%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU756^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:31:09 AM UTC 2026
% Result : Theorem 2.15s 0.65s
% Output : Refutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 155 ( 47 unt; 0 typ; 18 def)
% Number of atoms : 6055 (1639 equ; 0 cnn)
% Maximal formula atoms : 277 ( 39 avg)
% Number of connectives : 3445 ( 191 ~; 181 |;1140 &; 776 @)
% ( 32 <=>;1125 =>; 0 <=; 0 <~>)
% Maximal formula depth : 287 ( 18 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 526 ( 523 usr; 331 con; 0-4 aty)
% Number of variables : 220 ( 0 sgn 178 !; 42 ?; 220 :)
% 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_313,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_314,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_315,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_316,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_317,type,
vNOT: $o > $o ).
thf(func_def_318,type,
vOR: $o > $o > $o ).
thf(func_def_319,type,
vAND: $o > $o > $o ).
thf(func_def_320,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_321,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_322,type,
vIMP: $o > $o > $o ).
thf(func_def_323,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_324,type,
sP0: $o ).
thf(func_def_325,type,
sP1: $i > $i > $o ).
thf(func_def_326,type,
sP2: $i > $o ).
thf(func_def_327,type,
sP3: $o ).
thf(func_def_331,type,
sK7: $i > $i > $i > $i ).
thf(func_def_348,type,
sK24: $i > $o ).
thf(func_def_350,type,
sK26: ( $i > $o ) > $i > $i ).
thf(func_def_351,type,
sK27: $o ).
thf(func_def_358,type,
sK34: $i > $o ).
thf(func_def_385,type,
sK61: $i > $i > $i ).
thf(func_def_386,type,
sK62: $i > $i > $i ).
thf(func_def_387,type,
sK63: ( $i > $o ) > $i > $i ).
thf(func_def_388,type,
sK64: ( $i > $o ) > $i > $i ).
thf(func_def_390,type,
sK66: $i > $o ).
thf(func_def_393,type,
sK69: $o ).
thf(func_def_407,type,
sK83: $o ).
thf(func_def_420,type,
sK96: ( $i > $i ) > $i > $i > $i ).
thf(func_def_423,type,
sK99: $i > $i ).
thf(func_def_428,type,
sK104: $i > $o ).
thf(func_def_430,type,
sK106: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_431,type,
sK107: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_456,type,
sK132: $i > $o ).
thf(func_def_491,type,
sK167: $i > $i > $i ).
thf(func_def_498,type,
sK174: $i > $i > $i ).
thf(func_def_502,type,
sK178: $i > $i > $o ).
thf(func_def_511,type,
sK187: $i > $i > $i > $i > $i ).
thf(func_def_520,type,
sK196: $i > $i > $i > $i > $i ).
thf(func_def_521,type,
sK197: $i > $i > $i > $i > $i ).
thf(func_def_522,type,
sK198: $i > $i > $i > $i > $i ).
thf(func_def_523,type,
sK199: $i > $i > $i > $i > $i ).
thf(func_def_524,type,
sK200: $o ).
thf(func_def_527,type,
sK203: $i > $i > $i ).
thf(func_def_531,type,
sK207: $o ).
thf(func_def_536,type,
sK212: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_537,type,
sK213: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_540,type,
sK216: $i > $o ).
thf(func_def_541,type,
sK217: $i > $o ).
thf(func_def_545,type,
sK221: $i > $o ).
thf(func_def_558,type,
sK234: $i > $o ).
thf(func_def_560,type,
sK236: ( $i > $o ) > $i > $i ).
thf(func_def_561,type,
sK237: ( $i > $o ) > $i > $i ).
thf(func_def_563,type,
sK239: $i > $i ).
thf(func_def_565,type,
sK241: $i > ( $i > $i ) > $i > $i ).
thf(func_def_570,type,
sK246: $i > $o ).
thf(func_def_571,type,
sK247: $i > $i ).
thf(func_def_572,type,
sK248: ( $i > $o ) > $i ).
thf(func_def_577,type,
sK253: $i > $i ).
thf(func_def_578,type,
sK254: ( $i > $i ) > $i > $i > $i ).
thf(func_def_581,type,
sK257: ( $i > $o ) > $i > $i ).
thf(func_def_583,type,
sK259: $i > $o ).
thf(func_def_587,type,
sK263: $o ).
thf(func_def_605,type,
sK281: $i > $o ).
thf(func_def_638,type,
sK314: $o ).
thf(func_def_663,type,
sK339: $i > $i > $i > $i ).
thf(func_def_678,type,
sK354: $i > $o ).
thf(func_def_684,type,
sK360: $i > $o ).
thf(func_def_692,type,
sK368: $i > $o ).
thf(func_def_693,type,
sK369: $i > $i ).
thf(func_def_695,type,
sK371: $i > $o ).
thf(func_def_697,type,
sK373: $i > ( $i > $o ) > $i ).
thf(func_def_700,type,
sK376: $i > $o ).
thf(func_def_702,type,
sK378: ( $i > $o ) > $i > $i ).
thf(func_def_704,type,
sK380: $i > $o ).
thf(func_def_721,type,
sK397: $o ).
thf(func_def_732,type,
sK408: $i > $i > $i > $i > $i ).
thf(func_def_735,type,
sK411: ( $i > $o ) > $i ).
thf(func_def_736,type,
sK412: $i > $o ).
thf(func_def_737,type,
sK413: $i > $i ).
thf(func_def_740,type,
sK416: $i > $i ).
thf(func_def_742,type,
sK418: $i > $i > $i ).
thf(func_def_745,type,
sK421: $i > $o ).
thf(func_def_747,type,
sK423: $i > ( $i > $o ) > $i ).
thf(func_def_756,type,
sK432: $i > $i ).
thf(func_def_757,type,
sK433: ( $i > $i ) > $i > $i > $i ).
thf(func_def_762,type,
sK438: $i > $i > $i > $i > $i ).
thf(func_def_774,type,
sK450: $i > $o ).
thf(func_def_776,type,
sK452: $i > $i > $o ).
thf(func_def_778,type,
sK454: $i > $i ).
thf(func_def_779,type,
sK455: $i > $i ).
thf(func_def_780,type,
sK456: $i > ( $i > $i > $o ) > $i ).
thf(func_def_781,type,
sK457: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_782,type,
sK458: $i > ( $i > $i > $o ) > $i ).
thf(func_def_785,type,
sK461: $i > $i > $o ).
thf(func_def_791,type,
sK467: $o ).
thf(func_def_797,type,
sK473: $o ).
thf(func_def_803,type,
sK479: $i > $o ).
thf(func_def_807,type,
sK483: $i > $o ).
thf(func_def_809,type,
sK485: ( $i > $o ) > $i > $i ).
thf(func_def_810,type,
sK486: $o ).
thf(func_def_824,type,
sK500: $i > $o ).
thf(func_def_826,type,
sK502: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_827,type,
sK503: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_831,type,
sK507: $i > $i > $i ).
thf(func_def_834,type,
sK510: $i > $i > $i > $i ).
thf(func_def_835,type,
sK511: $i > $i > $i > $i ).
thf(func_def_845,type,
sK521: $i > $o ).
thf(func_def_862,type,
sK538: $i > $i > $o ).
thf(func_def_876,type,
sK552: $i > $i ).
thf(func_def_901,type,
sK577: $i > $i > $i > $i > $i ).
thf(func_def_902,type,
sK578: $i > $i > $i > $i > $i ).
thf(func_def_913,type,
sK589: $i > $i > $i ).
thf(func_def_914,type,
sK590: $i > $o ).
thf(func_def_916,type,
sK592: ( $i > $o ) > $i ).
thf(func_def_917,type,
sK593: ( $i > $o ) > $i ).
thf(func_def_929,type,
sK605: $i > $i > $o ).
thf(func_def_938,type,
sK614: $i > $o ).
thf(func_def_954,type,
sK630: $i > $i > $i ).
thf(func_def_958,type,
sK634: $i > $o ).
thf(func_def_960,type,
sK636: $i > ( $i > $o ) > $i > $i ).
thf(func_def_965,type,
sK641: $o ).
thf(func_def_978,type,
sK654: ( $i > $i ) > $i > $i > $i ).
thf(func_def_981,type,
sK657: $i > $i ).
thf(func_def_986,type,
sK662: $i > $o ).
thf(func_def_988,type,
sK664: $i > $i ).
thf(func_def_995,type,
sK671: $o > $i > $i > $i ).
thf(func_def_998,type,
sK674: $o ).
thf(func_def_1012,type,
sK688: $i > ( $i > $o ) > $i ).
thf(func_def_1013,type,
sK689: $i > $o ).
thf(func_def_1017,type,
sK693: $o ).
thf(func_def_1033,type,
sK709: $i > $i ).
thf(func_def_1037,type,
sK713: $o ).
thf(func_def_1042,type,
sK718: $i > $i > $o ).
thf(func_def_1044,type,
sK720: $i > ( $i > $o ) > $i ).
thf(func_def_1045,type,
sK721: $i > $o ).
thf(func_def_1070,type,
sK746: $i > $i > $i > $i ).
thf(func_def_1071,type,
sK747: $i > $i > $i > $i ).
thf(func_def_1094,type,
sK770: ( $i > $o ) > $i ).
thf(func_def_1095,type,
sK771: $i > $o ).
thf(func_def_1098,type,
sK774: $i > $i > $i ).
thf(func_def_1101,type,
sK777: $o ).
thf(func_def_1109,type,
sK785: $i > $i ).
thf(func_def_1111,type,
sK787: $i > $i ).
thf(func_def_1128,type,
sK804: $i > ( $i > $o ) > $i ).
thf(func_def_1129,type,
sK805: $i > $o ).
thf(func_def_1139,type,
sK815: $i > $o ).
thf(func_def_1140,type,
sK816: $i > $o ).
thf(func_def_1141,type,
sK817: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1142,type,
sK818: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1143,type,
sK819: $i > $i > $o ).
thf(func_def_1151,type,
sK827: $o ).
thf(func_def_1152,type,
sK828: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1153,type,
sK829: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1154,type,
sK830: $i > $o ).
thf(func_def_1155,type,
sK831: $i > $o ).
thf(func_def_1157,type,
sK833: $i > $i ).
thf(func_def_1159,type,
sK835: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1163,type,
sK839: $o ).
thf(func_def_1168,type,
sK844: $i > $i > $o ).
thf(func_def_1173,type,
sK849: $i > $i ).
thf(func_def_1174,type,
sK850: $i > $i ).
thf(func_def_1175,type,
sK851: $i > $i ).
thf(func_def_1176,type,
sK852: $i > $i ).
thf(func_def_1177,type,
sK853: $i > $i ).
thf(func_def_1178,type,
sK854: $i > $i > $i > $i ).
thf(func_def_1179,type,
sK855: $i > $i ).
thf(func_def_1180,type,
sK856: $i > $i ).
thf(func_def_1181,type,
sK857: $i > $i ).
thf(func_def_1182,type,
sK858: $i > $i ).
thf(func_def_1183,type,
sK859: $i > $i > $i ).
thf(func_def_1184,type,
sK860: $i > $i > $i > $i ).
thf(func_def_1185,type,
sK861: $i > $i > $i > $i ).
thf(func_def_1186,type,
sK862: $i > $i > $i > $i ).
thf(func_def_1187,type,
sK863: $i > $i > $i ).
thf(func_def_1188,type,
sK864: $i > $i > $i ).
thf(func_def_1189,type,
sK865: $i > $i > $i ).
thf(func_def_1190,type,
sK866: $i > $i > $i ).
thf(f105,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) )
= binunionE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(f110,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) )
= binintersectEL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(f114,axiom,
( binintersectER
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(f122,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(f124,axiom,
( setminusERneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(f277,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b) ).
thf(f278,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f277]) ).
thf(f430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ X0 @ X2 )
| ( in @ X0 @ X1 ) ) )
= binunionE ),
inference(rectify,[],[f105]) ).
thf(f431,plain,
( ( binunionE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f430]) ).
thf(f436,plain,
( setminusERneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f124]) ).
thf(f437,plain,
( ( setminusERneg = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f436]) ).
thf(f473,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
=> ( in @ X1 @ X2 ) )
= binintersectEL ),
inference(rectify,[],[f110]) ).
thf(f474,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
=> ( ( in @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f473]) ).
thf(f544,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f278]) ).
thf(f545,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f544]) ).
thf(f595,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) )
= setminusER ),
inference(rectify,[],[f122]) ).
thf(f596,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[],[f595]) ).
thf(f708,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
=> ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f114]) ).
thf(f709,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
=> ( ( in @ X1 @ X0 )
= $true ) )
<=> ( binintersectER = $true ) ),
inference(fool_elimination,[],[f708]) ).
thf(f839,plain,
( ( setminusERneg = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(flattening,[],[f437]) ).
thf(f850,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[],[f596]) ).
thf(f890,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
<=> ( binintersectER = $true ) ),
inference(ennf_transformation,[],[f709]) ).
thf(f969,plain,
( ( setminusERneg = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f839]) ).
thf(f970,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
<=> ( setminusERneg = $true ) ),
inference(flattening,[],[f969]) ).
thf(f1078,plain,
( ( binintersectEL = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f474]) ).
thf(f1088,plain,
( ( binunionE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f431]) ).
thf(f1089,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
!= $true )
| ( $true
= ( in @ X0 @ X2 ) ) )
<=> ( binunionE = $true ) ),
inference(flattening,[],[f1088]) ).
thf(f1093,plain,
( ( setminusER = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f850]) ).
thf(f1192,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $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,[],[f545]) ).
thf(f1193,plain,
( ( binunionEcases = $true )
& ( replAx = $true )
& ( funcext2 = $true )
& ( nonemptyI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusLsub = $true )
& ( binunionIL = $true )
& ( setminusILneg = $true )
& ( singletonsswitch = $true )
& ( powerset__Cong = $true )
& ( demorgan2a2 = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinOr = $true )
& ( upairequniteq = $true )
& ( noeltsimpempty = $true )
& ( cartprodpairmemEL = $true )
& ( prop2setE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( demorgan1b = $true )
& ( binunionTEcontra = $true )
& ( emptyinunitempty = $true )
& ( kpairsurjEq = $true )
& ( cartprodpairmemER = $true )
& ( setminusERneg = $true )
& ( brelnall2 = $true )
& ( subsetRefl = $true )
& ( setminusEL = $true )
& ( iftrueProp2 = $true )
& ( demorgan2a1 = $true )
& ( binunionT_lem = $true )
& ( ap2p = $true )
& ( binunionLsub = $true )
& ( kfstpairEq = $true )
& ( notinemptyset = $true )
& ( ksndpairEq = $true )
& ( eqinunit = $true )
& ( doubleComplementSub2 = $true )
& ( demorgan1 = $true )
& ( setunionE = $true )
& ( secondinupair = $true )
& ( nonemptyImpWitness = $true )
& ( exuE3u = $true )
& ( powersetAx = $true )
& ( ap2apEq2 = $true )
& ( setunionI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( subsetI1 = $true )
& ( emptysetsubset = $true )
& ( setunionsingleton = $true )
& ( setukpairinjR2 = $true )
& ( cartprodmempair1 = $true )
& ( infuncsetfunc = $true )
& ( binintersectI = $true )
& ( setukpairinjL1 = $true )
& ( nonemptyI = $true )
& ( setadjoinSub = $true )
& ( eta2 = $true )
& ( notdexE = $true )
& ( funcGraphProp1 = $true )
& ( dsetconstrEL = $true )
& ( setextAx = $true )
& ( dpsetconstrI = $true )
& ( setukpairIR = $true )
& ( binintersectEL = $true )
& ( kpairp = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( complementTE1 = $true )
& ( inIntersectImpInUnion = $true )
& ( upairset2E = $true )
& ( emptyset__Cong = $true )
& ( dpsetconstrEL2 = $true )
& ( exu__Cong = $true )
& ( contrasubsetT = $true )
& ( ifSingleton = $true )
& ( iftrueProp1 = $true )
& ( sepInPowerset = $true )
& ( funcGraphProp2 = $true )
& ( doubleComplementEq = $true )
& ( binintersectSubset2 = $true )
& ( iffalseProp2 = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset4 = $true )
& ( emptyinPowerset = $true )
& ( contraSubsetComplement = $true )
& ( eqimpsubset1 = $true )
& ( emptysetimpfalse = $true )
& ( binintersectTERcontra = $true )
& ( subbreln = $true )
& ( funcImageSingleton = $true )
& ( binintersectLsub = $true )
& ( singletonprop = $true )
& ( dpsetconstrEL1 = $true )
& ( setext = $true )
& ( ubforcartprodlem2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( in__Cong = $true )
& ( exuE1 = $true )
& ( descrp = $true )
& ( contrasubsetT1 = $true )
& ( demorgan1a = $true )
& ( setukpairinjL = $true )
& ( kfstsingleton = $true )
& ( emptysetE = $true )
& ( upairsubunion = $true )
& ( symdiffI1 = $true )
& ( upairsetIR = $true )
& ( setadjoinSub2 = $true )
& ( singletonsuniq = $true )
& ( setunionE2 = $true )
& ( emptysetAx = $true )
& ( powersetE1 = $true )
& ( setminusER = $true )
& ( setukpairinjR = $true )
& ( bs114d = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( omegaSAx = $true )
& ( eta1 = $true )
& ( powersetsubset = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( inPowerset = $true )
& ( demorgan2b2 = $true )
& ( beta1 = $true )
& ( complementT_lem = $true )
& ( inCongP = $true )
& ( omegaIndAx = $true )
& ( symdiffIneg1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subsetI2 = $true )
& ( setminusIRneg = $true )
& ( nonemptyE1 = $true )
& ( iftrue = $true )
& ( demorgan2a = $true )
& ( setukpairinjR12 = $true )
& ( cartprodsndpairEq = $true )
& ( prop2setI = $true )
& ( setminusELneg = $true )
& ( binintersectRsub = $true )
& ( cartprodpairsurjEq = $true )
& ( setunionsingleton2 = $true )
& ( contrasubsetT3 = $true )
& ( exuI1 = $true )
& ( powersetI = $true )
& ( apProp = $true )
& ( ap2apEq1 = $true )
& ( doubleComplementI1 = $true )
& ( singletonsubset = $true )
& ( setadjoinE = $true )
& ( lamProp = $true )
& ( ifp = $true )
& ( setadjoinIL = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodmempaircEq = $true )
& ( notequalI1 = $true )
& ( funcext = $true )
& ( theeq = $true )
& ( funcGraphProp4 = $true )
& ( setminusT_lem = $true )
& ( notinsingleton = $true )
& ( setbeta = $true )
& ( lamp = $true )
& ( upairsetIL = $true )
& ( setminusSubset1 = $true )
& ( cartprodmempair = $true )
& ( binintersectT_lem = $true )
& ( exuI2 = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset1 = $true )
& ( powersetE = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetE = $true )
& ( setukpairinjR11 = $true )
& ( exuI3 = $true )
& ( setukpairinjL2 = $true )
& ( subsetE2 = $true )
& ( setadjoinAx = $true )
& ( binunionTE = $true )
& ( emptyI = $true )
& ( dsetconstrI = $true )
& ( binunionE = $true )
& ( complementImpComplementIntersect = $true )
& ( prop2set2propI = $true )
& ( app = $true )
& ( lam2p = $true )
& ( setadjoinIR = $true )
& ( emptyInPowerset = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetemptysetimpeq = $true )
& ( setunion__Cong = $true )
& ( cartprodfstin = $true )
& ( funcGraphProp3 = $true )
& ( quantDeMorgan4 = $true )
& ( ex1E1 = $true )
& ( funcinfuncset = $true )
& ( ubforcartprodlem3 = $true )
& ( subsetTrans = $true )
& ( powersetTI1 = $true )
& ( setextT = $true )
& ( binintersectTELcontra = $true )
& ( subsetE = $true )
& ( brelnall1 = $true )
& ( powersetI1 = $true )
& ( symdiffE = $true )
& ( eqbreln = $true )
& ( exuE2 = $true )
& ( beta2 = $true )
& ( notsubsetI = $true )
& ( ex1I2 = $true )
& ( powersetT_lem = $true )
& ( iftrueorfalse = $true )
& ( dpsetconstrSub = $true )
& ( foundationAx = $true )
& ( complementTnotintersectT = $true )
& ( upairinpowunion = $true )
& ( notdallE = $true )
& ( setextsub = $true )
& ( subsetTI = $true )
& ( powersetTE1 = $true )
& ( dsetconstr__Cong = $true )
& ( sepSubset = $true )
& ( setunionsingleton1 = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrER = $true )
& ( setadjoin__Cong = $true )
& ( theprop = $true )
& ( cartprodpairin = $true )
& ( setunionAx = $true )
& ( subPowSU = $true )
& ( uniqinunit = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset3 = $true )
& ( ex1E2 = $true )
& ( iffalseProp1 = $true )
& ( upairset2IR = $true )
& ( dpsetconstrERa = $true )
& ( ex1I = $true )
& ( ksndsingleton = $true )
& ( setukpairIL = $true )
& ( lam2lamEq = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( singletoninpowunion = $true )
& ( binunionIR = $true )
& ( doubleComplementE1 = $true )
& ( subset2powerset = $true )
& ( setoftrueEq = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( setOfPairsIsBReln = $true )
& ( notequalI2 = $true )
& ( dsetconstrER = $true )
& ( exuEu = $true )
& ( doubleComplementSub1 = $true )
& ( symdiffI2 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( kpairiskpair = $true )
& ( funcextLem = $true )
& ( omega__Cong = $true )
& ( complementTcontraSubset = $true )
& ( quantDeMorgan2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( iffalse = $true )
& ( contrasubsetT2 = $true )
& ( setminusI = $true )
& ( complementTI1 = $true )
& ( descr__Cong = $true )
& ( binunionRsub = $true )
& ( cartprodsndin = $true )
& ( eqimpsubset2 = $true )
& ( exuE3e = $true )
& ( cartprodfstpairEq = $true ) ),
inference(flattening,[],[f1192]) ).
thf(f1259,plain,
( ( ( setminusER = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X1 @ X2 )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[],[f1093]) ).
thf(f1260,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
& ( $true
= ( in @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(rectify,[],[f1259]) ).
thf(f1261,plain,
( ( ( setminusER = $true )
| ( ( $true
= ( in @ sK49 @ ( setminus @ sK51 @ sK50 ) ) )
& ( ( in @ sK49 @ sK50 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50,sK51]),skolemize(X0,sK49),skolemize(X1,sK50),skolemize(X2,sK51)],[f1260]) ).
thf(f1512,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( setminusERneg != $true ) )
& ( ( setminusERneg = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f970]) ).
thf(f1513,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( $true
= ( in @ X0 @ X1 ) ) )
| ( setminusERneg != $true ) )
& ( ( setminusERneg = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true )
& ( ( in @ X3 @ X4 )
!= $true ) ) ) ),
inference(rectify,[],[f1512]) ).
thf(f1514,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( $true
= ( in @ X0 @ X1 ) ) )
| ( setminusERneg != $true ) )
& ( ( setminusERneg = $true )
| ( ( ( in @ sK329 @ sK331 )
= $true )
& ( ( in @ sK329 @ ( setminus @ sK331 @ sK330 ) )
!= $true )
& ( ( in @ sK329 @ sK330 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK329,sK330,sK331]),skolemize(X3,sK329),skolemize(X4,sK330),skolemize(X5,sK331)],[f1513]) ).
thf(f1536,plain,
( ( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
!= $true )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true )
& ( $true
!= ( in @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[],[f1089]) ).
thf(f1537,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
& ( $true
= ( in @ X4 @ ( binunion @ X3 @ X5 ) ) )
& ( ( in @ X4 @ X5 )
!= $true ) ) ) ),
inference(rectify,[],[f1536]) ).
thf(f1538,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ( ( ( in @ sK351 @ sK350 )
!= $true )
& ( ( in @ sK351 @ ( binunion @ sK350 @ sK352 ) )
= $true )
& ( ( in @ sK351 @ sK352 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK350,sK351,sK352]),skolemize(X3,sK350),skolemize(X4,sK351),skolemize(X5,sK352)],[f1537]) ).
thf(f1760,plain,
( ( ( binintersectEL = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X2 )
!= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[],[f1078]) ).
thf(f1761,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X4 @ X5 ) ) )
| ( ( in @ X3 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[],[f1760]) ).
thf(f1762,plain,
( ( ( binintersectEL = $true )
| ( ( ( in @ sK594 @ ( binintersect @ sK595 @ sK596 ) )
= $true )
& ( ( in @ sK594 @ sK595 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X4 @ X5 ) ) )
| ( ( in @ X3 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK594,sK595,sK596]),skolemize(X0,sK594),skolemize(X1,sK595),skolemize(X2,sK596)],[f1761]) ).
thf(f1835,plain,
( ( binunionEcases = $true )
& ( replAx = $true )
& ( funcext2 = $true )
& ( nonemptyI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusLsub = $true )
& ( binunionIL = $true )
& ( setminusILneg = $true )
& ( singletonsswitch = $true )
& ( powerset__Cong = $true )
& ( demorgan2a2 = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinOr = $true )
& ( upairequniteq = $true )
& ( noeltsimpempty = $true )
& ( cartprodpairmemEL = $true )
& ( prop2setE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( demorgan1b = $true )
& ( binunionTEcontra = $true )
& ( emptyinunitempty = $true )
& ( kpairsurjEq = $true )
& ( cartprodpairmemER = $true )
& ( setminusERneg = $true )
& ( brelnall2 = $true )
& ( subsetRefl = $true )
& ( setminusEL = $true )
& ( iftrueProp2 = $true )
& ( demorgan2a1 = $true )
& ( binunionT_lem = $true )
& ( ap2p = $true )
& ( binunionLsub = $true )
& ( kfstpairEq = $true )
& ( notinemptyset = $true )
& ( ksndpairEq = $true )
& ( eqinunit = $true )
& ( doubleComplementSub2 = $true )
& ( demorgan1 = $true )
& ( setunionE = $true )
& ( secondinupair = $true )
& ( nonemptyImpWitness = $true )
& ( exuE3u = $true )
& ( powersetAx = $true )
& ( ap2apEq2 = $true )
& ( setunionI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( subsetI1 = $true )
& ( emptysetsubset = $true )
& ( setunionsingleton = $true )
& ( setukpairinjR2 = $true )
& ( cartprodmempair1 = $true )
& ( infuncsetfunc = $true )
& ( binintersectI = $true )
& ( setukpairinjL1 = $true )
& ( nonemptyI = $true )
& ( setadjoinSub = $true )
& ( eta2 = $true )
& ( notdexE = $true )
& ( funcGraphProp1 = $true )
& ( dsetconstrEL = $true )
& ( setextAx = $true )
& ( dpsetconstrI = $true )
& ( setukpairIR = $true )
& ( binintersectEL = $true )
& ( kpairp = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( complementTE1 = $true )
& ( inIntersectImpInUnion = $true )
& ( upairset2E = $true )
& ( emptyset__Cong = $true )
& ( dpsetconstrEL2 = $true )
& ( exu__Cong = $true )
& ( contrasubsetT = $true )
& ( ifSingleton = $true )
& ( iftrueProp1 = $true )
& ( sepInPowerset = $true )
& ( funcGraphProp2 = $true )
& ( doubleComplementEq = $true )
& ( binintersectSubset2 = $true )
& ( iffalseProp2 = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset4 = $true )
& ( emptyinPowerset = $true )
& ( contraSubsetComplement = $true )
& ( eqimpsubset1 = $true )
& ( emptysetimpfalse = $true )
& ( binintersectTERcontra = $true )
& ( subbreln = $true )
& ( funcImageSingleton = $true )
& ( binintersectLsub = $true )
& ( singletonprop = $true )
& ( dpsetconstrEL1 = $true )
& ( setext = $true )
& ( ubforcartprodlem2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( in__Cong = $true )
& ( exuE1 = $true )
& ( descrp = $true )
& ( contrasubsetT1 = $true )
& ( demorgan1a = $true )
& ( setukpairinjL = $true )
& ( kfstsingleton = $true )
& ( emptysetE = $true )
& ( upairsubunion = $true )
& ( symdiffI1 = $true )
& ( upairsetIR = $true )
& ( setadjoinSub2 = $true )
& ( singletonsuniq = $true )
& ( setunionE2 = $true )
& ( emptysetAx = $true )
& ( powersetE1 = $true )
& ( setminusER = $true )
& ( setukpairinjR = $true )
& ( bs114d = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( omegaSAx = $true )
& ( eta1 = $true )
& ( powersetsubset = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( inPowerset = $true )
& ( demorgan2b2 = $true )
& ( beta1 = $true )
& ( complementT_lem = $true )
& ( inCongP = $true )
& ( omegaIndAx = $true )
& ( symdiffIneg1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subsetI2 = $true )
& ( setminusIRneg = $true )
& ( nonemptyE1 = $true )
& ( iftrue = $true )
& ( demorgan2a = $true )
& ( setukpairinjR12 = $true )
& ( cartprodsndpairEq = $true )
& ( prop2setI = $true )
& ( setminusELneg = $true )
& ( binintersectRsub = $true )
& ( cartprodpairsurjEq = $true )
& ( setunionsingleton2 = $true )
& ( contrasubsetT3 = $true )
& ( exuI1 = $true )
& ( powersetI = $true )
& ( apProp = $true )
& ( ap2apEq1 = $true )
& ( doubleComplementI1 = $true )
& ( singletonsubset = $true )
& ( setadjoinE = $true )
& ( lamProp = $true )
& ( ifp = $true )
& ( setadjoinIL = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodmempaircEq = $true )
& ( notequalI1 = $true )
& ( funcext = $true )
& ( theeq = $true )
& ( funcGraphProp4 = $true )
& ( setminusT_lem = $true )
& ( notinsingleton = $true )
& ( setbeta = $true )
& ( lamp = $true )
& ( upairsetIL = $true )
& ( setminusSubset1 = $true )
& ( cartprodmempair = $true )
& ( binintersectT_lem = $true )
& ( exuI2 = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset1 = $true )
& ( powersetE = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetE = $true )
& ( setukpairinjR11 = $true )
& ( exuI3 = $true )
& ( setukpairinjL2 = $true )
& ( subsetE2 = $true )
& ( setadjoinAx = $true )
& ( binunionTE = $true )
& ( emptyI = $true )
& ( dsetconstrI = $true )
& ( binunionE = $true )
& ( complementImpComplementIntersect = $true )
& ( prop2set2propI = $true )
& ( app = $true )
& ( lam2p = $true )
& ( setadjoinIR = $true )
& ( emptyInPowerset = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetemptysetimpeq = $true )
& ( setunion__Cong = $true )
& ( cartprodfstin = $true )
& ( funcGraphProp3 = $true )
& ( quantDeMorgan4 = $true )
& ( ex1E1 = $true )
& ( funcinfuncset = $true )
& ( ubforcartprodlem3 = $true )
& ( subsetTrans = $true )
& ( powersetTI1 = $true )
& ( setextT = $true )
& ( binintersectTELcontra = $true )
& ( subsetE = $true )
& ( brelnall1 = $true )
& ( powersetI1 = $true )
& ( symdiffE = $true )
& ( eqbreln = $true )
& ( exuE2 = $true )
& ( beta2 = $true )
& ( notsubsetI = $true )
& ( ex1I2 = $true )
& ( powersetT_lem = $true )
& ( iftrueorfalse = $true )
& ( dpsetconstrSub = $true )
& ( foundationAx = $true )
& ( complementTnotintersectT = $true )
& ( upairinpowunion = $true )
& ( notdallE = $true )
& ( setextsub = $true )
& ( subsetTI = $true )
& ( powersetTE1 = $true )
& ( dsetconstr__Cong = $true )
& ( sepSubset = $true )
& ( setunionsingleton1 = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrER = $true )
& ( setadjoin__Cong = $true )
& ( theprop = $true )
& ( cartprodpairin = $true )
& ( setunionAx = $true )
& ( subPowSU = $true )
& ( uniqinunit = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset3 = $true )
& ( ex1E2 = $true )
& ( iffalseProp1 = $true )
& ( upairset2IR = $true )
& ( dpsetconstrERa = $true )
& ( ex1I = $true )
& ( ksndsingleton = $true )
& ( setukpairIL = $true )
& ( lam2lamEq = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( singletoninpowunion = $true )
& ( binunionIR = $true )
& ( doubleComplementE1 = $true )
& ( subset2powerset = $true )
& ( setoftrueEq = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( setOfPairsIsBReln = $true )
& ( notequalI2 = $true )
& ( dsetconstrER = $true )
& ( exuEu = $true )
& ( doubleComplementSub1 = $true )
& ( symdiffI2 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( kpairiskpair = $true )
& ( funcextLem = $true )
& ( omega__Cong = $true )
& ( complementTcontraSubset = $true )
& ( quantDeMorgan2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( iffalse = $true )
& ( contrasubsetT2 = $true )
& ( setminusI = $true )
& ( complementTI1 = $true )
& ( descr__Cong = $true )
& ( binunionRsub = $true )
& ( cartprodsndin = $true )
& ( eqimpsubset2 = $true )
& ( exuE3e = $true )
& ( cartprodfstpairEq = $true ) ),
inference(rectify,[],[f1193]) ).
thf(f1836,plain,
( ( binunionEcases = $true )
& ( replAx = $true )
& ( funcext2 = $true )
& ( nonemptyI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusLsub = $true )
& ( binunionIL = $true )
& ( setminusILneg = $true )
& ( singletonsswitch = $true )
& ( powerset__Cong = $true )
& ( demorgan2a2 = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinOr = $true )
& ( upairequniteq = $true )
& ( noeltsimpempty = $true )
& ( cartprodpairmemEL = $true )
& ( prop2setE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( demorgan1b = $true )
& ( binunionTEcontra = $true )
& ( emptyinunitempty = $true )
& ( kpairsurjEq = $true )
& ( cartprodpairmemER = $true )
& ( setminusERneg = $true )
& ( brelnall2 = $true )
& ( subsetRefl = $true )
& ( setminusEL = $true )
& ( iftrueProp2 = $true )
& ( demorgan2a1 = $true )
& ( binunionT_lem = $true )
& ( ap2p = $true )
& ( binunionLsub = $true )
& ( kfstpairEq = $true )
& ( notinemptyset = $true )
& ( ksndpairEq = $true )
& ( eqinunit = $true )
& ( doubleComplementSub2 = $true )
& ( demorgan1 = $true )
& ( setunionE = $true )
& ( secondinupair = $true )
& ( nonemptyImpWitness = $true )
& ( exuE3u = $true )
& ( powersetAx = $true )
& ( ap2apEq2 = $true )
& ( setunionI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( subsetI1 = $true )
& ( emptysetsubset = $true )
& ( setunionsingleton = $true )
& ( setukpairinjR2 = $true )
& ( cartprodmempair1 = $true )
& ( infuncsetfunc = $true )
& ( binintersectI = $true )
& ( setukpairinjL1 = $true )
& ( nonemptyI = $true )
& ( setadjoinSub = $true )
& ( eta2 = $true )
& ( notdexE = $true )
& ( funcGraphProp1 = $true )
& ( dsetconstrEL = $true )
& ( setextAx = $true )
& ( dpsetconstrI = $true )
& ( setukpairIR = $true )
& ( binintersectEL = $true )
& ( kpairp = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( complementTE1 = $true )
& ( inIntersectImpInUnion = $true )
& ( upairset2E = $true )
& ( emptyset__Cong = $true )
& ( dpsetconstrEL2 = $true )
& ( exu__Cong = $true )
& ( contrasubsetT = $true )
& ( ifSingleton = $true )
& ( iftrueProp1 = $true )
& ( sepInPowerset = $true )
& ( funcGraphProp2 = $true )
& ( doubleComplementEq = $true )
& ( binintersectSubset2 = $true )
& ( iffalseProp2 = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset4 = $true )
& ( emptyinPowerset = $true )
& ( contraSubsetComplement = $true )
& ( eqimpsubset1 = $true )
& ( emptysetimpfalse = $true )
& ( binintersectTERcontra = $true )
& ( subbreln = $true )
& ( funcImageSingleton = $true )
& ( binintersectLsub = $true )
& ( singletonprop = $true )
& ( dpsetconstrEL1 = $true )
& ( setext = $true )
& ( ubforcartprodlem2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( in__Cong = $true )
& ( exuE1 = $true )
& ( descrp = $true )
& ( contrasubsetT1 = $true )
& ( demorgan1a = $true )
& ( setukpairinjL = $true )
& ( kfstsingleton = $true )
& ( emptysetE = $true )
& ( upairsubunion = $true )
& ( symdiffI1 = $true )
& ( upairsetIR = $true )
& ( setadjoinSub2 = $true )
& ( singletonsuniq = $true )
& ( setunionE2 = $true )
& ( emptysetAx = $true )
& ( powersetE1 = $true )
& ( setminusER = $true )
& ( setukpairinjR = $true )
& ( bs114d = $true )
& ( ( in @ sK667 @ ( powerset @ sK666 ) )
= $true )
& ( ( in @ sK668 @ ( binintersect @ ( setminus @ sK666 @ sK665 ) @ ( setminus @ sK666 @ sK667 ) ) )
= $true )
& ( ( in @ sK668 @ ( setminus @ sK666 @ ( binunion @ sK665 @ sK667 ) ) )
!= $true )
& ( ( in @ sK668 @ sK666 )
= $true )
& ( $true
= ( in @ sK665 @ ( powerset @ sK666 ) ) )
& ( omegaSAx = $true )
& ( eta1 = $true )
& ( powersetsubset = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( inPowerset = $true )
& ( demorgan2b2 = $true )
& ( beta1 = $true )
& ( complementT_lem = $true )
& ( inCongP = $true )
& ( omegaIndAx = $true )
& ( symdiffIneg1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subsetI2 = $true )
& ( setminusIRneg = $true )
& ( nonemptyE1 = $true )
& ( iftrue = $true )
& ( demorgan2a = $true )
& ( setukpairinjR12 = $true )
& ( cartprodsndpairEq = $true )
& ( prop2setI = $true )
& ( setminusELneg = $true )
& ( binintersectRsub = $true )
& ( cartprodpairsurjEq = $true )
& ( setunionsingleton2 = $true )
& ( contrasubsetT3 = $true )
& ( exuI1 = $true )
& ( powersetI = $true )
& ( apProp = $true )
& ( ap2apEq1 = $true )
& ( doubleComplementI1 = $true )
& ( singletonsubset = $true )
& ( setadjoinE = $true )
& ( lamProp = $true )
& ( ifp = $true )
& ( setadjoinIL = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodmempaircEq = $true )
& ( notequalI1 = $true )
& ( funcext = $true )
& ( theeq = $true )
& ( funcGraphProp4 = $true )
& ( setminusT_lem = $true )
& ( notinsingleton = $true )
& ( setbeta = $true )
& ( lamp = $true )
& ( upairsetIL = $true )
& ( setminusSubset1 = $true )
& ( cartprodmempair = $true )
& ( binintersectT_lem = $true )
& ( exuI2 = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset1 = $true )
& ( powersetE = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetE = $true )
& ( setukpairinjR11 = $true )
& ( exuI3 = $true )
& ( setukpairinjL2 = $true )
& ( subsetE2 = $true )
& ( setadjoinAx = $true )
& ( binunionTE = $true )
& ( emptyI = $true )
& ( dsetconstrI = $true )
& ( binunionE = $true )
& ( complementImpComplementIntersect = $true )
& ( prop2set2propI = $true )
& ( app = $true )
& ( lam2p = $true )
& ( setadjoinIR = $true )
& ( emptyInPowerset = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetemptysetimpeq = $true )
& ( setunion__Cong = $true )
& ( cartprodfstin = $true )
& ( funcGraphProp3 = $true )
& ( quantDeMorgan4 = $true )
& ( ex1E1 = $true )
& ( funcinfuncset = $true )
& ( ubforcartprodlem3 = $true )
& ( subsetTrans = $true )
& ( powersetTI1 = $true )
& ( setextT = $true )
& ( binintersectTELcontra = $true )
& ( subsetE = $true )
& ( brelnall1 = $true )
& ( powersetI1 = $true )
& ( symdiffE = $true )
& ( eqbreln = $true )
& ( exuE2 = $true )
& ( beta2 = $true )
& ( notsubsetI = $true )
& ( ex1I2 = $true )
& ( powersetT_lem = $true )
& ( iftrueorfalse = $true )
& ( dpsetconstrSub = $true )
& ( foundationAx = $true )
& ( complementTnotintersectT = $true )
& ( upairinpowunion = $true )
& ( notdallE = $true )
& ( setextsub = $true )
& ( subsetTI = $true )
& ( powersetTE1 = $true )
& ( dsetconstr__Cong = $true )
& ( sepSubset = $true )
& ( setunionsingleton1 = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrER = $true )
& ( setadjoin__Cong = $true )
& ( theprop = $true )
& ( cartprodpairin = $true )
& ( setunionAx = $true )
& ( subPowSU = $true )
& ( uniqinunit = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset3 = $true )
& ( ex1E2 = $true )
& ( iffalseProp1 = $true )
& ( upairset2IR = $true )
& ( dpsetconstrERa = $true )
& ( ex1I = $true )
& ( ksndsingleton = $true )
& ( setukpairIL = $true )
& ( lam2lamEq = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( singletoninpowunion = $true )
& ( binunionIR = $true )
& ( doubleComplementE1 = $true )
& ( subset2powerset = $true )
& ( setoftrueEq = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( setOfPairsIsBReln = $true )
& ( notequalI2 = $true )
& ( dsetconstrER = $true )
& ( exuEu = $true )
& ( doubleComplementSub1 = $true )
& ( symdiffI2 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( kpairiskpair = $true )
& ( funcextLem = $true )
& ( omega__Cong = $true )
& ( complementTcontraSubset = $true )
& ( quantDeMorgan2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( iffalse = $true )
& ( contrasubsetT2 = $true )
& ( setminusI = $true )
& ( complementTI1 = $true )
& ( descr__Cong = $true )
& ( binunionRsub = $true )
& ( cartprodsndin = $true )
& ( eqimpsubset2 = $true )
& ( exuE3e = $true )
& ( cartprodfstpairEq = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK665,sK666,sK667,sK668]),skolemize(X0,sK665),skolemize(X1,sK666),skolemize(X2,sK667),skolemize(X3,sK668)],[f1835]) ).
thf(f1945,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f890]) ).
thf(f1946,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binintersect @ X5 @ X3 ) )
= $true )
& ( ( in @ X4 @ X3 )
!= $true ) ) ) ),
inference(rectify,[],[f1945]) ).
thf(f1947,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ( ( ( in @ sK782 @ ( binintersect @ sK783 @ sK781 ) )
= $true )
& ( ( in @ sK782 @ sK781 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK781,sK782,sK783]),skolemize(X3,sK781),skolemize(X4,sK782),skolemize(X5,sK783)],[f1946]) ).
thf(f2091,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( setminusER != $true )
| ( ( in @ X3 @ X4 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true ) ),
inference(cnf_transformation,[],[f1261]) ).
thf(f2474,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( setminusERneg != $true )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f1514]) ).
thf(f2506,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( binunionE != $true )
| ( ( in @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f1538]) ).
thf(f2842,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X4 @ X5 ) ) )
| ( binintersectEL != $true )
| ( ( in @ X3 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f1762]) ).
thf(f2964,plain,
binintersectER = $true,
inference(cnf_transformation,[],[f1836]) ).
thf(f3025,plain,
binunionE = $true,
inference(cnf_transformation,[],[f1836]) ).
thf(f3091,plain,
( ( in @ sK668 @ sK666 )
= $true ),
inference(cnf_transformation,[],[f1836]) ).
thf(f3092,plain,
( ( in @ sK668 @ ( setminus @ sK666 @ ( binunion @ sK665 @ sK667 ) ) )
!= $true ),
inference(cnf_transformation,[],[f1836]) ).
thf(f3093,plain,
( ( in @ sK668 @ ( binintersect @ ( setminus @ sK666 @ sK665 ) @ ( setminus @ sK666 @ sK667 ) ) )
= $true ),
inference(cnf_transformation,[],[f1836]) ).
thf(f3097,plain,
setminusER = $true,
inference(cnf_transformation,[],[f1836]) ).
thf(f3146,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f1836]) ).
thf(f3187,plain,
setminusERneg = $true,
inference(cnf_transformation,[],[f1836]) ).
thf(f3348,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersectER != $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f1947]) ).
thf(f3969,definition,
( spl872_60
<=> ( ( in @ sK668 @ ( setminus @ sK666 @ ( binunion @ sK665 @ sK667 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl872_60])],[avatar_definition]) ).
thf(f3971,plain,
( ( ( in @ sK668 @ ( setminus @ sK666 @ ( binunion @ sK665 @ sK667 ) ) )
!= $true )
| spl872_60 ),
inference(avatar_component_clause,[],[f3969]) ).
thf(f3972,plain,
~ spl872_60,
inference(avatar_split_clause,[],[f3092,f3969]) ).
thf(f4182,definition,
( spl872_109
<=> ( binunionE = $true ) ),
introduced(definition,[new_symbols(definition,[spl872_109])],[avatar_definition]) ).
thf(f4703,definition,
( spl872_226
<=> ( ( in @ sK668 @ ( binintersect @ ( setminus @ sK666 @ sK665 ) @ ( setminus @ sK666 @ sK667 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl872_226])],[avatar_definition]) ).
thf(f4705,plain,
( ( ( in @ sK668 @ ( binintersect @ ( setminus @ sK666 @ sK665 ) @ ( setminus @ sK666 @ sK667 ) ) )
= $true )
| ~ spl872_226 ),
inference(avatar_component_clause,[],[f4703]) ).
thf(f4706,plain,
spl872_226,
inference(avatar_split_clause,[],[f3093,f4703]) ).
thf(f4851,definition,
( spl872_259
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( ( in @ X5 @ ( binunion @ X7 @ X6 ) )
!= $true )
| ( $true
= ( in @ X5 @ X7 ) )
| ( $true
= ( in @ X5 @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl872_259])],[avatar_definition]) ).
thf(f4852,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( ( in @ X5 @ ( binunion @ X7 @ X6 ) )
!= $true )
| ( $true
= ( in @ X5 @ X7 ) )
| ( $true
= ( in @ X5 @ X6 ) ) )
| ~ spl872_259 ),
inference(avatar_component_clause,[],[f4851]) ).
thf(f5095,definition,
( spl872_313
<=> ( setminusERneg = $true ) ),
introduced(definition,[new_symbols(definition,[spl872_313])],[avatar_definition]) ).
thf(f5165,definition,
( spl872_329
<=> ( ( in @ sK668 @ sK666 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl872_329])],[avatar_definition]) ).
thf(f5167,plain,
( ( ( in @ sK668 @ sK666 )
= $true )
| ~ spl872_329 ),
inference(avatar_component_clause,[],[f5165]) ).
thf(f5168,plain,
spl872_329,
inference(avatar_split_clause,[],[f3091,f5165]) ).
thf(f5207,definition,
( spl872_338
<=> ( binintersectER = $true ) ),
introduced(definition,[new_symbols(definition,[spl872_338])],[avatar_definition]) ).
thf(f5791,plain,
spl872_109,
inference(avatar_split_clause,[],[f3025,f4182]) ).
thf(f6326,definition,
( spl872_579
<=> ( binintersectEL = $true ) ),
introduced(definition,[new_symbols(definition,[spl872_579])],[avatar_definition]) ).
thf(f6385,plain,
spl872_313,
inference(avatar_split_clause,[],[f3187,f5095]) ).
thf(f6405,plain,
( ~ spl872_109
| spl872_259 ),
inference(avatar_split_clause,[],[f2506,f4851,f4182]) ).
thf(f6687,definition,
( spl872_656
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl872_656])],[avatar_definition]) ).
thf(f6688,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ~ spl872_656 ),
inference(avatar_component_clause,[],[f6687]) ).
thf(f6690,definition,
( spl872_657
<=> ( setminusER = $true ) ),
introduced(definition,[new_symbols(definition,[spl872_657])],[avatar_definition]) ).
thf(f6693,plain,
( spl872_656
| ~ spl872_657 ),
inference(avatar_split_clause,[],[f2091,f6690,f6687]) ).
thf(f6729,definition,
( spl872_665
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( $true
= ( in @ X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl872_665])],[avatar_definition]) ).
thf(f6730,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ~ spl872_665 ),
inference(avatar_component_clause,[],[f6729]) ).
thf(f6731,plain,
( ~ spl872_313
| spl872_665 ),
inference(avatar_split_clause,[],[f2474,f6729,f5095]) ).
thf(f6855,plain,
spl872_338,
inference(avatar_split_clause,[],[f2964,f5207]) ).
thf(f6923,definition,
( spl872_707
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X4 @ X5 ) ) )
| ( ( in @ X3 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl872_707])],[avatar_definition]) ).
thf(f6924,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X4 @ X5 ) ) )
| ( ( in @ X3 @ X4 )
= $true ) )
| ~ spl872_707 ),
inference(avatar_component_clause,[],[f6923]) ).
thf(f6925,plain,
( ~ spl872_579
| spl872_707 ),
inference(avatar_split_clause,[],[f2842,f6923,f6326]) ).
thf(f7368,plain,
spl872_579,
inference(avatar_split_clause,[],[f3146,f6326]) ).
thf(f7654,plain,
spl872_657,
inference(avatar_split_clause,[],[f3097,f6690]) ).
thf(f9736,definition,
( spl872_1283
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl872_1283])],[avatar_definition]) ).
thf(f9737,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ~ spl872_1283 ),
inference(avatar_component_clause,[],[f9736]) ).
thf(f9738,plain,
( spl872_1283
| ~ spl872_338 ),
inference(avatar_split_clause,[],[f3348,f5207,f9736]) ).
thf(f10797,definition,
( spl872_1413
<=> ( ( in @ sK668 @ ( setminus @ sK666 @ sK667 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl872_1413])],[avatar_definition]) ).
thf(f10799,plain,
( ( ( in @ sK668 @ ( setminus @ sK666 @ sK667 ) )
= $true )
| ~ spl872_1413 ),
inference(avatar_component_clause,[],[f10797]) ).
thf(f10845,definition,
( spl872_1418
<=> ( ( in @ sK668 @ ( setminus @ sK666 @ sK665 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl872_1418])],[avatar_definition]) ).
thf(f10847,plain,
( ( ( in @ sK668 @ ( setminus @ sK666 @ sK665 ) )
= $true )
| ~ spl872_1418 ),
inference(avatar_component_clause,[],[f10845]) ).
thf(f11314,plain,
( ( $true != $true )
| ( ( in @ sK668 @ ( setminus @ sK666 @ sK665 ) )
= $true )
| ~ spl872_226
| ~ spl872_707 ),
inference(superposition,[],[f6924,f4705]) ).
thf(f11320,plain,
( ( ( in @ sK668 @ ( setminus @ sK666 @ sK665 ) )
= $true )
| ~ spl872_226
| ~ spl872_707 ),
inference(trivial_inequality_removal,[],[f11314]) ).
thf(f11325,plain,
( spl872_1418
| ~ spl872_226
| ~ spl872_707 ),
inference(avatar_split_clause,[],[f11320,f6923,f4703,f10845]) ).
thf(f11399,plain,
( ( $true != $true )
| ( ( in @ sK668 @ sK665 )
!= $true )
| ~ spl872_656
| ~ spl872_1418 ),
inference(superposition,[],[f6688,f10847]) ).
thf(f11404,plain,
( ( ( in @ sK668 @ sK665 )
!= $true )
| ~ spl872_656
| ~ spl872_1418 ),
inference(trivial_inequality_removal,[],[f11399]) ).
thf(f11411,definition,
( spl872_1449
<=> ( ( in @ sK668 @ sK665 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl872_1449])],[avatar_definition]) ).
thf(f11413,plain,
( ( ( in @ sK668 @ sK665 )
!= $true )
| spl872_1449 ),
inference(avatar_component_clause,[],[f11411]) ).
thf(f11414,plain,
( ~ spl872_1449
| ~ spl872_656
| ~ spl872_1418 ),
inference(avatar_split_clause,[],[f11404,f10845,f6687,f11411]) ).
thf(f11463,plain,
( ( $true != $true )
| ( ( in @ sK668 @ ( setminus @ sK666 @ sK667 ) )
= $true )
| ~ spl872_226
| ~ spl872_1283 ),
inference(superposition,[],[f9737,f4705]) ).
thf(f11470,plain,
( ( ( in @ sK668 @ ( setminus @ sK666 @ sK667 ) )
= $true )
| ~ spl872_226
| ~ spl872_1283 ),
inference(trivial_inequality_removal,[],[f11463]) ).
thf(f11476,plain,
( spl872_1413
| ~ spl872_226
| ~ spl872_1283 ),
inference(avatar_split_clause,[],[f11470,f9736,f4703,f10797]) ).
thf(f11669,plain,
( ( $true != $true )
| ( ( in @ sK668 @ sK667 )
!= $true )
| ~ spl872_656
| ~ spl872_1413 ),
inference(superposition,[],[f6688,f10799]) ).
thf(f11674,plain,
( ( ( in @ sK668 @ sK667 )
!= $true )
| ~ spl872_656
| ~ spl872_1413 ),
inference(trivial_inequality_removal,[],[f11669]) ).
thf(f11680,definition,
( spl872_1454
<=> ( ( in @ sK668 @ sK667 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl872_1454])],[avatar_definition]) ).
thf(f11683,plain,
( ~ spl872_1454
| ~ spl872_656
| ~ spl872_1413 ),
inference(avatar_split_clause,[],[f11674,f10797,f6687,f11680]) ).
thf(f12705,plain,
( ( ( in @ sK668 @ ( binunion @ sK665 @ sK667 ) )
= $true )
| ( ( in @ sK668 @ sK666 )
!= $true )
| ( $true != $true )
| spl872_60
| ~ spl872_665 ),
inference(superposition,[],[f3971,f6730]) ).
thf(f12716,plain,
( ( ( in @ sK668 @ sK666 )
!= $true )
| ( ( in @ sK668 @ ( binunion @ sK665 @ sK667 ) )
= $true )
| spl872_60
| ~ spl872_665 ),
inference(trivial_inequality_removal,[],[f12705]) ).
thf(f12721,plain,
( ( ( in @ sK668 @ ( binunion @ sK665 @ sK667 ) )
= $true )
| spl872_60
| ~ spl872_329
| ~ spl872_665 ),
inference(forward_subsumption_resolution,[],[f12716,f5167]) ).
thf(f12724,definition,
( spl872_1469
<=> ( ( in @ sK668 @ ( binunion @ sK665 @ sK667 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl872_1469])],[avatar_definition]) ).
thf(f12726,plain,
( ( ( in @ sK668 @ ( binunion @ sK665 @ sK667 ) )
= $true )
| ~ spl872_1469 ),
inference(avatar_component_clause,[],[f12724]) ).
thf(f12727,plain,
( spl872_1469
| spl872_60
| ~ spl872_329
| ~ spl872_665 ),
inference(avatar_split_clause,[],[f12721,f6729,f5165,f3969,f12724]) ).
thf(f12778,plain,
( ( ( in @ sK668 @ sK667 )
= $true )
| ( ( in @ sK668 @ sK665 )
= $true )
| ( $true != $true )
| ~ spl872_259
| ~ spl872_1469 ),
inference(superposition,[],[f4852,f12726]) ).
thf(f12786,plain,
( ( ( in @ sK668 @ sK665 )
= $true )
| ( ( in @ sK668 @ sK667 )
= $true )
| ~ spl872_259
| ~ spl872_1469 ),
inference(trivial_inequality_removal,[],[f12778]) ).
thf(f12807,plain,
( ( ( in @ sK668 @ sK667 )
= $true )
| ~ spl872_259
| spl872_1449
| ~ spl872_1469 ),
inference(forward_subsumption_resolution,[],[f12786,f11413]) ).
thf(f12813,plain,
( spl872_1454
| ~ spl872_259
| spl872_1449
| ~ spl872_1469 ),
inference(avatar_split_clause,[],[f12807,f12724,f11411,f4851,f11680]) ).
cnf(s34,plain,
~ spl872_60,
inference(sat_conversion,[],[f3972]) ).
cnf(s137,plain,
spl872_226,
inference(sat_conversion,[],[f4706]) ).
cnf(s212,plain,
spl872_329,
inference(sat_conversion,[],[f5168]) ).
cnf(s324,plain,
spl872_109,
inference(sat_conversion,[],[f5791]) ).
cnf(s443,plain,
spl872_313,
inference(sat_conversion,[],[f6385]) ).
cnf(s448,plain,
( ~ spl872_109
| spl872_259 ),
inference(sat_conversion,[],[f6405]) ).
cnf(s505,plain,
( spl872_656
| ~ spl872_657 ),
inference(sat_conversion,[],[f6693]) ).
cnf(s514,plain,
( ~ spl872_313
| spl872_665 ),
inference(sat_conversion,[],[f6731]) ).
cnf(s539,plain,
spl872_338,
inference(sat_conversion,[],[f6855]) ).
cnf(s555,plain,
( ~ spl872_579
| spl872_707 ),
inference(sat_conversion,[],[f6925]) ).
cnf(s656,plain,
spl872_579,
inference(sat_conversion,[],[f7368]) ).
cnf(s728,plain,
spl872_657,
inference(sat_conversion,[],[f7654]) ).
cnf(s1277,plain,
( ~ spl872_338
| spl872_1283 ),
inference(sat_conversion,[],[f9738]) ).
cnf(s1473,plain,
( ~ spl872_226
| ~ spl872_707
| spl872_1418 ),
inference(sat_conversion,[],[f11325]) ).
cnf(s1478,plain,
( ~ spl872_656
| ~ spl872_1418
| ~ spl872_1449 ),
inference(sat_conversion,[],[f11414]) ).
cnf(s1483,plain,
( ~ spl872_226
| ~ spl872_1283
| spl872_1413 ),
inference(sat_conversion,[],[f11476]) ).
cnf(s1489,plain,
( ~ spl872_656
| ~ spl872_1413
| ~ spl872_1454 ),
inference(sat_conversion,[],[f11683]) ).
cnf(s1508,plain,
( spl872_60
| ~ spl872_329
| ~ spl872_665
| spl872_1469 ),
inference(sat_conversion,[],[f12727]) ).
cnf(s1515,plain,
( ~ spl872_259
| spl872_1449
| spl872_1454
| ~ spl872_1469 ),
inference(sat_conversion,[],[f12813]) ).
cnf(s1640,plain,
spl872_707,
inference(rat,[],[s555,s656]) ).
cnf(s1644,plain,
spl872_1283,
inference(rat,[],[s1277,s539]) ).
cnf(s1655,plain,
spl872_656,
inference(rat,[],[s505,s728]) ).
cnf(s1676,plain,
spl872_665,
inference(rat,[],[s514,s443]) ).
cnf(s1737,plain,
spl872_259,
inference(rat,[],[s448,s324]) ).
cnf(s1815,plain,
spl872_1413,
inference(rat,[],[s1483,s1644,s137]) ).
cnf(s1816,plain,
spl872_1418,
inference(rat,[],[s1473,s1640,s137]) ).
cnf(s1819,plain,
~ spl872_1454,
inference(rat,[],[s1489,s1655,s1815]) ).
cnf(s1821,plain,
~ spl872_1449,
inference(rat,[],[s1478,s1655,s1816]) ).
cnf(s1824,plain,
~ spl872_1469,
inference(rat,[],[s1515,s1819,s1737,s1821]) ).
cnf(s1825,plain,
spl872_60,
inference(rat,[],[s1508,s212,s1676,s1824]) ).
cnf(s1873,plain,
$false,
inference(rat,[],[s34,s1825]) ).
thf(f12814,plain,
$false,
inference(avatar_sat_refutation,[],[s1873]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU756^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:20:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.43 % (3433903)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.49/0.43 % (3433910)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3555199576:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.49/0.43 % (3433910)Instruction limit reached!
% 0.49/0.43 % (3433910)------------------------------
% 0.49/0.43 % (3433910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.43 % (3433910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.43 % (3433910)CaDiCaL version: 2.1.3
% 0.49/0.43 % (3433910)Termination reason: Instruction limit
% 0.49/0.43 % (3433910)Termination phase: shuffling
% 0.49/0.43 % (3433910)Time elapsed: 0.002 s
% 0.49/0.43 % (3433910)Peak memory usage: 10 MB
% 0.49/0.43 % (3433910)Instructions burned: 7 (million)
% 0.49/0.43 % (3433914)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.49/0.43 % (3433914)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.49/0.43 % (3433908)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2367778672:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.49/0.43 % (3433911)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=3057824506:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.49/0.43 % (3433912)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2470647370:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.49/0.43 % (3433914)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=4091250897:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.49/0.43 % (3433913)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3818593114:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.49/0.43 % (3433916)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2221553453:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.43 % (3433916)Instruction limit reached!
% 0.49/0.43 % (3433916)------------------------------
% 0.49/0.43 % (3433916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.43 % (3433916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.43 % (3433916)CaDiCaL version: 2.1.3
% 0.49/0.43 % (3433916)Termination reason: Instruction limit
% 0.49/0.43 % (3433916)Termination phase: shuffling
% 0.49/0.43 % (3433916)Time elapsed: 0.002 s
% 0.49/0.43 % (3433916)Peak memory usage: 10 MB
% 0.49/0.43 % (3433916)Instructions burned: 7 (million)
% 0.49/0.43 % (3433909)lrs+10_16_si=on:nwc=1.5:random_seed=3658193540:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.49/0.43 % (3433912)Instruction limit reached!
% 0.49/0.43 % (3433912)------------------------------
% 0.49/0.43 % (3433912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.43 % (3433912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.43 % (3433912)CaDiCaL version: 2.1.3
% 0.49/0.43 % (3433912)Termination reason: Instruction limit
% 0.49/0.43 % (3433912)Termination phase: shuffling
% 0.49/0.43 % (3433912)Time elapsed: 0.012 s
% 0.49/0.43 % (3433912)Peak memory usage: 10 MB
% 0.49/0.43 % (3433912)Instructions burned: 25 (million)
% 0.49/0.43 % (3433909)Instruction limit reached!
% 0.49/0.43 % (3433909)------------------------------
% 0.49/0.43 % (3433909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.43 % (3433909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.43 % (3433909)CaDiCaL version: 2.1.3
% 0.49/0.43 % (3433909)Termination reason: Instruction limit
% 0.49/0.43 % (3433909)Termination phase: shuffling
% 0.49/0.43 % (3433909)Time elapsed: 0.009 s
% 0.49/0.43 % (3433909)Peak memory usage: 10 MB
% 0.49/0.43 % (3433909)Instructions burned: 18 (million)
% 0.49/0.43 % (3433923)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=368443395:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.49/0.47 % (3433923)Instruction limit reached!
% 0.49/0.47 % (3433923)------------------------------
% 0.49/0.47 % (3433923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.47 % (3433923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.47 % (3433923)CaDiCaL version: 2.1.3
% 0.49/0.47 % (3433923)Termination reason: Instruction limit
% 0.49/0.47 % (3433923)Termination phase: shuffling
% 0.49/0.47 % (3433923)Time elapsed: 0.003 s
% 0.49/0.47 % (3433923)Peak memory usage: 10 MB
% 0.49/0.47 % (3433923)Instructions burned: 12 (million)
% 0.49/0.47 % (3433925)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.47 % (3433925)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3166570433:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.49/0.47 % (3433913)Instruction limit reached!
% 0.49/0.47 % (3433913)------------------------------
% 0.49/0.47 % (3433913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.47 % (3433913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.47 % (3433913)CaDiCaL version: 2.1.3
% 1.12/0.47 % (3433913)Termination reason: Instruction limit
% 1.12/0.47 % (3433913)Termination phase: Preprocessing 3
% 1.12/0.47 % (3433913)Time elapsed: 0.034 s
% 1.12/0.47 % (3433913)Peak memory usage: 12 MB
% 1.12/0.47 % (3433913)Instructions burned: 76 (million)
% 1.12/0.47 % (3433925)Instruction limit reached!
% 1.12/0.47 % (3433925)------------------------------
% 1.12/0.47 % (3433925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.47 % (3433925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.47 % (3433925)CaDiCaL version: 2.1.3
% 1.12/0.47 % (3433925)Termination reason: Instruction limit
% 1.12/0.47 % (3433925)Termination phase: shuffling
% 1.12/0.47 % (3433925)Time elapsed: 0.004 s
% 1.12/0.47 % (3433925)Peak memory usage: 10 MB
% 1.12/0.47 % (3433925)Instructions burned: 9 (million)
% 1.12/0.47 % (3433926)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1890637585:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.12/0.47 % (3433908)Instruction limit reached!
% 1.12/0.47 % (3433908)------------------------------
% 1.12/0.47 % (3433908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.47 % (3433928)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
% 1.12/0.47 % (3433908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.47 % (3433908)CaDiCaL version: 2.1.3
% 1.12/0.47 % (3433908)Termination reason: Instruction limit
% 1.12/0.47 % (3433908)Termination phase: Preprocessing 3
% 1.12/0.47 % (3433908)Time elapsed: 0.040 s
% 1.12/0.47 % (3433928)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.12/0.47 % (3433908)Peak memory usage: 12 MB
% 1.12/0.47 % (3433908)Instructions burned: 87 (million)
% 1.12/0.47 % (3433928)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3948658912:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.12/0.47 % (3433926)Instruction limit reached!
% 1.12/0.47 % (3433926)------------------------------
% 1.12/0.47 % (3433926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.47 % (3433926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.47 % (3433926)CaDiCaL version: 2.1.3
% 1.12/0.47 % (3433926)Termination reason: Instruction limit
% 1.12/0.47 % (3433926)Termination phase: shuffling
% 1.12/0.47 % (3433926)Time elapsed: 0.006 s
% 1.12/0.47 % (3433926)Peak memory usage: 10 MB
% 1.12/0.47 % (3433926)Instructions burned: 13 (million)
% 1.12/0.47 % (3433930)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=705941193:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.12/0.47 % (3433933)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.12/0.50 % (3433928)Instruction limit reached!
% 1.12/0.50 % (3433928)------------------------------
% 1.12/0.50 % (3433928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.50 % (3433928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.50 % (3433928)CaDiCaL version: 2.1.3
% 1.12/0.50 % (3433928)Termination reason: Instruction limit
% 1.12/0.50 % (3433928)Termination phase: shuffling
% 1.12/0.50 % (3433928)Time elapsed: 0.013 s
% 1.12/0.50 % (3433928)Peak memory usage: 10 MB
% 1.12/0.50 % (3433928)Instructions burned: 29 (million)
% 1.12/0.50 % (3433931)lrs+10_1_si=on:cs=on:random_seed=1727997233:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.12/0.50 % (3433933)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=2329620997:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.12/0.50 % (3433933)Instruction limit reached!
% 1.12/0.50 % (3433933)------------------------------
% 1.12/0.50 % (3433933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.50 % (3433933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.50 % (3433933)CaDiCaL version: 2.1.3
% 1.12/0.50 % (3433933)Termination reason: Instruction limit
% 1.12/0.50 % (3433933)Termination phase: shuffling
% 1.12/0.50 % (3433933)Time elapsed: 0.002 s
% 1.12/0.50 % (3433933)Peak memory usage: 10 MB
% 1.12/0.50 % (3433933)Instructions burned: 3 (million)
% 1.12/0.50 % (3433931)Instruction limit reached!
% 1.12/0.50 % (3433931)------------------------------
% 1.12/0.50 % (3433931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.50 % (3433931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.50 % (3433931)CaDiCaL version: 2.1.3
% 1.12/0.50 % (3433931)Termination reason: Instruction limit
% 1.12/0.50 % (3433931)Termination phase: shuffling
% 1.12/0.50 % (3433931)Time elapsed: 0.005 s
% 1.12/0.50 % (3433931)Peak memory usage: 10 MB
% 1.12/0.50 % (3433931)Instructions burned: 10 (million)
% 1.12/0.50 % (3433935)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1779339351:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.12/0.50 % (3433930)Instruction limit reached!
% 1.12/0.50 % (3433930)------------------------------
% 1.12/0.50 % (3433930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.50 % (3433930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.50 % (3433930)CaDiCaL version: 2.1.3
% 1.12/0.50 % (3433930)Termination reason: Instruction limit
% 1.12/0.50 % (3433930)Termination phase: Property scanning
% 1.12/0.50 % (3433930)Time elapsed: 0.019 s
% 1.12/0.50 % (3433930)Peak memory usage: 11 MB
% 1.12/0.50 % (3433930)Instructions burned: 88 (million)
% 1.12/0.50 % (3433914)Instruction limit reached!
% 1.12/0.50 % (3433914)------------------------------
% 1.12/0.50 % (3433914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.50 % (3433914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.50 % (3433914)CaDiCaL version: 2.1.3
% 1.12/0.50 % (3433914)Termination reason: Instruction limit
% 1.12/0.50 % (3433914)Termination phase: Property scanning
% 1.12/0.50 % (3433914)Time elapsed: 0.067 s
% 1.12/0.50 % (3433914)Peak memory usage: 12 MB
% 1.12/0.50 % (3433914)Instructions burned: 159 (million)
% 1.12/0.50 % (3433938)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1644327814:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.12/0.50 % (3433943)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=367294813:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.12/0.50 % (3433940)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1749753779:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.12/0.50 % (3433935)Instruction limit reached!
% 1.12/0.50 % (3433935)------------------------------
% 1.12/0.50 % (3433935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.50 % (3433935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.50 % (3433935)CaDiCaL version: 2.1.3
% 1.12/0.50 % (3433935)Termination reason: Instruction limit
% 1.12/0.50 % (3433935)Termination phase: Property scanning
% 1.12/0.50 % (3433935)Time elapsed: 0.017 s
% 1.12/0.50 % (3433935)Peak memory usage: 11 MB
% 1.12/0.54 % (3433935)Instructions burned: 39 (million)
% 1.12/0.54 % (3433941)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3218053561:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.12/0.54 % (3433944)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1553428214:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.12/0.54 % (3433941)Instruction limit reached!
% 1.12/0.54 % (3433941)------------------------------
% 1.12/0.54 % (3433941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.54 % (3433941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.54 % (3433941)CaDiCaL version: 2.1.3
% 1.12/0.54 % (3433941)Termination reason: Instruction limit
% 1.12/0.54 % (3433941)Termination phase: shuffling
% 1.12/0.54 % (3433941)Time elapsed: 0.007 s
% 1.12/0.54 % (3433941)Peak memory usage: 10 MB
% 1.12/0.54 % (3433941)Instructions burned: 14 (million)
% 1.12/0.54 % (3433944)Instruction limit reached!
% 1.12/0.54 % (3433944)------------------------------
% 1.12/0.54 % (3433944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.54 % (3433944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.54 % (3433944)CaDiCaL version: 2.1.3
% 1.12/0.54 % (3433944)Termination reason: Instruction limit
% 1.12/0.54 % (3433944)Termination phase: shuffling
% 1.12/0.54 % (3433944)Time elapsed: 0.007 s
% 1.12/0.54 % (3433944)Peak memory usage: 10 MB
% 1.12/0.54 % (3433944)Instructions burned: 14 (million)
% 1.12/0.54 % (3433940)Instruction limit reached!
% 1.12/0.54 % (3433940)------------------------------
% 1.12/0.54 % (3433940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.54 % (3433940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.54 % (3433940)CaDiCaL version: 2.1.3
% 1.12/0.54 % (3433940)Termination reason: Instruction limit
% 1.12/0.54 % (3433940)Termination phase: Property scanning
% 1.12/0.54 % (3433940)Time elapsed: 0.013 s
% 1.12/0.54 % (3433940)Peak memory usage: 11 MB
% 1.12/0.54 % (3433940)Instructions burned: 28 (million)
% 1.12/0.54 % (3433949)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=655502108:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.12/0.54 % (3433949)Instruction limit reached!
% 1.12/0.54 % (3433949)------------------------------
% 1.12/0.54 % (3433949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.54 % (3433949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.54 % (3433949)CaDiCaL version: 2.1.3
% 1.12/0.54 % (3433949)Termination reason: Instruction limit
% 1.12/0.54 % (3433949)Termination phase: shuffling
% 1.12/0.54 % (3433949)Time elapsed: 0.003 s
% 1.12/0.54 % (3433949)Peak memory usage: 10 MB
% 1.12/0.54 % (3433949)Instructions burned: 6 (million)
% 1.12/0.54 % (3433951)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2214634155:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.12/0.54 % (3433953)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2436709963:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.12/0.54 % (3433952)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1156597973:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.12/0.54 % (3433955)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.12/0.54 % (3433955)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.12/0.54 % (3433951)Instruction limit reached!
% 1.12/0.54 % (3433951)------------------------------
% 1.12/0.54 % (3433951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.54 % (3433951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.54 % (3433951)CaDiCaL version: 2.1.3
% 1.12/0.54 % (3433951)Termination reason: Instruction limit
% 1.12/0.54 % (3433951)Termination phase: shuffling
% 1.12/0.54 % (3433951)Time elapsed: 0.012 s
% 1.12/0.54 % (3433951)Peak memory usage: 10 MB
% 1.83/0.60 % (3433951)Instructions burned: 27 (million)
% 1.83/0.60 % (3433955)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=1320117458:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.83/0.60 % (3433952)Instruction limit reached!
% 1.83/0.60 % (3433952)------------------------------
% 1.83/0.60 % (3433952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (3433952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (3433952)CaDiCaL version: 2.1.3
% 1.83/0.60 % (3433952)Termination reason: Instruction limit
% 1.83/0.60 % (3433952)Termination phase: shuffling
% 1.83/0.60 % (3433952)Time elapsed: 0.011 s
% 1.83/0.60 % (3433952)Peak memory usage: 10 MB
% 1.83/0.60 % (3433952)Instructions burned: 24 (million)
% 1.83/0.60 % (3433955)Instruction limit reached!
% 1.83/0.60 % (3433955)------------------------------
% 1.83/0.60 % (3433955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (3433955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (3433955)CaDiCaL version: 2.1.3
% 1.83/0.60 % (3433955)Termination reason: Instruction limit
% 1.83/0.60 % (3433955)Termination phase: shuffling
% 1.83/0.60 % (3433955)Time elapsed: 0.007 s
% 1.83/0.60 % (3433955)Peak memory usage: 10 MB
% 1.83/0.60 % (3433955)Instructions burned: 16 (million)
% 1.83/0.60 % (3433959)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.83/0.60 % (3433959)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=2109627489:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.83/0.60 % (3433953)Instruction limit reached!
% 1.83/0.60 % (3433953)------------------------------
% 1.83/0.60 % (3433953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (3433953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (3433953)CaDiCaL version: 2.1.3
% 1.83/0.60 % (3433953)Termination reason: Instruction limit
% 1.83/0.60 % (3433953)Termination phase: Preprocessing 3
% 1.83/0.60 % (3433953)Time elapsed: 0.028 s
% 1.83/0.60 % (3433953)Peak memory usage: 12 MB
% 1.83/0.60 % (3433953)Instructions burned: 62 (million)
% 1.83/0.60 % (3433959)Instruction limit reached!
% 1.83/0.60 % (3433959)------------------------------
% 1.83/0.60 % (3433959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (3433961)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=2325726014:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.83/0.60 % (3433959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (3433959)CaDiCaL version: 2.1.3
% 1.83/0.60 % (3433959)Termination reason: Instruction limit
% 1.83/0.60 % (3433959)Termination phase: shuffling
% 1.83/0.60 % (3433959)Time elapsed: 0.004 s
% 1.83/0.60 % (3433959)Peak memory usage: 10 MB
% 1.83/0.60 % (3433959)Instructions burned: 8 (million)
% 1.83/0.60 % (3433962)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=946632043:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.83/0.60 % (3433962)Instruction limit reached!
% 1.83/0.60 % (3433962)------------------------------
% 1.83/0.60 % (3433962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (3433962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (3433962)CaDiCaL version: 2.1.3
% 1.83/0.60 % (3433962)Termination reason: Instruction limit
% 1.83/0.60 % (3433962)Termination phase: shuffling
% 1.83/0.60 % (3433962)Time elapsed: 0.004 s
% 1.83/0.60 % (3433962)Peak memory usage: 10 MB
% 1.83/0.60 % (3433962)Instructions burned: 8 (million)
% 1.83/0.60 % (3433943)Instruction limit reached!
% 1.83/0.60 % (3433943)------------------------------
% 1.83/0.60 % (3433943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (3433943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (3433943)CaDiCaL version: 2.1.3
% 1.83/0.60 % (3433943)Termination reason: Instruction limit
% 1.83/0.60 % (3433943)Termination phase: Saturation
% 1.83/0.60 % (3433943)Time elapsed: 0.077 s
% 1.83/0.60 % (3433943)Peak memory usage: 15 MB
% 2.15/0.65 % (3433943)Instructions burned: 329 (million)
% 2.15/0.65 % (3433961)Instruction limit reached!
% 2.15/0.65 % (3433961)------------------------------
% 2.15/0.65 % (3433961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433961)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433961)Termination reason: Instruction limit
% 2.15/0.65 % (3433961)Termination phase: shuffling
% 2.15/0.65 % (3433961)Time elapsed: 0.014 s
% 2.15/0.65 % (3433961)Peak memory usage: 10 MB
% 2.15/0.65 % (3433961)Instructions burned: 31 (million)
% 2.15/0.65 % (3433964)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=4187496043:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.15/0.65 % (3433966)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=118087147:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.15/0.65 % (3433969)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1065734642:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.15/0.65 % (3433964)Instruction limit reached!
% 2.15/0.65 % (3433964)------------------------------
% 2.15/0.65 % (3433964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433964)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433964)Termination reason: Instruction limit
% 2.15/0.65 % (3433964)Termination phase: shuffling
% 2.15/0.65 % (3433964)Time elapsed: 0.011 s
% 2.15/0.65 % (3433964)Peak memory usage: 10 MB
% 2.15/0.65 % (3433964)Instructions burned: 24 (million)
% 2.15/0.65 % (3433968)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2579163163:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.15/0.65 % (3433966)Instruction limit reached!
% 2.15/0.65 % (3433966)------------------------------
% 2.15/0.65 % (3433966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433966)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433966)Termination reason: Instruction limit
% 2.15/0.65 % (3433966)Termination phase: shuffling
% 2.15/0.65 % (3433966)Time elapsed: 0.010 s
% 2.15/0.65 % (3433966)Peak memory usage: 10 MB
% 2.15/0.65 % (3433966)Instructions burned: 21 (million)
% 2.15/0.65 % (3433970)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2368083810:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.15/0.65 % (3433938)Instruction limit reached!
% 2.15/0.65 % (3433938)------------------------------
% 2.15/0.65 % (3433938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433938)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433938)Termination reason: Instruction limit
% 2.15/0.65 % (3433938)Termination phase: Saturation
% 2.15/0.65 % (3433938)Time elapsed: 0.111 s
% 2.15/0.65 % (3433938)Peak memory usage: 15 MB
% 2.15/0.65 % (3433938)Instructions burned: 251 (million)
% 2.15/0.65 % (3433976)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.15/0.65 % (3433974)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3750877429:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.15/0.65 % (3433976)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=483865492:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.15/0.65 % (3433969)Instruction limit reached!
% 2.15/0.65 % (3433969)------------------------------
% 2.15/0.65 % (3433969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433969)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433969)Termination reason: Instruction limit
% 2.15/0.65 % (3433969)Termination phase: Property scanning
% 2.15/0.65 % (3433969)Time elapsed: 0.032 s
% 2.15/0.65 % (3433969)Peak memory usage: 12 MB
% 2.15/0.65 % (3433969)Instructions burned: 145 (million)
% 2.15/0.65 % (3433976)Instruction limit reached!
% 2.15/0.65 % (3433976)------------------------------
% 2.15/0.65 % (3433976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433976)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433976)Termination reason: Instruction limit
% 2.15/0.65 % (3433976)Termination phase: shuffling
% 2.15/0.65 % (3433976)Time elapsed: 0.004 s
% 2.15/0.65 % (3433976)Peak memory usage: 10 MB
% 2.15/0.65 % (3433976)Instructions burned: 9 (million)
% 2.15/0.65 % (3433978)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1786762076:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.15/0.65 % (3433981)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=1558787004:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.15/0.65 % (3433974)Instruction limit reached!
% 2.15/0.65 % (3433974)------------------------------
% 2.15/0.65 % (3433974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433974)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433974)Termination reason: Instruction limit
% 2.15/0.65 % (3433974)Termination phase: Property scanning
% 2.15/0.65 % (3433974)Time elapsed: 0.020 s
% 2.15/0.65 % (3433974)Peak memory usage: 11 MB
% 2.15/0.65 % (3433974)Instructions burned: 44 (million)
% 2.15/0.65 % (3433982)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.15/0.65 % (3433982)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=4105513141:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.15/0.65 % (3433982)Instruction limit reached!
% 2.15/0.65 % (3433982)------------------------------
% 2.15/0.65 % (3433982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433982)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433982)Termination reason: Instruction limit
% 2.15/0.65 % (3433982)Termination phase: shuffling
% 2.15/0.65 % (3433982)Time elapsed: 0.003 s
% 2.15/0.65 % (3433982)Peak memory usage: 10 MB
% 2.15/0.65 % (3433982)Instructions burned: 6 (million)
% 2.15/0.65 % (3433985)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1868324898:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.15/0.65 % (3433987)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2240307168:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.15/0.65 % (3433985)Instruction limit reached!
% 2.15/0.65 % (3433985)------------------------------
% 2.15/0.65 % (3433985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433985)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433985)Termination reason: Instruction limit
% 2.15/0.65 % (3433985)Termination phase: shuffling
% 2.15/0.65 % (3433985)Time elapsed: 0.010 s
% 2.15/0.65 % (3433985)Peak memory usage: 11 MB
% 2.15/0.65 % (3433985)Instructions burned: 23 (million)
% 2.15/0.65 % (3433981)Instruction limit reached!
% 2.15/0.65 % (3433981)------------------------------
% 2.15/0.65 % (3433981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433981)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433981)Termination reason: Instruction limit
% 2.15/0.65 % (3433981)Termination phase: Saturation
% 2.15/0.65 % (3433981)Time elapsed: 0.037 s
% 2.15/0.65 % (3433981)Peak memory usage: 12 MB
% 2.15/0.65 % (3433981)Instructions burned: 170 (million)
% 2.15/0.65 % (3433987)Instruction limit reached!
% 2.15/0.65 % (3433987)------------------------------
% 2.15/0.65 % (3433987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433987)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433987)Termination reason: Instruction limit
% 2.15/0.65 % (3433987)Termination phase: shuffling
% 2.15/0.65 % (3433987)Time elapsed: 0.009 s
% 2.15/0.65 % (3433987)Peak memory usage: 10 MB
% 2.15/0.65 % (3433987)Instructions burned: 21 (million)
% 2.15/0.65 % (3433991)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=1946965138:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.15/0.65 % (3433970)Instruction limit reached!
% 2.15/0.65 % (3433970)------------------------------
% 2.15/0.65 % (3433970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433970)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433970)Termination reason: Instruction limit
% 2.15/0.65 % (3433970)Termination phase: Saturation
% 2.15/0.65 % (3433970)Time elapsed: 0.080 s
% 2.15/0.65 % (3433970)Peak memory usage: 13 MB
% 2.15/0.65 % (3433970)Instructions burned: 194 (million)
% 2.15/0.65 % (3433990)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=368895444:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.15/0.65 % (3433992)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=4087679437:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.15/0.65 % (3433994)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2546389574:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.15/0.65 % (3433978)Instruction limit reached!
% 2.15/0.65 % (3433978)------------------------------
% 2.15/0.65 % (3433978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433978)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433978)Termination reason: Instruction limit
% 2.15/0.65 % (3433978)Termination phase: Saturation
% 2.15/0.65 % (3433978)Time elapsed: 0.076 s
% 2.15/0.65 % (3433978)Peak memory usage: 14 MB
% 2.15/0.65 % (3433978)Instructions burned: 183 (million)
% 2.15/0.65 % (3433992)Instruction limit reached!
% 2.15/0.65 % (3433992)------------------------------
% 2.15/0.65 % (3433992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.65 % (3433992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.65 % (3433992)CaDiCaL version: 2.1.3
% 2.15/0.65 % (3433992)Termination reason: Instruction limit
% 2.15/0.65 % (3433992)Termination phase: Property scanning
% 2.15/0.65 % (3433992)Time elapsed: 0.020 s
% 2.15/0.65 % (3433992)Peak memory usage: 11 MB
% 2.15/0.65 % (3433992)Instructions burned: 46 (million)
% 2.15/0.65 % (3433911) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3433903-3433911"...
% 2.15/0.65 % (3433998)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1426833534:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.15/0.65 % (3433911)...printing done.
% 2.15/0.65 % (3433999)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.15/0.65 % (3433911)Refutation found. Thanks to Tanya!
% 2.15/0.65 % SZS status Theorem for theBenchmark
% 2.15/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 2.15/0.66 % (3433911)------------------------------
% 2.15/0.66 % (3433911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.66 % (3433911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.66 % (3433911)CaDiCaL version: 2.1.3
% 2.15/0.66 % (3433911)Termination reason: Refutation
% 2.15/0.66 % (3433911)Time elapsed: 0.303 s
% 2.15/0.66 % (3433911)Peak memory usage: 22 MB
% 2.15/0.66 % (3433911)Instructions burned: 590 (million)
% 2.15/0.66 % (3433903)Success in time 0.359 s
% 2.15/0.66 % Vampire exiting
%------------------------------------------------------------------------------