%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU763^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:31:12 AM UTC 2026
% Result : Theorem 5.70s 1.23s
% Output : Refutation 5.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 5276 (1462 equ; 0 cnn)
% Maximal formula atoms : 282 ( 211 avg)
% Number of connectives : 2641 ( 35 ~; 23 |;1133 &; 318 @)
% ( 2 <=>;1130 =>; 0 <=; 0 <~>)
% Maximal formula depth : 291 ( 94 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 511 ( 508 usr; 311 con; 0-4 aty)
% Number of variables : 51 ( 0 ^; 36 !; 15 ?; 51 :)
% 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_303,type,
demorgan2a1: $o ).
thf(func_def_304,type,
complementUnionInPowersetComplement: $o ).
thf(func_def_305,type,
demorgan2a2: $o ).
thf(func_def_306,type,
demorgan1a: $o ).
thf(func_def_307,type,
demorgan1b: $o ).
thf(func_def_308,type,
demorgan1: $o ).
thf(func_def_309,type,
demorgan2a: $o ).
thf(func_def_310,type,
demorgan2b2: $o ).
thf(func_def_311,type,
demorgan2b: $o ).
thf(func_def_312,type,
demorgan2: $o ).
thf(func_def_313,type,
woz13rule0: $o ).
thf(func_def_314,type,
woz13rule1: $o ).
thf(func_def_315,type,
woz13rule2: $o ).
thf(func_def_316,type,
woz13rule3: $o ).
thf(func_def_317,type,
woz13rule4: $o ).
thf(func_def_320,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_321,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_322,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_323,type,
vAND: $o > $o > $o ).
thf(func_def_324,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_325,type,
vIMP: $o > $o > $o ).
thf(func_def_326,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_327,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_328,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_329,type,
vOR: $o > $o > $o ).
thf(func_def_330,type,
vNOT: $o > $o ).
thf(func_def_331,type,
sP0: $i > $i > $o ).
thf(func_def_332,type,
sP1: $i > $o ).
thf(func_def_333,type,
sP2: $i > $i > $o ).
thf(func_def_334,type,
sP3: $i > $i > $o ).
thf(func_def_335,type,
sP4: $o ).
thf(func_def_336,type,
sP5: $o ).
thf(func_def_337,type,
sP6: $o ).
thf(func_def_338,type,
sP7: $o ).
thf(func_def_339,type,
sP8: $o ).
thf(func_def_340,type,
sP9: $i > $i > $i > $i > $o ).
thf(func_def_341,type,
sP10: $o ).
thf(func_def_342,type,
sP11: $i > $i > $i > $o ).
thf(func_def_343,type,
sP12: $i > $i > $i > $o > $o ).
thf(func_def_348,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_349,type,
sK18: $i > $o ).
thf(func_def_357,type,
sK26: $i > $i > $i ).
thf(func_def_360,type,
sK29: $i > $o ).
thf(func_def_361,type,
sK30: $i > $o ).
thf(func_def_362,type,
sK31: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_363,type,
sK32: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_364,type,
sK33: $i > $i > $o ).
thf(func_def_382,type,
sK51: $i > $i > $i ).
thf(func_def_383,type,
sK52: $i > $i > $i ).
thf(func_def_384,type,
sK53: $i > $i > $i ).
thf(func_def_385,type,
sK54: $i > $i > $i ).
thf(func_def_386,type,
sK55: $i > $i > $i ).
thf(func_def_387,type,
sK56: $i > $i > $i > $i ).
thf(func_def_388,type,
sK57: $i > $i ).
thf(func_def_389,type,
sK58: $i > $i ).
thf(func_def_390,type,
sK59: $i > $i ).
thf(func_def_391,type,
sK60: $i > $i ).
thf(func_def_392,type,
sK61: $i > $i > $i > $i ).
thf(func_def_393,type,
sK62: $i > $i > $i > $i ).
thf(func_def_394,type,
sK63: $i > $i > $i ).
thf(func_def_395,type,
sK64: $i > $i > $i ).
thf(func_def_396,type,
sK65: $i > $i > $i ).
thf(func_def_398,type,
sK67: $i > $i ).
thf(func_def_399,type,
sK68: $i > $i ).
thf(func_def_400,type,
sK69: $i > $i ).
thf(func_def_404,type,
sK73: $i > $i > $i ).
thf(func_def_410,type,
sK79: $i > $i ).
thf(func_def_413,type,
sK82: $i > $i ).
thf(func_def_416,type,
sK85: $i > $i ).
thf(func_def_417,type,
sK86: ( $i > $i ) > $i > $i > $i ).
thf(func_def_443,type,
sK112: $o ).
thf(func_def_445,type,
sK114: $i > $i > $i ).
thf(func_def_450,type,
sK119: $i > $i ).
thf(func_def_458,type,
sK127: $i > $i > $o ).
thf(func_def_490,type,
sK159: $i > $i ).
thf(func_def_491,type,
sK160: $o ).
thf(func_def_496,type,
sK165: $i > $o ).
thf(func_def_497,type,
sK166: $i > $i ).
thf(func_def_511,type,
sK180: $o ).
thf(func_def_515,type,
sK184: $i > $o ).
thf(func_def_519,type,
sK188: $i > $i > $o ).
thf(func_def_521,type,
sK190: $i > $i > $i > $i ).
thf(func_def_522,type,
sK191: $i > $i > $i > $i ).
thf(func_def_551,type,
sK220: $i > $i ).
thf(func_def_558,type,
sK227: $i > $o ).
thf(func_def_572,type,
sK241: $i > $i > $i > $i ).
thf(func_def_585,type,
sK254: $i > $i > $i > $i > $i ).
thf(func_def_587,type,
sK256: $o ).
thf(func_def_601,type,
sK270: $i > $o ).
thf(func_def_611,type,
sK280: $o ).
thf(func_def_618,type,
sK287: $i > $o ).
thf(func_def_619,type,
sK288: ( $i > $o ) > $i ).
thf(func_def_625,type,
sK294: $i > $i > $o ).
thf(func_def_627,type,
sK296: $i > $i ).
thf(func_def_628,type,
sK297: $i > $i ).
thf(func_def_629,type,
sK298: $i > ( $i > $i > $o ) > $i ).
thf(func_def_630,type,
sK299: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_631,type,
sK300: $i > ( $i > $i > $o ) > $i ).
thf(func_def_635,type,
sK304: $i > $i > $o ).
thf(func_def_638,type,
sK307: $i > $i ).
thf(func_def_642,type,
sK311: $i > $i > ( $i > $i ) > $i ).
thf(func_def_648,type,
sK317: $o ).
thf(func_def_660,type,
sK329: $o ).
thf(func_def_661,type,
sK330: $o > $i > $i > $i ).
thf(func_def_666,type,
sK335: $i > $i > $i > $i > $i ).
thf(func_def_668,type,
sK337: $i > $i > $o ).
thf(func_def_670,type,
sK339: $i > $o ).
thf(func_def_695,type,
sK364: $i > $i > $i > $i > $i ).
thf(func_def_707,type,
sK376: $i > $o ).
thf(func_def_708,type,
sK377: $i > $o ).
thf(func_def_709,type,
sK378: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_710,type,
sK379: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_712,type,
sK381: $i > $i ).
thf(func_def_714,type,
sK383: $i > ( $i > $i ) > $i > $i ).
thf(func_def_724,type,
sK393: $o ).
thf(func_def_730,type,
sK399: $i > $i > $i ).
thf(func_def_734,type,
sK403: ( $i > $i ) > $i > $i > $i ).
thf(func_def_737,type,
sK406: $i > $i ).
thf(func_def_744,type,
sK413: $i > $o ).
thf(func_def_746,type,
sK415: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_747,type,
sK416: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_768,type,
sK437: $i > $i > $i ).
thf(func_def_785,type,
sK454: $i > $i > $o ).
thf(func_def_790,type,
sK459: $i > $i ).
thf(func_def_793,type,
sK462: $i > ( $i > $i ) > $i > $i ).
thf(func_def_794,type,
sK463: $i > $i > $i ).
thf(func_def_795,type,
sK464: $i > $i > $i ).
thf(func_def_815,type,
sK484: $o ).
thf(func_def_825,type,
sK494: $i > $o ).
thf(func_def_826,type,
sK495: $i > $i ).
thf(func_def_827,type,
sK496: ( $i > $o ) > $i ).
thf(func_def_841,type,
sK510: $o ).
thf(func_def_844,type,
sK513: $i > $o ).
thf(func_def_863,type,
sK532: $i > $o ).
thf(func_def_865,type,
sK534: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_866,type,
sK535: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_873,type,
sK542: $o ).
thf(func_def_896,type,
sK565: $i > $i > ( $i > $o ) > $i ).
thf(func_def_897,type,
sK566: $i > $o ).
thf(func_def_913,type,
sK582: $i > ( $i > $o ) > $i ).
thf(func_def_914,type,
sK583: $i > $o ).
thf(func_def_926,type,
sK595: $o ).
thf(func_def_932,type,
sK601: $i > ( $i > $i ) > $i > $i ).
thf(func_def_934,type,
sK603: $i > $i ).
thf(func_def_937,type,
sK606: $i > $o ).
thf(func_def_940,type,
sK609: $i > $i > $i ).
thf(func_def_949,type,
sK618: $i > $o ).
thf(func_def_950,type,
sK619: $i > $i ).
thf(func_def_951,type,
sK620: ( $i > $o ) > $i ).
thf(func_def_953,type,
sK622: $i > $o ).
thf(func_def_955,type,
sK624: ( $i > $o ) > $i > $i ).
thf(func_def_956,type,
sK625: ( $i > $o ) > $i > $i ).
thf(func_def_964,type,
sK633: $o ).
thf(func_def_993,type,
sK662: $i > $o ).
thf(func_def_995,type,
sK664: ( $i > $o ) > $i > $i ).
thf(func_def_996,type,
sK665: ( $i > $o ) > $i > $i ).
thf(func_def_1003,type,
sK672: $i > $i > $i > $i > $i ).
thf(func_def_1004,type,
sK673: $i > $i > $i > $i > $i ).
thf(func_def_1010,type,
sK679: $i > $o ).
thf(func_def_1025,type,
sK694: $i > $i > $i ).
thf(func_def_1034,type,
sK703: $i > $i > $i ).
thf(func_def_1036,type,
sK705: $o ).
thf(func_def_1037,type,
sK706: $i > ( $i > $o ) > $i ).
thf(func_def_1038,type,
sK707: $i > $o ).
thf(func_def_1042,type,
sK711: ( $i > $o ) > $i > $i ).
thf(func_def_1044,type,
sK713: $i > $o ).
thf(func_def_1046,type,
sK715: ( $i > $o ) > $i ).
thf(func_def_1047,type,
sK716: ( $i > $o ) > $i ).
thf(func_def_1048,type,
sK717: $i > $o ).
thf(func_def_1065,type,
sK734: $i > $i > $o ).
thf(func_def_1072,type,
sK741: $i > $o ).
thf(func_def_1074,type,
sK743: $i > ( $i > $o ) > $i ).
thf(func_def_1075,type,
sK744: $o ).
thf(func_def_1083,type,
sK752: $i > $i > $i > $i > $i ).
thf(func_def_1084,type,
sK753: $i > $i > $i > $i > $i ).
thf(func_def_1085,type,
sK754: $i > $i > $i > $i > $i ).
thf(func_def_1086,type,
sK755: $i > $i > $i > $i > $i ).
thf(func_def_1104,type,
sK773: $i > $i > $i > $i ).
thf(func_def_1108,type,
sK777: $i > $i > $i > $i ).
thf(func_def_1110,type,
sK779: $i > $o ).
thf(func_def_1113,type,
sK782: $o ).
thf(func_def_1144,type,
sK813: $i > $o ).
thf(func_def_1147,type,
sK816: ( $i > $o ) > $i > $i ).
thf(func_def_1149,type,
sK818: $i > $o ).
thf(func_def_1156,type,
sK825: $i > ( $i > $o ) > $i ).
thf(func_def_1157,type,
sK826: $i > $o ).
thf(func_def_1162,type,
sK831: $i > $i > $i > $i ).
thf(func_def_1163,type,
sK832: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1164,type,
sK833: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1165,type,
sK834: $i > $o ).
thf(func_def_1166,type,
sK835: $i > $o ).
thf(func_def_1171,type,
sK840: $i > $o ).
thf(func_def_1189,type,
sK858: $i > $o ).
thf(func_def_1192,type,
sK861: $o ).
thf(func_def_1199,type,
sK868: $o ).
thf(func_def_1202,type,
sK871: $i > $i ).
thf(func_def_1210,type,
sK879: $i > $o ).
thf(func_def_1220,type,
sK889: ( $i > $o ) > $i > $i ).
thf(func_def_1222,type,
sK891: $i > $o ).
thf(func_def_1228,type,
sK897: $i > ( $i > $o ) > $i ).
thf(func_def_1229,type,
sK898: $i > $o ).
thf(f256,axiom,
( complementInPowersetComplementIntersect
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(f284,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
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_1) ).
thf(f285,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
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f284]) ).
thf(f633,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
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f285]) ).
thf(f634,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 )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f633]) ).
thf(f701,plain,
( complementInPowersetComplementIntersect
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f256]) ).
thf(f702,plain,
( ( complementInPowersetComplementIntersect = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f701]) ).
thf(f992,plain,
( ( complementInPowersetComplementIntersect = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
= $true ) ) ) ),
inference(ennf_transformation,[],[f702]) ).
thf(f1032,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $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,[],[f634]) ).
thf(f1033,plain,
( ( app = $true )
& ( setukpairIR = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( singletonsuniq = $true )
& ( inIntersectImpInUnion = $true )
& ( setukpairinjR11 = $true )
& ( upairinpowunion = $true )
& ( setukpairIL = $true )
& ( funcextLem = $true )
& ( binunionEcases = $true )
& ( binunionTILcontra = $true )
& ( cartprodmempair = $true )
& ( eqimpsubset2 = $true )
& ( secondinupair = $true )
& ( binunionT_lem = $true )
& ( funcGraphProp1 = $true )
& ( binintersectTERcontra = $true )
& ( doubleComplementE1 = $true )
& ( noeltsimpempty = $true )
& ( theprop = $true )
& ( contrasubsetT3 = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( setminusIRneg = $true )
& ( singletonsswitch = $true )
& ( demorgan2b = $true )
& ( lam2lamEq = $true )
& ( woz13rule1 = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrER = $true )
& ( kpairsurjEq = $true )
& ( contraSubsetComplement = $true )
& ( doubleComplementSub2 = $true )
& ( exuE2 = $true )
& ( setoftrueEq = $true )
& ( nonemptyI1 = $true )
& ( upairsubunion = $true )
& ( binintersectER = $true )
& ( iffalseProp1 = $true )
& ( subsetI2 = $true )
& ( omegaSAx = $true )
& ( binintersectSubset3 = $true )
& ( setukpairinjR2 = $true )
& ( nonemptyI = $true )
& ( dpsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( binunionLsub = $true )
& ( emptyE1 = $true )
& ( setminusLsub = $true )
& ( funcImageSingleton = $true )
& ( ubforcartprodlem3 = $true )
& ( exuI1 = $true )
& ( powersetI = $true )
& ( subsetI1 = $true )
& ( ap2apEq1 = $true )
& ( prop2setI = $true )
& ( demorgan2a1 = $true )
& ( infuncsetfunc = $true )
& ( demorgan2a2 = $true )
& ( binunionRsub = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( symdiffE = $true )
& ( inCongP = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( cartprodfstpairEq = $true )
& ( dsetconstr__Cong = $true )
& ( inPowerset = $true )
& ( upairset2E = $true )
& ( woz13rule3 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setadjoinOr = $true )
& ( symdiffI1 = $true )
& ( woz13rule0 = $true )
& ( setminusEL = $true )
& ( emptyinPowerset = $true )
& ( notdallE = $true )
& ( setunionI = $true )
& ( setminusER = $true )
& ( exuI3 = $true )
& ( binintersectSubset4 = $true )
& ( demorgan2 = $true )
& ( cartprodpairin = $true )
& ( powersetTI1 = $true )
& ( binunionTIRcontra = $true )
& ( binintersectRsub = $true )
& ( ex1E1 = $true )
& ( contrasubsetT1 = $true )
& ( setadjoinIR = $true )
& ( upairsetE = $true )
& ( emptyinunitempty = $true )
& ( demorgan2b2 = $true )
& ( powersetAx = $true )
& ( subsetRefl = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( kpairp = $true )
& ( subsetE2 = $true )
& ( funcinfuncset = $true )
& ( notinsingleton = $true )
& ( nonemptyImpWitness = $true )
& ( setminusELneg = $true )
& ( setextT = $true )
& ( ksndpairEq = $true )
& ( ap2apEq2 = $true )
& ( quantDeMorgan3 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectT_lem = $true )
& ( dpsetconstrER = $true )
& ( upairsetIL = $true )
& ( cartprodfstin = $true )
& ( brelnall1 = $true )
& ( descrp = $true )
& ( setukpairinjL = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( binintersectSubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyI = $true )
& ( exuEu = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset5 = $true )
& ( notinemptyset = $true )
& ( funcGraphProp3 = $true )
& ( setadjoinIL = $true )
& ( iffalse = $true )
& ( kfstsingleton = $true )
& ( setext = $true )
& ( uniqinunit = $true )
& ( binintersectLsub = $true )
& ( iftrue = $true )
& ( singletonsubset = $true )
& ( beta1 = $true )
& ( setadjoinSub = $true )
& ( brelnall2 = $true )
& ( funcext = $true )
& ( setminusI = $true )
& ( sepInPowerset = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( setbeta = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( exuE3u = $true )
& ( symdiffIneg2 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setadjoinE = $true )
& ( eta1 = $true )
& ( notequalI1 = $true )
& ( cartprodpairsurjEq = $true )
& ( doubleComplementI1 = $true )
& ( cartprodpairmemEL = $true )
& ( setukpairinjL1 = $true )
& ( setukpairinjR = $true )
& ( disjointsetsI1 = $true )
& ( replAx = $true )
& ( emptysetimpfalse = $true )
& ( complementT_lem = $true )
& ( binintersectTELcontra = $true )
& ( foundationAx = $true )
& ( setukpairinjR1 = $true )
& ( ap2p = $true )
& ( binunionIR = $true )
& ( powersetE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementTE1 = $true )
& ( lamp = $true )
& ( complementTcontraSubset = $true )
& ( dsetconstrI = $true )
& ( ex1I = $true )
& ( powersetI1 = $true )
& ( iftrueProp2 = $true )
& ( woz13rule4 = $true )
& ( emptysetsubset = $true )
& ( setunion__Cong = $true )
& ( cartprodsndpairEq = $true )
& ( upairequniteq = $true )
& ( powersetT_lem = $true )
& ( complementTI1 = $true )
& ( quantDeMorgan2 = $true )
& ( singletoninpowunion = $true )
& ( subbreln = $true )
& ( dsetconstrEL = $true )
& ( powersetTE1 = $true )
& ( funcext2 = $true )
& ( setadjoinAx = $true )
& ( doubleComplementEq = $true )
& ( iftrueProp1 = $true )
& ( setunionsingleton1 = $true )
& ( emptyset__Cong = $true )
& ( lamProp = $true )
& ( symdiffIneg1 = $true )
& ( setunionAx = $true )
& ( kfstpairEq = $true )
& ( contrasubsetT2 = $true )
& ( ksndsingleton = $true )
& ( setukpairinjL2 = $true )
& ( sepSubset = $true )
& ( setunionE2 = $true )
& ( lam2p = $true )
& ( binunionTE = $true )
& ( omega__Cong = $true )
& ( complementImpComplementIntersect = $true )
& ( ifp = $true )
& ( dpsetconstrEL2 = $true )
& ( setminusSubset2 = $true )
& ( singletonprop = $true )
& ( cartprodsndin = $true )
& ( setminusT_lem = $true )
& ( doubleComplementSub1 = $true )
& ( notsubsetI = $true )
& ( upairset2IR = $true )
& ( binintersectSubset2 = $true )
& ( setminusILneg = $true )
& ( powersetsubset = $true )
& ( setunionsingleton2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR12 = $true )
& ( prop2setE = $true )
& ( subset2powerset = $true )
& ( beta2 = $true )
& ( emptyInPowerset = $true )
& ( setunionsingleton = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( dpsetconstrERa = $true )
& ( eqimpsubset1 = $true )
& ( binunionIL = $true )
& ( emptysetE = $true )
& ( setOfPairsIsBReln = $true )
& ( binintersectEL = $true )
& ( notdexE = $true )
& ( exuI2 = $true )
& ( ubforcartprodlem1 = $true )
& ( demorgan1a = $true )
& ( setminusSubset1 = $true )
& ( notequalI2 = $true )
& ( cartprodmempair1 = $true )
& ( exu__Cong = $true )
& ( powersetE1 = $true )
& ( symdiffI2 = $true )
& ( funcGraphProp2 = $true )
& ( setunionE = $true )
& ( wellorderingAx = $true )
& ( setminusERneg = $true )
& ( iftrueorfalse = $true )
& ( ex1I2 = $true )
& ( setextAx = $true )
& ( iffalseProp2 = $true )
& ( demorgan1b = $true )
& ( funcGraphProp4 = $true )
& ( eqbreln = $true )
& ( dpsetconstrSub = $true )
& ( subsetTI = $true )
& ( theeq = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( demorgan1 = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( binunionTEcontra = $true )
& ( ifSingleton = $true )
& ( setadjoin__Cong = $true )
& ( subsetTrans = $true )
& ( eta2 = $true )
& ( in__Cong = $true )
& ( contrasubsetT = $true )
& ( complementTnotintersectT = $true )
& ( bs114d = $true )
& ( inIntersectImpInUnion2 = $true )
& ( ex1E2 = $true )
& ( upairsetIR = $true )
& ( woz13rule2 = $true )
& ( setadjoinSub2 = $true )
& ( demorgan2a = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( dpsetconstrEL1 = $true ) ),
inference(flattening,[],[f1032]) ).
thf(f1698,plain,
( ( ( complementInPowersetComplementIntersect = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
!= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
= $true ) ) )
| ( complementInPowersetComplementIntersect != $true ) ) ),
inference(nnf_transformation,[],[f992]) ).
thf(f1699,plain,
( ( ( complementInPowersetComplementIntersect = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ ( setminus @ X3 @ X4 ) @ ( powerset @ ( setminus @ X3 @ ( binintersect @ X4 @ X5 ) ) ) )
= $true ) ) )
| ( complementInPowersetComplementIntersect != $true ) ) ),
inference(rectify,[],[f1698]) ).
thf(f1700,plain,
( ( ( complementInPowersetComplementIntersect = $true )
| ( ( $true
= ( in @ sK492 @ ( powerset @ sK491 ) ) )
& ( $true
= ( in @ sK493 @ ( powerset @ sK491 ) ) )
& ( ( in @ ( setminus @ sK491 @ sK492 ) @ ( powerset @ ( setminus @ sK491 @ ( binintersect @ sK492 @ sK493 ) ) ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ ( setminus @ X3 @ X4 ) @ ( powerset @ ( setminus @ X3 @ ( binintersect @ X4 @ X5 ) ) ) )
= $true ) ) )
| ( complementInPowersetComplementIntersect != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK491,sK492,sK493]),skolemize(X0,sK491),skolemize(X1,sK492),skolemize(X2,sK493)],[f1699]) ).
thf(f1994,plain,
( ( app = $true )
& ( setukpairIR = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( singletonsuniq = $true )
& ( inIntersectImpInUnion = $true )
& ( setukpairinjR11 = $true )
& ( upairinpowunion = $true )
& ( setukpairIL = $true )
& ( funcextLem = $true )
& ( binunionEcases = $true )
& ( binunionTILcontra = $true )
& ( cartprodmempair = $true )
& ( eqimpsubset2 = $true )
& ( secondinupair = $true )
& ( binunionT_lem = $true )
& ( funcGraphProp1 = $true )
& ( binintersectTERcontra = $true )
& ( doubleComplementE1 = $true )
& ( noeltsimpempty = $true )
& ( theprop = $true )
& ( contrasubsetT3 = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( setminusIRneg = $true )
& ( singletonsswitch = $true )
& ( demorgan2b = $true )
& ( lam2lamEq = $true )
& ( woz13rule1 = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrER = $true )
& ( kpairsurjEq = $true )
& ( contraSubsetComplement = $true )
& ( doubleComplementSub2 = $true )
& ( exuE2 = $true )
& ( setoftrueEq = $true )
& ( nonemptyI1 = $true )
& ( upairsubunion = $true )
& ( binintersectER = $true )
& ( iffalseProp1 = $true )
& ( subsetI2 = $true )
& ( omegaSAx = $true )
& ( binintersectSubset3 = $true )
& ( setukpairinjR2 = $true )
& ( nonemptyI = $true )
& ( dpsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( binunionLsub = $true )
& ( emptyE1 = $true )
& ( setminusLsub = $true )
& ( funcImageSingleton = $true )
& ( ubforcartprodlem3 = $true )
& ( exuI1 = $true )
& ( powersetI = $true )
& ( subsetI1 = $true )
& ( ap2apEq1 = $true )
& ( prop2setI = $true )
& ( demorgan2a1 = $true )
& ( infuncsetfunc = $true )
& ( demorgan2a2 = $true )
& ( binunionRsub = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( symdiffE = $true )
& ( inCongP = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( cartprodfstpairEq = $true )
& ( dsetconstr__Cong = $true )
& ( inPowerset = $true )
& ( upairset2E = $true )
& ( woz13rule3 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setadjoinOr = $true )
& ( symdiffI1 = $true )
& ( woz13rule0 = $true )
& ( setminusEL = $true )
& ( emptyinPowerset = $true )
& ( notdallE = $true )
& ( setunionI = $true )
& ( setminusER = $true )
& ( exuI3 = $true )
& ( binintersectSubset4 = $true )
& ( demorgan2 = $true )
& ( cartprodpairin = $true )
& ( powersetTI1 = $true )
& ( binunionTIRcontra = $true )
& ( binintersectRsub = $true )
& ( ex1E1 = $true )
& ( contrasubsetT1 = $true )
& ( setadjoinIR = $true )
& ( upairsetE = $true )
& ( emptyinunitempty = $true )
& ( demorgan2b2 = $true )
& ( powersetAx = $true )
& ( subsetRefl = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( kpairp = $true )
& ( subsetE2 = $true )
& ( funcinfuncset = $true )
& ( notinsingleton = $true )
& ( nonemptyImpWitness = $true )
& ( setminusELneg = $true )
& ( setextT = $true )
& ( ksndpairEq = $true )
& ( ap2apEq2 = $true )
& ( quantDeMorgan3 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectT_lem = $true )
& ( dpsetconstrER = $true )
& ( upairsetIL = $true )
& ( cartprodfstin = $true )
& ( brelnall1 = $true )
& ( descrp = $true )
& ( setukpairinjL = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( binintersectSubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyI = $true )
& ( exuEu = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset5 = $true )
& ( notinemptyset = $true )
& ( funcGraphProp3 = $true )
& ( setadjoinIL = $true )
& ( iffalse = $true )
& ( kfstsingleton = $true )
& ( setext = $true )
& ( uniqinunit = $true )
& ( binintersectLsub = $true )
& ( iftrue = $true )
& ( singletonsubset = $true )
& ( beta1 = $true )
& ( setadjoinSub = $true )
& ( brelnall2 = $true )
& ( funcext = $true )
& ( setminusI = $true )
& ( sepInPowerset = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( setbeta = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( exuE3u = $true )
& ( symdiffIneg2 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setadjoinE = $true )
& ( eta1 = $true )
& ( notequalI1 = $true )
& ( cartprodpairsurjEq = $true )
& ( doubleComplementI1 = $true )
& ( cartprodpairmemEL = $true )
& ( setukpairinjL1 = $true )
& ( setukpairinjR = $true )
& ( disjointsetsI1 = $true )
& ( replAx = $true )
& ( emptysetimpfalse = $true )
& ( complementT_lem = $true )
& ( binintersectTELcontra = $true )
& ( foundationAx = $true )
& ( setukpairinjR1 = $true )
& ( ap2p = $true )
& ( binunionIR = $true )
& ( powersetE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementTE1 = $true )
& ( lamp = $true )
& ( complementTcontraSubset = $true )
& ( dsetconstrI = $true )
& ( ex1I = $true )
& ( powersetI1 = $true )
& ( iftrueProp2 = $true )
& ( woz13rule4 = $true )
& ( emptysetsubset = $true )
& ( setunion__Cong = $true )
& ( cartprodsndpairEq = $true )
& ( upairequniteq = $true )
& ( powersetT_lem = $true )
& ( complementTI1 = $true )
& ( quantDeMorgan2 = $true )
& ( singletoninpowunion = $true )
& ( subbreln = $true )
& ( dsetconstrEL = $true )
& ( powersetTE1 = $true )
& ( funcext2 = $true )
& ( setadjoinAx = $true )
& ( doubleComplementEq = $true )
& ( iftrueProp1 = $true )
& ( setunionsingleton1 = $true )
& ( emptyset__Cong = $true )
& ( lamProp = $true )
& ( symdiffIneg1 = $true )
& ( setunionAx = $true )
& ( kfstpairEq = $true )
& ( contrasubsetT2 = $true )
& ( ksndsingleton = $true )
& ( setukpairinjL2 = $true )
& ( sepSubset = $true )
& ( setunionE2 = $true )
& ( lam2p = $true )
& ( binunionTE = $true )
& ( omega__Cong = $true )
& ( complementImpComplementIntersect = $true )
& ( ifp = $true )
& ( dpsetconstrEL2 = $true )
& ( setminusSubset2 = $true )
& ( singletonprop = $true )
& ( cartprodsndin = $true )
& ( setminusT_lem = $true )
& ( doubleComplementSub1 = $true )
& ( notsubsetI = $true )
& ( upairset2IR = $true )
& ( binintersectSubset2 = $true )
& ( setminusILneg = $true )
& ( powersetsubset = $true )
& ( setunionsingleton2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR12 = $true )
& ( prop2setE = $true )
& ( subset2powerset = $true )
& ( beta2 = $true )
& ( emptyInPowerset = $true )
& ( setunionsingleton = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( dpsetconstrERa = $true )
& ( eqimpsubset1 = $true )
& ( binunionIL = $true )
& ( emptysetE = $true )
& ( setOfPairsIsBReln = $true )
& ( binintersectEL = $true )
& ( notdexE = $true )
& ( exuI2 = $true )
& ( ubforcartprodlem1 = $true )
& ( demorgan1a = $true )
& ( setminusSubset1 = $true )
& ( notequalI2 = $true )
& ( cartprodmempair1 = $true )
& ( exu__Cong = $true )
& ( powersetE1 = $true )
& ( symdiffI2 = $true )
& ( funcGraphProp2 = $true )
& ( setunionE = $true )
& ( wellorderingAx = $true )
& ( setminusERneg = $true )
& ( iftrueorfalse = $true )
& ( ex1I2 = $true )
& ( setextAx = $true )
& ( iffalseProp2 = $true )
& ( demorgan1b = $true )
& ( funcGraphProp4 = $true )
& ( eqbreln = $true )
& ( dpsetconstrSub = $true )
& ( subsetTI = $true )
& ( theeq = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan1 = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( binunionTEcontra = $true )
& ( ifSingleton = $true )
& ( setadjoin__Cong = $true )
& ( subsetTrans = $true )
& ( eta2 = $true )
& ( in__Cong = $true )
& ( contrasubsetT = $true )
& ( complementTnotintersectT = $true )
& ( bs114d = $true )
& ( inIntersectImpInUnion2 = $true )
& ( ex1E2 = $true )
& ( upairsetIR = $true )
& ( woz13rule2 = $true )
& ( setadjoinSub2 = $true )
& ( demorgan2a = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( dpsetconstrEL1 = $true ) ),
inference(rectify,[],[f1033]) ).
thf(f1995,plain,
( ( app = $true )
& ( setukpairIR = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( singletonsuniq = $true )
& ( inIntersectImpInUnion = $true )
& ( setukpairinjR11 = $true )
& ( upairinpowunion = $true )
& ( setukpairIL = $true )
& ( funcextLem = $true )
& ( binunionEcases = $true )
& ( binunionTILcontra = $true )
& ( cartprodmempair = $true )
& ( eqimpsubset2 = $true )
& ( secondinupair = $true )
& ( binunionT_lem = $true )
& ( funcGraphProp1 = $true )
& ( binintersectTERcontra = $true )
& ( doubleComplementE1 = $true )
& ( noeltsimpempty = $true )
& ( theprop = $true )
& ( contrasubsetT3 = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( setminusIRneg = $true )
& ( singletonsswitch = $true )
& ( demorgan2b = $true )
& ( lam2lamEq = $true )
& ( woz13rule1 = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrER = $true )
& ( kpairsurjEq = $true )
& ( contraSubsetComplement = $true )
& ( doubleComplementSub2 = $true )
& ( exuE2 = $true )
& ( setoftrueEq = $true )
& ( nonemptyI1 = $true )
& ( upairsubunion = $true )
& ( binintersectER = $true )
& ( iffalseProp1 = $true )
& ( subsetI2 = $true )
& ( omegaSAx = $true )
& ( binintersectSubset3 = $true )
& ( setukpairinjR2 = $true )
& ( nonemptyI = $true )
& ( dpsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( binunionLsub = $true )
& ( emptyE1 = $true )
& ( setminusLsub = $true )
& ( funcImageSingleton = $true )
& ( ubforcartprodlem3 = $true )
& ( exuI1 = $true )
& ( powersetI = $true )
& ( subsetI1 = $true )
& ( ap2apEq1 = $true )
& ( prop2setI = $true )
& ( demorgan2a1 = $true )
& ( infuncsetfunc = $true )
& ( demorgan2a2 = $true )
& ( binunionRsub = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( symdiffE = $true )
& ( inCongP = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( cartprodfstpairEq = $true )
& ( dsetconstr__Cong = $true )
& ( inPowerset = $true )
& ( upairset2E = $true )
& ( woz13rule3 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setadjoinOr = $true )
& ( symdiffI1 = $true )
& ( woz13rule0 = $true )
& ( setminusEL = $true )
& ( emptyinPowerset = $true )
& ( notdallE = $true )
& ( setunionI = $true )
& ( setminusER = $true )
& ( exuI3 = $true )
& ( binintersectSubset4 = $true )
& ( demorgan2 = $true )
& ( cartprodpairin = $true )
& ( powersetTI1 = $true )
& ( binunionTIRcontra = $true )
& ( binintersectRsub = $true )
& ( ex1E1 = $true )
& ( contrasubsetT1 = $true )
& ( setadjoinIR = $true )
& ( upairsetE = $true )
& ( emptyinunitempty = $true )
& ( demorgan2b2 = $true )
& ( powersetAx = $true )
& ( subsetRefl = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( kpairp = $true )
& ( subsetE2 = $true )
& ( funcinfuncset = $true )
& ( notinsingleton = $true )
& ( nonemptyImpWitness = $true )
& ( setminusELneg = $true )
& ( setextT = $true )
& ( ksndpairEq = $true )
& ( ap2apEq2 = $true )
& ( quantDeMorgan3 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectT_lem = $true )
& ( dpsetconstrER = $true )
& ( upairsetIL = $true )
& ( cartprodfstin = $true )
& ( brelnall1 = $true )
& ( descrp = $true )
& ( setukpairinjL = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( binintersectSubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyI = $true )
& ( exuEu = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset5 = $true )
& ( notinemptyset = $true )
& ( funcGraphProp3 = $true )
& ( setadjoinIL = $true )
& ( iffalse = $true )
& ( kfstsingleton = $true )
& ( setext = $true )
& ( uniqinunit = $true )
& ( binintersectLsub = $true )
& ( iftrue = $true )
& ( singletonsubset = $true )
& ( beta1 = $true )
& ( setadjoinSub = $true )
& ( brelnall2 = $true )
& ( funcext = $true )
& ( setminusI = $true )
& ( sepInPowerset = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( setbeta = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( exuE3u = $true )
& ( symdiffIneg2 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setadjoinE = $true )
& ( eta1 = $true )
& ( notequalI1 = $true )
& ( cartprodpairsurjEq = $true )
& ( doubleComplementI1 = $true )
& ( cartprodpairmemEL = $true )
& ( setukpairinjL1 = $true )
& ( setukpairinjR = $true )
& ( disjointsetsI1 = $true )
& ( replAx = $true )
& ( emptysetimpfalse = $true )
& ( complementT_lem = $true )
& ( binintersectTELcontra = $true )
& ( foundationAx = $true )
& ( setukpairinjR1 = $true )
& ( ap2p = $true )
& ( binunionIR = $true )
& ( powersetE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementTE1 = $true )
& ( lamp = $true )
& ( complementTcontraSubset = $true )
& ( dsetconstrI = $true )
& ( ex1I = $true )
& ( powersetI1 = $true )
& ( iftrueProp2 = $true )
& ( woz13rule4 = $true )
& ( emptysetsubset = $true )
& ( setunion__Cong = $true )
& ( cartprodsndpairEq = $true )
& ( upairequniteq = $true )
& ( powersetT_lem = $true )
& ( complementTI1 = $true )
& ( quantDeMorgan2 = $true )
& ( singletoninpowunion = $true )
& ( subbreln = $true )
& ( dsetconstrEL = $true )
& ( powersetTE1 = $true )
& ( funcext2 = $true )
& ( setadjoinAx = $true )
& ( doubleComplementEq = $true )
& ( iftrueProp1 = $true )
& ( setunionsingleton1 = $true )
& ( emptyset__Cong = $true )
& ( lamProp = $true )
& ( symdiffIneg1 = $true )
& ( setunionAx = $true )
& ( kfstpairEq = $true )
& ( contrasubsetT2 = $true )
& ( ksndsingleton = $true )
& ( setukpairinjL2 = $true )
& ( sepSubset = $true )
& ( setunionE2 = $true )
& ( lam2p = $true )
& ( binunionTE = $true )
& ( omega__Cong = $true )
& ( complementImpComplementIntersect = $true )
& ( ifp = $true )
& ( dpsetconstrEL2 = $true )
& ( setminusSubset2 = $true )
& ( singletonprop = $true )
& ( cartprodsndin = $true )
& ( setminusT_lem = $true )
& ( doubleComplementSub1 = $true )
& ( notsubsetI = $true )
& ( upairset2IR = $true )
& ( binintersectSubset2 = $true )
& ( setminusILneg = $true )
& ( powersetsubset = $true )
& ( setunionsingleton2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR12 = $true )
& ( prop2setE = $true )
& ( subset2powerset = $true )
& ( beta2 = $true )
& ( emptyInPowerset = $true )
& ( setunionsingleton = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( dpsetconstrERa = $true )
& ( eqimpsubset1 = $true )
& ( binunionIL = $true )
& ( emptysetE = $true )
& ( setOfPairsIsBReln = $true )
& ( binintersectEL = $true )
& ( notdexE = $true )
& ( exuI2 = $true )
& ( ubforcartprodlem1 = $true )
& ( demorgan1a = $true )
& ( setminusSubset1 = $true )
& ( notequalI2 = $true )
& ( cartprodmempair1 = $true )
& ( exu__Cong = $true )
& ( powersetE1 = $true )
& ( symdiffI2 = $true )
& ( funcGraphProp2 = $true )
& ( setunionE = $true )
& ( wellorderingAx = $true )
& ( setminusERneg = $true )
& ( iftrueorfalse = $true )
& ( ex1I2 = $true )
& ( setextAx = $true )
& ( iffalseProp2 = $true )
& ( demorgan1b = $true )
& ( funcGraphProp4 = $true )
& ( eqbreln = $true )
& ( dpsetconstrSub = $true )
& ( subsetTI = $true )
& ( theeq = $true )
& ( ( in @ ( setminus @ sK784 @ sK785 ) @ ( powerset @ ( setminus @ sK784 @ ( binintersect @ sK785 @ sK786 ) ) ) )
!= $true )
& ( $true
= ( in @ sK786 @ ( powerset @ sK784 ) ) )
& ( ( in @ sK785 @ ( powerset @ sK784 ) )
= $true )
& ( demorgan1 = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( binunionTEcontra = $true )
& ( ifSingleton = $true )
& ( setadjoin__Cong = $true )
& ( subsetTrans = $true )
& ( eta2 = $true )
& ( in__Cong = $true )
& ( contrasubsetT = $true )
& ( complementTnotintersectT = $true )
& ( bs114d = $true )
& ( inIntersectImpInUnion2 = $true )
& ( ex1E2 = $true )
& ( upairsetIR = $true )
& ( woz13rule2 = $true )
& ( setadjoinSub2 = $true )
& ( demorgan2a = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( dpsetconstrEL1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK784,sK785,sK786]),skolemize(X0,sK784),skolemize(X1,sK785),skolemize(X2,sK786)],[f1994]) ).
thf(f2753,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setminus @ X3 @ X4 ) @ ( powerset @ ( setminus @ X3 @ ( binintersect @ X4 @ X5 ) ) ) )
= $true )
| ( ( in @ X5 @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true )
| ( complementInPowersetComplementIntersect != $true ) ),
inference(cnf_transformation,[],[f1700]) ).
thf(f3189,plain,
( ( in @ sK785 @ ( powerset @ sK784 ) )
= $true ),
inference(cnf_transformation,[],[f1995]) ).
thf(f3190,plain,
( $true
= ( in @ sK786 @ ( powerset @ sK784 ) ) ),
inference(cnf_transformation,[],[f1995]) ).
thf(f3191,plain,
( ( in @ ( setminus @ sK784 @ sK785 ) @ ( powerset @ ( setminus @ sK784 @ ( binintersect @ sK785 @ sK786 ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f1995]) ).
thf(f3306,plain,
complementInPowersetComplementIntersect = $true,
inference(cnf_transformation,[],[f1995]) ).
thf(f3840,plain,
( ( $true != $true )
| ( ( in @ sK785 @ ( powerset @ sK784 ) )
!= $true )
| ( $true
!= ( in @ sK786 @ ( powerset @ sK784 ) ) )
| ( complementInPowersetComplementIntersect != $true ) ),
inference(constrained_superposition,[],[f3191,f2753]) ).
thf(f3855,plain,
( ( ( in @ sK785 @ ( powerset @ sK784 ) )
!= $true )
| ( $true
!= ( in @ sK786 @ ( powerset @ sK784 ) ) )
| ( complementInPowersetComplementIntersect != $true ) ),
inference(trivial_inequality_removal,[],[f3840]) ).
thf(f3867,plain,
( ( complementInPowersetComplementIntersect != $true )
| ( $true
!= ( in @ sK786 @ ( powerset @ sK784 ) ) ) ),
inference(forward_subsumption_resolution,[],[f3855,f3189]) ).
thf(f3914,plain,
( $true
!= ( in @ sK786 @ ( powerset @ sK784 ) ) ),
inference(forward_subsumption_resolution,[],[f3867,f3306]) ).
thf(f3915,plain,
$false,
inference(forward_subsumption_resolution,[],[f3914,f3190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU763^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n017.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 14:18:37 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.30 Running higher-order theorem proving
% 0.26/0.37 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/0.57 % (406599)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.05/0.57 % (406607)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=774073529:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.05/0.57 % (406613)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.05/0.57 % (406613)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
% 1.05/0.57 % (406608)lrs+10_16_si=on:nwc=1.5:random_seed=545922029:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.05/0.57 % (406609)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3923958971:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.05/0.57 % (406611)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2909337990:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.05/0.57 % (406613)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=726080601:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.05/0.57 % (406610)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=3941567613: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)
% 1.05/0.57 % (406612)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3346325268:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.05/0.57 % (406609)Instruction limit reached!
% 1.05/0.57 % (406609)------------------------------
% 1.05/0.57 % (406609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.57 % (406609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.57 % (406609)CaDiCaL version: 2.1.3
% 1.05/0.57 % (406609)Termination reason: Instruction limit
% 1.05/0.57 % (406609)Termination phase: shuffling
% 1.05/0.57 % (406609)Time elapsed: 0.003 s
% 1.05/0.57 % (406609)Peak memory usage: 10 MB
% 1.05/0.57 % (406609)Instructions burned: 3 (million)
% 1.05/0.57 % (406608)Instruction limit reached!
% 1.05/0.57 % (406608)------------------------------
% 1.05/0.57 % (406608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.57 % (406608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.57 % (406608)CaDiCaL version: 2.1.3
% 1.05/0.57 % (406608)Termination reason: Instruction limit
% 1.05/0.57 % (406608)Termination phase: shuffling
% 1.05/0.57 % (406608)Time elapsed: 0.016 s
% 1.05/0.57 % (406608)Peak memory usage: 10 MB
% 1.05/0.57 % (406608)Instructions burned: 19 (million)
% 1.05/0.57 % (406611)Instruction limit reached!
% 1.05/0.57 % (406611)------------------------------
% 1.05/0.57 % (406611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.57 % (406611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.57 % (406611)CaDiCaL version: 2.1.3
% 1.05/0.57 % (406611)Termination reason: Instruction limit
% 1.05/0.57 % (406611)Termination phase: shuffling
% 1.05/0.57 % (406611)Time elapsed: 0.021 s
% 1.05/0.57 % (406611)Peak memory usage: 10 MB
% 1.05/0.57 % (406611)Instructions burned: 25 (million)
% 1.05/0.57 % (406622)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3841731963:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.05/0.57 % (406622)Instruction limit reached!
% 1.05/0.57 % (406622)------------------------------
% 1.05/0.57 % (406622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.57 % (406622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.57 % (406622)CaDiCaL version: 2.1.3
% 1.05/0.57 % (406622)Termination reason: Instruction limit
% 1.05/0.57 % (406622)Termination phase: shuffling
% 1.05/0.57 % (406622)Time elapsed: 0.004 s
% 1.05/0.57 % (406622)Peak memory usage: 10 MB
% 1.05/0.57 % (406622)Instructions burned: 9 (million)
% 1.05/0.57 % (406607)Instruction limit reached!
% 1.05/0.57 % (406607)------------------------------
% 1.05/0.57 % (406607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.57 % (406607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.65 % (406607)CaDiCaL version: 2.1.3
% 1.74/0.65 % (406607)Termination reason: Instruction limit
% 1.74/0.65 % (406607)Termination phase: Preprocessing 3
% 1.74/0.65 % (406607)Time elapsed: 0.045 s
% 1.74/0.65 % (406607)Peak memory usage: 13 MB
% 1.74/0.65 % (406607)Instructions burned: 88 (million)
% 1.74/0.65 % (406626)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=421986813:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.74/0.65 % (406623)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3305615127:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.74/0.65 % (406625)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.74/0.65 % (406626)Instruction limit reached!
% 1.74/0.65 % (406626)------------------------------
% 1.74/0.65 % (406626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.65 % (406626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.65 % (406626)CaDiCaL version: 2.1.3
% 1.74/0.65 % (406626)Termination reason: Instruction limit
% 1.74/0.65 % (406626)Termination phase: shuffling
% 1.74/0.65 % (406626)Time elapsed: 0.006 s
% 1.74/0.65 % (406626)Peak memory usage: 10 MB
% 1.74/0.65 % (406626)Instructions burned: 13 (million)
% 1.74/0.65 % (406627)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
% 1.74/0.65 % (406627)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.74/0.65 % (406623)Instruction limit reached!
% 1.74/0.65 % (406623)------------------------------
% 1.74/0.65 % (406623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.65 % (406623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.65 % (406623)CaDiCaL version: 2.1.3
% 1.74/0.65 % (406623)Termination reason: Instruction limit
% 1.74/0.65 % (406623)Termination phase: shuffling
% 1.74/0.65 % (406623)Time elapsed: 0.005 s
% 1.74/0.65 % (406623)Peak memory usage: 10 MB
% 1.74/0.65 % (406623)Instructions burned: 5 (million)
% 1.74/0.65 % (406625)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4038564229:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.74/0.65 % (406627)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2979717176:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.74/0.65 % (406625)Instruction limit reached!
% 1.74/0.65 % (406625)------------------------------
% 1.74/0.65 % (406625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.65 % (406625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.65 % (406625)CaDiCaL version: 2.1.3
% 1.74/0.65 % (406625)Termination reason: Instruction limit
% 1.74/0.65 % (406625)Termination phase: shuffling
% 1.74/0.65 % (406625)Time elapsed: 0.006 s
% 1.74/0.65 % (406625)Peak memory usage: 10 MB
% 1.74/0.65 % (406625)Instructions burned: 7 (million)
% 1.74/0.65 % (406631)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=1552737089:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.74/0.65 % (406627)Instruction limit reached!
% 1.74/0.65 % (406627)------------------------------
% 1.74/0.65 % (406627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.65 % (406627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.65 % (406627)CaDiCaL version: 2.1.3
% 1.74/0.65 % (406627)Termination reason: Instruction limit
% 1.74/0.65 % (406627)Termination phase: shuffling
% 1.74/0.65 % (406627)Time elapsed: 0.014 s
% 1.74/0.65 % (406627)Peak memory usage: 11 MB
% 1.74/0.65 % (406627)Instructions burned: 29 (million)
% 1.74/0.65 % (406632)lrs+10_1_si=on:cs=on:random_seed=2292613266:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.74/0.65 % (406612)Instruction limit reached!
% 1.74/0.65 % (406612)------------------------------
% 1.74/0.65 % (406612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.71 % (406612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.71 % (406612)CaDiCaL version: 2.1.3
% 2.34/0.71 % (406612)Termination reason: Instruction limit
% 2.34/0.71 % (406612)Termination phase: Preprocessing 3
% 2.34/0.71 % (406612)Time elapsed: 0.089 s
% 2.34/0.71 % (406612)Peak memory usage: 12 MB
% 2.34/0.71 % (406612)Instructions burned: 76 (million)
% 2.34/0.71 % (406638)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2360701171:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 2.34/0.71 % (406632)Instruction limit reached!
% 2.34/0.71 % (406632)------------------------------
% 2.34/0.71 % (406632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.71 % (406632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.71 % (406632)CaDiCaL version: 2.1.3
% 2.34/0.71 % (406632)Termination reason: Instruction limit
% 2.34/0.71 % (406632)Termination phase: shuffling
% 2.34/0.71 % (406632)Time elapsed: 0.008 s
% 2.34/0.71 % (406632)Peak memory usage: 10 MB
% 2.34/0.71 % (406632)Instructions burned: 9 (million)
% 2.34/0.71 % (406636)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 2.34/0.71 % (406636)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=2771785860:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.34/0.71 % (406636)Instruction limit reached!
% 2.34/0.71 % (406636)------------------------------
% 2.34/0.71 % (406636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.71 % (406636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.71 % (406636)CaDiCaL version: 2.1.3
% 2.34/0.71 % (406636)Termination reason: Instruction limit
% 2.34/0.71 % (406636)Termination phase: shuffling
% 2.34/0.71 % (406636)Time elapsed: 0.003 s
% 2.34/0.71 % (406636)Peak memory usage: 10 MB
% 2.34/0.71 % (406636)Instructions burned: 2 (million)
% 2.34/0.71 % (406631)Instruction limit reached!
% 2.34/0.71 % (406631)------------------------------
% 2.34/0.71 % (406631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.71 % (406631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.71 % (406631)CaDiCaL version: 2.1.3
% 2.34/0.71 % (406631)Termination reason: Instruction limit
% 2.34/0.71 % (406631)Termination phase: Property scanning
% 2.34/0.71 % (406631)Time elapsed: 0.040 s
% 2.34/0.71 % (406631)Peak memory usage: 11 MB
% 2.34/0.71 % (406631)Instructions burned: 96 (million)
% 2.34/0.71 % (406638)Instruction limit reached!
% 2.34/0.71 % (406638)------------------------------
% 2.34/0.71 % (406638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.71 % (406638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.71 % (406638)CaDiCaL version: 2.1.3
% 2.34/0.71 % (406638)Termination reason: Instruction limit
% 2.34/0.71 % (406638)Termination phase: Property scanning
% 2.34/0.71 % (406638)Time elapsed: 0.020 s
% 2.34/0.71 % (406638)Peak memory usage: 11 MB
% 2.34/0.71 % (406638)Instructions burned: 38 (million)
% 2.34/0.71 % (406640)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1271051591:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 2.34/0.71 % (406613)Instruction limit reached!
% 2.34/0.71 % (406613)------------------------------
% 2.34/0.71 % (406613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.71 % (406613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.71 % (406613)CaDiCaL version: 2.1.3
% 2.34/0.71 % (406613)Termination reason: Instruction limit
% 2.34/0.71 % (406613)Termination phase: Property scanning
% 2.34/0.71 % (406613)Time elapsed: 0.123 s
% 2.34/0.71 % (406613)Peak memory usage: 12 MB
% 2.34/0.71 % (406613)Instructions burned: 157 (million)
% 2.34/0.71 % (406642)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3781176120:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 2.34/0.71 % (406645)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2701674373:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.34/0.71 % (406644)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4096530248:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.34/0.77 % (406646)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2784403696:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.34/0.77 % (406642)Instruction limit reached!
% 2.34/0.77 % (406642)------------------------------
% 2.34/0.77 % (406642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.77 % (406642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.77 % (406642)CaDiCaL version: 2.1.3
% 2.34/0.77 % (406642)Termination reason: Instruction limit
% 2.34/0.77 % (406642)Termination phase: shuffling
% 2.34/0.77 % (406642)Time elapsed: 0.021 s
% 2.34/0.77 % (406642)Peak memory usage: 10 MB
% 2.34/0.77 % (406642)Instructions burned: 25 (million)
% 2.34/0.77 % (406644)Instruction limit reached!
% 2.34/0.77 % (406644)------------------------------
% 2.34/0.77 % (406644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.77 % (406644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.77 % (406644)CaDiCaL version: 2.1.3
% 2.34/0.77 % (406644)Termination reason: Instruction limit
% 2.34/0.77 % (406644)Termination phase: shuffling
% 2.34/0.77 % (406644)Time elapsed: 0.013 s
% 2.34/0.77 % (406644)Peak memory usage: 10 MB
% 2.34/0.77 % (406644)Instructions burned: 15 (million)
% 2.34/0.77 % (406646)Instruction limit reached!
% 2.34/0.77 % (406646)------------------------------
% 2.34/0.77 % (406646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.77 % (406646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.77 % (406646)CaDiCaL version: 2.1.3
% 2.34/0.77 % (406646)Termination reason: Instruction limit
% 2.34/0.77 % (406646)Termination phase: shuffling
% 2.34/0.77 % (406646)Time elapsed: 0.016 s
% 2.34/0.77 % (406646)Peak memory usage: 10 MB
% 2.34/0.77 % (406646)Instructions burned: 19 (million)
% 2.34/0.77 % (406648)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4095283669: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)
% 2.34/0.77 % (406648)Instruction limit reached!
% 2.34/0.77 % (406648)------------------------------
% 2.34/0.77 % (406648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.77 % (406648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.77 % (406648)CaDiCaL version: 2.1.3
% 2.34/0.77 % (406648)Termination reason: Instruction limit
% 2.34/0.77 % (406648)Termination phase: shuffling
% 2.34/0.77 % (406648)Time elapsed: 0.003 s
% 2.34/0.77 % (406648)Peak memory usage: 10 MB
% 2.34/0.77 % (406648)Instructions burned: 2 (million)
% 2.34/0.77 % (406654)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2269365458:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.34/0.77 % (406653)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3414502292:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.34/0.77 % (406655)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=934686023:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.34/0.77 % (406658)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.34/0.78 % (406658)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.34/0.78 % (406658)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=1009797277:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.34/0.78 % (406654)Instruction limit reached!
% 2.34/0.78 % (406654)------------------------------
% 2.34/0.78 % (406654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.78 % (406654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.78 % (406654)CaDiCaL version: 2.1.3
% 2.34/0.78 % (406654)Termination reason: Instruction limit
% 2.34/0.78 % (406654)Termination phase: shuffling
% 2.34/0.78 % (406654)Time elapsed: 0.020 s
% 2.34/0.78 % (406654)Peak memory usage: 10 MB
% 2.34/0.78 % (406654)Instructions burned: 24 (million)
% 3.26/0.90 % (406653)Instruction limit reached!
% 3.26/0.90 % (406653)------------------------------
% 3.26/0.90 % (406653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.90 % (406653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.90 % (406653)CaDiCaL version: 2.1.3
% 3.26/0.90 % (406653)Termination reason: Instruction limit
% 3.26/0.90 % (406653)Termination phase: shuffling
% 3.26/0.90 % (406653)Time elapsed: 0.023 s
% 3.26/0.90 % (406653)Peak memory usage: 11 MB
% 3.26/0.90 % (406653)Instructions burned: 26 (million)
% 3.26/0.90 % (406658)Instruction limit reached!
% 3.26/0.90 % (406658)------------------------------
% 3.26/0.90 % (406658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.90 % (406658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.90 % (406658)CaDiCaL version: 2.1.3
% 3.26/0.90 % (406658)Termination reason: Instruction limit
% 3.26/0.90 % (406658)Termination phase: shuffling
% 3.26/0.90 % (406658)Time elapsed: 0.013 s
% 3.26/0.90 % (406658)Peak memory usage: 10 MB
% 3.26/0.90 % (406658)Instructions burned: 15 (million)
% 3.26/0.90 % (406665)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=2341735097:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 3.26/0.90 % (406664)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 3.26/0.90 % (406664)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=4155776021:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 3.26/0.90 % (406655)Instruction limit reached!
% 3.26/0.90 % (406655)------------------------------
% 3.26/0.90 % (406655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.90 % (406655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.90 % (406655)CaDiCaL version: 2.1.3
% 3.26/0.90 % (406655)Termination reason: Instruction limit
% 3.26/0.90 % (406655)Termination phase: Preprocessing 3
% 3.26/0.90 % (406655)Time elapsed: 0.051 s
% 3.26/0.90 % (406655)Peak memory usage: 12 MB
% 3.26/0.90 % (406655)Instructions burned: 61 (million)
% 3.26/0.90 % (406666)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=410398695:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 3.26/0.90 % (406664)Instruction limit reached!
% 3.26/0.90 % (406664)------------------------------
% 3.26/0.90 % (406664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.90 % (406664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.90 % (406664)CaDiCaL version: 2.1.3
% 3.26/0.90 % (406664)Termination reason: Instruction limit
% 3.26/0.90 % (406664)Termination phase: shuffling
% 3.26/0.90 % (406664)Time elapsed: 0.008 s
% 3.26/0.90 % (406664)Peak memory usage: 10 MB
% 3.26/0.90 % (406664)Instructions burned: 9 (million)
% 3.26/0.90 % (406665)Instruction limit reached!
% 3.26/0.90 % (406665)------------------------------
% 3.26/0.90 % (406665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.90 % (406665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.90 % (406665)CaDiCaL version: 2.1.3
% 3.26/0.90 % (406665)Termination reason: Instruction limit
% 3.26/0.90 % (406665)Termination phase: shuffling
% 3.26/0.90 % (406665)Time elapsed: 0.016 s
% 3.26/0.90 % (406665)Peak memory usage: 11 MB
% 3.26/0.90 % (406665)Instructions burned: 32 (million)
% 3.26/0.90 % (406666)Instruction limit reached!
% 3.26/0.90 % (406666)------------------------------
% 3.26/0.90 % (406666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.90 % (406666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.90 % (406666)CaDiCaL version: 2.1.3
% 3.26/0.90 % (406666)Termination reason: Instruction limit
% 3.26/0.90 % (406666)Termination phase: shuffling
% 3.26/0.90 % (406666)Time elapsed: 0.009 s
% 3.26/0.90 % (406666)Peak memory usage: 10 MB
% 3.26/0.90 % (406666)Instructions burned: 9 (million)
% 3.26/0.90 % (406645)Instruction limit reached!
% 3.26/0.90 % (406645)------------------------------
% 3.26/0.90 % (406645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.90 % (406645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.99 % (406645)CaDiCaL version: 2.1.3
% 3.26/0.99 % (406645)Termination reason: Instruction limit
% 3.26/0.99 % (406645)Termination phase: Saturation
% 3.26/0.99 % (406645)Time elapsed: 0.142 s
% 3.26/0.99 % (406645)Peak memory usage: 15 MB
% 3.26/0.99 % (406645)Instructions burned: 330 (million)
% 3.26/0.99 % (406672)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4224426006:i=1240:rtra=on:ixr=off_2996 on theBenchmark for (2996ds/1240Mi)
% 3.26/0.99 % (406669)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=106040606:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 3.26/0.99 % (406671)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2684758036:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/20Mi)
% 3.26/0.99 % (406673)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2663326798:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2996 on theBenchmark for (2996ds/143Mi)
% 3.26/0.99 % (406674)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1806390419:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/193Mi)
% 3.26/0.99 % (406669)Instruction limit reached!
% 3.26/0.99 % (406669)------------------------------
% 3.26/0.99 % (406669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.99 % (406669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.99 % (406669)CaDiCaL version: 2.1.3
% 3.26/0.99 % (406669)Termination reason: Instruction limit
% 3.26/0.99 % (406669)Termination phase: shuffling
% 3.26/0.99 % (406669)Time elapsed: 0.020 s
% 3.26/0.99 % (406669)Peak memory usage: 10 MB
% 3.26/0.99 % (406669)Instructions burned: 24 (million)
% 3.26/0.99 % (406671)Instruction limit reached!
% 3.26/0.99 % (406671)------------------------------
% 3.26/0.99 % (406671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.99 % (406671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.99 % (406671)CaDiCaL version: 2.1.3
% 3.26/0.99 % (406671)Termination reason: Instruction limit
% 3.26/0.99 % (406671)Termination phase: shuffling
% 3.26/0.99 % (406671)Time elapsed: 0.020 s
% 3.26/0.99 % (406671)Peak memory usage: 11 MB
% 3.26/0.99 % (406671)Instructions burned: 24 (million)
% 3.26/0.99 % (406680)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1644408327:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 3.26/0.99 % (406640)Instruction limit reached!
% 3.26/0.99 % (406640)------------------------------
% 3.26/0.99 % (406640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.99 % (406640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.99 % (406640)CaDiCaL version: 2.1.3
% 3.26/0.99 % (406640)Termination reason: Instruction limit
% 3.26/0.99 % (406640)Termination phase: Saturation
% 3.26/0.99 % (406640)Time elapsed: 0.199 s
% 3.26/0.99 % (406640)Peak memory usage: 15 MB
% 3.26/0.99 % (406640)Instructions burned: 249 (million)
% 3.26/0.99 % (406681)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.26/0.99 % (406681)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1377925477:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 3.26/0.99 % (406681)Instruction limit reached!
% 3.26/0.99 % (406681)------------------------------
% 3.26/0.99 % (406681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.99 % (406681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.99 % (406681)CaDiCaL version: 2.1.3
% 3.26/0.99 % (406681)Termination reason: Instruction limit
% 3.26/0.99 % (406681)Termination phase: shuffling
% 3.26/0.99 % (406681)Time elapsed: 0.006 s
% 3.26/0.99 % (406681)Peak memory usage: 10 MB
% 3.26/0.99 % (406681)Instructions burned: 7 (million)
% 3.26/0.99 % (406680)Instruction limit reached!
% 3.26/0.99 % (406680)------------------------------
% 3.26/0.99 % (406680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.26/0.99 % (406680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/0.99 % (406680)CaDiCaL version: 2.1.3
% 3.26/0.99 % (406680)Termination reason: Instruction limit
% 3.26/0.99 % (406680)Termination phase: Property scanning
% 3.26/0.99 % (406680)Time elapsed: 0.019 s
% 3.26/0.99 % (406680)Peak memory usage: 11 MB
% 5.36/1.16 % (406680)Instructions burned: 44 (million)
% 5.36/1.16 % (406684)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1949849903:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 5.36/1.16 % (406687)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 5.36/1.16 % (406686)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=1695947469:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 5.36/1.16 % (406687)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2564464546:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 5.36/1.16 % (406687)Instruction limit reached!
% 5.36/1.16 % (406687)------------------------------
% 5.36/1.16 % (406687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.16 % (406687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.16 % (406687)CaDiCaL version: 2.1.3
% 5.36/1.16 % (406687)Termination reason: Instruction limit
% 5.36/1.16 % (406687)Termination phase: shuffling
% 5.36/1.16 % (406687)Time elapsed: 0.006 s
% 5.36/1.16 % (406687)Peak memory usage: 10 MB
% 5.36/1.16 % (406687)Instructions burned: 6 (million)
% 5.36/1.16 % (406673)Instruction limit reached!
% 5.36/1.16 % (406673)------------------------------
% 5.36/1.16 % (406673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.16 % (406673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.16 % (406673)CaDiCaL version: 2.1.3
% 5.36/1.16 % (406673)Termination reason: Instruction limit
% 5.36/1.16 % (406673)Termination phase: Property scanning
% 5.36/1.16 % (406673)Time elapsed: 0.114 s
% 5.36/1.16 % (406673)Peak memory usage: 12 MB
% 5.36/1.16 % (406673)Instructions burned: 143 (million)
% 5.36/1.16 % (406692)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3198345903:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2995 on theBenchmark for (2995ds/22Mi)
% 5.36/1.16 % (406692)Instruction limit reached!
% 5.36/1.16 % (406692)------------------------------
% 5.36/1.16 % (406692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.16 % (406692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.16 % (406692)CaDiCaL version: 2.1.3
% 5.36/1.16 % (406692)Termination reason: Instruction limit
% 5.36/1.16 % (406692)Termination phase: shuffling
% 5.36/1.16 % (406692)Time elapsed: 0.020 s
% 5.36/1.16 % (406692)Peak memory usage: 11 MB
% 5.36/1.16 % (406692)Instructions burned: 23 (million)
% 5.36/1.16 % (406674)Instruction limit reached!
% 5.36/1.16 % (406674)------------------------------
% 5.36/1.16 % (406674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.16 % (406674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.16 % (406674)CaDiCaL version: 2.1.3
% 5.36/1.16 % (406674)Termination reason: Instruction limit
% 5.36/1.16 % (406674)Termination phase: Saturation
% 5.36/1.16 % (406674)Time elapsed: 0.140 s
% 5.36/1.16 % (406674)Peak memory usage: 13 MB
% 5.36/1.16 % (406674)Instructions burned: 193 (million)
% 5.36/1.16 % (406693)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3562535236:i=19:add=on:rtra=on_2995 on theBenchmark for (2995ds/19Mi)
% 5.36/1.16 % (406696)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=1600153211:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 5.36/1.16 % (406693)Instruction limit reached!
% 5.36/1.16 % (406693)------------------------------
% 5.36/1.16 % (406693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.16 % (406693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.16 % (406693)CaDiCaL version: 2.1.3
% 5.36/1.16 % (406693)Termination reason: Instruction limit
% 5.36/1.16 % (406693)Termination phase: shuffling
% 5.36/1.16 % (406693)Time elapsed: 0.017 s
% 5.36/1.16 % (406693)Peak memory usage: 10 MB
% 5.36/1.16 % (406693)Instructions burned: 20 (million)
% 5.36/1.16 % (406695)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=2436391138:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 5.70/1.23 % (406610)Instruction limit reached!
% 5.70/1.23 % (406610)------------------------------
% 5.70/1.23 % (406610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406610)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406610)Termination reason: Instruction limit
% 5.70/1.23 % (406610)Termination phase: Saturation
% 5.70/1.23 % (406610)Time elapsed: 0.479 s
% 5.70/1.23 % (406610)Peak memory usage: 21 MB
% 5.70/1.23 % (406610)Instructions burned: 634 (million)
% 5.70/1.23 % (406699)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3092699338:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2994 on theBenchmark for (2994ds/45Mi)
% 5.70/1.23 % (406684)Instruction limit reached!
% 5.70/1.23 % (406684)------------------------------
% 5.70/1.23 % (406684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406684)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406684)Termination reason: Instruction limit
% 5.70/1.23 % (406684)Termination phase: Saturation
% 5.70/1.23 % (406684)Time elapsed: 0.142 s
% 5.70/1.23 % (406684)Peak memory usage: 14 MB
% 5.70/1.23 % (406684)Instructions burned: 181 (million)
% 5.70/1.23 % (406701)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3777257257:i=480:rtra=on_2994 on theBenchmark for (2994ds/480Mi)
% 5.70/1.23 % (406686)Instruction limit reached!
% 5.70/1.23 % (406686)------------------------------
% 5.70/1.23 % (406686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406686)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406686)Termination reason: Instruction limit
% 5.70/1.23 % (406686)Termination phase: Property scanning
% 5.70/1.23 % (406686)Time elapsed: 0.133 s
% 5.70/1.23 % (406686)Peak memory usage: 12 MB
% 5.70/1.23 % (406686)Instructions burned: 170 (million)
% 5.70/1.23 % (406699)Instruction limit reached!
% 5.70/1.23 % (406699)------------------------------
% 5.70/1.23 % (406699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406699)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406699)Termination reason: Instruction limit
% 5.70/1.23 % (406699)Termination phase: Property scanning
% 5.70/1.23 % (406699)Time elapsed: 0.038 s
% 5.70/1.23 % (406699)Peak memory usage: 11 MB
% 5.70/1.23 % (406699)Instructions burned: 46 (million)
% 5.70/1.23 % (406705)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 5.70/1.23 % (406704)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1085699618:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2994 on theBenchmark for (2994ds/21Mi)
% 5.70/1.23 % (406705)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2749986498:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/200Mi)
% 5.70/1.23 % (406706)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3938330433:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2994 on theBenchmark for (2994ds/13Mi)
% 5.70/1.23 % (406704)Instruction limit reached!
% 5.70/1.23 % (406704)------------------------------
% 5.70/1.23 % (406704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406704)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406704)Termination reason: Instruction limit
% 5.70/1.23 % (406704)Termination phase: shuffling
% 5.70/1.23 % (406704)Time elapsed: 0.018 s
% 5.70/1.23 % (406704)Peak memory usage: 10 MB
% 5.70/1.23 % (406704)Instructions burned: 22 (million)
% 5.70/1.23 % (406706)Instruction limit reached!
% 5.70/1.23 % (406706)------------------------------
% 5.70/1.23 % (406706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406706)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406706)Termination reason: Instruction limit
% 5.70/1.23 % (406706)Termination phase: shuffling
% 5.70/1.23 % (406706)Time elapsed: 0.007 s
% 5.70/1.23 % (406706)Peak memory usage: 10 MB
% 5.70/1.23 % (406706)Instructions burned: 14 (million)
% 5.70/1.23 % (406710)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=974633765:i=66:s2at=3:nm=2:rtra=on:rawr=on_2993 on theBenchmark for (2993ds/66Mi)
% 5.70/1.23 % (406711)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3425284676:i=51:fsr=off:rtra=on_2993 on theBenchmark for (2993ds/51Mi)
% 5.70/1.23 % (406710)Instruction limit reached!
% 5.70/1.23 % (406710)------------------------------
% 5.70/1.23 % (406710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406710)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406710)Termination reason: Instruction limit
% 5.70/1.23 % (406710)Termination phase: Property scanning
% 5.70/1.23 % (406710)Time elapsed: 0.029 s
% 5.70/1.23 % (406710)Peak memory usage: 11 MB
% 5.70/1.23 % (406710)Instructions burned: 67 (million)
% 5.70/1.23 % (406715)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1837969323:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/31Mi)
% 5.70/1.23 % (406711)Instruction limit reached!
% 5.70/1.23 % (406711)------------------------------
% 5.70/1.23 % (406711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406711)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406711)Termination reason: Instruction limit
% 5.70/1.23 % (406711)Termination phase: Property scanning
% 5.70/1.23 % (406711)Time elapsed: 0.046 s
% 5.70/1.23 % (406711)Peak memory usage: 11 MB
% 5.70/1.23 % (406711)Instructions burned: 52 (million)
% 5.70/1.23 % (406715)Instruction limit reached!
% 5.70/1.23 % (406715)------------------------------
% 5.70/1.23 % (406715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406715)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406715)Termination reason: Instruction limit
% 5.70/1.23 % (406715)Termination phase: shuffling
% 5.70/1.23 % (406715)Time elapsed: 0.015 s
% 5.70/1.23 % (406715)Peak memory usage: 11 MB
% 5.70/1.23 % (406715)Instructions burned: 32 (million)
% 5.70/1.23 % (406718)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2980146178:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2993 on theBenchmark for (2993ds/137Mi)
% 5.70/1.23 % (406719)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=280938852:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 5.70/1.23 % (406705)Instruction limit reached!
% 5.70/1.23 % (406705)------------------------------
% 5.70/1.23 % (406705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406705)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406705)Termination reason: Instruction limit
% 5.70/1.23 % (406705)Termination phase: Saturation
% 5.70/1.23 % (406705)Time elapsed: 0.161 s
% 5.70/1.23 % (406705)Peak memory usage: 14 MB
% 5.70/1.23 % (406705)Instructions burned: 200 (million)
% 5.70/1.23 % (406719)Instruction limit reached!
% 5.70/1.23 % (406719)------------------------------
% 5.70/1.23 % (406719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406719)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406719)Termination reason: Instruction limit
% 5.70/1.23 % (406719)Termination phase: shuffling
% 5.70/1.23 % (406719)Time elapsed: 0.029 s
% 5.70/1.23 % (406719)Peak memory usage: 11 MB
% 5.70/1.23 % (406719)Instructions burned: 34 (million)
% 5.70/1.23 % (406718)Instruction limit reached!
% 5.70/1.23 % (406718)------------------------------
% 5.70/1.23 % (406718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406718)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406718)Termination reason: Instruction limit
% 5.70/1.23 % (406718)Termination phase: Property scanning
% 5.70/1.23 % (406718)Time elapsed: 0.062 s
% 5.70/1.23 % (406718)Peak memory usage: 12 MB
% 5.70/1.23 % (406718)Instructions burned: 146 (million)
% 5.70/1.23 % (406695)Instruction limit reached!
% 5.70/1.23 % (406695)------------------------------
% 5.70/1.23 % (406695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406695)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406695)Termination reason: Instruction limit
% 5.70/1.23 % (406695)Termination phase: Saturation
% 5.70/1.23 % (406695)Time elapsed: 0.256 s
% 5.70/1.23 % (406695)Peak memory usage: 16 MB
% 5.70/1.23 % (406695)Instructions burned: 317 (million)
% 5.70/1.23 % (406723)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.70/1.23 % (406722)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=4262304508:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2992 on theBenchmark for (2992ds/67Mi)
% 5.70/1.23 % (406723)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=520454731:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2992 on theBenchmark for (2992ds/180Mi)
% 5.70/1.23 % (406725)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3290316618:cond=on:i=96:bd=all:rtra=on_2992 on theBenchmark for (2992ds/96Mi)
% 5.70/1.23 % (406724)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=78385562:st=2:i=246:sd=3:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/246Mi)
% 5.70/1.23 % (406701) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-406599-406701"...
% 5.70/1.23 % (406701)...printing done.
% 5.70/1.23 % (406701)Refutation found. Thanks to Tanya!
% 5.70/1.23 % SZS status Theorem for theBenchmark
% 5.70/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 5.70/1.23 % (406701)------------------------------
% 5.70/1.23 % (406701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.23 % (406701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.23 % (406701)CaDiCaL version: 2.1.3
% 5.70/1.23 % (406701)Termination reason: Refutation
% 5.70/1.23 % (406701)Time elapsed: 0.277 s
% 5.70/1.23 % (406701)Peak memory usage: 18 MB
% 5.70/1.23 % (406701)Instructions burned: 326 (million)
% 5.70/1.23 % (406599)Success in time 0.844 s
% 5.70/1.23 % Vampire exiting
%------------------------------------------------------------------------------