%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU748^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:06 AM UTC 2026
% Result : Theorem 1.80s 0.62s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 89 ( 31 unt; 0 typ; 10 def)
% Number of atoms : 4770 (1248 equ; 0 cnn)
% Maximal formula atoms : 269 ( 53 avg)
% Number of connectives : 2816 ( 156 ~; 130 |; 828 &; 588 @)
% ( 18 <=>;1096 =>; 0 <=; 0 <~>)
% Maximal formula depth : 278 ( 26 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 : 502 ( 499 usr; 307 con; 0-4 aty)
% Number of variables : 122 ( 0 sgn 100 !; 22 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_279,type,
contrasubsetT1: $o ).
thf(func_def_280,type,
contrasubsetT2: $o ).
thf(func_def_281,type,
contrasubsetT3: $o ).
thf(func_def_282,type,
doubleComplementI1: $o ).
thf(func_def_283,type,
doubleComplementE1: $o ).
thf(func_def_284,type,
doubleComplementSub1: $o ).
thf(func_def_285,type,
doubleComplementSub2: $o ).
thf(func_def_286,type,
doubleComplementEq: $o ).
thf(func_def_287,type,
complementTnotintersectT: $o ).
thf(func_def_288,type,
complementImpComplementIntersect: $o ).
thf(func_def_289,type,
complementSubsetComplementIntersect: $o ).
thf(func_def_290,type,
complementInPowersetComplementIntersect: $o ).
thf(func_def_291,type,
contraSubsetComplement: $o ).
thf(func_def_292,type,
complementTcontraSubset: $o ).
thf(func_def_293,type,
binunionTILcontra: $o ).
thf(func_def_294,type,
binunionTIRcontra: $o ).
thf(func_def_295,type,
inIntersectImpInUnion: $o ).
thf(func_def_296,type,
inIntersectImpInUnion2: $o ).
thf(func_def_297,type,
inIntersectImpInIntersectUnions: $o ).
thf(func_def_298,type,
intersectInPowersetIntersectUnions: $o ).
thf(func_def_299,type,
inComplementUnionImpNotIn1: $o ).
thf(func_def_300,type,
inComplementUnionImpInComplement1: $o ).
thf(func_def_301,type,
binunionTE: $o ).
thf(func_def_302,type,
binunionTEcontra: $o ).
thf(func_def_305,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_306,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_307,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_308,type,
vOR: $o > $o > $o ).
thf(func_def_309,type,
vAND: $o > $o > $o ).
thf(func_def_310,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_311,type,
vNOT: $o > $o ).
thf(func_def_312,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_313,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_314,type,
vIMP: $o > $o > $o ).
thf(func_def_315,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_316,type,
sP0: $i > $i > $o ).
thf(func_def_317,type,
sP1: $i > $o ).
thf(func_def_318,type,
sP2: $o ).
thf(func_def_319,type,
sP3: $o ).
thf(func_def_323,type,
sK7: $i > $i > $i ).
thf(func_def_337,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_338,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_339,type,
sK23: $i > $o ).
thf(func_def_357,type,
sK41: $i > $i > $i > $i ).
thf(func_def_368,type,
sK52: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_369,type,
sK53: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_372,type,
sK56: $i > $o ).
thf(func_def_373,type,
sK57: $i > $o ).
thf(func_def_378,type,
sK62: $i > $i ).
thf(func_def_384,type,
sK68: $i > $i ).
thf(func_def_387,type,
sK71: $i > $o ).
thf(func_def_396,type,
sK80: $i > $i > $i > $i ).
thf(func_def_397,type,
sK81: $i > $i > $i > $i ).
thf(func_def_406,type,
sK90: $o ).
thf(func_def_409,type,
sK93: $i > $o ).
thf(func_def_412,type,
sK96: $i > ( $i > $o ) > $i ).
thf(func_def_422,type,
sK106: $i > $i > $o ).
thf(func_def_423,type,
sK107: $i > $o ).
thf(func_def_427,type,
sK111: $i > $i ).
thf(func_def_430,type,
sK114: $i > ( $i > $i ) > $i > $i ).
thf(func_def_432,type,
sK116: $i > $i ).
thf(func_def_433,type,
sK117: $i > $i ).
thf(func_def_434,type,
sK118: $i > $i ).
thf(func_def_435,type,
sK119: $i > $i ).
thf(func_def_436,type,
sK120: $i > $i ).
thf(func_def_437,type,
sK121: $i > $i > $i > $i ).
thf(func_def_438,type,
sK122: $i > $i ).
thf(func_def_439,type,
sK123: $i > $i ).
thf(func_def_440,type,
sK124: $i > $i ).
thf(func_def_441,type,
sK125: $i > $i ).
thf(func_def_442,type,
sK126: $i > $i > $i ).
thf(func_def_443,type,
sK127: $i > $i > $i ).
thf(func_def_444,type,
sK128: $i > $i > $i > $i ).
thf(func_def_445,type,
sK129: $i > $i > $i > $i ).
thf(func_def_446,type,
sK130: $i > $i > $i > $i ).
thf(func_def_447,type,
sK131: $i > $i > $i ).
thf(func_def_448,type,
sK132: $i > $i > $i ).
thf(func_def_449,type,
sK133: $i > $i > $i ).
thf(func_def_451,type,
sK135: $o ).
thf(func_def_454,type,
sK138: $o ).
thf(func_def_476,type,
sK160: ( $i > $o ) > $i > $i ).
thf(func_def_478,type,
sK162: $i > $o ).
thf(func_def_483,type,
sK167: $i > $i > $i > $i > $i ).
thf(func_def_492,type,
sK176: $i > $i > $i > $i > $i ).
thf(func_def_493,type,
sK177: $i > $i > $i > $i > $i ).
thf(func_def_494,type,
sK178: $i > $i > $i > $i > $i ).
thf(func_def_495,type,
sK179: $i > $i > $i > $i > $i ).
thf(func_def_506,type,
sK190: $i > $i > $o ).
thf(func_def_510,type,
sK194: $o ).
thf(func_def_516,type,
sK200: $i > $o ).
thf(func_def_518,type,
sK202: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_519,type,
sK203: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_544,type,
sK228: $o ).
thf(func_def_548,type,
sK232: $i > $o ).
thf(func_def_551,type,
sK235: $i > ( $i > $o ) > $i ).
thf(func_def_552,type,
sK236: $i > $o ).
thf(func_def_554,type,
sK238: $i > ( $i > $o ) > $i ).
thf(func_def_556,type,
sK240: $i > $o ).
thf(func_def_562,type,
sK246: $i > $i ).
thf(func_def_565,type,
sK249: $i > $i > ( $i > $i ) > $i ).
thf(func_def_571,type,
sK255: ( $i > $o ) > $i > $i ).
thf(func_def_573,type,
sK257: $i > $o ).
thf(func_def_577,type,
sK261: $i > $i > $i ).
thf(func_def_583,type,
sK267: $o ).
thf(func_def_590,type,
sK274: $o > $i > $i > $i ).
thf(func_def_593,type,
sK277: $o ).
thf(func_def_594,type,
sK278: $i > $i > $i > $i ).
thf(func_def_595,type,
sK279: $i > $i > $i > $i ).
thf(func_def_599,type,
sK283: $i > $i > $i ).
thf(func_def_623,type,
sK307: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_624,type,
sK308: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_628,type,
sK312: $i > $o ).
thf(func_def_633,type,
sK317: $o ).
thf(func_def_641,type,
sK325: $o ).
thf(func_def_646,type,
sK330: $i > $o ).
thf(func_def_647,type,
sK331: $i > $i ).
thf(func_def_648,type,
sK332: ( $i > $o ) > $i ).
thf(func_def_654,type,
sK338: $o ).
thf(func_def_667,type,
sK351: $o ).
thf(func_def_669,type,
sK353: $i > $i ).
thf(func_def_672,type,
sK356: $i > $i > ( $i > $i ) > $i ).
thf(func_def_681,type,
sK365: $i > $i > $i ).
thf(func_def_685,type,
sK369: $i > $o ).
thf(func_def_686,type,
sK370: $i > $i ).
thf(func_def_687,type,
sK371: ( $i > $o ) > $i ).
thf(func_def_690,type,
sK374: $i > $i ).
thf(func_def_695,type,
sK379: $i > $i > $o ).
thf(func_def_697,type,
sK381: $i > $i ).
thf(func_def_698,type,
sK382: $i > $i ).
thf(func_def_699,type,
sK383: $i > ( $i > $i > $o ) > $i ).
thf(func_def_700,type,
sK384: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_701,type,
sK385: $i > ( $i > $i > $o ) > $i ).
thf(func_def_706,type,
sK390: $i > ( $i > $o ) > $i ).
thf(func_def_707,type,
sK391: $i > ( $i > $o ) > $i ).
thf(func_def_708,type,
sK392: $i > $o ).
thf(func_def_717,type,
sK401: $i > $i > $i ).
thf(func_def_718,type,
sK402: $i > $i > $i ).
thf(func_def_731,type,
sK415: $i > $o ).
thf(func_def_733,type,
sK417: $i > $i > $i ).
thf(func_def_742,type,
sK426: $i > $i ).
thf(func_def_745,type,
sK429: $i > $i ).
thf(func_def_752,type,
sK436: $i > $o ).
thf(func_def_755,type,
sK439: $i > ( $i > $o ) > $i ).
thf(func_def_768,type,
sK452: $i > $i > $i > $i ).
thf(func_def_774,type,
sK458: $i > $i > $i > $i > $i ).
thf(func_def_775,type,
sK459: $i > $i > $i > $i > $i ).
thf(func_def_780,type,
sK464: $i > $i ).
thf(func_def_784,type,
sK468: $i > $o ).
thf(func_def_790,type,
sK474: $i > $o ).
thf(func_def_792,type,
sK476: $i > ( $i > $o ) > $i ).
thf(func_def_799,type,
sK483: $i > $o ).
thf(func_def_800,type,
sK484: $i > $o ).
thf(func_def_801,type,
sK485: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_802,type,
sK486: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_803,type,
sK487: $i > $o ).
thf(func_def_806,type,
sK490: $i > ( $i > $o ) > $i ).
thf(func_def_819,type,
sK503: $i > $o ).
thf(func_def_820,type,
sK504: $i > $o ).
thf(func_def_821,type,
sK505: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_822,type,
sK506: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_823,type,
sK507: $i > $o ).
thf(func_def_831,type,
sK515: $i > $i > $o ).
thf(func_def_841,type,
sK525: $i > $i > $o ).
thf(func_def_846,type,
sK530: $i > $i > $i > $i > $i ).
thf(func_def_861,type,
sK545: $i > $o ).
thf(func_def_864,type,
sK548: $i > $o ).
thf(func_def_867,type,
sK551: $i > $i > $i ).
thf(func_def_877,type,
sK561: $i > $o ).
thf(func_def_903,type,
sK587: $o ).
thf(func_def_912,type,
sK596: $o ).
thf(func_def_922,type,
sK606: $i > $o ).
thf(func_def_923,type,
sK607: ( $i > $o ) > $i ).
thf(func_def_927,type,
sK611: $i > $i > $o ).
thf(func_def_965,type,
sK649: $i > ( $i > $o ) > $i ).
thf(func_def_966,type,
sK650: $i > ( $i > $o ) > $i ).
thf(func_def_967,type,
sK651: $i > $o ).
thf(func_def_979,type,
sK663: $i > $o ).
thf(func_def_983,type,
sK667: $o ).
thf(func_def_986,type,
sK670: $i > $i > $o ).
thf(func_def_990,type,
sK674: $i > $o ).
thf(func_def_1001,type,
sK685: $i > $o ).
thf(func_def_1027,type,
sK711: $i > $i > $i > $i > $i ).
thf(func_def_1036,type,
sK720: $o ).
thf(func_def_1044,type,
sK728: $i > $i ).
thf(func_def_1046,type,
sK730: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1050,type,
sK734: $o ).
thf(func_def_1087,type,
sK771: $o ).
thf(func_def_1090,type,
sK774: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1092,type,
sK776: $i > $i ).
thf(func_def_1095,type,
sK779: $i > $i > $o ).
thf(func_def_1115,type,
sK799: $i > $i > $i ).
thf(func_def_1118,type,
sK802: $i > $o ).
thf(func_def_1126,type,
sK810: $i > $i ).
thf(func_def_1128,type,
sK812: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1130,type,
sK814: $o ).
thf(func_def_1133,type,
sK817: $i > $i ).
thf(func_def_1134,type,
sK818: $i > $i > $i ).
thf(func_def_1138,type,
sK822: $i > $o ).
thf(func_def_1141,type,
sK825: $i > ( $i > $o ) > $i ).
thf(func_def_1142,type,
sK826: $i > $o ).
thf(func_def_1145,type,
sK829: $i > $i > ( $i > $o ) > $i ).
thf(f125,axiom,
( setminusELneg
= ( ! [X1: $i,X2: $i,X0: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(f265,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) )
= inComplementUnionImpNotIn1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(f269,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a1) ).
thf(f270,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f269]) ).
thf(f513,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f270]) ).
thf(f514,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f513]) ).
thf(f565,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) )
= inComplementUnionImpNotIn1 ),
inference(rectify,[],[f265]) ).
thf(f566,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(fool_elimination,[],[f565]) ).
thf(f607,plain,
( setminusELneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ( ~ ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f125]) ).
thf(f608,plain,
( ( setminusELneg = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) ) ) ),
inference(fool_elimination,[],[f607]) ).
thf(f830,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(flattening,[],[f566]) ).
thf(f834,plain,
( ( setminusELneg = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) ) ) ),
inference(flattening,[],[f608]) ).
thf(f868,plain,
( ( setminusELneg = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f834]) ).
thf(f869,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) )
<=> ( setminusELneg = $true ) ),
inference(flattening,[],[f868]) ).
thf(f1071,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(ennf_transformation,[],[f830]) ).
thf(f1072,plain,
( ( inComplementUnionImpNotIn1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ),
inference(flattening,[],[f1071]) ).
thf(f1125,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f514]) ).
thf(f1126,plain,
( ( emptysetAx = $true )
& ( subbreln = $true )
& ( upairset2E = $true )
& ( singletonsswitch = $true )
& ( setukpairinjL = $true )
& ( emptyE1 = $true )
& ( complementTnotintersectT = $true )
& ( setminusEL = $true )
& ( setunionsingleton1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( sepSubset = $true )
& ( upairinpowunion = $true )
& ( upairsetIL = $true )
& ( setunionE = $true )
& ( setadjoinSub = $true )
& ( binunionTE = $true )
& ( powersetAx = $true )
& ( binunionE = $true )
& ( complementT_lem = $true )
& ( setunionsingleton = $true )
& ( dsetconstr__Cong = $true )
& ( cartprodpairmemER = $true )
& ( emptysetE = $true )
& ( setunionAx = $true )
& ( cartprodfstin = $true )
& ( upairsubunion = $true )
& ( notequalI1 = $true )
& ( powersetTE1 = $true )
& ( in__Cong = $true )
& ( notdallE = $true )
& ( ksndsingleton = $true )
& ( setminusT_lem = $true )
& ( app = $true )
& ( setukpairinjR12 = $true )
& ( noeltsimpempty = $true )
& ( setukpairinjR11 = $true )
& ( nonemptyI = $true )
& ( exuE1 = $true )
& ( contrasubsetT3 = $true )
& ( setminusILneg = $true )
& ( binintersectEL = $true )
& ( subsetI2 = $true )
& ( notequalI2 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectTELcontra = $true )
& ( subsetE2 = $true )
& ( binintersectTERcontra = $true )
& ( setadjoinE = $true )
& ( foundationAx = $true )
& ( funcImageSingleton = $true )
& ( funcinfuncset = $true )
& ( vacuousDall = $true )
& ( dpsetconstrER = $true )
& ( lamp = $true )
& ( funcextLem = $true )
& ( lam2p = $true )
& ( omegaIndAx = $true )
& ( setminusIRneg = $true )
& ( subsetI1 = $true )
& ( upairsetIR = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectER = $true )
& ( ap2p = $true )
& ( kpairiskpair = $true )
& ( theprop = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( binunionRsub = $true )
& ( cartprodpairin = $true )
& ( subsetTrans = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset2 = $true )
& ( funcGraphProp2 = $true )
& ( ifp = $true )
& ( setunion__Cong = $true )
& ( binintersectSubset2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( doubleComplementSub2 = $true )
& ( funcGraphProp4 = $true )
& ( doubleComplementSub1 = $true )
& ( setunionE2 = $true )
& ( symdiffIneg2 = $true )
& ( singletoninpowunion = $true )
& ( eta1 = $true )
& ( funcGraphProp1 = $true )
& ( notinemptyset = $true )
& ( exuE3e = $true )
& ( binintersectSubset3 = $true )
& ( inPowerset = $true )
& ( ap2apEq2 = $true )
& ( setoftrueEq = $true )
& ( notsubsetI = $true )
& ( binunionTILcontra = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan3 = $true )
& ( kpairp = $true )
& ( inCongP = $true )
& ( subsetE = $true )
& ( ex1I2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( symdiffI1 = $true )
& ( singletonsuniq = $true )
& ( upairset2IR = $true )
& ( singletoninpowerset = $true )
& ( dsetconstrI = $true )
& ( setminusER = $true )
& ( setext = $true )
& ( cartprodpairsurjEq = $true )
& ( symdiffE = $true )
& ( secondinupair = $true )
& ( binintersectT_lem = $true )
& ( setminusSubset1 = $true )
& ( complementImpComplementIntersect = $true )
& ( exuE2 = $true )
& ( ex1I = $true )
& ( infuncsetfunc = $true )
& ( disjointsetsI1 = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffI2 = $true )
& ( cartprodmempair1 = $true )
& ( binunionLsub = $true )
& ( setukpairinjR2 = $true )
& ( setukpairinjR1 = $true )
& ( powersetTI1 = $true )
& ( complementTE1 = $true )
& ( funcext = $true )
& ( powersetE = $true )
& ( kpairsurjEq = $true )
& ( binunionIR = $true )
& ( setadjoinIR = $true )
& ( powersetsubset = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( powerset__Cong = $true )
& ( subsetTI = $true )
& ( notinsingleton = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( setadjoin__Cong = $true )
& ( iffalseProp1 = $true )
& ( setukpairinjR = $true )
& ( prop2set2propI = $true )
& ( setukpairIR = $true )
& ( eta2 = $true )
& ( wellorderingAx = $true )
& ( setadjoinSub2 = $true )
& ( setukpairinjL2 = $true )
& ( lam2lamEq = $true )
& ( doubleComplementI1 = $true )
& ( ifSingleton = $true )
& ( setukpairIL = $true )
& ( exuE3u = $true )
& ( descrp = $true )
& ( notdexE = $true )
& ( binintersectSubset5 = $true )
& ( complementTcontraSubset = $true )
& ( nonemptyI1 = $true )
& ( contrasubsetT2 = $true )
& ( dpsetconstrSub = $true )
& ( subPowSU = $true )
& ( bs114d = $true )
& ( dsetconstrER = $true )
& ( doubleComplementEq = $true )
& ( setadjoinIL = $true )
& ( setunionsingleton2 = $true )
& ( theeq = $true )
& ( exuI2 = $true )
& ( eqimpsubset1 = $true )
& ( setOfPairsIsBReln = $true )
& ( kfstsingleton = $true )
& ( brelnall1 = $true )
& ( dpsetconstrI = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyImpWitness = $true )
& ( contrasubsetT1 = $true )
& ( setminusERneg = $true )
& ( binintersectRsub = $true )
& ( ap2apEq1 = $true )
& ( setadjoinAx = $true )
& ( setminusLsub = $true )
& ( symdiffIneg1 = $true )
& ( ubforcartprodlem2 = $true )
& ( binunionIL = $true )
& ( sepInPowerset = $true )
& ( upairsetE = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( binintersectSubset4 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( emptyinPowerset = $true )
& ( emptyInPowerset = $true )
& ( binunionEcases = $true )
& ( brelnall2 = $true )
& ( ex1E2 = $true )
& ( ksndpairEq = $true )
& ( quantDeMorgan1 = $true )
& ( kfstpairEq = $true )
& ( iffalse = $true )
& ( cartprodmempaircEq = $true )
& ( exuI3 = $true )
& ( prop2setI = $true )
& ( powersetT_lem = $true )
& ( eqbreln = $true )
& ( omega__Cong = $true )
& ( binunionTEcontra = $true )
& ( complementTI1 = $true )
& ( descr__Cong = $true )
& ( cartprodmempair = $true )
& ( emptysetimpfalse = $true )
& ( contraSubsetComplement = $true )
& ( binintersectI = $true )
& ( beta1 = $true )
& ( setminusI = $true )
& ( iftrue = $true )
& ( setbeta = $true )
& ( nonemptyE1 = $true )
& ( emptyset__Cong = $true )
& ( cartprodsndin = $true )
& ( iftrueProp2 = $true )
& ( setunionI = $true )
& ( cartprodsndpairEq = $true )
& ( singletonsubset = $true )
& ( prop2setE = $true )
& ( dpsetconstrEL1 = $true )
& ( apProp = $true )
& ( iftrueorfalse = $true )
& ( exu__Cong = $true )
& ( setminusSubset2 = $true )
& ( binunionT_lem = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( omegaSAx = $true )
& ( powersetE1 = $true )
& ( setextT = $true )
& ( ubforcartprodlem1 = $true )
& ( lamProp = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( funcext2 = $true )
& ( ex1E1 = $true )
& ( beta2 = $true )
& ( singletonprop = $true )
& ( contrasubsetT = $true )
& ( iffalseProp2 = $true )
& ( binintersectSubset1 = $true )
& ( setminusELneg = $true )
& ( powersetI = $true )
& ( setadjoinOr = $true )
& ( setextsub = $true )
& ( uniqinunit = $true )
& ( binunionTIRcontra = $true )
& ( doubleComplementE1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( iftrueProp1 = $true )
& ( cartprodpairmemEL = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem3 = $true )
& ( upairequniteq = $true )
& ( cartprodfstpairEq = $true )
& ( dpsetconstrERa = $true )
& ( subsetemptysetimpeq = $true )
& ( exuI1 = $true )
& ( funcGraphProp3 = $true )
& ( dsetconstrEL = $true )
& ( replAx = $true )
& ( dpsetconstrEL2 = $true )
& ( emptyinunitempty = $true )
& ( emptyI = $true ) ),
inference(flattening,[],[f1125]) ).
thf(f1348,plain,
( ( ( inComplementUnionImpNotIn1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) )
| ( inComplementUnionImpNotIn1 != $true ) ) ),
inference(nnf_transformation,[],[f1072]) ).
thf(f1349,plain,
( ( ( inComplementUnionImpNotIn1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ) ) )
| ( inComplementUnionImpNotIn1 != $true ) ) ),
inference(rectify,[],[f1348]) ).
thf(f1350,plain,
( ( ( inComplementUnionImpNotIn1 = $true )
| ( ( ( in @ sK207 @ ( powerset @ sK206 ) )
= $true )
& ( $true
= ( in @ sK208 @ ( powerset @ sK206 ) ) )
& ( ( in @ sK209 @ ( setminus @ sK206 @ ( binunion @ sK207 @ sK208 ) ) )
= $true )
& ( $true
= ( in @ sK209 @ sK207 ) )
& ( ( in @ sK209 @ sK206 )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ) ) )
| ( inComplementUnionImpNotIn1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206,sK207,sK208,sK209]),skolemize(X0,sK206),skolemize(X1,sK207),skolemize(X2,sK208),skolemize(X3,sK209)],[f1349]) ).
thf(f1420,plain,
( ( emptysetAx = $true )
& ( subbreln = $true )
& ( upairset2E = $true )
& ( singletonsswitch = $true )
& ( setukpairinjL = $true )
& ( emptyE1 = $true )
& ( complementTnotintersectT = $true )
& ( setminusEL = $true )
& ( setunionsingleton1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( sepSubset = $true )
& ( upairinpowunion = $true )
& ( upairsetIL = $true )
& ( setunionE = $true )
& ( setadjoinSub = $true )
& ( binunionTE = $true )
& ( powersetAx = $true )
& ( binunionE = $true )
& ( complementT_lem = $true )
& ( setunionsingleton = $true )
& ( dsetconstr__Cong = $true )
& ( cartprodpairmemER = $true )
& ( emptysetE = $true )
& ( setunionAx = $true )
& ( cartprodfstin = $true )
& ( upairsubunion = $true )
& ( notequalI1 = $true )
& ( powersetTE1 = $true )
& ( in__Cong = $true )
& ( notdallE = $true )
& ( ksndsingleton = $true )
& ( setminusT_lem = $true )
& ( app = $true )
& ( setukpairinjR12 = $true )
& ( noeltsimpempty = $true )
& ( setukpairinjR11 = $true )
& ( nonemptyI = $true )
& ( exuE1 = $true )
& ( contrasubsetT3 = $true )
& ( setminusILneg = $true )
& ( binintersectEL = $true )
& ( subsetI2 = $true )
& ( notequalI2 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectTELcontra = $true )
& ( subsetE2 = $true )
& ( binintersectTERcontra = $true )
& ( setadjoinE = $true )
& ( foundationAx = $true )
& ( funcImageSingleton = $true )
& ( funcinfuncset = $true )
& ( vacuousDall = $true )
& ( dpsetconstrER = $true )
& ( lamp = $true )
& ( funcextLem = $true )
& ( lam2p = $true )
& ( omegaIndAx = $true )
& ( setminusIRneg = $true )
& ( subsetI1 = $true )
& ( upairsetIR = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectER = $true )
& ( ap2p = $true )
& ( kpairiskpair = $true )
& ( theprop = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( binunionRsub = $true )
& ( cartprodpairin = $true )
& ( subsetTrans = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset2 = $true )
& ( funcGraphProp2 = $true )
& ( ifp = $true )
& ( setunion__Cong = $true )
& ( binintersectSubset2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( doubleComplementSub2 = $true )
& ( funcGraphProp4 = $true )
& ( doubleComplementSub1 = $true )
& ( setunionE2 = $true )
& ( symdiffIneg2 = $true )
& ( singletoninpowunion = $true )
& ( eta1 = $true )
& ( funcGraphProp1 = $true )
& ( notinemptyset = $true )
& ( exuE3e = $true )
& ( binintersectSubset3 = $true )
& ( inPowerset = $true )
& ( ap2apEq2 = $true )
& ( setoftrueEq = $true )
& ( notsubsetI = $true )
& ( binunionTILcontra = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan3 = $true )
& ( kpairp = $true )
& ( inCongP = $true )
& ( subsetE = $true )
& ( ex1I2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( symdiffI1 = $true )
& ( singletonsuniq = $true )
& ( upairset2IR = $true )
& ( singletoninpowerset = $true )
& ( dsetconstrI = $true )
& ( setminusER = $true )
& ( setext = $true )
& ( cartprodpairsurjEq = $true )
& ( symdiffE = $true )
& ( secondinupair = $true )
& ( binintersectT_lem = $true )
& ( setminusSubset1 = $true )
& ( complementImpComplementIntersect = $true )
& ( exuE2 = $true )
& ( ex1I = $true )
& ( infuncsetfunc = $true )
& ( disjointsetsI1 = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffI2 = $true )
& ( cartprodmempair1 = $true )
& ( binunionLsub = $true )
& ( setukpairinjR2 = $true )
& ( setukpairinjR1 = $true )
& ( powersetTI1 = $true )
& ( complementTE1 = $true )
& ( funcext = $true )
& ( powersetE = $true )
& ( kpairsurjEq = $true )
& ( binunionIR = $true )
& ( setadjoinIR = $true )
& ( powersetsubset = $true )
& ( ( in @ sK288 @ ( powerset @ sK287 ) )
= $true )
& ( $true
= ( in @ sK289 @ ( setminus @ sK287 @ ( binunion @ sK286 @ sK288 ) ) ) )
& ( ( in @ sK289 @ sK287 )
= $true )
& ( ( in @ sK289 @ ( setminus @ sK287 @ sK286 ) )
!= $true )
& ( ( in @ sK286 @ ( powerset @ sK287 ) )
= $true )
& ( powerset__Cong = $true )
& ( subsetTI = $true )
& ( notinsingleton = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( setadjoin__Cong = $true )
& ( iffalseProp1 = $true )
& ( setukpairinjR = $true )
& ( prop2set2propI = $true )
& ( setukpairIR = $true )
& ( eta2 = $true )
& ( wellorderingAx = $true )
& ( setadjoinSub2 = $true )
& ( setukpairinjL2 = $true )
& ( lam2lamEq = $true )
& ( doubleComplementI1 = $true )
& ( ifSingleton = $true )
& ( setukpairIL = $true )
& ( exuE3u = $true )
& ( descrp = $true )
& ( notdexE = $true )
& ( binintersectSubset5 = $true )
& ( complementTcontraSubset = $true )
& ( nonemptyI1 = $true )
& ( contrasubsetT2 = $true )
& ( dpsetconstrSub = $true )
& ( subPowSU = $true )
& ( bs114d = $true )
& ( dsetconstrER = $true )
& ( doubleComplementEq = $true )
& ( setadjoinIL = $true )
& ( setunionsingleton2 = $true )
& ( theeq = $true )
& ( exuI2 = $true )
& ( eqimpsubset1 = $true )
& ( setOfPairsIsBReln = $true )
& ( kfstsingleton = $true )
& ( brelnall1 = $true )
& ( dpsetconstrI = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyImpWitness = $true )
& ( contrasubsetT1 = $true )
& ( setminusERneg = $true )
& ( binintersectRsub = $true )
& ( ap2apEq1 = $true )
& ( setadjoinAx = $true )
& ( setminusLsub = $true )
& ( symdiffIneg1 = $true )
& ( ubforcartprodlem2 = $true )
& ( binunionIL = $true )
& ( sepInPowerset = $true )
& ( upairsetE = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( binintersectSubset4 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( emptyinPowerset = $true )
& ( emptyInPowerset = $true )
& ( binunionEcases = $true )
& ( brelnall2 = $true )
& ( ex1E2 = $true )
& ( ksndpairEq = $true )
& ( quantDeMorgan1 = $true )
& ( kfstpairEq = $true )
& ( iffalse = $true )
& ( cartprodmempaircEq = $true )
& ( exuI3 = $true )
& ( prop2setI = $true )
& ( powersetT_lem = $true )
& ( eqbreln = $true )
& ( omega__Cong = $true )
& ( binunionTEcontra = $true )
& ( complementTI1 = $true )
& ( descr__Cong = $true )
& ( cartprodmempair = $true )
& ( emptysetimpfalse = $true )
& ( contraSubsetComplement = $true )
& ( binintersectI = $true )
& ( beta1 = $true )
& ( setminusI = $true )
& ( iftrue = $true )
& ( setbeta = $true )
& ( nonemptyE1 = $true )
& ( emptyset__Cong = $true )
& ( cartprodsndin = $true )
& ( iftrueProp2 = $true )
& ( setunionI = $true )
& ( cartprodsndpairEq = $true )
& ( singletonsubset = $true )
& ( prop2setE = $true )
& ( dpsetconstrEL1 = $true )
& ( apProp = $true )
& ( iftrueorfalse = $true )
& ( exu__Cong = $true )
& ( setminusSubset2 = $true )
& ( binunionT_lem = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( omegaSAx = $true )
& ( powersetE1 = $true )
& ( setextT = $true )
& ( ubforcartprodlem1 = $true )
& ( lamProp = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( funcext2 = $true )
& ( ex1E1 = $true )
& ( beta2 = $true )
& ( singletonprop = $true )
& ( contrasubsetT = $true )
& ( iffalseProp2 = $true )
& ( binintersectSubset1 = $true )
& ( setminusELneg = $true )
& ( powersetI = $true )
& ( setadjoinOr = $true )
& ( setextsub = $true )
& ( uniqinunit = $true )
& ( binunionTIRcontra = $true )
& ( doubleComplementE1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( iftrueProp1 = $true )
& ( cartprodpairmemEL = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem3 = $true )
& ( upairequniteq = $true )
& ( cartprodfstpairEq = $true )
& ( dpsetconstrERa = $true )
& ( subsetemptysetimpeq = $true )
& ( exuI1 = $true )
& ( funcGraphProp3 = $true )
& ( dsetconstrEL = $true )
& ( replAx = $true )
& ( dpsetconstrEL2 = $true )
& ( emptyinunitempty = $true )
& ( emptyI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286,sK287,sK288,sK289]),skolemize(X0,sK286),skolemize(X1,sK287),skolemize(X2,sK288),skolemize(X3,sK289)],[f1126]) ).
thf(f1880,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) )
| ( setminusELneg != $true ) )
& ( ( setminusELneg = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f869]) ).
thf(f1881,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusELneg != $true ) )
& ( ( setminusELneg = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true ) ) ) ),
inference(rectify,[],[f1880]) ).
thf(f1882,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusELneg != $true ) )
& ( ( setminusELneg = $true )
| ( ( ( in @ sK767 @ sK765 )
= $true )
& ( $true
!= ( in @ sK767 @ sK766 ) )
& ( ( in @ sK767 @ ( setminus @ sK765 @ sK766 ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK765,sK766,sK767]),skolemize(X3,sK765),skolemize(X4,sK766),skolemize(X5,sK767)],[f1881]) ).
thf(f2250,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( inComplementUnionImpNotIn1 != $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f1350]) ).
thf(f2392,plain,
setminusELneg = $true,
inference(cnf_transformation,[],[f1420]) ).
thf(f2400,plain,
inComplementUnionImpNotIn1 = $true,
inference(cnf_transformation,[],[f1420]) ).
thf(f2504,plain,
( ( in @ sK286 @ ( powerset @ sK287 ) )
= $true ),
inference(cnf_transformation,[],[f1420]) ).
thf(f2505,plain,
( ( in @ sK289 @ ( setminus @ sK287 @ sK286 ) )
!= $true ),
inference(cnf_transformation,[],[f1420]) ).
thf(f2506,plain,
( ( in @ sK289 @ sK287 )
= $true ),
inference(cnf_transformation,[],[f1420]) ).
thf(f2507,plain,
( $true
= ( in @ sK289 @ ( setminus @ sK287 @ ( binunion @ sK286 @ sK288 ) ) ) ),
inference(cnf_transformation,[],[f1420]) ).
thf(f2508,plain,
( ( in @ sK288 @ ( powerset @ sK287 ) )
= $true ),
inference(cnf_transformation,[],[f1420]) ).
thf(f3270,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( setminusELneg != $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f1882]) ).
thf(f4370,definition,
( spl842_176
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl842_176])],[avatar_definition]) ).
thf(f4371,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ~ spl842_176 ),
inference(avatar_component_clause,[],[f4370]) ).
thf(f4541,definition,
( spl842_215
<=> ( ( in @ sK289 @ ( setminus @ sK287 @ sK286 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl842_215])],[avatar_definition]) ).
thf(f4543,plain,
( ( ( in @ sK289 @ ( setminus @ sK287 @ sK286 ) )
!= $true )
| spl842_215 ),
inference(avatar_component_clause,[],[f4541]) ).
thf(f4544,plain,
~ spl842_215,
inference(avatar_split_clause,[],[f2505,f4541]) ).
thf(f4779,definition,
( spl842_270
<=> ( inComplementUnionImpNotIn1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl842_270])],[avatar_definition]) ).
thf(f5441,definition,
( spl842_417
<=> ( setminusELneg = $true ) ),
introduced(definition,[new_symbols(definition,[spl842_417])],[avatar_definition]) ).
thf(f5829,definition,
( spl842_501
<=> ( ( in @ sK286 @ ( powerset @ sK287 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl842_501])],[avatar_definition]) ).
thf(f5831,plain,
( ( ( in @ sK286 @ ( powerset @ sK287 ) )
= $true )
| ~ spl842_501 ),
inference(avatar_component_clause,[],[f5829]) ).
thf(f5832,plain,
spl842_501,
inference(avatar_split_clause,[],[f2504,f5829]) ).
thf(f6265,definition,
( spl842_593
<=> ( $true
= ( in @ sK289 @ ( setminus @ sK287 @ ( binunion @ sK286 @ sK288 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl842_593])],[avatar_definition]) ).
thf(f6267,plain,
( ( $true
= ( in @ sK289 @ ( setminus @ sK287 @ ( binunion @ sK286 @ sK288 ) ) ) )
| ~ spl842_593 ),
inference(avatar_component_clause,[],[f6265]) ).
thf(f6268,plain,
spl842_593,
inference(avatar_split_clause,[],[f2507,f6265]) ).
thf(f7516,plain,
spl842_417,
inference(avatar_split_clause,[],[f2392,f5441]) ).
thf(f7567,plain,
spl842_270,
inference(avatar_split_clause,[],[f2400,f4779]) ).
thf(f7996,plain,
( ~ spl842_417
| spl842_176 ),
inference(avatar_split_clause,[],[f3270,f4370,f5441]) ).
thf(f8369,definition,
( spl842_1028
<=> ( ( in @ sK289 @ sK287 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl842_1028])],[avatar_definition]) ).
thf(f8371,plain,
( ( ( in @ sK289 @ sK287 )
= $true )
| ~ spl842_1028 ),
inference(avatar_component_clause,[],[f8369]) ).
thf(f8372,plain,
spl842_1028,
inference(avatar_split_clause,[],[f2506,f8369]) ).
thf(f9510,definition,
( spl842_1261
<=> ( ( in @ sK288 @ ( powerset @ sK287 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl842_1261])],[avatar_definition]) ).
thf(f9512,plain,
( ( ( in @ sK288 @ ( powerset @ sK287 ) )
= $true )
| ~ spl842_1261 ),
inference(avatar_component_clause,[],[f9510]) ).
thf(f9513,plain,
spl842_1261,
inference(avatar_split_clause,[],[f2508,f9510]) ).
thf(f9924,definition,
( spl842_1345
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl842_1345])],[avatar_definition]) ).
thf(f9925,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) )
| ~ spl842_1345 ),
inference(avatar_component_clause,[],[f9924]) ).
thf(f9926,plain,
( ~ spl842_270
| spl842_1345 ),
inference(avatar_split_clause,[],[f2250,f9924,f4779]) ).
thf(f10009,plain,
( ( ( in @ sK286 @ ( powerset @ sK287 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK289 @ sK286 ) )
| ( ( in @ sK289 @ sK287 )
!= $true )
| ( ( in @ sK288 @ ( powerset @ sK287 ) )
!= $true )
| ~ spl842_593
| ~ spl842_1345 ),
inference(superposition,[],[f9925,f6267]) ).
thf(f10014,plain,
( ( $true
!= ( in @ sK289 @ sK286 ) )
| ( ( in @ sK288 @ ( powerset @ sK287 ) )
!= $true )
| ( ( in @ sK289 @ sK287 )
!= $true )
| ( ( in @ sK286 @ ( powerset @ sK287 ) )
!= $true )
| ~ spl842_593
| ~ spl842_1345 ),
inference(trivial_inequality_removal,[],[f10009]) ).
thf(f10021,plain,
( ( $true
!= ( in @ sK289 @ sK286 ) )
| ( ( in @ sK289 @ sK287 )
!= $true )
| ( ( in @ sK286 @ ( powerset @ sK287 ) )
!= $true )
| ~ spl842_593
| ~ spl842_1261
| ~ spl842_1345 ),
inference(forward_subsumption_resolution,[],[f10014,f9512]) ).
thf(f10030,plain,
( ( $true
!= ( in @ sK289 @ sK286 ) )
| ( ( in @ sK286 @ ( powerset @ sK287 ) )
!= $true )
| ~ spl842_593
| ~ spl842_1028
| ~ spl842_1261
| ~ spl842_1345 ),
inference(forward_subsumption_resolution,[],[f10021,f8371]) ).
thf(f10031,plain,
( ( $true
!= ( in @ sK289 @ sK286 ) )
| ~ spl842_501
| ~ spl842_593
| ~ spl842_1028
| ~ spl842_1261
| ~ spl842_1345 ),
inference(forward_subsumption_resolution,[],[f10030,f5831]) ).
thf(f10033,definition,
( spl842_1353
<=> ( $true
= ( in @ sK289 @ sK286 ) ) ),
introduced(definition,[new_symbols(definition,[spl842_1353])],[avatar_definition]) ).
thf(f10035,plain,
( ( $true
!= ( in @ sK289 @ sK286 ) )
| spl842_1353 ),
inference(avatar_component_clause,[],[f10033]) ).
thf(f10036,plain,
( ~ spl842_1353
| ~ spl842_501
| ~ spl842_593
| ~ spl842_1028
| ~ spl842_1261
| ~ spl842_1345 ),
inference(avatar_split_clause,[],[f10031,f9924,f9510,f8369,f6265,f5829,f10033]) ).
thf(f11954,plain,
( ( $true
= ( in @ sK289 @ sK286 ) )
| ( ( in @ sK289 @ sK287 )
!= $true )
| ( $true != $true )
| ~ spl842_176
| spl842_215 ),
inference(superposition,[],[f4543,f4371]) ).
thf(f11958,plain,
( ( $true
= ( in @ sK289 @ sK286 ) )
| ( ( in @ sK289 @ sK287 )
!= $true )
| ~ spl842_176
| spl842_215 ),
inference(trivial_inequality_removal,[],[f11954]) ).
thf(f11975,plain,
( ( ( in @ sK289 @ sK287 )
!= $true )
| ~ spl842_176
| spl842_215
| spl842_1353 ),
inference(forward_subsumption_resolution,[],[f11958,f10035]) ).
thf(f11976,plain,
( $false
| ~ spl842_176
| spl842_215
| ~ spl842_1028
| spl842_1353 ),
inference(forward_subsumption_resolution,[],[f11975,f8371]) ).
thf(f11977,plain,
( ~ spl842_176
| spl842_215
| ~ spl842_1028
| spl842_1353 ),
inference(avatar_contradiction_clause,[],[f11976]) ).
cnf(s135,plain,
~ spl842_215,
inference(sat_conversion,[],[f4544]) ).
cnf(s361,plain,
spl842_501,
inference(sat_conversion,[],[f5832]) ).
cnf(s454,plain,
spl842_593,
inference(sat_conversion,[],[f6268]) ).
cnf(s753,plain,
spl842_417,
inference(sat_conversion,[],[f7516]) ).
cnf(s767,plain,
spl842_270,
inference(sat_conversion,[],[f7567]) ).
cnf(s869,plain,
( spl842_176
| ~ spl842_417 ),
inference(sat_conversion,[],[f7996]) ).
cnf(s967,plain,
spl842_1028,
inference(sat_conversion,[],[f8372]) ).
cnf(s1256,plain,
spl842_1261,
inference(sat_conversion,[],[f9513]) ).
cnf(s1369,plain,
( ~ spl842_270
| spl842_1345 ),
inference(sat_conversion,[],[f9926]) ).
cnf(s1378,plain,
( ~ spl842_501
| ~ spl842_593
| ~ spl842_1028
| ~ spl842_1261
| ~ spl842_1345
| ~ spl842_1353 ),
inference(sat_conversion,[],[f10036]) ).
cnf(s1424,plain,
( ~ spl842_176
| spl842_215
| ~ spl842_1028
| spl842_1353 ),
inference(sat_conversion,[],[f11977]) ).
cnf(s1496,plain,
spl842_1345,
inference(rat,[],[s1369,s767]) ).
cnf(s1504,plain,
spl842_176,
inference(rat,[],[s869,s753]) ).
cnf(s1613,plain,
~ spl842_1353,
inference(rat,[],[s1378,s454,s1496,s1256,s967,s361]) ).
cnf(s1614,plain,
spl842_215,
inference(rat,[],[s1424,s1504,s967,s1613]) ).
cnf(s1709,plain,
$false,
inference(rat,[],[s135,s1614]) ).
thf(f11978,plain,
$false,
inference(avatar_sat_refutation,[],[s1709]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU748^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:23:58 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.43 % (3599602)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.47/0.43 % (3599607)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=796706224:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.47/0.43 % (3599613)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.47/0.43 % (3599613)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.47/0.43 % (3599608)lrs+10_16_si=on:nwc=1.5:random_seed=3226748292:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.47/0.43 % (3599610)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=2849837479:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.47/0.43 % (3599611)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3477037744:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.47/0.43 % (3599612)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3186213177:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.47/0.43 % (3599613)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=2878091313:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.47/0.43 % (3599609)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=983195922:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.47/0.43 % (3599609)Instruction limit reached!
% 0.47/0.43 % (3599609)------------------------------
% 0.47/0.43 % (3599609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (3599609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (3599609)CaDiCaL version: 2.1.3
% 0.47/0.43 % (3599609)Termination reason: Instruction limit
% 0.47/0.43 % (3599609)Termination phase: shuffling
% 0.47/0.43 % (3599609)Time elapsed: 0.002 s
% 0.47/0.43 % (3599609)Peak memory usage: 10 MB
% 0.47/0.43 % (3599609)Instructions burned: 3 (million)
% 0.47/0.43 % (3599608)Instruction limit reached!
% 0.47/0.43 % (3599608)------------------------------
% 0.47/0.43 % (3599608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (3599608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (3599608)CaDiCaL version: 2.1.3
% 0.47/0.43 % (3599608)Termination reason: Instruction limit
% 0.47/0.43 % (3599608)Termination phase: shuffling
% 0.47/0.43 % (3599608)Time elapsed: 0.008 s
% 0.47/0.43 % (3599608)Peak memory usage: 10 MB
% 0.47/0.43 % (3599608)Instructions burned: 18 (million)
% 0.47/0.43 % (3599611)Instruction limit reached!
% 0.47/0.43 % (3599611)------------------------------
% 0.47/0.43 % (3599611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (3599611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (3599611)CaDiCaL version: 2.1.3
% 0.47/0.43 % (3599611)Termination reason: Instruction limit
% 0.47/0.43 % (3599611)Termination phase: shuffling
% 0.47/0.43 % (3599611)Time elapsed: 0.011 s
% 0.47/0.43 % (3599611)Peak memory usage: 10 MB
% 0.47/0.43 % (3599611)Instructions burned: 25 (million)
% 0.47/0.43 % (3599607)Instruction limit reached!
% 0.47/0.43 % (3599607)------------------------------
% 0.47/0.43 % (3599607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (3599607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (3599607)CaDiCaL version: 2.1.3
% 0.47/0.43 % (3599607)Termination reason: Instruction limit
% 0.47/0.43 % (3599607)Termination phase: Preprocessing 3
% 0.47/0.43 % (3599607)Time elapsed: 0.021 s
% 0.47/0.43 % (3599607)Peak memory usage: 12 MB
% 0.47/0.43 % (3599607)Instructions burned: 89 (million)
% 0.47/0.43 % (3599624)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2843297257:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.47/0.43 % (3599623)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.47/0.46 % (3599624)Instruction limit reached!
% 0.47/0.46 % (3599624)------------------------------
% 0.47/0.46 % (3599624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (3599624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (3599624)CaDiCaL version: 2.1.3
% 0.47/0.46 % (3599624)Termination reason: Instruction limit
% 0.47/0.46 % (3599624)Termination phase: shuffling
% 0.47/0.46 % (3599624)Time elapsed: 0.003 s
% 0.47/0.46 % (3599624)Peak memory usage: 10 MB
% 0.47/0.46 % (3599624)Instructions burned: 12 (million)
% 0.47/0.46 % (3599621)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3966341467:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.47/0.46 % (3599622)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3885583853:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.47/0.46 % (3599621)Instruction limit reached!
% 0.47/0.46 % (3599621)------------------------------
% 0.47/0.46 % (3599621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (3599621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (3599621)CaDiCaL version: 2.1.3
% 0.47/0.46 % (3599621)Termination reason: Instruction limit
% 0.47/0.46 % (3599621)Termination phase: shuffling
% 0.47/0.46 % (3599621)Time elapsed: 0.002 s
% 0.47/0.46 % (3599621)Peak memory usage: 10 MB
% 0.47/0.46 % (3599621)Instructions burned: 3 (million)
% 0.47/0.46 % (3599623)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1526916923:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.47/0.46 % (3599622)Instruction limit reached!
% 0.47/0.46 % (3599622)------------------------------
% 0.47/0.46 % (3599622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (3599622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (3599622)CaDiCaL version: 2.1.3
% 0.47/0.46 % (3599622)Termination reason: Instruction limit
% 0.47/0.46 % (3599622)Termination phase: shuffling
% 0.47/0.46 % (3599622)Time elapsed: 0.003 s
% 0.47/0.46 % (3599622)Peak memory usage: 10 MB
% 0.47/0.46 % (3599622)Instructions burned: 6 (million)
% 0.47/0.46 % (3599612)Instruction limit reached!
% 0.47/0.46 % (3599612)------------------------------
% 0.47/0.46 % (3599612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (3599612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (3599612)CaDiCaL version: 2.1.3
% 0.47/0.46 % (3599612)Termination reason: Instruction limit
% 0.47/0.46 % (3599612)Termination phase: Preprocessing 3
% 0.47/0.46 % (3599612)Time elapsed: 0.035 s
% 0.47/0.46 % (3599612)Peak memory usage: 12 MB
% 0.47/0.46 % (3599612)Instructions burned: 77 (million)
% 0.47/0.46 % (3599623)Instruction limit reached!
% 0.47/0.46 % (3599623)------------------------------
% 0.47/0.46 % (3599623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (3599623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (3599623)CaDiCaL version: 2.1.3
% 0.47/0.46 % (3599623)Termination reason: Instruction limit
% 0.47/0.46 % (3599623)Termination phase: shuffling
% 0.47/0.46 % (3599623)Time elapsed: 0.004 s
% 0.47/0.46 % (3599623)Peak memory usage: 10 MB
% 0.47/0.46 % (3599623)Instructions burned: 9 (million)
% 0.47/0.46 % (3599627)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.47/0.46 % (3599627)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.47/0.46 % (3599627)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2441389403:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.47/0.46 % (3599627)Instruction limit reached!
% 0.47/0.46 % (3599627)------------------------------
% 0.47/0.46 % (3599627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.46 % (3599627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.46 % (3599627)CaDiCaL version: 2.1.3
% 0.47/0.46 % (3599627)Termination reason: Instruction limit
% 1.12/0.49 % (3599627)Termination phase: shuffling
% 1.12/0.49 % (3599627)Time elapsed: 0.007 s
% 1.12/0.49 % (3599627)Peak memory usage: 11 MB
% 1.12/0.49 % (3599627)Instructions burned: 33 (million)
% 1.12/0.49 % (3599629)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=775385328:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.12/0.49 % (3599632)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.12/0.49 % (3599631)lrs+10_1_si=on:cs=on:random_seed=2414033875:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.12/0.49 % (3599633)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=569765260:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.12/0.49 % (3599632)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=1784201319:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.12/0.49 % (3599631)Instruction limit reached!
% 1.12/0.49 % (3599631)------------------------------
% 1.12/0.49 % (3599631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.49 % (3599631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.49 % (3599631)CaDiCaL version: 2.1.3
% 1.12/0.49 % (3599631)Termination reason: Instruction limit
% 1.12/0.49 % (3599631)Termination phase: shuffling
% 1.12/0.49 % (3599631)Time elapsed: 0.004 s
% 1.12/0.49 % (3599631)Peak memory usage: 10 MB
% 1.12/0.49 % (3599631)Instructions burned: 8 (million)
% 1.12/0.49 % (3599635)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=702392546:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.12/0.49 % (3599632)Instruction limit reached!
% 1.12/0.49 % (3599632)------------------------------
% 1.12/0.49 % (3599632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.49 % (3599632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.49 % (3599632)CaDiCaL version: 2.1.3
% 1.12/0.49 % (3599632)Termination reason: Instruction limit
% 1.12/0.49 % (3599632)Termination phase: shuffling
% 1.12/0.49 % (3599632)Time elapsed: 0.002 s
% 1.12/0.49 % (3599632)Peak memory usage: 10 MB
% 1.12/0.49 % (3599632)Instructions burned: 3 (million)
% 1.12/0.49 % (3599613)Instruction limit reached!
% 1.12/0.49 % (3599613)------------------------------
% 1.12/0.49 % (3599613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.49 % (3599613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.49 % (3599613)CaDiCaL version: 2.1.3
% 1.12/0.49 % (3599613)Termination reason: Instruction limit
% 1.12/0.49 % (3599613)Termination phase: Property scanning
% 1.12/0.49 % (3599613)Time elapsed: 0.065 s
% 1.12/0.49 % (3599613)Peak memory usage: 12 MB
% 1.12/0.49 % (3599613)Instructions burned: 157 (million)
% 1.12/0.49 % (3599633)Instruction limit reached!
% 1.12/0.49 % (3599633)------------------------------
% 1.12/0.49 % (3599633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.49 % (3599633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.49 % (3599633)CaDiCaL version: 2.1.3
% 1.12/0.49 % (3599633)Termination reason: Instruction limit
% 1.12/0.49 % (3599633)Termination phase: Property scanning
% 1.12/0.49 % (3599633)Time elapsed: 0.017 s
% 1.12/0.49 % (3599633)Peak memory usage: 11 MB
% 1.12/0.49 % (3599633)Instructions burned: 40 (million)
% 1.12/0.49 % (3599641)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2246068711:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.12/0.49 % (3599642)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3013559197:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.12/0.49 % (3599642)Instruction limit reached!
% 1.12/0.49 % (3599642)------------------------------
% 1.12/0.49 % (3599642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.49 % (3599642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.49 % (3599642)CaDiCaL version: 2.1.3
% 1.12/0.49 % (3599642)Termination reason: Instruction limit
% 1.12/0.49 % (3599642)Termination phase: shuffling
% 1.12/0.49 % (3599642)Time elapsed: 0.007 s
% 1.12/0.55 % (3599642)Peak memory usage: 10 MB
% 1.12/0.55 % (3599642)Instructions burned: 16 (million)
% 1.12/0.55 % (3599643)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3191944361:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.12/0.55 % (3599629)Instruction limit reached!
% 1.12/0.55 % (3599629)------------------------------
% 1.12/0.55 % (3599629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.55 % (3599629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.55 % (3599629)CaDiCaL version: 2.1.3
% 1.12/0.55 % (3599629)Termination reason: Instruction limit
% 1.12/0.55 % (3599629)Termination phase: Property scanning
% 1.12/0.55 % (3599629)Time elapsed: 0.036 s
% 1.12/0.55 % (3599629)Peak memory usage: 11 MB
% 1.12/0.55 % (3599629)Instructions burned: 87 (million)
% 1.12/0.55 % (3599641)Instruction limit reached!
% 1.12/0.55 % (3599641)------------------------------
% 1.12/0.55 % (3599641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.55 % (3599641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.55 % (3599641)CaDiCaL version: 2.1.3
% 1.12/0.55 % (3599641)Termination reason: Instruction limit
% 1.12/0.55 % (3599641)Termination phase: Property scanning
% 1.12/0.55 % (3599641)Time elapsed: 0.012 s
% 1.12/0.55 % (3599641)Peak memory usage: 11 MB
% 1.12/0.55 % (3599641)Instructions burned: 26 (million)
% 1.12/0.55 % (3599644)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=675964927:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.12/0.55 % (3599644)Instruction limit reached!
% 1.12/0.55 % (3599644)------------------------------
% 1.12/0.55 % (3599644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.55 % (3599644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.55 % (3599644)CaDiCaL version: 2.1.3
% 1.12/0.55 % (3599644)Termination reason: Instruction limit
% 1.12/0.55 % (3599644)Termination phase: shuffling
% 1.12/0.55 % (3599644)Time elapsed: 0.007 s
% 1.12/0.55 % (3599644)Peak memory usage: 10 MB
% 1.12/0.55 % (3599644)Instructions burned: 15 (million)
% 1.12/0.55 % (3599647)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=294913071: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)
% 1.12/0.55 % (3599649)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1643148862:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.12/0.55 % (3599650)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4100092336:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.12/0.55 % (3599647)Instruction limit reached!
% 1.12/0.55 % (3599647)------------------------------
% 1.12/0.55 % (3599647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.55 % (3599647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.55 % (3599647)CaDiCaL version: 2.1.3
% 1.12/0.55 % (3599647)Termination reason: Instruction limit
% 1.12/0.55 % (3599647)Termination phase: shuffling
% 1.12/0.55 % (3599647)Time elapsed: 0.002 s
% 1.12/0.55 % (3599647)Peak memory usage: 10 MB
% 1.12/0.55 % (3599647)Instructions burned: 4 (million)
% 1.12/0.55 % (3599635)Instruction limit reached!
% 1.12/0.55 % (3599635)------------------------------
% 1.12/0.55 % (3599635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.55 % (3599635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.55 % (3599635)CaDiCaL version: 2.1.3
% 1.12/0.55 % (3599635)Termination reason: Instruction limit
% 1.12/0.55 % (3599635)Termination phase: Saturation
% 1.12/0.55 % (3599635)Time elapsed: 0.057 s
% 1.12/0.55 % (3599635)Peak memory usage: 15 MB
% 1.12/0.55 % (3599635)Instructions burned: 252 (million)
% 1.12/0.55 % (3599652)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3359398176:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.12/0.55 % (3599650)Instruction limit reached!
% 1.12/0.55 % (3599650)------------------------------
% 1.12/0.55 % (3599650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.55 % (3599650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.55 % (3599650)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3599650)Termination reason: Instruction limit
% 1.80/0.60 % (3599650)Termination phase: shuffling
% 1.80/0.60 % (3599650)Time elapsed: 0.011 s
% 1.80/0.60 % (3599650)Peak memory usage: 11 MB
% 1.80/0.60 % (3599650)Instructions burned: 25 (million)
% 1.80/0.60 % (3599649)Instruction limit reached!
% 1.80/0.60 % (3599649)------------------------------
% 1.80/0.60 % (3599649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3599649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3599649)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3599649)Termination reason: Instruction limit
% 1.80/0.60 % (3599649)Termination phase: shuffling
% 1.80/0.60 % (3599649)Time elapsed: 0.012 s
% 1.80/0.60 % (3599649)Peak memory usage: 11 MB
% 1.80/0.60 % (3599649)Instructions burned: 29 (million)
% 1.80/0.60 % (3599656)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
% 1.80/0.60 % (3599656)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.80/0.60 % (3599656)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=3627660571:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.80/0.60 % (3599657)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.80/0.60 % (3599657)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=1406134920:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.80/0.60 % (3599656)Instruction limit reached!
% 1.80/0.60 % (3599656)------------------------------
% 1.80/0.60 % (3599656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3599656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3599656)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3599656)Termination reason: Instruction limit
% 1.80/0.60 % (3599656)Termination phase: shuffling
% 1.80/0.60 % (3599656)Time elapsed: 0.007 s
% 1.80/0.60 % (3599656)Peak memory usage: 10 MB
% 1.80/0.60 % (3599656)Instructions burned: 16 (million)
% 1.80/0.60 % (3599657)Instruction limit reached!
% 1.80/0.60 % (3599657)------------------------------
% 1.80/0.60 % (3599657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3599657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3599657)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3599657)Termination reason: Instruction limit
% 1.80/0.60 % (3599657)Termination phase: shuffling
% 1.80/0.60 % (3599657)Time elapsed: 0.006 s
% 1.80/0.60 % (3599657)Peak memory usage: 10 MB
% 1.80/0.60 % (3599657)Instructions burned: 8 (million)
% 1.80/0.60 % (3599659)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=1058803901:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.80/0.60 % (3599660)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=727317689:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.80/0.60 % (3599652)Instruction limit reached!
% 1.80/0.60 % (3599652)------------------------------
% 1.80/0.60 % (3599652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3599652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3599652)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3599652)Termination reason: Instruction limit
% 1.80/0.60 % (3599652)Termination phase: Preprocessing 3
% 1.80/0.60 % (3599652)Time elapsed: 0.027 s
% 1.80/0.60 % (3599652)Peak memory usage: 12 MB
% 1.80/0.60 % (3599652)Instructions burned: 60 (million)
% 1.80/0.60 % (3599660)Instruction limit reached!
% 1.80/0.60 % (3599660)------------------------------
% 1.80/0.60 % (3599660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3599660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3599660)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3599660)Termination reason: Instruction limit
% 1.80/0.60 % (3599660)Termination phase: shuffling
% 1.80/0.60 % (3599660)Time elapsed: 0.004 s
% 1.80/0.60 % (3599660)Peak memory usage: 10 MB
% 1.80/0.62 % (3599660)Instructions burned: 8 (million)
% 1.80/0.62 % (3599664)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3287644148:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.80/0.62 % (3599664)Instruction limit reached!
% 1.80/0.62 % (3599664)------------------------------
% 1.80/0.62 % (3599664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599664)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599664)Termination reason: Instruction limit
% 1.80/0.62 % (3599664)Termination phase: shuffling
% 1.80/0.62 % (3599664)Time elapsed: 0.005 s
% 1.80/0.62 % (3599664)Peak memory usage: 10 MB
% 1.80/0.62 % (3599664)Instructions burned: 22 (million)
% 1.80/0.62 % (3599663)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=4165981343:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.80/0.62 % (3599659)Instruction limit reached!
% 1.80/0.62 % (3599659)------------------------------
% 1.80/0.62 % (3599659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599659)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599659)Termination reason: Instruction limit
% 1.80/0.62 % (3599659)Termination phase: shuffling
% 1.80/0.62 % (3599659)Time elapsed: 0.014 s
% 1.80/0.62 % (3599659)Peak memory usage: 10 MB
% 1.80/0.62 % (3599659)Instructions burned: 32 (million)
% 1.80/0.62 % (3599670)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2681535228:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.80/0.62 % (3599667)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3488334428:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.80/0.62 % (3599663)Instruction limit reached!
% 1.80/0.62 % (3599663)------------------------------
% 1.80/0.62 % (3599663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599663)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599663)Termination reason: Instruction limit
% 1.80/0.62 % (3599663)Termination phase: shuffling
% 1.80/0.62 % (3599663)Time elapsed: 0.011 s
% 1.80/0.62 % (3599663)Peak memory usage: 10 MB
% 1.80/0.62 % (3599663)Instructions burned: 24 (million)
% 1.80/0.62 % (3599669)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=42931069:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.80/0.62 % (3599672)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2685306306:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.80/0.62 % (3599676)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.80/0.62 % (3599676)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1019848115:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.80/0.62 % (3599676)Instruction limit reached!
% 1.80/0.62 % (3599676)------------------------------
% 1.80/0.62 % (3599676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599676)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599676)Termination reason: Instruction limit
% 1.80/0.62 % (3599676)Termination phase: shuffling
% 1.80/0.62 % (3599676)Time elapsed: 0.007 s
% 1.80/0.62 % (3599676)Peak memory usage: 10 MB
% 1.80/0.62 % (3599676)Instructions burned: 11 (million)
% 1.80/0.62 % (3599672)Instruction limit reached!
% 1.80/0.62 % (3599672)------------------------------
% 1.80/0.62 % (3599672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599672)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599672)Termination reason: Instruction limit
% 1.80/0.62 % (3599672)Termination phase: Property scanning
% 1.80/0.62 % (3599672)Time elapsed: 0.019 s
% 1.80/0.62 % (3599672)Peak memory usage: 11 MB
% 1.80/0.62 % (3599672)Instructions burned: 43 (million)
% 1.80/0.62 % (3599670)Instruction limit reached!
% 1.80/0.62 % (3599670)------------------------------
% 1.80/0.62 % (3599670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599670)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599670)Termination reason: Instruction limit
% 1.80/0.62 % (3599670)Termination phase: Saturation
% 1.80/0.62 % (3599670)Time elapsed: 0.042 s
% 1.80/0.62 % (3599670)Peak memory usage: 14 MB
% 1.80/0.62 % (3599670)Instructions burned: 194 (million)
% 1.80/0.62 % (3599680)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=2196683378:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.80/0.62 % (3599679)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1621614487:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.80/0.62 % (3599681)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.80/0.62 % (3599681)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1659995237:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.80/0.62 % (3599681)Instruction limit reached!
% 1.80/0.62 % (3599681)------------------------------
% 1.80/0.62 % (3599681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599681)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599681)Termination reason: Instruction limit
% 1.80/0.62 % (3599681)Termination phase: shuffling
% 1.80/0.62 % (3599681)Time elapsed: 0.002 s
% 1.80/0.62 % (3599681)Peak memory usage: 10 MB
% 1.80/0.62 % (3599681)Instructions burned: 9 (million)
% 1.80/0.62 % (3599669)Instruction limit reached!
% 1.80/0.62 % (3599669)------------------------------
% 1.80/0.62 % (3599669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599669)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599669)Termination reason: Instruction limit
% 1.80/0.62 % (3599669)Termination phase: Property scanning
% 1.80/0.62 % (3599669)Time elapsed: 0.059 s
% 1.80/0.62 % (3599669)Peak memory usage: 12 MB
% 1.80/0.62 % (3599669)Instructions burned: 143 (million)
% 1.80/0.62 % (3599685)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=610187237:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.80/0.62 % (3599643)Instruction limit reached!
% 1.80/0.62 % (3599643)------------------------------
% 1.80/0.62 % (3599643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599643)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599643)Termination reason: Instruction limit
% 1.80/0.62 % (3599643)Termination phase: Saturation
% 1.80/0.62 % (3599643)Time elapsed: 0.148 s
% 1.80/0.62 % (3599643)Peak memory usage: 15 MB
% 1.80/0.62 % (3599643)Instructions burned: 327 (million)
% 1.80/0.62 % (3599685)Instruction limit reached!
% 1.80/0.62 % (3599685)------------------------------
% 1.80/0.62 % (3599685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599685)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599685)Termination reason: Instruction limit
% 1.80/0.62 % (3599685)Termination phase: shuffling
% 1.80/0.62 % (3599685)Time elapsed: 0.005 s
% 1.80/0.62 % (3599685)Peak memory usage: 10 MB
% 1.80/0.62 % (3599685)Instructions burned: 22 (million)
% 1.80/0.62 % (3599686)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=589381029:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 1.80/0.62 % (3599689)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=761525979:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 1.80/0.62 % (3599686)Instruction limit reached!
% 1.80/0.62 % (3599686)------------------------------
% 1.80/0.62 % (3599686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599686)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599686)Termination reason: Instruction limit
% 1.80/0.62 % (3599686)Termination phase: shuffling
% 1.80/0.62 % (3599686)Time elapsed: 0.008 s
% 1.80/0.62 % (3599686)Peak memory usage: 10 MB
% 1.80/0.62 % (3599686)Instructions burned: 19 (million)
% 1.80/0.62 % (3599688)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=2672119834:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 1.80/0.62 % (3599610) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3599602-3599610"...
% 1.80/0.62 % (3599610)...printing done.
% 1.80/0.62 % (3599610)Refutation found. Thanks to Tanya!
% 1.80/0.62 % SZS status Theorem for theBenchmark
% 1.80/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 1.80/0.62 % (3599610)------------------------------
% 1.80/0.62 % (3599610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.62 % (3599610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.62 % (3599610)CaDiCaL version: 2.1.3
% 1.80/0.62 % (3599610)Termination reason: Refutation
% 1.80/0.62 % (3599610)Time elapsed: 0.266 s
% 1.80/0.62 % (3599610)Peak memory usage: 21 MB
% 1.80/0.62 % (3599610)Instructions burned: 527 (million)
% 1.80/0.62 % (3599602)Success in time 0.324 s
% 1.80/0.62 % Vampire exiting
%------------------------------------------------------------------------------