%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU745^1 : 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 : n020.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 08:31:05 AM UTC 2026
% Result : Theorem 2.30s 0.66s
% Output : Refutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 89 ( 30 unt; 0 typ; 10 def)
% Number of atoms : 5522 (1502 equ; 0 cnn)
% Maximal formula atoms : 266 ( 62 avg)
% Number of connectives : 3070 ( 148 ~; 130 |;1084 &; 606 @)
% ( 18 <=>;1084 =>; 0 <=; 0 <~>)
% Maximal formula depth : 275 ( 28 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 : 498 ( 495 usr; 303 con; 0-4 aty)
% Number of variables : 126 ( 0 sgn 100 !; 26 ?; 126 :)
% 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_302,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_303,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_304,type,
vOR: $o > $o > $o ).
thf(func_def_305,type,
vAND: $o > $o > $o ).
thf(func_def_306,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_307,type,
vNOT: $o > $o ).
thf(func_def_308,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_309,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_310,type,
vIMP: $o > $o > $o ).
thf(func_def_311,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_312,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_313,type,
sP0: $o ).
thf(func_def_314,type,
sP1: $i > $i > $o ).
thf(func_def_315,type,
sP2: $i > $o ).
thf(func_def_316,type,
sP3: $o ).
thf(func_def_319,type,
sK6: $i > $o ).
thf(func_def_324,type,
sK11: $i > $i > $i > $i ).
thf(func_def_329,type,
sK16: $i > $o ).
thf(func_def_348,type,
sK35: $i > ( $i > $o ) > $i ).
thf(func_def_349,type,
sK36: $i > $o ).
thf(func_def_365,type,
sK52: $i > $o ).
thf(func_def_368,type,
sK55: $i > $i > ( $i > $o ) > $i ).
thf(func_def_375,type,
sK62: $i > $i > $i > $i > $i ).
thf(func_def_376,type,
sK63: $i > $i > $i > $i > $i ).
thf(func_def_381,type,
sK68: $i > $i > $i > $i > $i ).
thf(func_def_386,type,
sK73: $i > $o ).
thf(func_def_388,type,
sK75: ( $i > $o ) > $i ).
thf(func_def_389,type,
sK76: ( $i > $o ) > $i ).
thf(func_def_390,type,
sK77: $i > $i ).
thf(func_def_393,type,
sK80: $i > $i > ( $i > $i ) > $i ).
thf(func_def_403,type,
sK90: $o ).
thf(func_def_404,type,
sK91: $i > $i > $i > $i > $i ).
thf(func_def_416,type,
sK103: $i > $o ).
thf(func_def_419,type,
sK106: $i > ( $i > $o ) > $i ).
thf(func_def_429,type,
sK116: $i > $o ).
thf(func_def_434,type,
sK121: $i > $i > $o ).
thf(func_def_436,type,
sK123: $o ).
thf(func_def_437,type,
sK124: $i > ( $i > $i > $o ) > $i ).
thf(func_def_438,type,
sK125: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_439,type,
sK126: $i > ( $i > $i > $o ) > $i ).
thf(func_def_440,type,
sK127: $i > $i > $o ).
thf(func_def_442,type,
sK129: $i > $i ).
thf(func_def_443,type,
sK130: $i > $i ).
thf(func_def_460,type,
sK147: $i > $i > $o ).
thf(func_def_485,type,
sK172: $i > $o ).
thf(func_def_491,type,
sK178: $i > $o ).
thf(func_def_493,type,
sK180: $i > $o ).
thf(func_def_495,type,
sK182: ( $i > $o ) > $i > $i ).
thf(func_def_511,type,
sK198: $i > $i > $i ).
thf(func_def_514,type,
sK201: $i > $i > $i > $i ).
thf(func_def_515,type,
sK202: $i > $i > $i > $i ).
thf(func_def_519,type,
sK206: $i > ( $i > $o ) > $i ).
thf(func_def_520,type,
sK207: $i > $o ).
thf(func_def_529,type,
sK216: $o ).
thf(func_def_543,type,
sK230: $i > $o ).
thf(func_def_544,type,
sK231: $i > ( $i > $i ) > $i > $i ).
thf(func_def_546,type,
sK233: $i > $i ).
thf(func_def_562,type,
sK249: $i > $i > $o ).
thf(func_def_573,type,
sK260: $i > $i ).
thf(func_def_574,type,
sK261: $i > $i ).
thf(func_def_575,type,
sK262: $i > $o ).
thf(func_def_578,type,
sK265: $i > $i > $i ).
thf(func_def_592,type,
sK279: $i > $i ).
thf(func_def_594,type,
sK281: $i > ( $i > $i ) > $i > $i ).
thf(func_def_599,type,
sK286: $o ).
thf(func_def_600,type,
sK287: $o > $i > $i > $i ).
thf(func_def_603,type,
sK290: $o ).
thf(func_def_606,type,
sK293: $i > $i > $o ).
thf(func_def_612,type,
sK299: $i > $o ).
thf(func_def_614,type,
sK301: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_615,type,
sK302: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_624,type,
sK311: $i > $i > $i ).
thf(func_def_627,type,
sK314: ( $i > $o ) > $i > $i ).
thf(func_def_629,type,
sK316: $i > $o ).
thf(func_def_631,type,
sK318: $o ).
thf(func_def_636,type,
sK323: $o ).
thf(func_def_644,type,
sK331: $i > $o ).
thf(func_def_657,type,
sK344: $i > $i > $i > $i ).
thf(func_def_658,type,
sK345: $i > $i > $i > $i ).
thf(func_def_666,type,
sK353: $i > $i > $i ).
thf(func_def_667,type,
sK354: $i > $i > $i ).
thf(func_def_669,type,
sK356: $i > $o ).
thf(func_def_671,type,
sK358: ( $i > $o ) > $i > $i ).
thf(func_def_689,type,
sK376: $i > $o ).
thf(func_def_692,type,
sK379: $i > ( $i > $o ) > $i ).
thf(func_def_693,type,
sK380: $i > ( $i > $o ) > $i ).
thf(func_def_697,type,
sK384: $o ).
thf(func_def_710,type,
sK397: $i > $i > $i ).
thf(func_def_711,type,
sK398: $o ).
thf(func_def_730,type,
sK417: $i > $i ).
thf(func_def_735,type,
sK422: $i > $i > $i ).
thf(func_def_755,type,
sK442: $i > $i > $i > $i > $i ).
thf(func_def_756,type,
sK443: $i > $i > $i > $i > $i ).
thf(func_def_757,type,
sK444: $i > $i > $i > $i > $i ).
thf(func_def_758,type,
sK445: $i > $i > $i > $i > $i ).
thf(func_def_759,type,
sK446: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_760,type,
sK447: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_761,type,
sK448: $i > $o ).
thf(func_def_762,type,
sK449: $i > $o ).
thf(func_def_764,type,
sK451: $i > $i ).
thf(func_def_765,type,
sK452: $i > $i ).
thf(func_def_766,type,
sK453: $i > $i ).
thf(func_def_767,type,
sK454: $i > $i ).
thf(func_def_768,type,
sK455: $i > $i ).
thf(func_def_769,type,
sK456: $i > $i > $i > $i ).
thf(func_def_770,type,
sK457: $i > $i ).
thf(func_def_771,type,
sK458: $i > $i ).
thf(func_def_772,type,
sK459: $i > $i ).
thf(func_def_773,type,
sK460: $i > $i ).
thf(func_def_774,type,
sK461: $i > $i > $i ).
thf(func_def_775,type,
sK462: $i > $i > $i > $i ).
thf(func_def_776,type,
sK463: $i > $i > $i > $i ).
thf(func_def_777,type,
sK464: $i > $i > $i > $i ).
thf(func_def_778,type,
sK465: $i > $i > $i ).
thf(func_def_779,type,
sK466: $i > $i > $i ).
thf(func_def_780,type,
sK467: $i > $i > $i ).
thf(func_def_781,type,
sK468: $i > $i > $i ).
thf(func_def_784,type,
sK471: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_785,type,
sK472: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_789,type,
sK476: $i > $o ).
thf(func_def_799,type,
sK486: $o ).
thf(func_def_804,type,
sK491: $i > $i ).
thf(func_def_806,type,
sK493: $i > ( $i > $i ) > $i > $i ).
thf(func_def_818,type,
sK505: $i > $i > $i ).
thf(func_def_841,type,
sK528: $i > $i > $o ).
thf(func_def_866,type,
sK553: $i > $i ).
thf(func_def_876,type,
sK563: $o ).
thf(func_def_880,type,
sK567: ( $i > $i ) > $i > $i > $i ).
thf(func_def_883,type,
sK570: $i > $i ).
thf(func_def_887,type,
sK574: $o ).
thf(func_def_889,type,
sK576: $i > ( $i > $i ) > $i > $i ).
thf(func_def_891,type,
sK578: $i > $i ).
thf(func_def_894,type,
sK581: $i > $i ).
thf(func_def_895,type,
sK582: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_896,type,
sK583: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_897,type,
sK584: $i > $o ).
thf(func_def_898,type,
sK585: $i > $o ).
thf(func_def_899,type,
sK586: ( $i > $o ) > $i ).
thf(func_def_900,type,
sK587: $i > $o ).
thf(func_def_901,type,
sK588: $i > $i ).
thf(func_def_904,type,
sK591: $i > $o ).
thf(func_def_907,type,
sK594: $i > $o ).
thf(func_def_909,type,
sK596: $i > ( $i > $o ) > $i ).
thf(func_def_910,type,
sK597: $i > $o ).
thf(func_def_914,type,
sK601: $i > $i > $i ).
thf(func_def_920,type,
sK607: $o ).
thf(func_def_924,type,
sK611: $o ).
thf(func_def_952,type,
sK639: $i > $o ).
thf(func_def_967,type,
sK654: $i > $o ).
thf(func_def_978,type,
sK665: $i > $o ).
thf(func_def_979,type,
sK666: ( $i > $o ) > $i > $i ).
thf(func_def_986,type,
sK673: $i > $i > $i > $i ).
thf(func_def_993,type,
sK680: $i > $i > $o ).
thf(func_def_1007,type,
sK694: $i > $i > $i ).
thf(func_def_1014,type,
sK701: $i > ( $i > $o ) > $i ).
thf(func_def_1015,type,
sK702: $i > ( $i > $o ) > $i ).
thf(func_def_1016,type,
sK703: $i > $o ).
thf(func_def_1023,type,
sK710: $o ).
thf(func_def_1041,type,
sK728: $o ).
thf(func_def_1052,type,
sK739: ( $i > $o ) > $i ).
thf(func_def_1053,type,
sK740: $i > $o ).
thf(func_def_1054,type,
sK741: $i > $i ).
thf(func_def_1060,type,
sK747: $i > $i ).
thf(func_def_1063,type,
sK750: $o ).
thf(func_def_1077,type,
sK764: $i > $i > $i > $i > $i ).
thf(func_def_1090,type,
sK777: $i > $o ).
thf(func_def_1095,type,
sK782: $i > $i > $o ).
thf(func_def_1109,type,
sK796: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1110,type,
sK797: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1113,type,
sK800: $i > $o ).
thf(func_def_1114,type,
sK801: $i > $o ).
thf(func_def_1120,type,
sK807: $i > $i ).
thf(func_def_1121,type,
sK808: $i > ( $i > $o ) > $i ).
thf(func_def_1122,type,
sK809: $i > $o ).
thf(func_def_1133,type,
sK820: ( $i > $o ) > $i ).
thf(func_def_1134,type,
sK821: $i > $o ).
thf(f120,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(f265,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) )
= inComplementUnionImpNotIn1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(f266,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
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
thf(f267,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
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f266]) ).
thf(f347,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
inference(rectify,[],[f120]) ).
thf(f348,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f347]) ).
thf(f527,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) )
= inComplementUnionImpNotIn1 ),
inference(rectify,[],[f265]) ).
thf(f528,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(fool_elimination,[],[f527]) ).
thf(f751,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
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f267]) ).
thf(f752,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f751]) ).
thf(f794,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f348]) ).
thf(f809,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(flattening,[],[f528]) ).
thf(f923,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(ennf_transformation,[],[f809]) ).
thf(f924,plain,
( ( inComplementUnionImpNotIn1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f923]) ).
thf(f997,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( 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,[],[f752]) ).
thf(f998,plain,
( ( cartprodmempaircEq = $true )
& ( theprop = $true )
& ( omegaIndAx = $true )
& ( eqinunit = $true )
& ( sepSubset = $true )
& ( symdiffI2 = $true )
& ( inCongP = $true )
& ( cartprodpairmemEL = $true )
& ( setunionAx = $true )
& ( cartprodsndin = $true )
& ( singletonprop = $true )
& ( in__Cong = $true )
& ( iffalseProp1 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR = $true )
& ( nonemptyI = $true )
& ( emptyset__Cong = $true )
& ( binunionTIRcontra = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true ) ) ) )
& ( setukpairIR = $true )
& ( doubleComplementSub1 = $true )
& ( cartprodpairmemER = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair = $true )
& ( setoftrueEq = $true )
& ( upairinpowunion = $true )
& ( complementImpComplementIntersect = $true )
& ( ksndsingleton = $true )
& ( funcext2 = $true )
& ( singletonsubset = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( iftrue = $true )
& ( subsetE2 = $true )
& ( complementTI1 = $true )
& ( subPowSU = $true )
& ( funcext = $true )
& ( brelnall1 = $true )
& ( setunionI = $true )
& ( lam2lamEq = $true )
& ( setadjoinE = $true )
& ( cartprodfstin = $true )
& ( notequalI2 = $true )
& ( eqbreln = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinOr = $true )
& ( ex1I = $true )
& ( nonemptyImpWitness = $true )
& ( funcGraphProp1 = $true )
& ( setukpairinjL1 = $true )
& ( iffalseProp2 = $true )
& ( iftrueProp2 = $true )
& ( funcGraphProp2 = $true )
& ( contrasubsetT3 = $true )
& ( funcGraphProp3 = $true )
& ( doubleComplementE1 = $true )
& ( setminusSubset2 = $true )
& ( complementTcontraSubset = $true )
& ( setminusIRneg = $true )
& ( nonemptyE1 = $true )
& ( cartprodpairin = $true )
& ( subsetE = $true )
& ( binunionTILcontra = $true )
& ( singletoninpowerset = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL = $true )
& ( emptyinunitempty = $true )
& ( binunionRsub = $true )
& ( contrasubsetT = $true )
& ( upairsetE = $true )
& ( setminusEL = $true )
& ( notsubsetI = $true )
& ( subsetI1 = $true )
& ( theeq = $true )
& ( powersetsubset = $true )
& ( ex1I2 = $true )
& ( dsetconstrI = $true )
& ( setadjoinSub = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( exuEu = $true )
& ( setunionsingleton1 = $true )
& ( subsetI2 = $true )
& ( lamp = $true )
& ( disjointsetsI1 = $true )
& ( upairsetIR = $true )
& ( kfstsingleton = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( iftrueProp1 = $true )
& ( setunionE2 = $true )
& ( powersetTE1 = $true )
& ( eqimpsubset1 = $true )
& ( powersetE = $true )
& ( binintersectER = $true )
& ( beta1 = $true )
& ( binintersectT_lem = $true )
& ( funcinfuncset = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( funcextLem = $true )
& ( binintersectSubset2 = $true )
& ( setOfPairsIsBReln = $true )
& ( subset2powerset = $true )
& ( dpsetconstrEL1 = $true )
& ( powersetAx = $true )
& ( ifp = $true )
& ( setminusILneg = $true )
& ( eqimpsubset2 = $true )
& ( cartprodsndpairEq = $true )
& ( inPowerset = $true )
& ( kpairp = $true )
& ( notinsingleton = $true )
& ( doubleComplementSub2 = $true )
& ( emptysetsubset = $true )
& ( emptyE1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( emptysetE = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectEL = $true )
& ( upairsubunion = $true )
& ( emptyinPowerset = $true )
& ( setminusSubset1 = $true )
& ( symdiffIneg2 = $true )
& ( exuE1 = $true )
& ( binunionIR = $true )
& ( noeltsimpempty = $true )
& ( exuE3e = $true )
& ( contraSubsetComplement = $true )
& ( setukpairinjL2 = $true )
& ( upairset2IR = $true )
& ( omega0Ax = $true )
& ( emptyI = $true )
& ( funcGraphProp4 = $true )
& ( funcImageSingleton = $true )
& ( bs114d = $true )
& ( ksndpairEq = $true )
& ( dsetconstrER = $true )
& ( ap2apEq2 = $true )
& ( setminusELneg = $true )
& ( singletonsuniq = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan1 = $true )
& ( setminusI = $true )
& ( dsetconstrEL = $true )
& ( setminusLsub = $true )
& ( binintersectRsub = $true )
& ( dpsetconstrEL2 = $true )
& ( eta2 = $true )
& ( setextsub = $true )
& ( cartprodfstpairEq = $true )
& ( complementT_lem = $true )
& ( contrasubsetT1 = $true )
& ( lamProp = $true )
& ( app = $true )
& ( binintersectI = $true )
& ( powersetTI1 = $true )
& ( binunionLsub = $true )
& ( setextT = $true )
& ( inIntersectImpInUnion = $true )
& ( exuI1 = $true )
& ( kfstpairEq = $true )
& ( dpsetconstrI = $true )
& ( replAx = $true )
& ( notequalI1 = $true )
& ( binintersectSubset3 = $true )
& ( wellorderingAx = $true )
& ( beta2 = $true )
& ( doubleComplementEq = $true )
& ( upairequniteq = $true )
& ( ubforcartprodlem3 = $true )
& ( complementTnotintersectT = $true )
& ( powerset__Cong = $true )
& ( complementTE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE2 = $true )
& ( lam2p = $true )
& ( upairset2E = $true )
& ( emptyInPowerset = $true )
& ( symdiffIneg1 = $true )
& ( setminusER = $true )
& ( infuncsetfunc = $true )
& ( notinemptyset = $true )
& ( dpsetconstrERa = $true )
& ( powersetI1 = $true )
& ( subsetTrans = $true )
& ( binintersectLsub = $true )
& ( binintersectTERcontra = $true )
& ( binunionIL = $true )
& ( setextAx = $true )
& ( binunionEcases = $true )
& ( subbreln = $true )
& ( iftrueorfalse = $true )
& ( exuI3 = $true )
& ( ap2apEq1 = $true )
& ( setadjoinAx = $true )
& ( binintersectTELcontra = $true )
& ( doubleComplementI1 = $true )
& ( descrp = $true )
& ( kpairsurjEq = $true )
& ( nonemptyI1 = $true )
& ( symdiffE = $true )
& ( setadjoinIR = $true )
& ( brelnall2 = $true )
& ( upairsetIL = $true )
& ( subsetTI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( sepInPowerset = $true )
& ( ubforcartprodlem1 = $true )
& ( foundationAx = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setunionsingleton = $true )
& ( subsetRefl = $true )
& ( powersetT_lem = $true )
& ( exuI2 = $true )
& ( binunionE = $true )
& ( notdallE = $true )
& ( dpsetconstrSub = $true )
& ( uniqinunit = $true )
& ( notdexE = $true )
& ( ex1E1 = $true )
& ( emptysetAx = $true )
& ( ex1E2 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( setunionsingleton2 = $true )
& ( exuE3u = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( secondinupair = $true )
& ( ap2p = $true )
& ( exu__Cong = $true )
& ( setukpairinjR1 = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( iffalse = $true )
& ( descr__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( eta1 = $true )
& ( cartprodmempair1 = $true )
& ( singletoninpowunion = $true )
& ( setminusT_lem = $true )
& ( powersetE1 = $true )
& ( setminusERneg = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR2 = $true )
& ( setukpairIL = $true )
& ( contrasubsetT2 = $true )
& ( setext = $true )
& ( binunionT_lem = $true )
& ( prop2set2propI = $true )
& ( setadjoinSub2 = $true )
& ( emptysetimpfalse = $true )
& ( ifSingleton = $true )
& ( setadjoinIL = $true )
& ( symdiffI1 = $true )
& ( dsetconstr__Cong = $true )
& ( omegaSAx = $true )
& ( setadjoin__Cong = $true )
& ( setunionE = $true ) ),
inference(flattening,[],[f997]) ).
thf(f1125,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[],[f794]) ).
thf(f1126,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f1125]) ).
thf(f1673,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f1126]) ).
thf(f1674,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( $true
!= ( in @ X3 @ X4 ) )
& ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true ) ) ) ),
inference(rectify,[],[f1673]) ).
thf(f1675,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( ( in @ sK564 @ sK566 )
= $true )
& ( ( in @ sK564 @ sK565 )
!= $true )
& ( $true
!= ( in @ sK564 @ ( setminus @ sK566 @ sK565 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK564,sK565,sK566]),skolemize(X3,sK564),skolemize(X4,sK565),skolemize(X5,sK566)],[f1674]) ).
thf(f1866,plain,
( ( ( inComplementUnionImpNotIn1 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( inComplementUnionImpNotIn1 != $true ) ) ),
inference(nnf_transformation,[],[f924]) ).
thf(f1867,plain,
( ( ( inComplementUnionImpNotIn1 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) ) )
| ( ( in @ X7 @ X5 )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( inComplementUnionImpNotIn1 != $true ) ) ),
inference(rectify,[],[f1866]) ).
thf(f1868,plain,
( ( ( inComplementUnionImpNotIn1 = $true )
| ( ( ( in @ sK762 @ ( powerset @ sK760 ) )
= $true )
& ( ( in @ sK763 @ ( setminus @ sK760 @ ( binunion @ sK761 @ sK762 ) ) )
= $true )
& ( ( in @ sK763 @ sK761 )
= $true )
& ( ( in @ sK763 @ sK760 )
= $true )
& ( ( in @ sK761 @ ( powerset @ sK760 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) ) )
| ( ( in @ X7 @ X5 )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( inComplementUnionImpNotIn1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK760,sK761,sK762,sK763]),skolemize(X0,sK760),skolemize(X1,sK761),skolemize(X2,sK762),skolemize(X3,sK763)],[f1867]) ).
thf(f1905,plain,
( ( cartprodmempaircEq = $true )
& ( theprop = $true )
& ( omegaIndAx = $true )
& ( eqinunit = $true )
& ( sepSubset = $true )
& ( symdiffI2 = $true )
& ( inCongP = $true )
& ( cartprodpairmemEL = $true )
& ( setunionAx = $true )
& ( cartprodsndin = $true )
& ( singletonprop = $true )
& ( in__Cong = $true )
& ( iffalseProp1 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR = $true )
& ( nonemptyI = $true )
& ( emptyset__Cong = $true )
& ( binunionTIRcontra = $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 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) )
& ( setukpairIR = $true )
& ( doubleComplementSub1 = $true )
& ( cartprodpairmemER = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair = $true )
& ( setoftrueEq = $true )
& ( upairinpowunion = $true )
& ( complementImpComplementIntersect = $true )
& ( ksndsingleton = $true )
& ( funcext2 = $true )
& ( singletonsubset = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( iftrue = $true )
& ( subsetE2 = $true )
& ( complementTI1 = $true )
& ( subPowSU = $true )
& ( funcext = $true )
& ( brelnall1 = $true )
& ( setunionI = $true )
& ( lam2lamEq = $true )
& ( setadjoinE = $true )
& ( cartprodfstin = $true )
& ( notequalI2 = $true )
& ( eqbreln = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinOr = $true )
& ( ex1I = $true )
& ( nonemptyImpWitness = $true )
& ( funcGraphProp1 = $true )
& ( setukpairinjL1 = $true )
& ( iffalseProp2 = $true )
& ( iftrueProp2 = $true )
& ( funcGraphProp2 = $true )
& ( contrasubsetT3 = $true )
& ( funcGraphProp3 = $true )
& ( doubleComplementE1 = $true )
& ( setminusSubset2 = $true )
& ( complementTcontraSubset = $true )
& ( setminusIRneg = $true )
& ( nonemptyE1 = $true )
& ( cartprodpairin = $true )
& ( subsetE = $true )
& ( binunionTILcontra = $true )
& ( singletoninpowerset = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL = $true )
& ( emptyinunitempty = $true )
& ( binunionRsub = $true )
& ( contrasubsetT = $true )
& ( upairsetE = $true )
& ( setminusEL = $true )
& ( notsubsetI = $true )
& ( subsetI1 = $true )
& ( theeq = $true )
& ( powersetsubset = $true )
& ( ex1I2 = $true )
& ( dsetconstrI = $true )
& ( setadjoinSub = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( exuEu = $true )
& ( setunionsingleton1 = $true )
& ( subsetI2 = $true )
& ( lamp = $true )
& ( disjointsetsI1 = $true )
& ( upairsetIR = $true )
& ( kfstsingleton = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( iftrueProp1 = $true )
& ( setunionE2 = $true )
& ( powersetTE1 = $true )
& ( eqimpsubset1 = $true )
& ( powersetE = $true )
& ( binintersectER = $true )
& ( beta1 = $true )
& ( binintersectT_lem = $true )
& ( funcinfuncset = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( funcextLem = $true )
& ( binintersectSubset2 = $true )
& ( setOfPairsIsBReln = $true )
& ( subset2powerset = $true )
& ( dpsetconstrEL1 = $true )
& ( powersetAx = $true )
& ( ifp = $true )
& ( setminusILneg = $true )
& ( eqimpsubset2 = $true )
& ( cartprodsndpairEq = $true )
& ( inPowerset = $true )
& ( kpairp = $true )
& ( notinsingleton = $true )
& ( doubleComplementSub2 = $true )
& ( emptysetsubset = $true )
& ( emptyE1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( emptysetE = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectEL = $true )
& ( upairsubunion = $true )
& ( emptyinPowerset = $true )
& ( setminusSubset1 = $true )
& ( symdiffIneg2 = $true )
& ( exuE1 = $true )
& ( binunionIR = $true )
& ( noeltsimpempty = $true )
& ( exuE3e = $true )
& ( contraSubsetComplement = $true )
& ( setukpairinjL2 = $true )
& ( upairset2IR = $true )
& ( omega0Ax = $true )
& ( emptyI = $true )
& ( funcGraphProp4 = $true )
& ( funcImageSingleton = $true )
& ( bs114d = $true )
& ( ksndpairEq = $true )
& ( dsetconstrER = $true )
& ( ap2apEq2 = $true )
& ( setminusELneg = $true )
& ( singletonsuniq = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan1 = $true )
& ( setminusI = $true )
& ( dsetconstrEL = $true )
& ( setminusLsub = $true )
& ( binintersectRsub = $true )
& ( dpsetconstrEL2 = $true )
& ( eta2 = $true )
& ( setextsub = $true )
& ( cartprodfstpairEq = $true )
& ( complementT_lem = $true )
& ( contrasubsetT1 = $true )
& ( lamProp = $true )
& ( app = $true )
& ( binintersectI = $true )
& ( powersetTI1 = $true )
& ( binunionLsub = $true )
& ( setextT = $true )
& ( inIntersectImpInUnion = $true )
& ( exuI1 = $true )
& ( kfstpairEq = $true )
& ( dpsetconstrI = $true )
& ( replAx = $true )
& ( notequalI1 = $true )
& ( binintersectSubset3 = $true )
& ( wellorderingAx = $true )
& ( beta2 = $true )
& ( doubleComplementEq = $true )
& ( upairequniteq = $true )
& ( ubforcartprodlem3 = $true )
& ( complementTnotintersectT = $true )
& ( powerset__Cong = $true )
& ( complementTE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE2 = $true )
& ( lam2p = $true )
& ( upairset2E = $true )
& ( emptyInPowerset = $true )
& ( symdiffIneg1 = $true )
& ( setminusER = $true )
& ( infuncsetfunc = $true )
& ( notinemptyset = $true )
& ( dpsetconstrERa = $true )
& ( powersetI1 = $true )
& ( subsetTrans = $true )
& ( binintersectLsub = $true )
& ( binintersectTERcontra = $true )
& ( binunionIL = $true )
& ( setextAx = $true )
& ( binunionEcases = $true )
& ( subbreln = $true )
& ( iftrueorfalse = $true )
& ( exuI3 = $true )
& ( ap2apEq1 = $true )
& ( setadjoinAx = $true )
& ( binintersectTELcontra = $true )
& ( doubleComplementI1 = $true )
& ( descrp = $true )
& ( kpairsurjEq = $true )
& ( nonemptyI1 = $true )
& ( symdiffE = $true )
& ( setadjoinIR = $true )
& ( brelnall2 = $true )
& ( upairsetIL = $true )
& ( subsetTI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( sepInPowerset = $true )
& ( ubforcartprodlem1 = $true )
& ( foundationAx = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setunionsingleton = $true )
& ( subsetRefl = $true )
& ( powersetT_lem = $true )
& ( exuI2 = $true )
& ( binunionE = $true )
& ( notdallE = $true )
& ( dpsetconstrSub = $true )
& ( uniqinunit = $true )
& ( notdexE = $true )
& ( ex1E1 = $true )
& ( emptysetAx = $true )
& ( ex1E2 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( setunionsingleton2 = $true )
& ( exuE3u = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( secondinupair = $true )
& ( ap2p = $true )
& ( exu__Cong = $true )
& ( setukpairinjR1 = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( iffalse = $true )
& ( descr__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( eta1 = $true )
& ( cartprodmempair1 = $true )
& ( singletoninpowunion = $true )
& ( setminusT_lem = $true )
& ( powersetE1 = $true )
& ( setminusERneg = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR2 = $true )
& ( setukpairIL = $true )
& ( contrasubsetT2 = $true )
& ( setext = $true )
& ( binunionT_lem = $true )
& ( prop2set2propI = $true )
& ( setadjoinSub2 = $true )
& ( emptysetimpfalse = $true )
& ( ifSingleton = $true )
& ( setadjoinIL = $true )
& ( symdiffI1 = $true )
& ( dsetconstr__Cong = $true )
& ( omegaSAx = $true )
& ( setadjoin__Cong = $true )
& ( setunionE = $true ) ),
inference(rectify,[],[f998]) ).
thf(f1906,plain,
( ( cartprodmempaircEq = $true )
& ( theprop = $true )
& ( omegaIndAx = $true )
& ( eqinunit = $true )
& ( sepSubset = $true )
& ( symdiffI2 = $true )
& ( inCongP = $true )
& ( cartprodpairmemEL = $true )
& ( setunionAx = $true )
& ( cartprodsndin = $true )
& ( singletonprop = $true )
& ( in__Cong = $true )
& ( iffalseProp1 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR = $true )
& ( nonemptyI = $true )
& ( emptyset__Cong = $true )
& ( binunionTIRcontra = $true )
& ( $true
= ( in @ sK803 @ ( powerset @ sK802 ) ) )
& ( $true
= ( in @ sK804 @ ( powerset @ sK802 ) ) )
& ( $true
= ( in @ sK805 @ sK802 ) )
& ( ( in @ sK805 @ ( setminus @ sK802 @ ( binunion @ sK803 @ sK804 ) ) )
= $true )
& ( ( in @ sK805 @ ( setminus @ sK802 @ sK803 ) )
!= $true )
& ( setukpairIR = $true )
& ( doubleComplementSub1 = $true )
& ( cartprodpairmemER = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair = $true )
& ( setoftrueEq = $true )
& ( upairinpowunion = $true )
& ( complementImpComplementIntersect = $true )
& ( ksndsingleton = $true )
& ( funcext2 = $true )
& ( singletonsubset = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( iftrue = $true )
& ( subsetE2 = $true )
& ( complementTI1 = $true )
& ( subPowSU = $true )
& ( funcext = $true )
& ( brelnall1 = $true )
& ( setunionI = $true )
& ( lam2lamEq = $true )
& ( setadjoinE = $true )
& ( cartprodfstin = $true )
& ( notequalI2 = $true )
& ( eqbreln = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinOr = $true )
& ( ex1I = $true )
& ( nonemptyImpWitness = $true )
& ( funcGraphProp1 = $true )
& ( setukpairinjL1 = $true )
& ( iffalseProp2 = $true )
& ( iftrueProp2 = $true )
& ( funcGraphProp2 = $true )
& ( contrasubsetT3 = $true )
& ( funcGraphProp3 = $true )
& ( doubleComplementE1 = $true )
& ( setminusSubset2 = $true )
& ( complementTcontraSubset = $true )
& ( setminusIRneg = $true )
& ( nonemptyE1 = $true )
& ( cartprodpairin = $true )
& ( subsetE = $true )
& ( binunionTILcontra = $true )
& ( singletoninpowerset = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL = $true )
& ( emptyinunitempty = $true )
& ( binunionRsub = $true )
& ( contrasubsetT = $true )
& ( upairsetE = $true )
& ( setminusEL = $true )
& ( notsubsetI = $true )
& ( subsetI1 = $true )
& ( theeq = $true )
& ( powersetsubset = $true )
& ( ex1I2 = $true )
& ( dsetconstrI = $true )
& ( setadjoinSub = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( exuEu = $true )
& ( setunionsingleton1 = $true )
& ( subsetI2 = $true )
& ( lamp = $true )
& ( disjointsetsI1 = $true )
& ( upairsetIR = $true )
& ( kfstsingleton = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( iftrueProp1 = $true )
& ( setunionE2 = $true )
& ( powersetTE1 = $true )
& ( eqimpsubset1 = $true )
& ( powersetE = $true )
& ( binintersectER = $true )
& ( beta1 = $true )
& ( binintersectT_lem = $true )
& ( funcinfuncset = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( funcextLem = $true )
& ( binintersectSubset2 = $true )
& ( setOfPairsIsBReln = $true )
& ( subset2powerset = $true )
& ( dpsetconstrEL1 = $true )
& ( powersetAx = $true )
& ( ifp = $true )
& ( setminusILneg = $true )
& ( eqimpsubset2 = $true )
& ( cartprodsndpairEq = $true )
& ( inPowerset = $true )
& ( kpairp = $true )
& ( notinsingleton = $true )
& ( doubleComplementSub2 = $true )
& ( emptysetsubset = $true )
& ( emptyE1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( emptysetE = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectEL = $true )
& ( upairsubunion = $true )
& ( emptyinPowerset = $true )
& ( setminusSubset1 = $true )
& ( symdiffIneg2 = $true )
& ( exuE1 = $true )
& ( binunionIR = $true )
& ( noeltsimpempty = $true )
& ( exuE3e = $true )
& ( contraSubsetComplement = $true )
& ( setukpairinjL2 = $true )
& ( upairset2IR = $true )
& ( omega0Ax = $true )
& ( emptyI = $true )
& ( funcGraphProp4 = $true )
& ( funcImageSingleton = $true )
& ( bs114d = $true )
& ( ksndpairEq = $true )
& ( dsetconstrER = $true )
& ( ap2apEq2 = $true )
& ( setminusELneg = $true )
& ( singletonsuniq = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan1 = $true )
& ( setminusI = $true )
& ( dsetconstrEL = $true )
& ( setminusLsub = $true )
& ( binintersectRsub = $true )
& ( dpsetconstrEL2 = $true )
& ( eta2 = $true )
& ( setextsub = $true )
& ( cartprodfstpairEq = $true )
& ( complementT_lem = $true )
& ( contrasubsetT1 = $true )
& ( lamProp = $true )
& ( app = $true )
& ( binintersectI = $true )
& ( powersetTI1 = $true )
& ( binunionLsub = $true )
& ( setextT = $true )
& ( inIntersectImpInUnion = $true )
& ( exuI1 = $true )
& ( kfstpairEq = $true )
& ( dpsetconstrI = $true )
& ( replAx = $true )
& ( notequalI1 = $true )
& ( binintersectSubset3 = $true )
& ( wellorderingAx = $true )
& ( beta2 = $true )
& ( doubleComplementEq = $true )
& ( upairequniteq = $true )
& ( ubforcartprodlem3 = $true )
& ( complementTnotintersectT = $true )
& ( powerset__Cong = $true )
& ( complementTE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE2 = $true )
& ( lam2p = $true )
& ( upairset2E = $true )
& ( emptyInPowerset = $true )
& ( symdiffIneg1 = $true )
& ( setminusER = $true )
& ( infuncsetfunc = $true )
& ( notinemptyset = $true )
& ( dpsetconstrERa = $true )
& ( powersetI1 = $true )
& ( subsetTrans = $true )
& ( binintersectLsub = $true )
& ( binintersectTERcontra = $true )
& ( binunionIL = $true )
& ( setextAx = $true )
& ( binunionEcases = $true )
& ( subbreln = $true )
& ( iftrueorfalse = $true )
& ( exuI3 = $true )
& ( ap2apEq1 = $true )
& ( setadjoinAx = $true )
& ( binintersectTELcontra = $true )
& ( doubleComplementI1 = $true )
& ( descrp = $true )
& ( kpairsurjEq = $true )
& ( nonemptyI1 = $true )
& ( symdiffE = $true )
& ( setadjoinIR = $true )
& ( brelnall2 = $true )
& ( upairsetIL = $true )
& ( subsetTI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( sepInPowerset = $true )
& ( ubforcartprodlem1 = $true )
& ( foundationAx = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setunionsingleton = $true )
& ( subsetRefl = $true )
& ( powersetT_lem = $true )
& ( exuI2 = $true )
& ( binunionE = $true )
& ( notdallE = $true )
& ( dpsetconstrSub = $true )
& ( uniqinunit = $true )
& ( notdexE = $true )
& ( ex1E1 = $true )
& ( emptysetAx = $true )
& ( ex1E2 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( setunionsingleton2 = $true )
& ( exuE3u = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( secondinupair = $true )
& ( ap2p = $true )
& ( exu__Cong = $true )
& ( setukpairinjR1 = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( iffalse = $true )
& ( descr__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( eta1 = $true )
& ( cartprodmempair1 = $true )
& ( singletoninpowunion = $true )
& ( setminusT_lem = $true )
& ( powersetE1 = $true )
& ( setminusERneg = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR2 = $true )
& ( setukpairIL = $true )
& ( contrasubsetT2 = $true )
& ( setext = $true )
& ( binunionT_lem = $true )
& ( prop2set2propI = $true )
& ( setadjoinSub2 = $true )
& ( emptysetimpfalse = $true )
& ( ifSingleton = $true )
& ( setadjoinIL = $true )
& ( symdiffI1 = $true )
& ( dsetconstr__Cong = $true )
& ( omegaSAx = $true )
& ( setadjoin__Cong = $true )
& ( setunionE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK802,sK803,sK804,sK805]),skolemize(X0,sK802),skolemize(X1,sK803),skolemize(X2,sK804),skolemize(X3,sK805)],[f1905]) ).
thf(f2697,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( setminusI != $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f1675]) ).
thf(f2967,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( inComplementUnionImpNotIn1 != $true )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) ) )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) ) ),
inference(cnf_transformation,[],[f1868]) ).
thf(f3135,plain,
setminusI = $true,
inference(cnf_transformation,[],[f1906]) ).
thf(f3192,plain,
inComplementUnionImpNotIn1 = $true,
inference(cnf_transformation,[],[f1906]) ).
thf(f3261,plain,
( ( in @ sK805 @ ( setminus @ sK802 @ sK803 ) )
!= $true ),
inference(cnf_transformation,[],[f1906]) ).
thf(f3262,plain,
( ( in @ sK805 @ ( setminus @ sK802 @ ( binunion @ sK803 @ sK804 ) ) )
= $true ),
inference(cnf_transformation,[],[f1906]) ).
thf(f3263,plain,
( $true
= ( in @ sK805 @ sK802 ) ),
inference(cnf_transformation,[],[f1906]) ).
thf(f3264,plain,
( $true
= ( in @ sK804 @ ( powerset @ sK802 ) ) ),
inference(cnf_transformation,[],[f1906]) ).
thf(f3265,plain,
( $true
= ( in @ sK803 @ ( powerset @ sK802 ) ) ),
inference(cnf_transformation,[],[f1906]) ).
thf(f3689,definition,
( spl829_34
<=> ( $true
= ( in @ sK805 @ sK802 ) ) ),
introduced(definition,[new_symbols(definition,[spl829_34])],[avatar_definition]) ).
thf(f3691,plain,
( ( $true
= ( in @ sK805 @ sK802 ) )
| ~ spl829_34 ),
inference(avatar_component_clause,[],[f3689]) ).
thf(f3692,plain,
spl829_34,
inference(avatar_split_clause,[],[f3263,f3689]) ).
thf(f5120,definition,
( spl829_357
<=> ( setminusI = $true ) ),
introduced(definition,[new_symbols(definition,[spl829_357])],[avatar_definition]) ).
thf(f5543,definition,
( spl829_450
<=> ( inComplementUnionImpNotIn1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl829_450])],[avatar_definition]) ).
thf(f6637,definition,
( spl829_681
<=> ( ( in @ sK805 @ ( setminus @ sK802 @ ( binunion @ sK803 @ sK804 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl829_681])],[avatar_definition]) ).
thf(f6639,plain,
( ( ( in @ sK805 @ ( setminus @ sK802 @ ( binunion @ sK803 @ sK804 ) ) )
= $true )
| ~ spl829_681 ),
inference(avatar_component_clause,[],[f6637]) ).
thf(f6640,plain,
spl829_681,
inference(avatar_split_clause,[],[f3262,f6637]) ).
thf(f6973,plain,
spl829_450,
inference(avatar_split_clause,[],[f3192,f5543]) ).
thf(f7800,definition,
( spl829_923
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl829_923])],[avatar_definition]) ).
thf(f7801,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ~ spl829_923 ),
inference(avatar_component_clause,[],[f7800]) ).
thf(f8219,definition,
( spl829_1008
<=> ( ( in @ sK805 @ ( setminus @ sK802 @ sK803 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl829_1008])],[avatar_definition]) ).
thf(f8221,plain,
( ( ( in @ sK805 @ ( setminus @ sK802 @ sK803 ) )
!= $true )
| spl829_1008 ),
inference(avatar_component_clause,[],[f8219]) ).
thf(f8222,plain,
~ spl829_1008,
inference(avatar_split_clause,[],[f3261,f8219]) ).
thf(f8284,definition,
( spl829_1022
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl829_1022])],[avatar_definition]) ).
thf(f8285,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( ( in @ X7 @ X5 )
!= $true ) )
| ~ spl829_1022 ),
inference(avatar_component_clause,[],[f8284]) ).
thf(f8286,plain,
( ~ spl829_450
| spl829_1022 ),
inference(avatar_split_clause,[],[f2967,f8284,f5543]) ).
thf(f8714,plain,
spl829_357,
inference(avatar_split_clause,[],[f3135,f5120]) ).
thf(f9235,plain,
( ~ spl829_357
| spl829_923 ),
inference(avatar_split_clause,[],[f2697,f7800,f5120]) ).
thf(f9254,definition,
( spl829_1220
<=> ( $true
= ( in @ sK804 @ ( powerset @ sK802 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl829_1220])],[avatar_definition]) ).
thf(f9256,plain,
( ( $true
= ( in @ sK804 @ ( powerset @ sK802 ) ) )
| ~ spl829_1220 ),
inference(avatar_component_clause,[],[f9254]) ).
thf(f9257,plain,
spl829_1220,
inference(avatar_split_clause,[],[f3264,f9254]) ).
thf(f9490,definition,
( spl829_1269
<=> ( $true
= ( in @ sK803 @ ( powerset @ sK802 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl829_1269])],[avatar_definition]) ).
thf(f9492,plain,
( ( $true
= ( in @ sK803 @ ( powerset @ sK802 ) ) )
| ~ spl829_1269 ),
inference(avatar_component_clause,[],[f9490]) ).
thf(f9493,plain,
spl829_1269,
inference(avatar_split_clause,[],[f3265,f9490]) ).
thf(f9831,plain,
( ( $true != $true )
| ( ( in @ sK805 @ sK803 )
!= $true )
| ( $true
!= ( in @ sK804 @ ( powerset @ sK802 ) ) )
| ( $true
!= ( in @ sK805 @ sK802 ) )
| ( $true
!= ( in @ sK803 @ ( powerset @ sK802 ) ) )
| ~ spl829_681
| ~ spl829_1022 ),
inference(superposition,[],[f8285,f6639]) ).
thf(f9834,plain,
( ( $true
!= ( in @ sK803 @ ( powerset @ sK802 ) ) )
| ( $true
!= ( in @ sK804 @ ( powerset @ sK802 ) ) )
| ( $true
!= ( in @ sK805 @ sK802 ) )
| ( ( in @ sK805 @ sK803 )
!= $true )
| ~ spl829_681
| ~ spl829_1022 ),
inference(trivial_inequality_removal,[],[f9831]) ).
thf(f9840,plain,
( ( ( in @ sK805 @ sK803 )
!= $true )
| ( $true
!= ( in @ sK805 @ sK802 ) )
| ( $true
!= ( in @ sK804 @ ( powerset @ sK802 ) ) )
| ~ spl829_681
| ~ spl829_1022
| ~ spl829_1269 ),
inference(forward_subsumption_resolution,[],[f9834,f9492]) ).
thf(f9841,plain,
( ( $true
!= ( in @ sK804 @ ( powerset @ sK802 ) ) )
| ( ( in @ sK805 @ sK803 )
!= $true )
| ~ spl829_34
| ~ spl829_681
| ~ spl829_1022
| ~ spl829_1269 ),
inference(forward_subsumption_resolution,[],[f9840,f3691]) ).
thf(f9842,plain,
( ( ( in @ sK805 @ sK803 )
!= $true )
| ~ spl829_34
| ~ spl829_681
| ~ spl829_1022
| ~ spl829_1220
| ~ spl829_1269 ),
inference(forward_subsumption_resolution,[],[f9841,f9256]) ).
thf(f9844,definition,
( spl829_1328
<=> ( ( in @ sK805 @ sK803 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl829_1328])],[avatar_definition]) ).
thf(f9846,plain,
( ( ( in @ sK805 @ sK803 )
!= $true )
| spl829_1328 ),
inference(avatar_component_clause,[],[f9844]) ).
thf(f9847,plain,
( ~ spl829_1328
| ~ spl829_34
| ~ spl829_681
| ~ spl829_1022
| ~ spl829_1220
| ~ spl829_1269 ),
inference(avatar_split_clause,[],[f9842,f9490,f9254,f8284,f6637,f3689,f9844]) ).
thf(f12256,plain,
( ( $true
!= ( in @ sK805 @ sK802 ) )
| ( $true != $true )
| ( ( in @ sK805 @ sK803 )
= $true )
| ~ spl829_923
| spl829_1008 ),
inference(superposition,[],[f8221,f7801]) ).
thf(f12266,plain,
( ( $true
!= ( in @ sK805 @ sK802 ) )
| ( ( in @ sK805 @ sK803 )
= $true )
| ~ spl829_923
| spl829_1008 ),
inference(trivial_inequality_removal,[],[f12256]) ).
thf(f12276,plain,
( ( ( in @ sK805 @ sK803 )
= $true )
| ~ spl829_34
| ~ spl829_923
| spl829_1008 ),
inference(forward_subsumption_resolution,[],[f12266,f3691]) ).
thf(f12277,plain,
( $false
| ~ spl829_34
| ~ spl829_923
| spl829_1008
| spl829_1328 ),
inference(forward_subsumption_resolution,[],[f12276,f9846]) ).
thf(f12278,plain,
( ~ spl829_34
| ~ spl829_923
| spl829_1008
| spl829_1328 ),
inference(avatar_contradiction_clause,[],[f12277]) ).
cnf(s21,plain,
spl829_34,
inference(sat_conversion,[],[f3692]) ).
cnf(s544,plain,
spl829_681,
inference(sat_conversion,[],[f6640]) ).
cnf(s619,plain,
spl829_450,
inference(sat_conversion,[],[f6973]) ).
cnf(s933,plain,
~ spl829_1008,
inference(sat_conversion,[],[f8222]) ).
cnf(s949,plain,
( ~ spl829_450
| spl829_1022 ),
inference(sat_conversion,[],[f8286]) ).
cnf(s1062,plain,
spl829_357,
inference(sat_conversion,[],[f8714]) ).
cnf(s1202,plain,
( ~ spl829_357
| spl829_923 ),
inference(sat_conversion,[],[f9235]) ).
cnf(s1208,plain,
spl829_1220,
inference(sat_conversion,[],[f9257]) ).
cnf(s1268,plain,
spl829_1269,
inference(sat_conversion,[],[f9493]) ).
cnf(s1353,plain,
( ~ spl829_34
| ~ spl829_681
| ~ spl829_1022
| ~ spl829_1220
| ~ spl829_1269
| ~ spl829_1328 ),
inference(sat_conversion,[],[f9847]) ).
cnf(s1411,plain,
( ~ spl829_34
| ~ spl829_923
| spl829_1008
| spl829_1328 ),
inference(sat_conversion,[],[f12278]) ).
cnf(s1426,plain,
spl829_923,
inference(rat,[],[s1202,s1062]) ).
cnf(s1514,plain,
spl829_1022,
inference(rat,[],[s949,s619]) ).
cnf(s1759,plain,
spl829_1328,
inference(rat,[],[s1411,s933,s1426,s21]) ).
cnf(s1762,plain,
$false,
inference(rat,[],[s1353,s544,s1268,s1208,s1514,s1759,s21]) ).
thf(f12279,plain,
$false,
inference(avatar_sat_refutation,[],[s1762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU745^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n020.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:20:49 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.19/0.30 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
% 0.29/0.45 % (1122205)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.29/0.45 % (1122214)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=312720860:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.29/0.45 % (1122214)Instruction limit reached!
% 0.29/0.45 % (1122214)------------------------------
% 0.29/0.45 % (1122214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.45 % (1122214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.45 % (1122214)CaDiCaL version: 2.1.3
% 0.29/0.45 % (1122214)Termination reason: Instruction limit
% 0.29/0.45 % (1122214)Termination phase: shuffling
% 0.29/0.45 % (1122214)Time elapsed: 0.007 s
% 0.29/0.45 % (1122214)Peak memory usage: 10 MB
% 0.29/0.45 % (1122214)Instructions burned: 26 (million)
% 0.29/0.45 % (1122212)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3048087112:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.29/0.45 % (1122211)lrs+10_16_si=on:nwc=1.5:random_seed=982003297:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.29/0.45 % (1122210)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2402042524:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.29/0.45 % (1122213)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=3382924096: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)
% 0.29/0.45 % (1122212)Instruction limit reached!
% 0.29/0.45 % (1122212)------------------------------
% 0.29/0.45 % (1122212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.45 % (1122212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.45 % (1122212)CaDiCaL version: 2.1.3
% 0.29/0.45 % (1122212)Termination reason: Instruction limit
% 0.29/0.45 % (1122212)Termination phase: shuffling
% 0.29/0.45 % (1122212)Time elapsed: 0.002 s
% 0.29/0.45 % (1122212)Peak memory usage: 10 MB
% 0.29/0.45 % (1122212)Instructions burned: 3 (million)
% 0.29/0.45 % (1122216)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.29/0.45 % (1122216)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
% 0.29/0.45 % (1122215)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2012591310:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.29/0.45 % (1122211)Instruction limit reached!
% 0.29/0.45 % (1122211)------------------------------
% 0.29/0.45 % (1122211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.45 % (1122211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.45 % (1122211)CaDiCaL version: 2.1.3
% 0.29/0.45 % (1122211)Termination reason: Instruction limit
% 0.29/0.45 % (1122211)Termination phase: shuffling
% 0.29/0.45 % (1122211)Time elapsed: 0.009 s
% 0.29/0.45 % (1122211)Peak memory usage: 10 MB
% 0.29/0.45 % (1122211)Instructions burned: 19 (million)
% 0.29/0.45 % (1122216)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=1457357567:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.29/0.45 % (1122222)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2630316547:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.29/0.45 % (1122222)Instruction limit reached!
% 0.29/0.45 % (1122222)------------------------------
% 0.29/0.45 % (1122222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.45 % (1122223)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2496563881:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.29/0.45 % (1122222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.45 % (1122222)CaDiCaL version: 2.1.3
% 0.29/0.45 % (1122222)Termination reason: Instruction limit
% 0.29/0.45 % (1122222)Termination phase: shuffling
% 0.29/0.45 % (1122222)Time elapsed: 0.002 s
% 0.29/0.45 % (1122222)Peak memory usage: 10 MB
% 0.29/0.45 % (1122222)Instructions burned: 4 (million)
% 0.29/0.48 % (1122225)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.29/0.48 % (1122223)Instruction limit reached!
% 0.29/0.48 % (1122223)------------------------------
% 0.29/0.48 % (1122223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.48 % (1122223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.48 % (1122223)CaDiCaL version: 2.1.3
% 0.29/0.48 % (1122223)Termination reason: Instruction limit
% 0.29/0.48 % (1122223)Termination phase: shuffling
% 0.29/0.48 % (1122223)Time elapsed: 0.003 s
% 0.29/0.48 % (1122223)Peak memory usage: 10 MB
% 0.29/0.48 % (1122223)Instructions burned: 6 (million)
% 0.29/0.48 % (1122225)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2042520505:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.29/0.48 % (1122215)Instruction limit reached!
% 0.29/0.48 % (1122215)------------------------------
% 0.29/0.48 % (1122215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.48 % (1122215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.48 % (1122215)CaDiCaL version: 2.1.3
% 0.29/0.48 % (1122215)Termination reason: Instruction limit
% 0.29/0.48 % (1122215)Termination phase: Preprocessing 3
% 0.29/0.48 % (1122215)Time elapsed: 0.022 s
% 0.29/0.48 % (1122215)Peak memory usage: 13 MB
% 0.29/0.48 % (1122215)Instructions burned: 89 (million)
% 0.29/0.48 % (1122225)Instruction limit reached!
% 0.29/0.48 % (1122225)------------------------------
% 0.29/0.48 % (1122225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.48 % (1122225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.48 % (1122225)CaDiCaL version: 2.1.3
% 0.29/0.48 % (1122225)Termination reason: Instruction limit
% 0.29/0.48 % (1122225)Termination phase: shuffling
% 0.29/0.48 % (1122225)Time elapsed: 0.004 s
% 0.29/0.48 % (1122225)Peak memory usage: 10 MB
% 0.29/0.48 % (1122225)Instructions burned: 8 (million)
% 0.29/0.48 % (1122210)Instruction limit reached!
% 0.29/0.48 % (1122210)------------------------------
% 0.29/0.48 % (1122210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.48 % (1122210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.48 % (1122210)CaDiCaL version: 2.1.3
% 0.29/0.48 % (1122210)Termination reason: Instruction limit
% 0.29/0.48 % (1122210)Termination phase: Preprocessing 3
% 0.29/0.48 % (1122210)Time elapsed: 0.041 s
% 0.29/0.48 % (1122210)Peak memory usage: 13 MB
% 0.29/0.48 % (1122210)Instructions burned: 88 (million)
% 0.29/0.48 % (1122232)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=1424284715:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.29/0.48 % (1122230)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
% 0.29/0.48 % (1122230)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.29/0.48 % (1122229)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1783843703:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.29/0.48 % (1122230)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2077846227:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.29/0.48 % (1122229)Instruction limit reached!
% 0.29/0.48 % (1122229)------------------------------
% 0.29/0.48 % (1122229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.48 % (1122229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.48 % (1122229)CaDiCaL version: 2.1.3
% 0.29/0.48 % (1122229)Termination reason: Instruction limit
% 0.29/0.48 % (1122229)Termination phase: shuffling
% 0.29/0.48 % (1122229)Time elapsed: 0.007 s
% 0.29/0.48 % (1122229)Peak memory usage: 10 MB
% 0.29/0.48 % (1122229)Instructions burned: 13 (million)
% 0.29/0.48 % (1122233)lrs+10_1_si=on:cs=on:random_seed=2330167406:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.29/0.48 % (1122233)Instruction limit reached!
% 1.20/0.52 % (1122233)------------------------------
% 1.20/0.52 % (1122233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.52 % (1122233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.52 % (1122233)CaDiCaL version: 2.1.3
% 1.20/0.52 % (1122233)Termination reason: Instruction limit
% 1.20/0.52 % (1122233)Termination phase: shuffling
% 1.20/0.52 % (1122233)Time elapsed: 0.004 s
% 1.20/0.52 % (1122233)Peak memory usage: 10 MB
% 1.20/0.52 % (1122233)Instructions burned: 8 (million)
% 1.20/0.52 % (1122230)Instruction limit reached!
% 1.20/0.52 % (1122230)------------------------------
% 1.20/0.52 % (1122230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.52 % (1122230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.52 % (1122230)CaDiCaL version: 2.1.3
% 1.20/0.52 % (1122230)Termination reason: Instruction limit
% 1.20/0.52 % (1122230)Termination phase: shuffling
% 1.20/0.52 % (1122230)Time elapsed: 0.013 s
% 1.20/0.52 % (1122230)Peak memory usage: 11 MB
% 1.20/0.52 % (1122230)Instructions burned: 28 (million)
% 1.20/0.52 % (1122232)Instruction limit reached!
% 1.20/0.52 % (1122232)------------------------------
% 1.20/0.52 % (1122232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.52 % (1122232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.52 % (1122232)CaDiCaL version: 2.1.3
% 1.20/0.52 % (1122232)Termination reason: Instruction limit
% 1.20/0.52 % (1122232)Termination phase: Property scanning
% 1.20/0.52 % (1122232)Time elapsed: 0.019 s
% 1.20/0.52 % (1122232)Peak memory usage: 11 MB
% 1.20/0.52 % (1122232)Instructions burned: 87 (million)
% 1.20/0.52 % (1122235)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.20/0.52 % (1122235)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=4083288178:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.20/0.52 % (1122235)Instruction limit reached!
% 1.20/0.52 % (1122235)------------------------------
% 1.20/0.52 % (1122235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.52 % (1122235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.52 % (1122235)CaDiCaL version: 2.1.3
% 1.20/0.52 % (1122235)Termination reason: Instruction limit
% 1.20/0.52 % (1122235)Termination phase: shuffling
% 1.20/0.52 % (1122235)Time elapsed: 0.002 s
% 1.20/0.52 % (1122235)Peak memory usage: 10 MB
% 1.20/0.52 % (1122235)Instructions burned: 3 (million)
% 1.20/0.52 % (1122242)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3740238443:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.20/0.52 % (1122238)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3010097368:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.20/0.52 % (1122216)Instruction limit reached!
% 1.20/0.52 % (1122216)------------------------------
% 1.20/0.52 % (1122216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.52 % (1122216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.52 % (1122216)CaDiCaL version: 2.1.3
% 1.20/0.52 % (1122216)Termination reason: Instruction limit
% 1.20/0.52 % (1122216)Termination phase: Saturation
% 1.20/0.52 % (1122216)Time elapsed: 0.065 s
% 1.20/0.52 % (1122216)Peak memory usage: 13 MB
% 1.20/0.52 % (1122216)Instructions burned: 157 (million)
% 1.20/0.52 % (1122242)Instruction limit reached!
% 1.20/0.52 % (1122242)------------------------------
% 1.20/0.52 % (1122242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.52 % (1122242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.52 % (1122242)CaDiCaL version: 2.1.3
% 1.20/0.52 % (1122242)Termination reason: Instruction limit
% 1.20/0.52 % (1122242)Termination phase: shuffling
% 1.20/0.52 % (1122242)Time elapsed: 0.004 s
% 1.20/0.52 % (1122242)Peak memory usage: 10 MB
% 1.20/0.52 % (1122242)Instructions burned: 19 (million)
% 1.20/0.52 % (1122240)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1286965232:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.20/0.52 % (1122247)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2527622530:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.20/0.58 % (1122244)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2949777262:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.20/0.58 % (1122241)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2173416561:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.20/0.58 % (1122238)Instruction limit reached!
% 1.20/0.58 % (1122238)------------------------------
% 1.20/0.58 % (1122238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.58 % (1122238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.58 % (1122238)CaDiCaL version: 2.1.3
% 1.20/0.58 % (1122238)Termination reason: Instruction limit
% 1.20/0.58 % (1122238)Termination phase: Property scanning
% 1.20/0.58 % (1122238)Time elapsed: 0.017 s
% 1.20/0.58 % (1122238)Peak memory usage: 11 MB
% 1.20/0.58 % (1122238)Instructions burned: 39 (million)
% 1.20/0.58 % (1122247)Instruction limit reached!
% 1.20/0.58 % (1122247)------------------------------
% 1.20/0.58 % (1122247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.58 % (1122247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.58 % (1122247)CaDiCaL version: 2.1.3
% 1.20/0.58 % (1122247)Termination reason: Instruction limit
% 1.20/0.58 % (1122247)Termination phase: shuffling
% 1.20/0.58 % (1122247)Time elapsed: 0.004 s
% 1.20/0.58 % (1122247)Peak memory usage: 10 MB
% 1.20/0.58 % (1122247)Instructions burned: 17 (million)
% 1.20/0.58 % (1122248)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1751780127: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)
% 1.20/0.58 % (1122248)Instruction limit reached!
% 1.20/0.58 % (1122248)------------------------------
% 1.20/0.58 % (1122248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.58 % (1122248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.58 % (1122248)CaDiCaL version: 2.1.3
% 1.20/0.58 % (1122248)Termination reason: Instruction limit
% 1.20/0.58 % (1122248)Termination phase: shuffling
% 1.20/0.58 % (1122248)Time elapsed: 0.003 s
% 1.20/0.58 % (1122248)Peak memory usage: 10 MB
% 1.20/0.58 % (1122248)Instructions burned: 5 (million)
% 1.20/0.58 % (1122253)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2810290292:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.20/0.58 % (1122253)Instruction limit reached!
% 1.20/0.58 % (1122253)------------------------------
% 1.20/0.58 % (1122253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.58 % (1122253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.58 % (1122253)CaDiCaL version: 2.1.3
% 1.20/0.58 % (1122253)Termination reason: Instruction limit
% 1.20/0.58 % (1122253)Termination phase: shuffling
% 1.20/0.58 % (1122253)Time elapsed: 0.007 s
% 1.20/0.58 % (1122253)Peak memory usage: 11 MB
% 1.20/0.58 % (1122253)Instructions burned: 30 (million)
% 1.20/0.58 % (1122254)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2010276940:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.20/0.58 % (1122241)Instruction limit reached!
% 1.20/0.58 % (1122241)------------------------------
% 1.20/0.58 % (1122241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.58 % (1122241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.58 % (1122241)CaDiCaL version: 2.1.3
% 1.20/0.58 % (1122241)Termination reason: Instruction limit
% 1.20/0.58 % (1122241)Termination phase: Property scanning
% 1.20/0.58 % (1122241)Time elapsed: 0.022 s
% 1.20/0.58 % (1122241)Peak memory usage: 11 MB
% 1.20/0.58 % (1122241)Instructions burned: 27 (million)
% 1.20/0.58 % (1122258)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
% 1.20/0.58 % (1122258)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.20/0.58 % (1122256)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2570207899:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.96/0.63 % (1122258)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=3549064430:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.96/0.63 % (1122254)Instruction limit reached!
% 1.96/0.63 % (1122254)------------------------------
% 1.96/0.63 % (1122254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.96/0.63 % (1122254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.96/0.63 % (1122254)CaDiCaL version: 2.1.3
% 1.96/0.63 % (1122254)Termination reason: Instruction limit
% 1.96/0.63 % (1122254)Termination phase: shuffling
% 1.96/0.63 % (1122254)Time elapsed: 0.010 s
% 1.96/0.63 % (1122254)Peak memory usage: 10 MB
% 1.96/0.63 % (1122254)Instructions burned: 23 (million)
% 1.96/0.63 % (1122258)Instruction limit reached!
% 1.96/0.63 % (1122258)------------------------------
% 1.96/0.63 % (1122258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.96/0.63 % (1122258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.96/0.63 % (1122258)CaDiCaL version: 2.1.3
% 1.96/0.63 % (1122258)Termination reason: Instruction limit
% 1.96/0.63 % (1122258)Termination phase: shuffling
% 1.96/0.63 % (1122258)Time elapsed: 0.004 s
% 1.96/0.63 % (1122258)Peak memory usage: 10 MB
% 1.96/0.63 % (1122258)Instructions burned: 17 (million)
% 1.96/0.63 % (1122264)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=333370073:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.96/0.63 % (1122264)Instruction limit reached!
% 1.96/0.63 % (1122264)------------------------------
% 1.96/0.63 % (1122264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.96/0.63 % (1122264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.96/0.63 % (1122264)CaDiCaL version: 2.1.3
% 1.96/0.63 % (1122264)Termination reason: Instruction limit
% 1.96/0.63 % (1122264)Termination phase: shuffling
% 1.96/0.63 % (1122264)Time elapsed: 0.002 s
% 1.96/0.63 % (1122264)Peak memory usage: 10 MB
% 1.96/0.63 % (1122264)Instructions burned: 10 (million)
% 1.96/0.63 % (1122260)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.96/0.63 % (1122263)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=1482178864:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.96/0.63 % (1122260)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=1056692164:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.96/0.63 % (1122256)Instruction limit reached!
% 1.96/0.63 % (1122256)------------------------------
% 1.96/0.63 % (1122256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.96/0.63 % (1122256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.96/0.63 % (1122256)CaDiCaL version: 2.1.3
% 1.96/0.63 % (1122256)Termination reason: Instruction limit
% 1.96/0.63 % (1122256)Termination phase: Preprocessing 3
% 1.96/0.63 % (1122256)Time elapsed: 0.027 s
% 1.96/0.63 % (1122256)Peak memory usage: 12 MB
% 1.96/0.63 % (1122256)Instructions burned: 61 (million)
% 1.96/0.63 % (1122260)Instruction limit reached!
% 1.96/0.63 % (1122260)------------------------------
% 1.96/0.63 % (1122260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.96/0.63 % (1122260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.96/0.63 % (1122260)CaDiCaL version: 2.1.3
% 1.96/0.63 % (1122260)Termination reason: Instruction limit
% 1.96/0.63 % (1122260)Termination phase: shuffling
% 1.96/0.63 % (1122260)Time elapsed: 0.005 s
% 1.96/0.63 % (1122260)Peak memory usage: 10 MB
% 1.96/0.63 % (1122260)Instructions burned: 10 (million)
% 1.96/0.63 % (1122266)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3571086389:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.96/0.63 % (1122266)Instruction limit reached!
% 1.96/0.63 % (1122266)------------------------------
% 1.96/0.63 % (1122266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.96/0.63 % (1122266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122266)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122266)Termination reason: Instruction limit
% 2.30/0.66 % (1122266)Termination phase: shuffling
% 2.30/0.66 % (1122266)Time elapsed: 0.005 s
% 2.30/0.66 % (1122266)Peak memory usage: 11 MB
% 2.30/0.66 % (1122266)Instructions burned: 23 (million)
% 2.30/0.66 % (1122263)Instruction limit reached!
% 2.30/0.66 % (1122263)------------------------------
% 2.30/0.66 % (1122263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122263)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122263)Termination reason: Instruction limit
% 2.30/0.66 % (1122263)Termination phase: shuffling
% 2.30/0.66 % (1122263)Time elapsed: 0.014 s
% 2.30/0.66 % (1122263)Peak memory usage: 11 MB
% 2.30/0.66 % (1122263)Instructions burned: 32 (million)
% 2.30/0.66 % (1122272)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3915622854:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.30/0.66 % (1122269)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1364403452:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.30/0.66 % (1122271)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=467332330:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.30/0.66 % (1122273)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1518599712:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.30/0.66 % (1122269)Instruction limit reached!
% 2.30/0.66 % (1122269)------------------------------
% 2.30/0.66 % (1122269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122269)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122269)Termination reason: Instruction limit
% 2.30/0.66 % (1122269)Termination phase: shuffling
% 2.30/0.66 % (1122269)Time elapsed: 0.010 s
% 2.30/0.66 % (1122269)Peak memory usage: 10 MB
% 2.30/0.66 % (1122269)Instructions burned: 22 (million)
% 2.30/0.66 % (1122278)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3126654610:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.30/0.66 % (1122272)Instruction limit reached!
% 2.30/0.66 % (1122272)------------------------------
% 2.30/0.66 % (1122272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122272)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122272)Termination reason: Instruction limit
% 2.30/0.66 % (1122272)Termination phase: Property scanning
% 2.30/0.66 % (1122272)Time elapsed: 0.031 s
% 2.30/0.66 % (1122272)Peak memory usage: 13 MB
% 2.30/0.66 % (1122272)Instructions burned: 144 (million)
% 2.30/0.66 % (1122240)Instruction limit reached!
% 2.30/0.66 % (1122240)------------------------------
% 2.30/0.66 % (1122240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122240)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122240)Termination reason: Instruction limit
% 2.30/0.66 % (1122240)Termination phase: Saturation
% 2.30/0.66 % (1122240)Time elapsed: 0.120 s
% 2.30/0.66 % (1122240)Peak memory usage: 15 MB
% 2.30/0.66 % (1122240)Instructions burned: 249 (million)
% 2.30/0.66 % (1122280)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.30/0.66 % (1122280)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=142788817:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.30/0.66 % (1122280)Instruction limit reached!
% 2.30/0.66 % (1122280)------------------------------
% 2.30/0.66 % (1122280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122280)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122280)Termination reason: Instruction limit
% 2.30/0.66 % (1122280)Termination phase: shuffling
% 2.30/0.66 % (1122280)Time elapsed: 0.002 s
% 2.30/0.66 % (1122280)Peak memory usage: 10 MB
% 2.30/0.66 % (1122280)Instructions burned: 8 (million)
% 2.30/0.66 % (1122278)Instruction limit reached!
% 2.30/0.66 % (1122278)------------------------------
% 2.30/0.66 % (1122278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122278)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122278)Termination reason: Instruction limit
% 2.30/0.66 % (1122278)Termination phase: Property scanning
% 2.30/0.66 % (1122278)Time elapsed: 0.019 s
% 2.30/0.66 % (1122278)Peak memory usage: 11 MB
% 2.30/0.66 % (1122278)Instructions burned: 42 (million)
% 2.30/0.66 % (1122281)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3782613479:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.30/0.66 % (1122283)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=1245566832: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)
% 2.30/0.66 % (1122284)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.30/0.66 % (1122284)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3848857989:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.30/0.66 % (1122244)Instruction limit reached!
% 2.30/0.66 % (1122244)------------------------------
% 2.30/0.66 % (1122244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122244)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122244)Termination reason: Instruction limit
% 2.30/0.66 % (1122244)Termination phase: Saturation
% 2.30/0.66 % (1122244)Time elapsed: 0.148 s
% 2.30/0.66 % (1122244)Peak memory usage: 15 MB
% 2.30/0.66 % (1122244)Instructions burned: 327 (million)
% 2.30/0.66 % (1122284)Instruction limit reached!
% 2.30/0.66 % (1122284)------------------------------
% 2.30/0.66 % (1122284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122284)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122284)Termination reason: Instruction limit
% 2.30/0.66 % (1122284)Termination phase: shuffling
% 2.30/0.66 % (1122284)Time elapsed: 0.003 s
% 2.30/0.66 % (1122284)Peak memory usage: 10 MB
% 2.30/0.66 % (1122284)Instructions burned: 6 (million)
% 2.30/0.66 % (1122288)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=393332499:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.30/0.66 % (1122273)Instruction limit reached!
% 2.30/0.66 % (1122273)------------------------------
% 2.30/0.66 % (1122273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122273)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122273)Termination reason: Instruction limit
% 2.30/0.66 % (1122273)Termination phase: Saturation
% 2.30/0.66 % (1122273)Time elapsed: 0.080 s
% 2.30/0.66 % (1122289)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2070979118:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.30/0.66 % (1122273)Peak memory usage: 14 MB
% 2.30/0.66 % (1122273)Instructions burned: 194 (million)
% 2.30/0.66 % (1122283)Instruction limit reached!
% 2.30/0.66 % (1122283)------------------------------
% 2.30/0.66 % (1122283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122283)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122283)Termination reason: Instruction limit
% 2.30/0.66 % (1122283)Termination phase: Saturation
% 2.30/0.66 % (1122283)Time elapsed: 0.037 s
% 2.30/0.66 % (1122283)Peak memory usage: 13 MB
% 2.30/0.66 % (1122283)Instructions burned: 171 (million)
% 2.30/0.66 % (1122289)Instruction limit reached!
% 2.30/0.66 % (1122289)------------------------------
% 2.30/0.66 % (1122289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122289)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122289)Termination reason: Instruction limit
% 2.30/0.66 % (1122289)Termination phase: shuffling
% 2.30/0.66 % (1122289)Time elapsed: 0.009 s
% 2.30/0.66 % (1122289)Peak memory usage: 10 MB
% 2.30/0.66 % (1122289)Instructions burned: 21 (million)
% 2.30/0.66 % (1122288)Instruction limit reached!
% 2.30/0.66 % (1122288)------------------------------
% 2.30/0.66 % (1122288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122288)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122288)Termination reason: Instruction limit
% 2.30/0.66 % (1122288)Termination phase: shuffling
% 2.30/0.66 % (1122288)Time elapsed: 0.011 s
% 2.30/0.66 % (1122288)Peak memory usage: 11 MB
% 2.30/0.66 % (1122288)Instructions burned: 24 (million)
% 2.30/0.66 % (1122293)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=2407399639:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.30/0.66 % (1122292)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=1510206130:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.30/0.66 % (1122294)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=1646678618: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)
% 2.30/0.66 % (1122295)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=504317678:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.30/0.66 % (1122213) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1122205-1122213"...
% 2.30/0.66 % (1122281)Instruction limit reached!
% 2.30/0.66 % (1122281)------------------------------
% 2.30/0.66 % (1122281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.66 % (1122281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.66 % (1122281)CaDiCaL version: 2.1.3
% 2.30/0.66 % (1122281)Termination reason: Instruction limit
% 2.30/0.66 % (1122281)Termination phase: Saturation
% 2.30/0.66 % (1122281)Time elapsed: 0.075 s
% 2.30/0.66 % (1122281)Peak memory usage: 14 MB
% 2.30/0.66 % (1122281)Instructions burned: 181 (million)
% 2.30/0.66 % (1122213)...printing done.
% 2.30/0.66 % (1122213)Refutation found. Thanks to Tanya!
% 2.30/0.66 % SZS status Theorem for theBenchmark
% 2.30/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.30/0.67 % (1122213)------------------------------
% 2.30/0.67 % (1122213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (1122213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (1122213)CaDiCaL version: 2.1.3
% 2.30/0.67 % (1122213)Termination reason: Refutation
% 2.30/0.67 % (1122213)Time elapsed: 0.295 s
% 2.30/0.67 % (1122213)Peak memory usage: 22 MB
% 2.30/0.67 % (1122213)Instructions burned: 575 (million)
% 2.30/0.67 % (1122205)Success in time 0.351 s
% 2.30/0.67 % Vampire exiting
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