_333
| spl703_524 ),
inference(sat_conversion,[],[f5797]) ).
cnf(s516,plain,
spl703_614,
inference(sat_conversion,[],[f5814]) ).
cnf(s570,plain,
( ~ spl703_538
| spl703_654 ),
inference(sat_conversion,[],[f6010]) ).
cnf(s571,plain,
spl703_538,
inference(sat_conversion,[],[f6011]) ).
cnf(s693,plain,
( ~ spl703_483
| spl703_609 ),
inference(sat_conversion,[],[f6496]) ).
cnf(s1008,plain,
spl703_1008,
inference(sat_conversion,[],[f7720]) ).
cnf(s1101,plain,
spl703_333,
inference(sat_conversion,[],[f8079]) ).
cnf(s1117,plain,
( spl703_313
| ~ spl703_1091
| spl703_1092 ),
inference(sat_conversion,[],[f8145]) ).
cnf(s1203,plain,
( ~ spl703_609
| ~ spl703_614
| ~ spl703_654
| ~ spl703_1008
| spl703_1091 ),
inference(sat_conversion,[],[f11110]) ).
cnf(s1210,plain,
( ~ spl703_155
| spl703_313
| ~ spl703_524
| ~ spl703_614
| ~ spl703_1008
| ~ spl703_1092 ),
inference(sat_conversion,[],[f11170]) ).
cnf(s1280,plain,
spl703_654,
inference(rat,[],[s570,s571]) ).
cnf(s1300,plain,
spl703_524,
inference(rat,[],[s510,s1101]) ).
cnf(s1351,plain,
spl703_609,
inference(rat,[],[s693,s358]) ).
cnf(s1352,plain,
spl703_1091,
inference(rat,[],[s1203,s516,s1008,s1280,s1351]) ).
cnf(s1417,plain,
spl703_1092,
inference(rat,[],[s1117,s1352,s212]) ).
cnf(s1422,plain,
~ spl703_155,
inference(rat,[],[s1210,s212,s1008,s516,s1300,s1417]) ).
cnf(s1479,plain,
$false,
inference(rat,[],[s99,s488,s1422]) ).
thf(f11171,plain,
$false,
inference(avatar_sat_refutation,[],[s1479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU709^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n009.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 14:13:15 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running higher-order theorem proving
% 0.06/0.26 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
% 0.62/0.42 % (4066031)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.62/0.42 % (4066036)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3792872695:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.62/0.42 % (4066037)lrs+10_16_si=on:nwc=1.5:random_seed=1050122564:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.62/0.42 % (4066038)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3865957891:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.62/0.42 % (4066041)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1674856036:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.62/0.42 % (4066040)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3635521414:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.62/0.42 % (4066038)Instruction limit reached!
% 0.62/0.42 % (4066038)------------------------------
% 0.62/0.42 % (4066038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.42 % (4066038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.42 % (4066038)CaDiCaL version: 2.1.3
% 0.62/0.42 % (4066038)Termination reason: Instruction limit
% 0.62/0.42 % (4066038)Termination phase: shuffling
% 0.62/0.42 % (4066038)Time elapsed: 0.003 s
% 0.62/0.42 % (4066038)Peak memory usage: 10 MB
% 0.62/0.42 % (4066038)Instructions burned: 4 (million)
% 0.62/0.42 % (4066037)Instruction limit reached!
% 0.62/0.42 % (4066037)------------------------------
% 0.62/0.42 % (4066037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.42 % (4066037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.42 % (4066037)CaDiCaL version: 2.1.3
% 0.62/0.42 % (4066037)Termination reason: Instruction limit
% 0.62/0.42 % (4066037)Termination phase: shuffling
% 0.62/0.42 % (4066037)Time elapsed: 0.009 s
% 0.62/0.42 % (4066037)Peak memory usage: 10 MB
% 0.62/0.42 % (4066037)Instructions burned: 18 (million)
% 0.62/0.42 % (4066040)Instruction limit reached!
% 0.62/0.42 % (4066040)------------------------------
% 0.62/0.42 % (4066040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.42 % (4066040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.42 % (4066040)CaDiCaL version: 2.1.3
% 0.62/0.42 % (4066040)Termination reason: Instruction limit
% 0.62/0.42 % (4066040)Termination phase: Property scanning
% 0.62/0.42 % (4066040)Time elapsed: 0.012 s
% 0.62/0.42 % (4066040)Peak memory usage: 10 MB
% 0.62/0.42 % (4066040)Instructions burned: 25 (million)
% 0.62/0.42 % (4066039)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=2909225403: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)
% 0.62/0.42 % (4066036)Instruction limit reached!
% 0.62/0.42 % (4066036)------------------------------
% 0.62/0.42 % (4066036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.42 % (4066036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.42 % (4066036)CaDiCaL version: 2.1.3
% 0.62/0.42 % (4066036)Termination reason: Instruction limit
% 0.62/0.42 % (4066036)Termination phase: Property scanning
% 0.62/0.42 % (4066042)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.62/0.42 % (4066036)Time elapsed: 0.023 s
% 0.62/0.42 % (4066036)Peak memory usage: 13 MB
% 0.62/0.42 % (4066036)Instructions burned: 89 (million)
% 0.62/0.42 % (4066042)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
% 0.62/0.42 % (4066042)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=718726302:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.62/0.42 % (4066048)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2406434210:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.62/0.42 % (4066048)Instruction limit reached!
% 0.62/0.42 % (4066048)------------------------------
% 0.62/0.42 % (4066048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.46 % (4066048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.46 % (4066048)CaDiCaL version: 2.1.3
% 0.62/0.46 % (4066048)Termination reason: Instruction limit
% 0.62/0.46 % (4066048)Termination phase: shuffling
% 0.62/0.46 % (4066048)Time elapsed: 0.002 s
% 0.62/0.46 % (4066048)Peak memory usage: 10 MB
% 0.62/0.46 % (4066048)Instructions burned: 4 (million)
% 0.62/0.46 % (4066052)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=954562814:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.62/0.46 % (4066050)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.62/0.46 % (4066052)Instruction limit reached!
% 0.62/0.46 % (4066052)------------------------------
% 0.62/0.46 % (4066052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.46 % (4066052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.46 % (4066052)CaDiCaL version: 2.1.3
% 0.62/0.46 % (4066052)Termination reason: Instruction limit
% 0.62/0.46 % (4066052)Termination phase: shuffling
% 0.62/0.46 % (4066052)Time elapsed: 0.003 s
% 0.62/0.46 % (4066052)Peak memory usage: 10 MB
% 0.62/0.46 % (4066052)Instructions burned: 12 (million)
% 0.62/0.46 % (4066050)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2951923922:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.62/0.46 % (4066041)Instruction limit reached!
% 0.62/0.46 % (4066041)------------------------------
% 0.62/0.46 % (4066041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.46 % (4066041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.46 % (4066041)CaDiCaL version: 2.1.3
% 0.62/0.46 % (4066041)Termination reason: Instruction limit
% 0.62/0.46 % (4066041)Termination phase: Preprocessing 3
% 0.62/0.46 % (4066041)Time elapsed: 0.037 s
% 0.62/0.46 % (4066041)Peak memory usage: 12 MB
% 0.62/0.46 % (4066041)Instructions burned: 76 (million)
% 0.62/0.46 % (4066049)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4020031516:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.62/0.46 % (4066057)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=2980517638:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.62/0.46 % (4066056)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
% 0.62/0.46 % (4066056)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.62/0.46 % (4066050)Instruction limit reached!
% 0.62/0.46 % (4066050)------------------------------
% 0.62/0.46 % (4066050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.46 % (4066050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.46 % (4066050)CaDiCaL version: 2.1.3
% 0.62/0.46 % (4066050)Termination reason: Instruction limit
% 0.62/0.46 % (4066050)Termination phase: shuffling
% 0.62/0.46 % (4066050)Time elapsed: 0.006 s
% 0.62/0.46 % (4066050)Peak memory usage: 10 MB
% 0.62/0.46 % (4066050)Instructions burned: 7 (million)
% 0.62/0.46 % (4066049)Instruction limit reached!
% 0.62/0.46 % (4066049)------------------------------
% 0.62/0.46 % (4066049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.46 % (4066049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.46 % (4066049)CaDiCaL version: 2.1.3
% 0.62/0.46 % (4066049)Termination reason: Instruction limit
% 0.62/0.46 % (4066049)Termination phase: shuffling
% 0.62/0.46 % (4066049)Time elapsed: 0.006 s
% 0.62/0.46 % (4066049)Peak memory usage: 10 MB
% 0.62/0.46 % (4066049)Instructions burned: 5 (million)
% 0.62/0.46 % (4066056)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3103617939:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.62/0.46 % (4066057)Instruction limit reached!
% 0.62/0.46 % (4066057)------------------------------
% 0.62/0.46 % (4066057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (4066057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (4066057)CaDiCaL version: 2.1.3
% 1.37/0.51 % (4066057)Termination reason: Instruction limit
% 1.37/0.51 % (4066057)Termination phase: Function definition elimination
% 1.37/0.51 % (4066057)Time elapsed: 0.019 s
% 1.37/0.51 % (4066057)Peak memory usage: 11 MB
% 1.37/0.51 % (4066057)Instructions burned: 87 (million)
% 1.37/0.51 % (4066059)lrs+10_1_si=on:cs=on:random_seed=1104469892:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.37/0.51 % (4066065)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2054375697:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.37/0.51 % (4066062)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.37/0.51 % (4066063)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=963855620:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.37/0.51 % (4066059)Instruction limit reached!
% 1.37/0.51 % (4066059)------------------------------
% 1.37/0.51 % (4066059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (4066059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (4066059)CaDiCaL version: 2.1.3
% 1.37/0.51 % (4066059)Termination reason: Instruction limit
% 1.37/0.51 % (4066059)Termination phase: shuffling
% 1.37/0.51 % (4066059)Time elapsed: 0.008 s
% 1.37/0.51 % (4066059)Peak memory usage: 10 MB
% 1.37/0.51 % (4066059)Instructions burned: 8 (million)
% 1.37/0.51 % (4066056)Instruction limit reached!
% 1.37/0.51 % (4066056)------------------------------
% 1.37/0.51 % (4066056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (4066056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (4066056)CaDiCaL version: 2.1.3
% 1.37/0.51 % (4066056)Termination reason: Instruction limit
% 1.37/0.51 % (4066056)Termination phase: shuffling
% 1.37/0.51 % (4066056)Time elapsed: 0.028 s
% 1.37/0.51 % (4066056)Peak memory usage: 10 MB
% 1.37/0.51 % (4066056)Instructions burned: 30 (million)
% 1.37/0.51 % (4066062)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=2829243756:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.37/0.51 % (4066062)Instruction limit reached!
% 1.37/0.51 % (4066062)------------------------------
% 1.37/0.51 % (4066062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (4066062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (4066062)CaDiCaL version: 2.1.3
% 1.37/0.51 % (4066062)Termination reason: Instruction limit
% 1.37/0.51 % (4066062)Termination phase: shuffling
% 1.37/0.51 % (4066062)Time elapsed: 0.004 s
% 1.37/0.51 % (4066062)Peak memory usage: 10 MB
% 1.37/0.51 % (4066062)Instructions burned: 7 (million)
% 1.37/0.51 % (4066042)Instruction limit reached!
% 1.37/0.51 % (4066042)------------------------------
% 1.37/0.51 % (4066042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (4066042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (4066042)CaDiCaL version: 2.1.3
% 1.37/0.51 % (4066042)Termination reason: Instruction limit
% 1.37/0.51 % (4066042)Termination phase: Saturation
% 1.37/0.51 % (4066042)Time elapsed: 0.068 s
% 1.37/0.51 % (4066042)Peak memory usage: 14 MB
% 1.37/0.51 % (4066042)Instructions burned: 159 (million)
% 1.37/0.51 % (4066072)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1845707791:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.37/0.51 % (4066063)Instruction limit reached!
% 1.37/0.51 % (4066063)------------------------------
% 1.37/0.51 % (4066063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (4066063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (4066063)CaDiCaL version: 2.1.3
% 1.37/0.51 % (4066063)Termination reason: Instruction limit
% 1.37/0.51 % (4066063)Termination phase: SInE selection
% 1.37/0.51 % (4066063)Time elapsed: 0.031 s
% 1.37/0.51 % (4066063)Peak memory usage: 11 MB
% 1.37/0.51 % (4066063)Instructions burned: 38 (million)
% 1.37/0.51 % (4066069)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3623776655:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.37/0.59 % (4066073)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1434271466:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.37/0.59 % (4066070)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1958252605:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.37/0.59 % (4066073)Instruction limit reached!
% 1.37/0.59 % (4066073)------------------------------
% 1.37/0.59 % (4066073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.59 % (4066073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.59 % (4066073)CaDiCaL version: 2.1.3
% 1.37/0.59 % (4066073)Termination reason: Instruction limit
% 1.37/0.59 % (4066073)Termination phase: shuffling
% 1.37/0.59 % (4066073)Time elapsed: 0.010 s
% 1.37/0.59 % (4066073)Peak memory usage: 10 MB
% 1.37/0.59 % (4066073)Instructions burned: 22 (million)
% 1.37/0.59 % (4066070)Instruction limit reached!
% 1.37/0.59 % (4066070)------------------------------
% 1.37/0.59 % (4066070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.59 % (4066070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.59 % (4066070)CaDiCaL version: 2.1.3
% 1.37/0.59 % (4066070)Termination reason: Instruction limit
% 1.37/0.59 % (4066070)Termination phase: shuffling
% 1.37/0.59 % (4066070)Time elapsed: 0.017 s
% 1.37/0.59 % (4066070)Peak memory usage: 10 MB
% 1.37/0.59 % (4066070)Instructions burned: 14 (million)
% 1.37/0.59 % (4066065)Instruction limit reached!
% 1.37/0.59 % (4066065)------------------------------
% 1.37/0.59 % (4066065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.59 % (4066065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.59 % (4066065)CaDiCaL version: 2.1.3
% 1.37/0.59 % (4066065)Termination reason: Instruction limit
% 1.37/0.59 % (4066065)Termination phase: Saturation
% 1.37/0.59 % (4066065)Time elapsed: 0.060 s
% 1.37/0.59 % (4066065)Peak memory usage: 15 MB
% 1.37/0.59 % (4066065)Instructions burned: 252 (million)
% 1.37/0.59 % (4066075)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3165395192: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)
% 1.37/0.59 % (4066075)Instruction limit reached!
% 1.37/0.59 % (4066075)------------------------------
% 1.37/0.59 % (4066075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.59 % (4066075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.59 % (4066075)CaDiCaL version: 2.1.3
% 1.37/0.59 % (4066075)Termination reason: Instruction limit
% 1.37/0.59 % (4066075)Termination phase: shuffling
% 1.37/0.59 % (4066075)Time elapsed: 0.003 s
% 1.37/0.59 % (4066075)Peak memory usage: 10 MB
% 1.37/0.59 % (4066075)Instructions burned: 3 (million)
% 1.37/0.59 % (4066082)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2868674893:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.37/0.59 % (4066069)Instruction limit reached!
% 1.37/0.59 % (4066069)------------------------------
% 1.37/0.59 % (4066069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.59 % (4066069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.59 % (4066069)CaDiCaL version: 2.1.3
% 1.37/0.59 % (4066069)Termination reason: Instruction limit
% 1.37/0.59 % (4066069)Termination phase: Property scanning
% 1.37/0.59 % (4066069)Time elapsed: 0.035 s
% 1.37/0.59 % (4066069)Peak memory usage: 10 MB
% 1.37/0.59 % (4066069)Instructions burned: 25 (million)
% 1.37/0.59 % (4066082)Instruction limit reached!
% 1.37/0.59 % (4066082)------------------------------
% 1.37/0.59 % (4066082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.59 % (4066081)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2154707117:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.37/0.59 % (4066082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.59 % (4066082)CaDiCaL version: 2.1.3
% 1.37/0.59 % (4066082)Termination reason: Instruction limit
% 1.37/0.59 % (4066082)Termination phase: shuffling
% 1.37/0.59 % (4066082)Time elapsed: 0.006 s
% 1.37/0.59 % (4066082)Peak memory usage: 10 MB
% 2.27/0.66 % (4066082)Instructions burned: 26 (million)
% 2.27/0.66 % (4066089)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=3354740116:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.27/0.66 % (4066089)Instruction limit reached!
% 2.27/0.66 % (4066089)------------------------------
% 2.27/0.66 % (4066089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.66 % (4066089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.66 % (4066089)CaDiCaL version: 2.1.3
% 2.27/0.66 % (4066089)Termination reason: Instruction limit
% 2.27/0.66 % (4066089)Termination phase: Property scanning
% 2.27/0.66 % (4066089)Time elapsed: 0.008 s
% 2.27/0.66 % (4066089)Peak memory usage: 10 MB
% 2.27/0.66 % (4066089)Instructions burned: 34 (million)
% 2.27/0.66 % (4066086)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
% 2.27/0.66 % (4066086)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.27/0.66 % (4066083)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=265592616:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.27/0.66 % (4066081)Instruction limit reached!
% 2.27/0.66 % (4066081)------------------------------
% 2.27/0.66 % (4066081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.66 % (4066081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.66 % (4066081)CaDiCaL version: 2.1.3
% 2.27/0.66 % (4066081)Termination reason: Instruction limit
% 2.27/0.66 % (4066081)Termination phase: shuffling
% 2.27/0.66 % (4066081)Time elapsed: 0.025 s
% 2.27/0.66 % (4066081)Peak memory usage: 10 MB
% 2.27/0.66 % (4066081)Instructions burned: 27 (million)
% 2.27/0.66 % (4066087)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.27/0.66 % (4066086)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=1874777712:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.27/0.66 % (4066087)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=3244315233:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.27/0.66 % (4066093)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3994032900:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.27/0.66 % (4066091)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2671458342:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.27/0.66 % (4066087)Instruction limit reached!
% 2.27/0.66 % (4066087)------------------------------
% 2.27/0.66 % (4066087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.66 % (4066087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.66 % (4066087)CaDiCaL version: 2.1.3
% 2.27/0.66 % (4066087)Termination reason: Instruction limit
% 2.27/0.66 % (4066087)Termination phase: shuffling
% 2.27/0.66 % (4066087)Time elapsed: 0.007 s
% 2.27/0.66 % (4066087)Peak memory usage: 10 MB
% 2.27/0.66 % (4066087)Instructions burned: 8 (million)
% 2.27/0.66 % (4066086)Instruction limit reached!
% 2.27/0.66 % (4066086)------------------------------
% 2.27/0.66 % (4066086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.66 % (4066086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.66 % (4066086)CaDiCaL version: 2.1.3
% 2.27/0.66 % (4066086)Termination reason: Instruction limit
% 2.27/0.66 % (4066086)Termination phase: shuffling
% 2.27/0.66 % (4066086)Time elapsed: 0.013 s
% 2.27/0.66 % (4066086)Peak memory usage: 10 MB
% 2.27/0.66 % (4066086)Instructions burned: 14 (million)
% 2.27/0.66 % (4066093)Instruction limit reached!
% 2.27/0.66 % (4066093)------------------------------
% 2.27/0.66 % (4066093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.66 % (4066093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (4066093)CaDiCaL version: 2.1.3
% 2.65/0.75 % (4066093)Termination reason: Instruction limit
% 2.65/0.75 % (4066093)Termination phase: shuffling
% 2.65/0.75 % (4066093)Time elapsed: 0.006 s
% 2.65/0.75 % (4066093)Peak memory usage: 10 MB
% 2.65/0.75 % (4066093)Instructions burned: 26 (million)
% 2.65/0.75 % (4066091)Instruction limit reached!
% 2.65/0.75 % (4066091)------------------------------
% 2.65/0.75 % (4066091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (4066091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (4066091)CaDiCaL version: 2.1.3
% 2.65/0.75 % (4066091)Termination reason: Instruction limit
% 2.65/0.75 % (4066091)Termination phase: shuffling
% 2.65/0.75 % (4066091)Time elapsed: 0.007 s
% 2.65/0.75 % (4066091)Peak memory usage: 10 MB
% 2.65/0.75 % (4066091)Instructions burned: 7 (million)
% 2.65/0.75 % (4066101)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1796763214:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.65/0.75 % (4066083)Instruction limit reached!
% 2.65/0.75 % (4066083)------------------------------
% 2.65/0.75 % (4066083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (4066083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (4066083)CaDiCaL version: 2.1.3
% 2.65/0.75 % (4066083)Termination reason: Instruction limit
% 2.65/0.75 % (4066083)Termination phase: Preprocessing 3
% 2.65/0.75 % (4066083)Time elapsed: 0.040 s
% 2.65/0.75 % (4066083)Peak memory usage: 12 MB
% 2.65/0.75 % (4066083)Instructions burned: 60 (million)
% 2.65/0.75 % (4066100)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1173240854:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.65/0.75 % (4066099)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3240553870:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.65/0.75 % (4066098)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3198962915:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.65/0.75 % (4066098)Instruction limit reached!
% 2.65/0.75 % (4066098)------------------------------
% 2.65/0.75 % (4066098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (4066098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (4066098)CaDiCaL version: 2.1.3
% 2.65/0.75 % (4066098)Termination reason: Instruction limit
% 2.65/0.75 % (4066098)Termination phase: shuffling
% 2.65/0.75 % (4066098)Time elapsed: 0.018 s
% 2.65/0.75 % (4066098)Peak memory usage: 10 MB
% 2.65/0.75 % (4066098)Instructions burned: 20 (million)
% 2.65/0.75 % (4066103)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3256974728:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.65/0.75 % (4066101)Instruction limit reached!
% 2.65/0.75 % (4066101)------------------------------
% 2.65/0.75 % (4066101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (4066101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (4066101)CaDiCaL version: 2.1.3
% 2.65/0.75 % (4066101)Termination reason: Instruction limit
% 2.65/0.75 % (4066101)Termination phase: Saturation
% 2.65/0.75 % (4066101)Time elapsed: 0.045 s
% 2.65/0.75 % (4066101)Peak memory usage: 14 MB
% 2.65/0.75 % (4066101)Instructions burned: 201 (million)
% 2.65/0.75 % (4066072)Instruction limit reached!
% 2.65/0.75 % (4066072)------------------------------
% 2.65/0.75 % (4066072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (4066072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (4066072)CaDiCaL version: 2.1.3
% 2.65/0.75 % (4066072)Termination reason: Instruction limit
% 2.65/0.75 % (4066072)Termination phase: Saturation
% 2.65/0.75 % (4066072)Time elapsed: 0.155 s
% 2.65/0.75 % (4066072)Peak memory usage: 15 MB
% 2.65/0.75 % (4066072)Instructions burned: 328 (million)
% 2.65/0.75 % (4066109)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=385639079:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.65/0.75 % (4066107)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.65/0.75 % (4066107)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=54825501:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.65/0.78 % (4066110)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1523730504:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 2.65/0.78 % (4066107)Instruction limit reached!
% 2.65/0.78 % (4066107)------------------------------
% 2.65/0.78 % (4066107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066107)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066107)Termination reason: Instruction limit
% 2.65/0.78 % (4066107)Termination phase: shuffling
% 2.65/0.78 % (4066107)Time elapsed: 0.007 s
% 2.65/0.78 % (4066107)Peak memory usage: 10 MB
% 2.65/0.78 % (4066107)Instructions burned: 7 (million)
% 2.65/0.78 % (4066103)Instruction limit reached!
% 2.65/0.78 % (4066103)------------------------------
% 2.65/0.78 % (4066103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066103)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066103)Termination reason: Instruction limit
% 2.65/0.78 % (4066103)Termination phase: Property scanning
% 2.65/0.78 % (4066103)Time elapsed: 0.034 s
% 2.65/0.78 % (4066103)Peak memory usage: 11 MB
% 2.65/0.78 % (4066103)Instructions burned: 42 (million)
% 2.65/0.78 % (4066109)Instruction limit reached!
% 2.65/0.78 % (4066109)------------------------------
% 2.65/0.78 % (4066109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066109)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066109)Termination reason: Instruction limit
% 2.65/0.78 % (4066109)Termination phase: Saturation
% 2.65/0.78 % (4066109)Time elapsed: 0.042 s
% 2.65/0.78 % (4066109)Peak memory usage: 14 MB
% 2.65/0.78 % (4066109)Instructions burned: 182 (million)
% 2.65/0.78 % (4066114)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.65/0.78 % (4066116)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=961551105:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.65/0.78 % (4066114)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2061047982:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 2.65/0.78 % (4066115)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=947241226:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.65/0.78 % (4066100)Instruction limit reached!
% 2.65/0.78 % (4066100)------------------------------
% 2.65/0.78 % (4066100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066100)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066100)Termination reason: Instruction limit
% 2.65/0.78 % (4066100)Termination phase: Saturation
% 2.65/0.78 % (4066100)Time elapsed: 0.112 s
% 2.65/0.78 % (4066100)Peak memory usage: 13 MB
% 2.65/0.78 % (4066100)Instructions burned: 143 (million)
% 2.65/0.78 % (4066114)Instruction limit reached!
% 2.65/0.78 % (4066114)------------------------------
% 2.65/0.78 % (4066114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066114)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066114)Termination reason: Instruction limit
% 2.65/0.78 % (4066114)Termination phase: shuffling
% 2.65/0.78 % (4066114)Time elapsed: 0.020 s
% 2.65/0.78 % (4066114)Peak memory usage: 10 MB
% 2.65/0.78 % (4066114)Instructions burned: 8 (million)
% 2.65/0.78 % (4066120)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2941219556:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.65/0.78 % (4066115)Instruction limit reached!
% 2.65/0.78 % (4066115)------------------------------
% 2.65/0.78 % (4066115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066115)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066115)Termination reason: Instruction limit
% 2.65/0.78 % (4066115)Termination phase: shuffling
% 2.65/0.78 % (4066115)Time elapsed: 0.029 s
% 2.65/0.78 % (4066115)Peak memory usage: 10 MB
% 2.65/0.78 % (4066115)Instructions burned: 22 (million)
% 2.65/0.78 % (4066110)Instruction limit reached!
% 2.65/0.78 % (4066110)------------------------------
% 2.65/0.78 % (4066110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066110)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066110)Termination reason: Instruction limit
% 2.65/0.78 % (4066110)Termination phase: Saturation
% 2.65/0.78 % (4066110)Time elapsed: 0.072 s
% 2.65/0.78 % (4066110)Peak memory usage: 13 MB
% 2.65/0.78 % (4066110)Instructions burned: 171 (million)
% 2.65/0.78 % (4066116)Instruction limit reached!
% 2.65/0.78 % (4066116)------------------------------
% 2.65/0.78 % (4066116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066116)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066116)Termination reason: Instruction limit
% 2.65/0.78 % (4066116)Termination phase: shuffling
% 2.65/0.78 % (4066116)Time elapsed: 0.034 s
% 2.65/0.78 % (4066116)Peak memory usage: 10 MB
% 2.65/0.78 % (4066116)Instructions burned: 19 (million)
% 2.65/0.78 % (4066125)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2390799213:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.65/0.78 % (4066124)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2789720517:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.65/0.78 % (4066125)Instruction limit reached!
% 2.65/0.78 % (4066125)------------------------------
% 2.65/0.78 % (4066125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066125)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066125)Termination reason: Instruction limit
% 2.65/0.78 % (4066125)Termination phase: shuffling
% 2.65/0.78 % (4066125)Time elapsed: 0.006 s
% 2.65/0.78 % (4066125)Peak memory usage: 10 MB
% 2.65/0.78 % (4066125)Instructions burned: 24 (million)
% 2.65/0.78 % (4066122)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=2245522122:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.65/0.78 % (4066129)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.65/0.78 % (4066129)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1314594363:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 2.65/0.78 % (4066123)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1433227263:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.65/0.78 % (4066129)Instruction limit reached!
% 2.65/0.78 % (4066129)------------------------------
% 2.65/0.78 % (4066129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066129)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066129)Termination reason: Instruction limit
% 2.65/0.78 % (4066129)Termination phase: Saturation
% 2.65/0.78 % (4066129)Time elapsed: 0.046 s
% 2.65/0.78 % (4066129)Peak memory usage: 14 MB
% 2.65/0.78 % (4066129)Instructions burned: 202 (million)
% 2.65/0.78 % (4066123)Instruction limit reached!
% 2.65/0.78 % (4066123)------------------------------
% 2.65/0.78 % (4066123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066123)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066123)Termination reason: Instruction limit
% 2.65/0.78 % (4066123)Termination phase: SInE selection
% 2.65/0.78 % (4066123)Time elapsed: 0.038 s
% 2.65/0.78 % (4066123)Peak memory usage: 10 MB
% 2.65/0.78 % (4066123)Instructions burned: 45 (million)
% 2.65/0.78 % (4066039) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4066031-4066039"...
% 2.65/0.78 % (4066133)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1834636342:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 2.65/0.78 % (4066132)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2992802521:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 2.65/0.78 % (4066039)...printing done.
% 2.65/0.78 % (4066039)Refutation found. Thanks to Tanya!
% 2.65/0.78 % SZS status Theorem for theBenchmark
% 2.65/0.78 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/0.78 % (4066039)------------------------------
% 2.65/0.78 % (4066039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.78 % (4066039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.78 % (4066039)CaDiCaL version: 2.1.3
% 2.65/0.78 % (4066039)Termination reason: Refutation
% 2.65/0.78 % (4066039)Time elapsed: 0.441 s
% 2.65/0.78 % (4066039)Peak memory usage: 21 MB
% 2.65/0.78 % (4066039)Instructions burned: 571 (million)
% 2.65/0.78 % (4066031)Success in time 0.509 s
% 2.65/0.78 % Vampire exiting
%------------------------------------------------------------------------------