%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU751^1 : 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 : n019.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 08:31:08 AM UTC 2026
% Result : Theorem 2.15s 0.67s
% Output : Refutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 156 ( 47 unt; 0 typ; 18 def)
% Number of atoms : 5984 (1617 equ; 0 cnn)
% Maximal formula atoms : 272 ( 38 avg)
% Number of connectives : 3434 ( 209 ~; 185 |;1120 &; 780 @)
% ( 32 <=>;1108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 282 ( 18 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 521 ( 518 usr; 326 con; 0-4 aty)
% Number of variables : 220 ( 0 sgn 178 !; 42 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_279,type,
contrasubsetT1: $o ).
thf(func_def_280,type,
contrasubsetT2: $o ).
thf(func_def_281,type,
contrasubsetT3: $o ).
thf(func_def_282,type,
doubleComplementI1: $o ).
thf(func_def_283,type,
doubleComplementE1: $o ).
thf(func_def_284,type,
doubleComplementSub1: $o ).
thf(func_def_285,type,
doubleComplementSub2: $o ).
thf(func_def_286,type,
doubleComplementEq: $o ).
thf(func_def_287,type,
complementTnotintersectT: $o ).
thf(func_def_288,type,
complementImpComplementIntersect: $o ).
thf(func_def_289,type,
complementSubsetComplementIntersect: $o ).
thf(func_def_290,type,
complementInPowersetComplementIntersect: $o ).
thf(func_def_291,type,
contraSubsetComplement: $o ).
thf(func_def_292,type,
complementTcontraSubset: $o ).
thf(func_def_293,type,
binunionTILcontra: $o ).
thf(func_def_294,type,
binunionTIRcontra: $o ).
thf(func_def_295,type,
inIntersectImpInUnion: $o ).
thf(func_def_296,type,
inIntersectImpInUnion2: $o ).
thf(func_def_297,type,
inIntersectImpInIntersectUnions: $o ).
thf(func_def_298,type,
intersectInPowersetIntersectUnions: $o ).
thf(func_def_299,type,
inComplementUnionImpNotIn1: $o ).
thf(func_def_300,type,
inComplementUnionImpInComplement1: $o ).
thf(func_def_301,type,
binunionTE: $o ).
thf(func_def_302,type,
binunionTEcontra: $o ).
thf(func_def_303,type,
demorgan2a1: $o ).
thf(func_def_304,type,
complementUnionInPowersetComplement: $o ).
thf(func_def_305,type,
demorgan2a2: $o ).
thf(func_def_308,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_309,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_310,type,
vOR: $o > $o > $o ).
thf(func_def_311,type,
vAND: $o > $o > $o ).
thf(func_def_312,type,
vNOT: $o > $o ).
thf(func_def_313,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_314,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_315,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_316,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_317,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_318,type,
vIMP: $o > $o > $o ).
thf(func_def_319,type,
sP0: $o ).
thf(func_def_320,type,
sP1: $i > $i > $o ).
thf(func_def_321,type,
sP2: $i > $o ).
thf(func_def_322,type,
sP3: $o ).
thf(func_def_327,type,
sK8: $i > $i > $i > $i > $i ).
thf(func_def_328,type,
sK9: $i > $i > $i > $i > $i ).
thf(func_def_329,type,
sK10: $i > $i > $i > $i > $i ).
thf(func_def_330,type,
sK11: $i > $i > $i > $i > $i ).
thf(func_def_333,type,
sK14: $i > $i ).
thf(func_def_334,type,
sK15: ( $i > $i ) > $i > $i > $i ).
thf(func_def_340,type,
sK21: $i > $i ).
thf(func_def_341,type,
sK22: $i > $i ).
thf(func_def_342,type,
sK23: $i > $i ).
thf(func_def_343,type,
sK24: $i > $i ).
thf(func_def_344,type,
sK25: $i > $i ).
thf(func_def_345,type,
sK26: $i > $i > $i > $i ).
thf(func_def_346,type,
sK27: $i > $i ).
thf(func_def_347,type,
sK28: $i > $i ).
thf(func_def_348,type,
sK29: $i > $i ).
thf(func_def_349,type,
sK30: $i > $i ).
thf(func_def_350,type,
sK31: $i > $i > $i ).
thf(func_def_351,type,
sK32: $i > $i > $i ).
thf(func_def_352,type,
sK33: $i > $i > $i > $i ).
thf(func_def_353,type,
sK34: $i > $i > $i > $i ).
thf(func_def_354,type,
sK35: $i > $i > $i > $i ).
thf(func_def_355,type,
sK36: $i > $i > $i ).
thf(func_def_356,type,
sK37: $i > $i > $i ).
thf(func_def_357,type,
sK38: $i > $i > $i ).
thf(func_def_363,type,
sK44: $o ).
thf(func_def_369,type,
sK50: $i > $i > $i > $i > $i ).
thf(func_def_370,type,
sK51: $i > $i > $i > $i > $i ).
thf(func_def_377,type,
sK58: $i > $i ).
thf(func_def_379,type,
sK60: ( $i > $i ) > $i > $i > $i ).
thf(func_def_390,type,
sK71: $i > $o ).
thf(func_def_401,type,
sK82: $i > $i > $o ).
thf(func_def_405,type,
sK86: $o ).
thf(func_def_409,type,
sK90: $i > $o ).
thf(func_def_415,type,
sK96: $i > $i > $i ).
thf(func_def_416,type,
sK97: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_417,type,
sK98: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_418,type,
sK99: $i > $o ).
thf(func_def_419,type,
sK100: $i > $o ).
thf(func_def_429,type,
sK110: $i > $o ).
thf(func_def_434,type,
sK115: $i > $o ).
thf(func_def_442,type,
sK123: $i > ( $i > $o ) > $i ).
thf(func_def_443,type,
sK124: $i > $o ).
thf(func_def_446,type,
sK127: $i > $i ).
thf(func_def_462,type,
sK143: $i > $i > $o ).
thf(func_def_469,type,
sK150: $i > $i > $i ).
thf(func_def_473,type,
sK154: $i > $i ).
thf(func_def_475,type,
sK156: $i > $o ).
thf(func_def_501,type,
sK182: $o ).
thf(func_def_504,type,
sK185: $i > $i > $o ).
thf(func_def_510,type,
sK191: $i > $i > $i ).
thf(func_def_513,type,
sK194: $i > $i > $i ).
thf(func_def_519,type,
sK200: $o ).
thf(func_def_521,type,
sK202: $i > $i > $i > $i ).
thf(func_def_531,type,
sK212: $i > $o ).
thf(func_def_534,type,
sK215: $i > ( $i > $o ) > $i ).
thf(func_def_535,type,
sK216: $i > ( $i > $o ) > $i ).
thf(func_def_536,type,
sK217: $i > $o ).
thf(func_def_541,type,
sK222: $i > $o ).
thf(func_def_542,type,
sK223: $i > $o ).
thf(func_def_543,type,
sK224: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_544,type,
sK225: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_545,type,
sK226: $o ).
thf(func_def_547,type,
sK228: $i > ( $i > $o ) > $i ).
thf(func_def_548,type,
sK229: $i > ( $i > $o ) > $i ).
thf(func_def_549,type,
sK230: $i > $o ).
thf(func_def_570,type,
sK251: $i > ( $i > $i ) > $i > $i ).
thf(func_def_572,type,
sK253: $i > $i ).
thf(func_def_575,type,
sK256: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_576,type,
sK257: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_580,type,
sK261: $i > $o ).
thf(func_def_583,type,
sK264: $o ).
thf(func_def_590,type,
sK271: $o ).
thf(func_def_594,type,
sK275: $o ).
thf(func_def_595,type,
sK276: $i > $o ).
thf(func_def_603,type,
sK284: $i > $i ).
thf(func_def_604,type,
sK285: $i > $o ).
thf(func_def_607,type,
sK288: $i > ( $i > $o ) > $i ).
thf(func_def_608,type,
sK289: $i > $o ).
thf(func_def_609,type,
sK290: $i > $i ).
thf(func_def_610,type,
sK291: ( $i > $o ) > $i ).
thf(func_def_613,type,
sK294: $o ).
thf(func_def_632,type,
sK313: $i > $o ).
thf(func_def_642,type,
sK323: $i > $i > ( $i > $o ) > $i ).
thf(func_def_643,type,
sK324: $i > $o ).
thf(func_def_685,type,
sK366: $i > $i > $i ).
thf(func_def_689,type,
sK370: $i > $i ).
thf(func_def_692,type,
sK373: $i > $i ).
thf(func_def_698,type,
sK379: $o ).
thf(func_def_699,type,
sK380: $o > $i > $i > $i ).
thf(func_def_703,type,
sK384: $o ).
thf(func_def_711,type,
sK392: $i > ( $i > $o ) > $i ).
thf(func_def_712,type,
sK393: $i > $o ).
thf(func_def_722,type,
sK403: $i > $i > $o ).
thf(func_def_725,type,
sK406: $i > ( $i > $o ) > $i ).
thf(func_def_726,type,
sK407: $i > $o ).
thf(func_def_735,type,
sK416: $i > $i > $i ).
thf(func_def_741,type,
sK422: $i > $i > $o ).
thf(func_def_788,type,
sK469: $i > $i > $o ).
thf(func_def_805,type,
sK486: $i > $i > $i > $i > $i ).
thf(func_def_811,type,
sK492: $i > $o ).
thf(func_def_814,type,
sK495: $i > ( $i > $o ) > $i ).
thf(func_def_816,type,
sK497: $i > $o ).
thf(func_def_817,type,
sK498: $i > $i > $i > $i > $i ).
thf(func_def_824,type,
sK505: $i > $i ).
thf(func_def_830,type,
sK511: $o ).
thf(func_def_833,type,
sK514: $i > $o ).
thf(func_def_834,type,
sK515: $i > $i > $i ).
thf(func_def_843,type,
sK524: $i > $o ).
thf(func_def_844,type,
sK525: $i > $o ).
thf(func_def_845,type,
sK526: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_846,type,
sK527: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_848,type,
sK529: $i > $i > $o ).
thf(func_def_849,type,
sK530: $i > $i ).
thf(func_def_850,type,
sK531: $i > $i ).
thf(func_def_851,type,
sK532: ( $i > $i > $o ) > $i > $i ).
thf(func_def_852,type,
sK533: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_853,type,
sK534: ( $i > $i > $o ) > $i > $i ).
thf(func_def_865,type,
sK546: $o ).
thf(func_def_870,type,
sK551: $i > $i ).
thf(func_def_873,type,
sK554: $i > $i > ( $i > $i ) > $i ).
thf(func_def_874,type,
sK555: $i > $o ).
thf(func_def_876,type,
sK557: ( $i > $o ) > $i ).
thf(func_def_877,type,
sK558: ( $i > $o ) > $i ).
thf(func_def_882,type,
sK563: $i > $i > $o ).
thf(func_def_886,type,
sK567: $i > $o ).
thf(func_def_891,type,
sK572: ( $i > $o ) > $i ).
thf(func_def_892,type,
sK573: $i > $o ).
thf(func_def_893,type,
sK574: $i > $i ).
thf(func_def_894,type,
sK575: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_895,type,
sK576: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_899,type,
sK580: $i > $o ).
thf(func_def_907,type,
sK588: $o ).
thf(func_def_928,type,
sK609: $i > $o ).
thf(func_def_937,type,
sK618: $o ).
thf(func_def_942,type,
sK623: $i > $o ).
thf(func_def_944,type,
sK625: $i > $i > $i > $i ).
thf(func_def_945,type,
sK626: $i > $i > $i > $i ).
thf(func_def_954,type,
sK635: $o ).
thf(func_def_979,type,
sK660: $i > $i > $i > $i ).
thf(func_def_989,type,
sK670: $i > $i > $i > $i > $i ).
thf(func_def_1016,type,
sK697: $i > $o ).
thf(func_def_1019,type,
sK700: $i > ( $i > $o ) > $i ).
thf(func_def_1020,type,
sK701: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1021,type,
sK702: $i > $i ).
thf(func_def_1029,type,
sK710: $i > ( $i > $o ) > $i ).
thf(func_def_1030,type,
sK711: $i > $o ).
thf(func_def_1032,type,
sK713: $i > $o ).
thf(func_def_1033,type,
sK714: ( $i > $o ) > $i ).
thf(func_def_1047,type,
sK728: $i > $i > $i > $i ).
thf(func_def_1048,type,
sK729: $i > $i > $i > $i ).
thf(func_def_1052,type,
sK733: $i > $i > $i ).
thf(func_def_1088,type,
sK769: $i > $o ).
thf(func_def_1101,type,
sK782: $o ).
thf(func_def_1116,type,
sK797: $i > $i > $i ).
thf(func_def_1117,type,
sK798: $i > $i > $i ).
thf(func_def_1124,type,
sK805: $i > $i ).
thf(func_def_1129,type,
sK810: $o ).
thf(func_def_1141,type,
sK822: $i > $i ).
thf(func_def_1143,type,
sK824: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1160,type,
sK841: ( $i > $o ) > $i > $i ).
thf(func_def_1161,type,
sK842: ( $i > $o ) > $i > $i ).
thf(func_def_1163,type,
sK844: $i > $o ).
thf(f101,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(f103,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(f108,axiom,
( binintersectI
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(f125,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) )
= setminusELneg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(f127,axiom,
( setminusIRneg
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(f272,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1a) ).
thf(f273,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f272]) ).
thf(f328,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
= binunionIL ),
inference(rectify,[],[f101]) ).
thf(f329,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) )
<=> ( binunionIL = $true ) ),
inference(fool_elimination,[],[f328]) ).
thf(f402,plain,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f108]) ).
thf(f403,plain,
( ( binintersectI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f402]) ).
thf(f492,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ~ ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ( ~ ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X2 ) ) )
= setminusELneg ),
inference(rectify,[],[f125]) ).
thf(f493,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) ) )
<=> ( setminusELneg = $true ) ),
inference(fool_elimination,[],[f492]) ).
thf(f648,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f273]) ).
thf(f649,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ! [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 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f648]) ).
thf(f715,plain,
( setminusIRneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f127]) ).
thf(f716,plain,
( ( setminusIRneg = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f715]) ).
thf(f745,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
= binunionIR ),
inference(rectify,[],[f103]) ).
thf(f746,plain,
( ( binunionIR = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f745]) ).
thf(f832,plain,
( ( setminusELneg = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) ) ) ),
inference(flattening,[],[f493]) ).
thf(f852,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
<=> ( setminusIRneg = $true ) ),
inference(flattening,[],[f716]) ).
thf(f871,plain,
( ( setminusIRneg = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ),
inference(ennf_transformation,[],[f852]) ).
thf(f982,plain,
( ( binintersectI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f403]) ).
thf(f983,plain,
( ( binintersectI = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f982]) ).
thf(f986,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( binunionIR = $true ) ),
inference(ennf_transformation,[],[f746]) ).
thf(f1061,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) )
<=> ( binunionIL = $true ) ),
inference(ennf_transformation,[],[f329]) ).
thf(f1144,plain,
( ( setminusELneg = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) ),
inference(ennf_transformation,[],[f832]) ).
thf(f1145,plain,
( ( setminusELneg = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) ),
inference(flattening,[],[f1144]) ).
thf(f1162,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f649]) ).
thf(f1163,plain,
( ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( setminusIRneg = $true )
& ( emptysetimpfalse = $true )
& ( cartprodmempaircEq = $true )
& ( setunion__Cong = $true )
& ( binunionIR = $true )
& ( symdiffI2 = $true )
& ( iftrue = $true )
& ( lam2p = $true )
& ( binunionEcases = $true )
& ( cartprodmempair1 = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( binunionTEcontra = $true )
& ( dsetconstrEL = $true )
& ( singletonsubset = $true )
& ( demorgan2a1 = $true )
& ( binunionTIRcontra = $true )
& ( sepSubset = $true )
& ( exuE2 = $true )
& ( binunionIL = $true )
& ( uniqinunit = $true )
& ( emptysetAx = $true )
& ( dpsetconstrEL2 = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectSubset5 = $true )
& ( exuEu = $true )
& ( inIntersectImpInUnion2 = $true )
& ( ksndpairEq = $true )
& ( setbeta = $true )
& ( emptyI = $true )
& ( funcGraphProp1 = $true )
& ( cartprodpairsurjEq = $true )
& ( singletoninpowerset = $true )
& ( replAx = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectSubset2 = $true )
& ( powersetAx = $true )
& ( powerset__Cong = $true )
& ( apProp = $true )
& ( singletonsuniq = $true )
& ( binintersectEL = $true )
& ( exuE1 = $true )
& ( kfstpairEq = $true )
& ( funcext2 = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( ubforcartprodlem2 = $true )
& ( ifp = $true )
& ( quantDeMorgan3 = $true )
& ( contrasubsetT3 = $true )
& ( nonemptyE1 = $true )
& ( setminusER = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subsetTI = $true )
& ( contrasubsetT = $true )
& ( binintersectER = $true )
& ( setukpairinjR1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIL = $true )
& ( cartprodpairmemER = $true )
& ( iffalseProp1 = $true )
& ( upairsetIL = $true )
& ( setadjoinSub = $true )
& ( cartprodfstin = $true )
& ( doubleComplementE1 = $true )
& ( inCongP = $true )
& ( doubleComplementEq = $true )
& ( eta2 = $true )
& ( emptyset__Cong = $true )
& ( setunionE = $true )
& ( setadjoin__Cong = $true )
& ( setminusSubset1 = $true )
& ( powersetI = $true )
& ( symdiffIneg1 = $true )
& ( dpsetconstrEL1 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setunionE2 = $true )
& ( binunionTILcontra = $true )
& ( iftrueorfalse = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetsubset = $true )
& ( binintersectTELcontra = $true )
& ( setunionsingleton2 = $true )
& ( ifSingleton = $true )
& ( binintersectSubset1 = $true )
& ( inPowerset = $true )
& ( ap2apEq1 = $true )
& ( in__Cong = $true )
& ( prop2setI = $true )
& ( binunionTE = $true )
& ( powersetE1 = $true )
& ( symdiffI1 = $true )
& ( upairequniteq = $true )
& ( kfstsingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binunionT_lem = $true )
& ( infuncsetfunc = $true )
& ( setminusELneg = $true )
& ( disjointsetsI1 = $true )
& ( sepInPowerset = $true )
& ( setadjoinAx = $true )
& ( upairsetIR = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementTI1 = $true )
& ( nonemptyImpWitness = $true )
& ( kpairp = $true )
& ( binintersectSubset4 = $true )
& ( lam2lamEq = $true )
& ( setminusI = $true )
& ( setukpairinjL = $true )
& ( binintersectT_lem = $true )
& ( kpairiskpair = $true )
& ( emptyE1 = $true )
& ( cartprodfstpairEq = $true )
& ( binunionRsub = $true )
& ( ex1I = $true )
& ( brelnall1 = $true )
& ( subsetRefl = $true )
& ( dpsetconstrSub = $true )
& ( binintersectSubset3 = $true )
& ( subset2powerset = $true )
& ( exuI3 = $true )
& ( binintersectRsub = $true )
& ( complementTcontraSubset = $true )
& ( notequalI2 = $true )
& ( contraSubsetComplement = $true )
& ( cartprodsndin = $true )
& ( dpsetconstrI = $true )
& ( powersetTI1 = $true )
& ( omegaIndAx = $true )
& ( setukpairinjL2 = $true )
& ( singletonprop = $true )
& ( subbreln = $true )
& ( setext = $true )
& ( setminusEL = $true )
& ( ksndsingleton = $true )
& ( nonemptyI = $true )
& ( emptyinunitempty = $true )
& ( funcGraphProp3 = $true )
& ( powersetT_lem = $true )
& ( doubleComplementI1 = $true )
& ( exuE3u = $true )
& ( binintersectI = $true )
& ( exuI2 = $true )
& ( setukpairinjR2 = $true )
& ( funcGraphProp2 = $true )
& ( setukpairinjL1 = $true )
& ( eqbreln = $true )
& ( brelnall2 = $true )
& ( setminusILneg = $true )
& ( cartprodpairin = $true )
& ( subsetI1 = $true )
& ( upairsubunion = $true )
& ( binunionLsub = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( lamProp = $true )
& ( binintersectTERcontra = $true )
& ( emptyInPowerset = $true )
& ( setminusT_lem = $true )
& ( singletoninpowunion = $true )
& ( subsetE = $true )
& ( theprop = $true )
& ( descr__Cong = $true )
& ( powersetTE1 = $true )
& ( exuE3e = $true )
& ( subsetTrans = $true )
& ( contrasubsetT2 = $true )
& ( setunionsingleton = $true )
& ( complementTE1 = $true )
& ( funcinfuncset = $true )
& ( setukpairinjR12 = $true )
& ( binintersectLsub = $true )
& ( funcextLem = $true )
& ( app = $true )
& ( setadjoinE = $true )
& ( setukpairinjR11 = $true )
& ( beta1 = $true )
& ( complementImpComplementIntersect = $true )
& ( powersetsubset = $true )
& ( theeq = $true )
& ( doubleComplementSub1 = $true )
& ( setOfPairsIsBReln = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionI = $true )
& ( setunionAx = $true )
& ( powersetE = $true )
& ( quantDeMorgan2 = $true )
& ( ex1E2 = $true )
& ( notequalI1 = $true )
& ( demorgan2a2 = $true )
& ( prop2set2propI = $true )
& ( kpairsurjEq = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( setukpairinjR = $true )
& ( inIntersectImpInUnion = $true )
& ( symdiffE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( emptyinPowerset = $true )
& ( subsetE2 = $true )
& ( ubforcartprodlem3 = $true )
& ( dpsetconstrERa = $true )
& ( vacuousDall = $true )
& ( subsetI2 = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( iftrueProp2 = $true )
& ( contrasubsetT1 = $true )
& ( setoftrueEq = $true )
& ( setextAx = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI1 = $true )
& ( secondinupair = $true )
& ( ap2apEq2 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset2 = $true )
& ( bs114d = $true )
& ( setminusLsub = $true )
& ( complementT_lem = $true )
& ( descrp = $true )
& ( eta1 = $true )
& ( iftrueProp1 = $true )
& ( upairsetE = $true )
& ( dsetconstr__Cong = $true )
& ( funcImageSingleton = $true )
& ( singletonsswitch = $true )
& ( setextT = $true )
& ( setextsub = $true )
& ( cartprodpairmemEL = $true )
& ( setukpairIL = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( lamp = $true )
& ( notinsingleton = $true )
& ( notdallE = $true )
& ( ex1I2 = $true )
& ( funcext = $true )
& ( setunionsingleton1 = $true )
& ( ex1E1 = $true )
& ( setminusERneg = $true )
& ( binunionE = $true )
& ( setukpairIR = $true )
& ( omegaSAx = $true )
& ( exu__Cong = $true )
& ( funcGraphProp4 = $true )
& ( wellorderingAx = $true )
& ( upairset2E = $true )
& ( doubleComplementSub2 = $true )
& ( notsubsetI = $true )
& ( notdexE = $true )
& ( ap2p = $true )
& ( upairinpowunion = $true )
& ( iffalseProp2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( complementTnotintersectT = $true )
& ( iffalse = $true )
& ( exuI1 = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( symdiffIneg2 = $true )
& ( cartprodmempair = $true )
& ( beta2 = $true ) ),
inference(flattening,[],[f1162]) ).
thf(f1501,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[],[f1061]) ).
thf(f1502,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
& ( $true
!= ( in @ X4 @ ( binunion @ X5 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f1501]) ).
thf(f1503,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ( ( $true
= ( in @ sK343 @ sK344 ) )
& ( ( in @ sK343 @ ( binunion @ sK344 @ sK342 ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK342,sK343,sK344]),skolemize(X3,sK342),skolemize(X4,sK343),skolemize(X5,sK344)],[f1502]) ).
thf(f1528,plain,
( ( ( setminusELneg = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) )
| ( setminusELneg != $true ) ) ),
inference(nnf_transformation,[],[f1145]) ).
thf(f1529,plain,
( ( ( setminusELneg = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) ) )
| ( setminusELneg != $true ) ) ),
inference(rectify,[],[f1528]) ).
thf(f1530,plain,
( ( ( setminusELneg = $true )
| ( ( ( in @ sK375 @ sK376 )
= $true )
& ( $true
!= ( in @ sK375 @ sK374 ) )
& ( $true
!= ( in @ sK375 @ ( setminus @ sK376 @ sK374 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) ) )
| ( setminusELneg != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK374,sK375,sK376]),skolemize(X0,sK374),skolemize(X1,sK375),skolemize(X2,sK376)],[f1529]) ).
thf(f1549,plain,
( ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( setminusIRneg = $true )
& ( emptysetimpfalse = $true )
& ( cartprodmempaircEq = $true )
& ( setunion__Cong = $true )
& ( binunionIR = $true )
& ( symdiffI2 = $true )
& ( iftrue = $true )
& ( lam2p = $true )
& ( binunionEcases = $true )
& ( cartprodmempair1 = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( binunionTEcontra = $true )
& ( dsetconstrEL = $true )
& ( singletonsubset = $true )
& ( demorgan2a1 = $true )
& ( binunionTIRcontra = $true )
& ( sepSubset = $true )
& ( exuE2 = $true )
& ( binunionIL = $true )
& ( uniqinunit = $true )
& ( emptysetAx = $true )
& ( dpsetconstrEL2 = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binintersectSubset5 = $true )
& ( exuEu = $true )
& ( inIntersectImpInUnion2 = $true )
& ( ksndpairEq = $true )
& ( setbeta = $true )
& ( emptyI = $true )
& ( funcGraphProp1 = $true )
& ( cartprodpairsurjEq = $true )
& ( singletoninpowerset = $true )
& ( replAx = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectSubset2 = $true )
& ( powersetAx = $true )
& ( powerset__Cong = $true )
& ( apProp = $true )
& ( singletonsuniq = $true )
& ( binintersectEL = $true )
& ( exuE1 = $true )
& ( kfstpairEq = $true )
& ( funcext2 = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( ubforcartprodlem2 = $true )
& ( ifp = $true )
& ( quantDeMorgan3 = $true )
& ( contrasubsetT3 = $true )
& ( nonemptyE1 = $true )
& ( setminusER = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subsetTI = $true )
& ( contrasubsetT = $true )
& ( binintersectER = $true )
& ( setukpairinjR1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIL = $true )
& ( cartprodpairmemER = $true )
& ( iffalseProp1 = $true )
& ( upairsetIL = $true )
& ( setadjoinSub = $true )
& ( cartprodfstin = $true )
& ( doubleComplementE1 = $true )
& ( inCongP = $true )
& ( doubleComplementEq = $true )
& ( eta2 = $true )
& ( emptyset__Cong = $true )
& ( setunionE = $true )
& ( setadjoin__Cong = $true )
& ( setminusSubset1 = $true )
& ( powersetI = $true )
& ( symdiffIneg1 = $true )
& ( dpsetconstrEL1 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setunionE2 = $true )
& ( binunionTILcontra = $true )
& ( iftrueorfalse = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetsubset = $true )
& ( binintersectTELcontra = $true )
& ( setunionsingleton2 = $true )
& ( ifSingleton = $true )
& ( binintersectSubset1 = $true )
& ( inPowerset = $true )
& ( ap2apEq1 = $true )
& ( in__Cong = $true )
& ( prop2setI = $true )
& ( binunionTE = $true )
& ( powersetE1 = $true )
& ( symdiffI1 = $true )
& ( upairequniteq = $true )
& ( kfstsingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binunionT_lem = $true )
& ( infuncsetfunc = $true )
& ( setminusELneg = $true )
& ( disjointsetsI1 = $true )
& ( sepInPowerset = $true )
& ( setadjoinAx = $true )
& ( upairsetIR = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementTI1 = $true )
& ( nonemptyImpWitness = $true )
& ( kpairp = $true )
& ( binintersectSubset4 = $true )
& ( lam2lamEq = $true )
& ( setminusI = $true )
& ( setukpairinjL = $true )
& ( binintersectT_lem = $true )
& ( kpairiskpair = $true )
& ( emptyE1 = $true )
& ( cartprodfstpairEq = $true )
& ( binunionRsub = $true )
& ( ex1I = $true )
& ( brelnall1 = $true )
& ( subsetRefl = $true )
& ( dpsetconstrSub = $true )
& ( binintersectSubset3 = $true )
& ( subset2powerset = $true )
& ( exuI3 = $true )
& ( binintersectRsub = $true )
& ( complementTcontraSubset = $true )
& ( notequalI2 = $true )
& ( contraSubsetComplement = $true )
& ( cartprodsndin = $true )
& ( dpsetconstrI = $true )
& ( powersetTI1 = $true )
& ( omegaIndAx = $true )
& ( setukpairinjL2 = $true )
& ( singletonprop = $true )
& ( subbreln = $true )
& ( setext = $true )
& ( setminusEL = $true )
& ( ksndsingleton = $true )
& ( nonemptyI = $true )
& ( emptyinunitempty = $true )
& ( funcGraphProp3 = $true )
& ( powersetT_lem = $true )
& ( doubleComplementI1 = $true )
& ( exuE3u = $true )
& ( binintersectI = $true )
& ( exuI2 = $true )
& ( setukpairinjR2 = $true )
& ( funcGraphProp2 = $true )
& ( setukpairinjL1 = $true )
& ( eqbreln = $true )
& ( brelnall2 = $true )
& ( setminusILneg = $true )
& ( cartprodpairin = $true )
& ( subsetI1 = $true )
& ( upairsubunion = $true )
& ( binunionLsub = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( lamProp = $true )
& ( binintersectTERcontra = $true )
& ( emptyInPowerset = $true )
& ( setminusT_lem = $true )
& ( singletoninpowunion = $true )
& ( subsetE = $true )
& ( theprop = $true )
& ( descr__Cong = $true )
& ( powersetTE1 = $true )
& ( exuE3e = $true )
& ( subsetTrans = $true )
& ( contrasubsetT2 = $true )
& ( setunionsingleton = $true )
& ( complementTE1 = $true )
& ( funcinfuncset = $true )
& ( setukpairinjR12 = $true )
& ( binintersectLsub = $true )
& ( funcextLem = $true )
& ( app = $true )
& ( setadjoinE = $true )
& ( setukpairinjR11 = $true )
& ( beta1 = $true )
& ( complementImpComplementIntersect = $true )
& ( powersetsubset = $true )
& ( theeq = $true )
& ( doubleComplementSub1 = $true )
& ( setOfPairsIsBReln = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionI = $true )
& ( setunionAx = $true )
& ( powersetE = $true )
& ( quantDeMorgan2 = $true )
& ( ex1E2 = $true )
& ( notequalI1 = $true )
& ( demorgan2a2 = $true )
& ( prop2set2propI = $true )
& ( kpairsurjEq = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( setukpairinjR = $true )
& ( inIntersectImpInUnion = $true )
& ( symdiffE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( emptyinPowerset = $true )
& ( subsetE2 = $true )
& ( ubforcartprodlem3 = $true )
& ( dpsetconstrERa = $true )
& ( vacuousDall = $true )
& ( subsetI2 = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( iftrueProp2 = $true )
& ( contrasubsetT1 = $true )
& ( setoftrueEq = $true )
& ( setextAx = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI1 = $true )
& ( secondinupair = $true )
& ( ap2apEq2 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset2 = $true )
& ( bs114d = $true )
& ( setminusLsub = $true )
& ( complementT_lem = $true )
& ( descrp = $true )
& ( eta1 = $true )
& ( iftrueProp1 = $true )
& ( upairsetE = $true )
& ( dsetconstr__Cong = $true )
& ( funcImageSingleton = $true )
& ( singletonsswitch = $true )
& ( setextT = $true )
& ( setextsub = $true )
& ( cartprodpairmemEL = $true )
& ( setukpairIL = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( lamp = $true )
& ( notinsingleton = $true )
& ( notdallE = $true )
& ( ex1I2 = $true )
& ( funcext = $true )
& ( setunionsingleton1 = $true )
& ( ex1E1 = $true )
& ( setminusERneg = $true )
& ( binunionE = $true )
& ( setukpairIR = $true )
& ( omegaSAx = $true )
& ( exu__Cong = $true )
& ( funcGraphProp4 = $true )
& ( wellorderingAx = $true )
& ( upairset2E = $true )
& ( doubleComplementSub2 = $true )
& ( notsubsetI = $true )
& ( notdexE = $true )
& ( ap2p = $true )
& ( upairinpowunion = $true )
& ( iffalseProp2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( complementTnotintersectT = $true )
& ( iffalse = $true )
& ( exuI1 = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( symdiffIneg2 = $true )
& ( cartprodmempair = $true )
& ( beta2 = $true ) ),
inference(rectify,[],[f1163]) ).
thf(f1550,plain,
( ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( setminusIRneg = $true )
& ( emptysetimpfalse = $true )
& ( cartprodmempaircEq = $true )
& ( setunion__Cong = $true )
& ( binunionIR = $true )
& ( symdiffI2 = $true )
& ( iftrue = $true )
& ( lam2p = $true )
& ( binunionEcases = $true )
& ( cartprodmempair1 = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( binunionTEcontra = $true )
& ( dsetconstrEL = $true )
& ( singletonsubset = $true )
& ( demorgan2a1 = $true )
& ( binunionTIRcontra = $true )
& ( sepSubset = $true )
& ( exuE2 = $true )
& ( binunionIL = $true )
& ( uniqinunit = $true )
& ( emptysetAx = $true )
& ( dpsetconstrEL2 = $true )
& ( ( in @ sK400 @ ( setminus @ sK398 @ ( binintersect @ sK397 @ sK399 ) ) )
= $true )
& ( $true
!= ( in @ sK400 @ ( binunion @ ( setminus @ sK398 @ sK397 ) @ ( setminus @ sK398 @ sK399 ) ) ) )
& ( $true
= ( in @ sK400 @ sK398 ) )
& ( $true
= ( in @ sK399 @ ( powerset @ sK398 ) ) )
& ( $true
= ( in @ sK397 @ ( powerset @ sK398 ) ) )
& ( binintersectSubset5 = $true )
& ( exuEu = $true )
& ( inIntersectImpInUnion2 = $true )
& ( ksndpairEq = $true )
& ( setbeta = $true )
& ( emptyI = $true )
& ( funcGraphProp1 = $true )
& ( cartprodpairsurjEq = $true )
& ( singletoninpowerset = $true )
& ( replAx = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectSubset2 = $true )
& ( powersetAx = $true )
& ( powerset__Cong = $true )
& ( apProp = $true )
& ( singletonsuniq = $true )
& ( binintersectEL = $true )
& ( exuE1 = $true )
& ( kfstpairEq = $true )
& ( funcext2 = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( ubforcartprodlem2 = $true )
& ( ifp = $true )
& ( quantDeMorgan3 = $true )
& ( contrasubsetT3 = $true )
& ( nonemptyE1 = $true )
& ( setminusER = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subsetTI = $true )
& ( contrasubsetT = $true )
& ( binintersectER = $true )
& ( setukpairinjR1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIL = $true )
& ( cartprodpairmemER = $true )
& ( iffalseProp1 = $true )
& ( upairsetIL = $true )
& ( setadjoinSub = $true )
& ( cartprodfstin = $true )
& ( doubleComplementE1 = $true )
& ( inCongP = $true )
& ( doubleComplementEq = $true )
& ( eta2 = $true )
& ( emptyset__Cong = $true )
& ( setunionE = $true )
& ( setadjoin__Cong = $true )
& ( setminusSubset1 = $true )
& ( powersetI = $true )
& ( symdiffIneg1 = $true )
& ( dpsetconstrEL1 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setunionE2 = $true )
& ( binunionTILcontra = $true )
& ( iftrueorfalse = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetsubset = $true )
& ( binintersectTELcontra = $true )
& ( setunionsingleton2 = $true )
& ( ifSingleton = $true )
& ( binintersectSubset1 = $true )
& ( inPowerset = $true )
& ( ap2apEq1 = $true )
& ( in__Cong = $true )
& ( prop2setI = $true )
& ( binunionTE = $true )
& ( powersetE1 = $true )
& ( symdiffI1 = $true )
& ( upairequniteq = $true )
& ( kfstsingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binunionT_lem = $true )
& ( infuncsetfunc = $true )
& ( setminusELneg = $true )
& ( disjointsetsI1 = $true )
& ( sepInPowerset = $true )
& ( setadjoinAx = $true )
& ( upairsetIR = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementTI1 = $true )
& ( nonemptyImpWitness = $true )
& ( kpairp = $true )
& ( binintersectSubset4 = $true )
& ( lam2lamEq = $true )
& ( setminusI = $true )
& ( setukpairinjL = $true )
& ( binintersectT_lem = $true )
& ( kpairiskpair = $true )
& ( emptyE1 = $true )
& ( cartprodfstpairEq = $true )
& ( binunionRsub = $true )
& ( ex1I = $true )
& ( brelnall1 = $true )
& ( subsetRefl = $true )
& ( dpsetconstrSub = $true )
& ( binintersectSubset3 = $true )
& ( subset2powerset = $true )
& ( exuI3 = $true )
& ( binintersectRsub = $true )
& ( complementTcontraSubset = $true )
& ( notequalI2 = $true )
& ( contraSubsetComplement = $true )
& ( cartprodsndin = $true )
& ( dpsetconstrI = $true )
& ( powersetTI1 = $true )
& ( omegaIndAx = $true )
& ( setukpairinjL2 = $true )
& ( singletonprop = $true )
& ( subbreln = $true )
& ( setext = $true )
& ( setminusEL = $true )
& ( ksndsingleton = $true )
& ( nonemptyI = $true )
& ( emptyinunitempty = $true )
& ( funcGraphProp3 = $true )
& ( powersetT_lem = $true )
& ( doubleComplementI1 = $true )
& ( exuE3u = $true )
& ( binintersectI = $true )
& ( exuI2 = $true )
& ( setukpairinjR2 = $true )
& ( funcGraphProp2 = $true )
& ( setukpairinjL1 = $true )
& ( eqbreln = $true )
& ( brelnall2 = $true )
& ( setminusILneg = $true )
& ( cartprodpairin = $true )
& ( subsetI1 = $true )
& ( upairsubunion = $true )
& ( binunionLsub = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( lamProp = $true )
& ( binintersectTERcontra = $true )
& ( emptyInPowerset = $true )
& ( setminusT_lem = $true )
& ( singletoninpowunion = $true )
& ( subsetE = $true )
& ( theprop = $true )
& ( descr__Cong = $true )
& ( powersetTE1 = $true )
& ( exuE3e = $true )
& ( subsetTrans = $true )
& ( contrasubsetT2 = $true )
& ( setunionsingleton = $true )
& ( complementTE1 = $true )
& ( funcinfuncset = $true )
& ( setukpairinjR12 = $true )
& ( binintersectLsub = $true )
& ( funcextLem = $true )
& ( app = $true )
& ( setadjoinE = $true )
& ( setukpairinjR11 = $true )
& ( beta1 = $true )
& ( complementImpComplementIntersect = $true )
& ( powersetsubset = $true )
& ( theeq = $true )
& ( doubleComplementSub1 = $true )
& ( setOfPairsIsBReln = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionI = $true )
& ( setunionAx = $true )
& ( powersetE = $true )
& ( quantDeMorgan2 = $true )
& ( ex1E2 = $true )
& ( notequalI1 = $true )
& ( demorgan2a2 = $true )
& ( prop2set2propI = $true )
& ( kpairsurjEq = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( setukpairinjR = $true )
& ( inIntersectImpInUnion = $true )
& ( symdiffE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( emptyinPowerset = $true )
& ( subsetE2 = $true )
& ( ubforcartprodlem3 = $true )
& ( dpsetconstrERa = $true )
& ( vacuousDall = $true )
& ( subsetI2 = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( iftrueProp2 = $true )
& ( contrasubsetT1 = $true )
& ( setoftrueEq = $true )
& ( setextAx = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI1 = $true )
& ( secondinupair = $true )
& ( ap2apEq2 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset2 = $true )
& ( bs114d = $true )
& ( setminusLsub = $true )
& ( complementT_lem = $true )
& ( descrp = $true )
& ( eta1 = $true )
& ( iftrueProp1 = $true )
& ( upairsetE = $true )
& ( dsetconstr__Cong = $true )
& ( funcImageSingleton = $true )
& ( singletonsswitch = $true )
& ( setextT = $true )
& ( setextsub = $true )
& ( cartprodpairmemEL = $true )
& ( setukpairIL = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( lamp = $true )
& ( notinsingleton = $true )
& ( notdallE = $true )
& ( ex1I2 = $true )
& ( funcext = $true )
& ( setunionsingleton1 = $true )
& ( ex1E1 = $true )
& ( setminusERneg = $true )
& ( binunionE = $true )
& ( setukpairIR = $true )
& ( omegaSAx = $true )
& ( exu__Cong = $true )
& ( funcGraphProp4 = $true )
& ( wellorderingAx = $true )
& ( upairset2E = $true )
& ( doubleComplementSub2 = $true )
& ( notsubsetI = $true )
& ( notdexE = $true )
& ( ap2p = $true )
& ( upairinpowunion = $true )
& ( iffalseProp2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( complementTnotintersectT = $true )
& ( iffalse = $true )
& ( exuI1 = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( symdiffIneg2 = $true )
& ( cartprodmempair = $true )
& ( beta2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK397,sK398,sK399,sK400]),skolemize(X0,sK397),skolemize(X1,sK398),skolemize(X2,sK399),skolemize(X3,sK400)],[f1549]) ).
thf(f1674,plain,
( ( ( binintersectI = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( binintersectI != $true ) ) ),
inference(nnf_transformation,[],[f983]) ).
thf(f1675,plain,
( ( ( binintersectI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
!= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( $true
!= ( in @ X5 @ X3 ) ) )
| ( binintersectI != $true ) ) ),
inference(rectify,[],[f1674]) ).
thf(f1676,plain,
( ( ( binintersectI = $true )
| ( ( $true
= ( in @ sK541 @ sK540 ) )
& ( ( in @ sK541 @ ( binintersect @ sK540 @ sK539 ) )
!= $true )
& ( $true
= ( in @ sK541 @ sK539 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( $true
!= ( in @ X5 @ X3 ) ) )
| ( binintersectI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK539,sK540,sK541]),skolemize(X0,sK539),skolemize(X1,sK540),skolemize(X2,sK541)],[f1675]) ).
thf(f1803,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( binunionIR != $true ) )
& ( ( binunionIR = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f986]) ).
thf(f1804,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( binunionIR != $true ) )
& ( ( binunionIR = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binunion @ X3 @ X4 ) ) )
& ( ( in @ X5 @ X4 )
= $true ) ) ) ),
inference(rectify,[],[f1803]) ).
thf(f1805,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( binunionIR != $true ) )
& ( ( binunionIR = $true )
| ( ( $true
!= ( in @ sK673 @ ( binunion @ sK671 @ sK672 ) ) )
& ( $true
= ( in @ sK673 @ sK672 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK671,sK672,sK673]),skolemize(X3,sK671),skolemize(X4,sK672),skolemize(X5,sK673)],[f1804]) ).
thf(f1967,plain,
( ( ( setminusIRneg = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
| ( setminusIRneg != $true ) ) ),
inference(nnf_transformation,[],[f871]) ).
thf(f1968,plain,
( ( ( setminusIRneg = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
!= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) ) )
| ( setminusIRneg != $true ) ) ),
inference(rectify,[],[f1967]) ).
thf(f1969,plain,
( ( ( setminusIRneg = $true )
| ( ( $true
= ( in @ sK839 @ sK838 ) )
& ( $true
= ( in @ sK839 @ ( setminus @ sK840 @ sK838 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
!= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) ) )
| ( setminusIRneg != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK838,sK839,sK840]),skolemize(X0,sK838),skolemize(X1,sK839),skolemize(X2,sK840)],[f1968]) ).
thf(f2474,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunionIL != $true )
| ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f1503]) ).
thf(f2508,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( ( in @ X4 @ X5 )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) )
| ( setminusELneg != $true ) ),
inference(cnf_transformation,[],[f1530]) ).
thf(f2660,plain,
binintersectI = $true,
inference(cnf_transformation,[],[f1550]) ).
thf(f2705,plain,
setminusELneg = $true,
inference(cnf_transformation,[],[f1550]) ).
thf(f2782,plain,
( $true
= ( in @ sK400 @ sK398 ) ),
inference(cnf_transformation,[],[f1550]) ).
thf(f2783,plain,
( $true
!= ( in @ sK400 @ ( binunion @ ( setminus @ sK398 @ sK397 ) @ ( setminus @ sK398 @ sK399 ) ) ) ),
inference(cnf_transformation,[],[f1550]) ).
thf(f2784,plain,
( ( in @ sK400 @ ( setminus @ sK398 @ ( binintersect @ sK397 @ sK399 ) ) )
= $true ),
inference(cnf_transformation,[],[f1550]) ).
thf(f2788,plain,
binunionIL = $true,
inference(cnf_transformation,[],[f1550]) ).
thf(f2803,plain,
binunionIR = $true,
inference(cnf_transformation,[],[f1550]) ).
thf(f2807,plain,
setminusIRneg = $true,
inference(cnf_transformation,[],[f1550]) ).
thf(f2995,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( binintersectI != $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( $true
!= ( in @ X5 @ X3 ) ) ),
inference(cnf_transformation,[],[f1676]) ).
thf(f3176,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( binunionIR != $true )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f1805]) ).
thf(f3389,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
!= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( setminusIRneg != $true ) ),
inference(cnf_transformation,[],[f1969]) ).
thf(f4378,definition,
( spl853_167
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl853_167])],[avatar_definition]) ).
thf(f4379,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ~ spl853_167 ),
inference(avatar_component_clause,[],[f4378]) ).
thf(f4425,definition,
( spl853_178
<=> ( binintersectI = $true ) ),
introduced(definition,[new_symbols(definition,[spl853_178])],[avatar_definition]) ).
thf(f4428,plain,
spl853_178,
inference(avatar_split_clause,[],[f2660,f4425]) ).
thf(f5046,definition,
( spl853_315
<=> ( setminusELneg = $true ) ),
introduced(definition,[new_symbols(definition,[spl853_315])],[avatar_definition]) ).
thf(f5223,definition,
( spl853_353
<=> ( setminusIRneg = $true ) ),
introduced(definition,[new_symbols(definition,[spl853_353])],[avatar_definition]) ).
thf(f5506,definition,
( spl853_416
<=> ( binunionIR = $true ) ),
introduced(definition,[new_symbols(definition,[spl853_416])],[avatar_definition]) ).
thf(f5509,plain,
spl853_416,
inference(avatar_split_clause,[],[f2803,f5506]) ).
thf(f5939,definition,
( spl853_509
<=> ( binunionIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl853_509])],[avatar_definition]) ).
thf(f5942,plain,
spl853_509,
inference(avatar_split_clause,[],[f2788,f5939]) ).
thf(f5970,definition,
( spl853_516
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl853_516])],[avatar_definition]) ).
thf(f5971,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ~ spl853_516 ),
inference(avatar_component_clause,[],[f5970]) ).
thf(f5972,plain,
( ~ spl853_509
| spl853_516 ),
inference(avatar_split_clause,[],[f2474,f5970,f5939]) ).
thf(f6418,definition,
( spl853_614
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl853_614])],[avatar_definition]) ).
thf(f6419,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ~ spl853_614 ),
inference(avatar_component_clause,[],[f6418]) ).
thf(f6785,definition,
( spl853_691
<=> ( $true
= ( in @ sK400 @ sK398 ) ) ),
introduced(definition,[new_symbols(definition,[spl853_691])],[avatar_definition]) ).
thf(f6787,plain,
( ( $true
= ( in @ sK400 @ sK398 ) )
| ~ spl853_691 ),
inference(avatar_component_clause,[],[f6785]) ).
thf(f6788,plain,
spl853_691,
inference(avatar_split_clause,[],[f2782,f6785]) ).
thf(f7268,definition,
( spl853_793
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl853_793])],[avatar_definition]) ).
thf(f7269,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ~ spl853_793 ),
inference(avatar_component_clause,[],[f7268]) ).
thf(f7270,plain,
( spl853_793
| ~ spl853_416 ),
inference(avatar_split_clause,[],[f3176,f5506,f7268]) ).
thf(f7521,definition,
( spl853_845
<=> ( $true
= ( in @ sK400 @ ( binunion @ ( setminus @ sK398 @ sK397 ) @ ( setminus @ sK398 @ sK399 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl853_845])],[avatar_definition]) ).
thf(f7523,plain,
( ( $true
!= ( in @ sK400 @ ( binunion @ ( setminus @ sK398 @ sK397 ) @ ( setminus @ sK398 @ sK399 ) ) ) )
| spl853_845 ),
inference(avatar_component_clause,[],[f7521]) ).
thf(f7524,plain,
~ spl853_845,
inference(avatar_split_clause,[],[f2783,f7521]) ).
thf(f8452,plain,
( ~ spl853_353
| spl853_167 ),
inference(avatar_split_clause,[],[f3389,f4378,f5223]) ).
thf(f8850,definition,
( spl853_1119
<=> ( ( in @ sK400 @ ( setminus @ sK398 @ ( binintersect @ sK397 @ sK399 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl853_1119])],[avatar_definition]) ).
thf(f8852,plain,
( ( ( in @ sK400 @ ( setminus @ sK398 @ ( binintersect @ sK397 @ sK399 ) ) )
= $true )
| ~ spl853_1119 ),
inference(avatar_component_clause,[],[f8850]) ).
thf(f8853,plain,
spl853_1119,
inference(avatar_split_clause,[],[f2784,f8850]) ).
thf(f8903,definition,
( spl853_1130
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl853_1130])],[avatar_definition]) ).
thf(f8904,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( in @ X5 @ X3 ) ) )
| ~ spl853_1130 ),
inference(avatar_component_clause,[],[f8903]) ).
thf(f8905,plain,
( spl853_1130
| ~ spl853_178 ),
inference(avatar_split_clause,[],[f2995,f4425,f8903]) ).
thf(f8979,plain,
spl853_315,
inference(avatar_split_clause,[],[f2705,f5046]) ).
thf(f9061,plain,
( ~ spl853_315
| spl853_614 ),
inference(avatar_split_clause,[],[f2508,f6418,f5046]) ).
thf(f9700,plain,
spl853_353,
inference(avatar_split_clause,[],[f2807,f5223]) ).
thf(f10143,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK400 @ ( binintersect @ sK397 @ sK399 ) ) )
| ~ spl853_167
| ~ spl853_1119 ),
inference(superposition,[],[f4379,f8852]) ).
thf(f10145,plain,
( ( $true
!= ( in @ sK400 @ ( binintersect @ sK397 @ sK399 ) ) )
| ~ spl853_167
| ~ spl853_1119 ),
inference(trivial_inequality_removal,[],[f10143]) ).
thf(f10148,definition,
( spl853_1368
<=> ( $true
= ( in @ sK400 @ ( binintersect @ sK397 @ sK399 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl853_1368])],[avatar_definition]) ).
thf(f10150,plain,
( ( $true
!= ( in @ sK400 @ ( binintersect @ sK397 @ sK399 ) ) )
| spl853_1368 ),
inference(avatar_component_clause,[],[f10148]) ).
thf(f10151,plain,
( ~ spl853_1368
| ~ spl853_167
| ~ spl853_1119 ),
inference(avatar_split_clause,[],[f10145,f8850,f4378,f10148]) ).
thf(f10545,definition,
( spl853_1378
<=> ( $true
= ( in @ sK400 @ sK399 ) ) ),
introduced(definition,[new_symbols(definition,[spl853_1378])],[avatar_definition]) ).
thf(f10546,plain,
( ( $true
= ( in @ sK400 @ sK399 ) )
| ~ spl853_1378 ),
inference(avatar_component_clause,[],[f10545]) ).
thf(f10555,definition,
( spl853_1380
<=> ( $true
= ( in @ sK400 @ ( setminus @ sK398 @ sK399 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl853_1380])],[avatar_definition]) ).
thf(f10556,plain,
( ( $true
!= ( in @ sK400 @ ( setminus @ sK398 @ sK399 ) ) )
| spl853_1380 ),
inference(avatar_component_clause,[],[f10555]) ).
thf(f10719,definition,
( spl853_1398
<=> ( $true
= ( in @ sK400 @ ( setminus @ sK398 @ sK397 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl853_1398])],[avatar_definition]) ).
thf(f10720,plain,
( ( $true
!= ( in @ sK400 @ ( setminus @ sK398 @ sK397 ) ) )
| spl853_1398 ),
inference(avatar_component_clause,[],[f10719]) ).
thf(f10724,definition,
( spl853_1399
<=> ( ( in @ sK400 @ sK397 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl853_1399])],[avatar_definition]) ).
thf(f11044,plain,
( ( $true
!= ( in @ sK400 @ ( setminus @ sK398 @ sK397 ) ) )
| ( $true != $true )
| ~ spl853_516
| spl853_845 ),
inference(superposition,[],[f7523,f5971]) ).
thf(f11047,plain,
( ( $true
!= ( in @ sK400 @ ( setminus @ sK398 @ sK397 ) ) )
| ~ spl853_516
| spl853_845 ),
inference(trivial_inequality_removal,[],[f11044]) ).
thf(f11052,plain,
( ~ spl853_1398
| ~ spl853_516
| spl853_845 ),
inference(avatar_split_clause,[],[f11047,f7521,f5970,f10719]) ).
thf(f11126,plain,
( ( $true
!= ( in @ sK400 @ ( setminus @ sK398 @ sK399 ) ) )
| ( $true != $true )
| ~ spl853_793
| spl853_845 ),
inference(superposition,[],[f7523,f7269]) ).
thf(f11130,plain,
( ( $true
!= ( in @ sK400 @ ( setminus @ sK398 @ sK399 ) ) )
| ~ spl853_793
| spl853_845 ),
inference(trivial_inequality_removal,[],[f11126]) ).
thf(f11136,plain,
( ~ spl853_1380
| ~ spl853_793
| spl853_845 ),
inference(avatar_split_clause,[],[f11130,f7521,f7268,f10555]) ).
thf(f12457,plain,
( ( $true
= ( in @ sK400 @ sK399 ) )
| ( $true != $true )
| ( $true
!= ( in @ sK400 @ sK398 ) )
| ~ spl853_614
| spl853_1380 ),
inference(superposition,[],[f10556,f6419]) ).
thf(f12458,plain,
( ( ( in @ sK400 @ sK397 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK400 @ sK398 ) )
| ~ spl853_614
| spl853_1398 ),
inference(superposition,[],[f10720,f6419]) ).
thf(f12468,plain,
( ( ( in @ sK400 @ sK397 )
= $true )
| ( $true
!= ( in @ sK400 @ sK398 ) )
| ~ spl853_614
| spl853_1398 ),
inference(trivial_inequality_removal,[],[f12458]) ).
thf(f12471,plain,
( ( $true
!= ( in @ sK400 @ sK398 ) )
| ( $true
= ( in @ sK400 @ sK399 ) )
| ~ spl853_614
| spl853_1380 ),
inference(trivial_inequality_removal,[],[f12457]) ).
thf(f12479,plain,
( ( ( in @ sK400 @ sK397 )
= $true )
| ~ spl853_614
| ~ spl853_691
| spl853_1398 ),
inference(forward_subsumption_resolution,[],[f12468,f6787]) ).
thf(f12480,plain,
( ( $true
= ( in @ sK400 @ sK399 ) )
| ~ spl853_614
| ~ spl853_691
| spl853_1380 ),
inference(forward_subsumption_resolution,[],[f12471,f6787]) ).
thf(f12481,plain,
( spl853_1399
| ~ spl853_614
| ~ spl853_691
| spl853_1398 ),
inference(avatar_split_clause,[],[f12479,f10719,f6785,f6418,f10724]) ).
thf(f12482,plain,
( spl853_1378
| ~ spl853_614
| ~ spl853_691
| spl853_1380 ),
inference(avatar_split_clause,[],[f12480,f10555,f6785,f6418,f10545]) ).
thf(f12728,plain,
( ( $true
!= ( in @ sK400 @ sK399 ) )
| ( ( in @ sK400 @ sK397 )
!= $true )
| ( $true != $true )
| ~ spl853_1130
| spl853_1368 ),
inference(superposition,[],[f10150,f8904]) ).
thf(f12729,plain,
( ( $true
!= ( in @ sK400 @ sK399 ) )
| ( ( in @ sK400 @ sK397 )
!= $true )
| ~ spl853_1130
| spl853_1368 ),
inference(trivial_inequality_removal,[],[f12728]) ).
thf(f12746,plain,
( ( ( in @ sK400 @ sK397 )
!= $true )
| ~ spl853_1130
| spl853_1368
| ~ spl853_1378 ),
inference(forward_subsumption_resolution,[],[f12729,f10546]) ).
thf(f12747,plain,
( ~ spl853_1399
| ~ spl853_1130
| spl853_1368
| ~ spl853_1378 ),
inference(avatar_split_clause,[],[f12746,f10545,f10148,f8903,f10724]) ).
cnf(s111,plain,
spl853_178,
inference(sat_conversion,[],[f4428]) ).
cnf(s305,plain,
spl853_416,
inference(sat_conversion,[],[f5509]) ).
cnf(s394,plain,
spl853_509,
inference(sat_conversion,[],[f5942]) ).
cnf(s399,plain,
( ~ spl853_509
| spl853_516 ),
inference(sat_conversion,[],[f5972]) ).
cnf(s575,plain,
spl853_691,
inference(sat_conversion,[],[f6788]) ).
cnf(s682,plain,
( ~ spl853_416
| spl853_793 ),
inference(sat_conversion,[],[f7270]) ).
cnf(s742,plain,
~ spl853_845,
inference(sat_conversion,[],[f7524]) ).
cnf(s961,plain,
( spl853_167
| ~ spl853_353 ),
inference(sat_conversion,[],[f8452]) ).
cnf(s1071,plain,
spl853_1119,
inference(sat_conversion,[],[f8853]) ).
cnf(s1083,plain,
( ~ spl853_178
| spl853_1130 ),
inference(sat_conversion,[],[f8905]) ).
cnf(s1099,plain,
spl853_315,
inference(sat_conversion,[],[f8979]) ).
cnf(s1122,plain,
( ~ spl853_315
| spl853_614 ),
inference(sat_conversion,[],[f9061]) ).
cnf(s1294,plain,
spl853_353,
inference(sat_conversion,[],[f9700]) ).
cnf(s1395,plain,
( ~ spl853_167
| ~ spl853_1119
| ~ spl853_1368 ),
inference(sat_conversion,[],[f10151]) ).
cnf(s1448,plain,
( ~ spl853_516
| spl853_845
| ~ spl853_1398 ),
inference(sat_conversion,[],[f11052]) ).
cnf(s1451,plain,
( ~ spl853_793
| spl853_845
| ~ spl853_1380 ),
inference(sat_conversion,[],[f11136]) ).
cnf(s1471,plain,
( ~ spl853_614
| ~ spl853_691
| spl853_1398
| spl853_1399 ),
inference(sat_conversion,[],[f12481]) ).
cnf(s1472,plain,
( ~ spl853_614
| ~ spl853_691
| spl853_1378
| spl853_1380 ),
inference(sat_conversion,[],[f12482]) ).
cnf(s1478,plain,
( ~ spl853_1130
| spl853_1368
| ~ spl853_1378
| ~ spl853_1399 ),
inference(sat_conversion,[],[f12747]) ).
cnf(s1492,plain,
spl853_614,
inference(rat,[],[s1122,s1099]) ).
cnf(s1506,plain,
spl853_167,
inference(rat,[],[s961,s1294]) ).
cnf(s1507,plain,
~ spl853_1368,
inference(rat,[],[s1395,s1071,s1506]) ).
cnf(s1650,plain,
spl853_516,
inference(rat,[],[s399,s394]) ).
cnf(s1651,plain,
~ spl853_1398,
inference(rat,[],[s1448,s742,s1650]) ).
cnf(s1652,plain,
spl853_1399,
inference(rat,[],[s1471,s575,s1492,s1651]) ).
cnf(s1690,plain,
spl853_793,
inference(rat,[],[s682,s305]) ).
cnf(s1691,plain,
~ spl853_1380,
inference(rat,[],[s1451,s742,s1690]) ).
cnf(s1692,plain,
spl853_1378,
inference(rat,[],[s1472,s575,s1492,s1691]) ).
cnf(s1694,plain,
~ spl853_1130,
inference(rat,[],[s1478,s1652,s1507,s1692]) ).
cnf(s1695,plain,
~ spl853_178,
inference(rat,[],[s1083,s1694]) ).
cnf(s1802,plain,
$false,
inference(rat,[],[s111,s1695]) ).
thf(f12748,plain,
$false,
inference(avatar_sat_refutation,[],[s1802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU751^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:21:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.20/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.44 % (846991)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.44 % (847000)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1724923300:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.44 % (847002)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.44 % (847002)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
% 0.30/0.44 % (847000)Instruction limit reached!
% 0.30/0.44 % (847000)------------------------------
% 0.30/0.44 % (847000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (847000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (847000)CaDiCaL version: 2.1.3
% 0.30/0.44 % (847000)Termination reason: Instruction limit
% 0.30/0.44 % (847000)Termination phase: shuffling
% 0.30/0.44 % (847000)Time elapsed: 0.006 s
% 0.30/0.44 % (847000)Peak memory usage: 10 MB
% 0.30/0.44 % (847000)Instructions burned: 24 (million)
% 0.30/0.44 % (846996)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=763058903:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.44 % (846997)lrs+10_16_si=on:nwc=1.5:random_seed=1566916782:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.44 % (846998)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1849834911:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.44 % (846999)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=1619082801: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)
% 0.30/0.44 % (847002)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=2429408652:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.44 % (847001)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1634271320:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.44 % (846998)Instruction limit reached!
% 0.30/0.44 % (846998)------------------------------
% 0.30/0.44 % (846998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (846998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (846998)CaDiCaL version: 2.1.3
% 0.30/0.44 % (846998)Termination reason: Instruction limit
% 0.30/0.44 % (846998)Termination phase: shuffling
% 0.30/0.44 % (846998)Time elapsed: 0.003 s
% 0.30/0.44 % (846998)Peak memory usage: 10 MB
% 0.30/0.44 % (846998)Instructions burned: 5 (million)
% 0.30/0.44 % (846997)Instruction limit reached!
% 0.30/0.44 % (846997)------------------------------
% 0.30/0.44 % (846997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (846997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (846997)CaDiCaL version: 2.1.3
% 0.30/0.44 % (846997)Termination reason: Instruction limit
% 0.30/0.44 % (846997)Termination phase: shuffling
% 0.30/0.44 % (846997)Time elapsed: 0.010 s
% 0.30/0.44 % (846997)Peak memory usage: 10 MB
% 0.30/0.44 % (846997)Instructions burned: 20 (million)
% 0.30/0.44 % (847004)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2370994540:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.44 % (847004)Instruction limit reached!
% 0.30/0.44 % (847004)------------------------------
% 0.30/0.44 % (847004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (847004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (847004)CaDiCaL version: 2.1.3
% 0.30/0.44 % (847004)Termination reason: Instruction limit
% 0.30/0.44 % (847004)Termination phase: shuffling
% 0.30/0.44 % (847004)Time elapsed: 0.001 s
% 0.30/0.44 % (847004)Peak memory usage: 10 MB
% 0.30/0.44 % (847004)Instructions burned: 3 (million)
% 0.30/0.44 % (847014)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=547470388:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.30/0.44 % (847011)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1479367019:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.05/0.47 % (847014)Instruction limit reached!
% 1.05/0.47 % (847014)------------------------------
% 1.05/0.47 % (847014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.47 % (847013)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.05/0.47 % (847014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.47 % (847014)CaDiCaL version: 2.1.3
% 1.05/0.47 % (847014)Termination reason: Instruction limit
% 1.05/0.47 % (847014)Termination phase: shuffling
% 1.05/0.47 % (847014)Time elapsed: 0.003 s
% 1.05/0.47 % (847014)Peak memory usage: 10 MB
% 1.05/0.47 % (847014)Instructions burned: 14 (million)
% 1.05/0.47 % (847011)Instruction limit reached!
% 1.05/0.47 % (847011)------------------------------
% 1.05/0.47 % (847011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.47 % (847011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.47 % (847011)CaDiCaL version: 2.1.3
% 1.05/0.47 % (847011)Termination reason: Instruction limit
% 1.05/0.47 % (847011)Termination phase: shuffling
% 1.05/0.47 % (847011)Time elapsed: 0.003 s
% 1.05/0.47 % (847011)Peak memory usage: 10 MB
% 1.05/0.47 % (847011)Instructions burned: 6 (million)
% 1.05/0.47 % (847013)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2569159762:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.05/0.47 % (847013)Instruction limit reached!
% 1.05/0.47 % (847013)------------------------------
% 1.05/0.47 % (847013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.47 % (847013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.47 % (847013)CaDiCaL version: 2.1.3
% 1.05/0.47 % (847013)Termination reason: Instruction limit
% 1.05/0.47 % (847013)Termination phase: shuffling
% 1.05/0.47 % (847013)Time elapsed: 0.004 s
% 1.05/0.47 % (847013)Peak memory usage: 10 MB
% 1.05/0.47 % (847013)Instructions burned: 8 (million)
% 1.05/0.47 % (847017)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.05/0.47 % (847017)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.05/0.47 % (847001)Instruction limit reached!
% 1.05/0.47 % (847001)------------------------------
% 1.05/0.47 % (847001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.47 % (847001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.47 % (847001)CaDiCaL version: 2.1.3
% 1.05/0.47 % (847001)Termination reason: Instruction limit
% 1.05/0.47 % (847001)Termination phase: Preprocessing 3
% 1.05/0.47 % (847001)Time elapsed: 0.035 s
% 1.05/0.47 % (847001)Peak memory usage: 12 MB
% 1.05/0.47 % (847001)Instructions burned: 76 (million)
% 1.05/0.47 % (847017)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3812593589:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.05/0.47 % (846996)Instruction limit reached!
% 1.05/0.47 % (846996)------------------------------
% 1.05/0.47 % (846996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.47 % (846996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.47 % (846996)CaDiCaL version: 2.1.3
% 1.05/0.47 % (846996)Termination reason: Instruction limit
% 1.05/0.47 % (846996)Termination phase: Preprocessing 3
% 1.05/0.47 % (846996)Time elapsed: 0.040 s
% 1.05/0.47 % (846996)Peak memory usage: 12 MB
% 1.05/0.47 % (846996)Instructions burned: 87 (million)
% 1.05/0.47 % (847017)Instruction limit reached!
% 1.05/0.47 % (847017)------------------------------
% 1.05/0.47 % (847017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.47 % (847017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.47 % (847017)CaDiCaL version: 2.1.3
% 1.05/0.47 % (847017)Termination reason: Instruction limit
% 1.05/0.47 % (847017)Termination phase: shuffling
% 1.05/0.47 % (847017)Time elapsed: 0.007 s
% 1.05/0.47 % (847017)Peak memory usage: 11 MB
% 1.05/0.47 % (847017)Instructions burned: 30 (million)
% 1.05/0.50 % (847018)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=2935964267:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.05/0.50 % (847021)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.05/0.50 % (847020)lrs+10_1_si=on:cs=on:random_seed=1334219871:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.05/0.50 % (847021)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=3515439986:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.05/0.50 % (847024)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4096084842:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.05/0.50 % (847021)Instruction limit reached!
% 1.05/0.50 % (847021)------------------------------
% 1.05/0.50 % (847021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (847021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (847021)CaDiCaL version: 2.1.3
% 1.05/0.50 % (847021)Termination reason: Instruction limit
% 1.05/0.50 % (847021)Termination phase: shuffling
% 1.05/0.50 % (847021)Time elapsed: 0.002 s
% 1.05/0.50 % (847021)Peak memory usage: 10 MB
% 1.05/0.50 % (847021)Instructions burned: 3 (million)
% 1.05/0.50 % (847020)Instruction limit reached!
% 1.05/0.50 % (847020)------------------------------
% 1.05/0.50 % (847020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (847020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (847020)CaDiCaL version: 2.1.3
% 1.05/0.50 % (847020)Termination reason: Instruction limit
% 1.05/0.50 % (847020)Termination phase: shuffling
% 1.05/0.50 % (847020)Time elapsed: 0.004 s
% 1.05/0.50 % (847020)Peak memory usage: 10 MB
% 1.05/0.50 % (847020)Instructions burned: 9 (million)
% 1.05/0.50 % (847023)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1475329615:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.05/0.50 % (847002)Instruction limit reached!
% 1.05/0.50 % (847002)------------------------------
% 1.05/0.50 % (847002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (847002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (847002)CaDiCaL version: 2.1.3
% 1.05/0.50 % (847002)Termination reason: Instruction limit
% 1.05/0.50 % (847002)Termination phase: Property scanning
% 1.05/0.50 % (847002)Time elapsed: 0.069 s
% 1.05/0.50 % (847002)Peak memory usage: 13 MB
% 1.05/0.50 % (847002)Instructions burned: 158 (million)
% 1.05/0.50 % (847029)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3486934324:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.05/0.50 % (847030)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3081618727:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.05/0.50 % (847023)Instruction limit reached!
% 1.05/0.50 % (847023)------------------------------
% 1.05/0.50 % (847023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (847023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (847023)CaDiCaL version: 2.1.3
% 1.05/0.50 % (847023)Termination reason: Instruction limit
% 1.05/0.50 % (847023)Termination phase: Property scanning
% 1.05/0.50 % (847023)Time elapsed: 0.018 s
% 1.05/0.50 % (847023)Peak memory usage: 11 MB
% 1.05/0.50 % (847023)Instructions burned: 41 (million)
% 1.05/0.50 % (847018)Instruction limit reached!
% 1.05/0.50 % (847018)------------------------------
% 1.05/0.50 % (847018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.50 % (847018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.50 % (847018)CaDiCaL version: 2.1.3
% 1.05/0.50 % (847018)Termination reason: Instruction limit
% 1.05/0.50 % (847018)Termination phase: Property scanning
% 1.05/0.50 % (847018)Time elapsed: 0.036 s
% 1.05/0.50 % (847018)Peak memory usage: 11 MB
% 1.05/0.50 % (847018)Instructions burned: 86 (million)
% 1.05/0.50 % (847030)Instruction limit reached!
% 1.05/0.50 % (847030)------------------------------
% 1.05/0.54 % (847030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.54 % (847030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.54 % (847030)CaDiCaL version: 2.1.3
% 1.05/0.54 % (847030)Termination reason: Instruction limit
% 1.05/0.54 % (847030)Termination phase: shuffling
% 1.05/0.54 % (847030)Time elapsed: 0.007 s
% 1.05/0.54 % (847030)Peak memory usage: 10 MB
% 1.05/0.54 % (847030)Instructions burned: 16 (million)
% 1.05/0.54 % (847032)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3482112558:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.05/0.54 % (847029)Instruction limit reached!
% 1.05/0.54 % (847029)------------------------------
% 1.05/0.54 % (847029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.54 % (847029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.54 % (847029)CaDiCaL version: 2.1.3
% 1.05/0.54 % (847029)Termination reason: Instruction limit
% 1.05/0.54 % (847029)Termination phase: shuffling
% 1.05/0.54 % (847029)Time elapsed: 0.012 s
% 1.05/0.54 % (847029)Peak memory usage: 10 MB
% 1.05/0.54 % (847029)Instructions burned: 26 (million)
% 1.05/0.54 % (847035)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=292456555:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.05/0.54 % (847036)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2739441956: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)
% 1.05/0.54 % (847036)Instruction limit reached!
% 1.05/0.54 % (847036)------------------------------
% 1.05/0.54 % (847036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.54 % (847036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.54 % (847036)CaDiCaL version: 2.1.3
% 1.05/0.54 % (847036)Termination reason: Instruction limit
% 1.05/0.54 % (847036)Termination phase: shuffling
% 1.05/0.54 % (847036)Time elapsed: 0.002 s
% 1.05/0.54 % (847036)Peak memory usage: 10 MB
% 1.05/0.54 % (847036)Instructions burned: 3 (million)
% 1.05/0.54 % (847035)Instruction limit reached!
% 1.05/0.54 % (847035)------------------------------
% 1.05/0.54 % (847035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.54 % (847035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.54 % (847035)CaDiCaL version: 2.1.3
% 1.05/0.54 % (847035)Termination reason: Instruction limit
% 1.05/0.54 % (847035)Termination phase: shuffling
% 1.05/0.54 % (847035)Time elapsed: 0.007 s
% 1.05/0.54 % (847035)Peak memory usage: 10 MB
% 1.05/0.54 % (847037)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3234258516:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.05/0.54 % (847035)Instructions burned: 14 (million)
% 1.05/0.54 % (847039)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3564783914:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.05/0.54 % (847024)Instruction limit reached!
% 1.05/0.54 % (847024)------------------------------
% 1.05/0.54 % (847024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.54 % (847024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.54 % (847024)CaDiCaL version: 2.1.3
% 1.05/0.54 % (847024)Termination reason: Instruction limit
% 1.05/0.54 % (847024)Termination phase: Saturation
% 1.05/0.54 % (847024)Time elapsed: 0.057 s
% 1.05/0.54 % (847024)Peak memory usage: 15 MB
% 1.05/0.54 % (847024)Instructions burned: 253 (million)
% 1.05/0.54 % (847037)Instruction limit reached!
% 1.05/0.54 % (847037)------------------------------
% 1.05/0.54 % (847037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.54 % (847037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.54 % (847037)CaDiCaL version: 2.1.3
% 1.05/0.54 % (847037)Termination reason: Instruction limit
% 1.05/0.54 % (847037)Termination phase: shuffling
% 1.05/0.54 % (847037)Time elapsed: 0.012 s
% 1.05/0.54 % (847037)Peak memory usage: 11 MB
% 1.05/0.54 % (847037)Instructions burned: 27 (million)
% 1.05/0.54 % (847039)Instruction limit reached!
% 1.05/0.54 % (847039)------------------------------
% 1.05/0.54 % (847039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.54 % (847039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.61 % (847039)CaDiCaL version: 2.1.3
% 1.80/0.61 % (847039)Termination reason: Instruction limit
% 1.80/0.61 % (847039)Termination phase: shuffling
% 1.80/0.61 % (847039)Time elapsed: 0.011 s
% 1.80/0.61 % (847039)Peak memory usage: 11 MB
% 1.80/0.61 % (847039)Instructions burned: 24 (million)
% 1.80/0.61 % (847044)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.80/0.61 % (847044)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.80/0.61 % (847046)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.80/0.61 % (847042)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2887297536:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.80/0.61 % (847046)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=1414160304:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.80/0.61 % (847044)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=240900199:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.80/0.61 % (847046)Instruction limit reached!
% 1.80/0.61 % (847046)------------------------------
% 1.80/0.61 % (847046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.61 % (847046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.61 % (847046)CaDiCaL version: 2.1.3
% 1.80/0.61 % (847046)Termination reason: Instruction limit
% 1.80/0.61 % (847046)Termination phase: shuffling
% 1.80/0.61 % (847046)Time elapsed: 0.003 s
% 1.80/0.61 % (847046)Peak memory usage: 10 MB
% 1.80/0.61 % (847046)Instructions burned: 12 (million)
% 1.80/0.61 % (847044)Instruction limit reached!
% 1.80/0.61 % (847044)------------------------------
% 1.80/0.61 % (847044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.61 % (847044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.61 % (847044)CaDiCaL version: 2.1.3
% 1.80/0.61 % (847044)Termination reason: Instruction limit
% 1.80/0.61 % (847044)Termination phase: shuffling
% 1.80/0.61 % (847044)Time elapsed: 0.007 s
% 1.80/0.61 % (847044)Peak memory usage: 10 MB
% 1.80/0.61 % (847044)Instructions burned: 16 (million)
% 1.80/0.61 % (847052)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3715755428:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.80/0.61 % (847047)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=2223238224:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.80/0.61 % (847048)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3925149624:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.80/0.61 % (847048)Instruction limit reached!
% 1.80/0.61 % (847048)------------------------------
% 1.80/0.61 % (847048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.61 % (847048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.61 % (847048)CaDiCaL version: 2.1.3
% 1.80/0.61 % (847048)Termination reason: Instruction limit
% 1.80/0.61 % (847048)Termination phase: shuffling
% 1.80/0.61 % (847048)Time elapsed: 0.004 s
% 1.80/0.61 % (847048)Peak memory usage: 10 MB
% 1.80/0.61 % (847048)Instructions burned: 8 (million)
% 1.80/0.61 % (847052)Instruction limit reached!
% 1.80/0.61 % (847052)------------------------------
% 1.80/0.61 % (847052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.61 % (847052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.61 % (847052)CaDiCaL version: 2.1.3
% 1.80/0.61 % (847052)Termination reason: Instruction limit
% 1.80/0.61 % (847052)Termination phase: shuffling
% 1.80/0.61 % (847052)Time elapsed: 0.006 s
% 1.80/0.61 % (847052)Peak memory usage: 11 MB
% 1.80/0.61 % (847052)Instructions burned: 27 (million)
% 1.80/0.61 % (847042)Instruction limit reached!
% 1.80/0.61 % (847042)------------------------------
% 2.15/0.66 % (847042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.66 % (847042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.66 % (847042)CaDiCaL version: 2.1.3
% 2.15/0.66 % (847042)Termination reason: Instruction limit
% 2.15/0.66 % (847042)Termination phase: Preprocessing 3
% 2.15/0.66 % (847042)Time elapsed: 0.028 s
% 2.15/0.66 % (847042)Peak memory usage: 12 MB
% 2.15/0.66 % (847042)Instructions burned: 62 (million)
% 2.15/0.66 % (847047)Instruction limit reached!
% 2.15/0.66 % (847047)------------------------------
% 2.15/0.66 % (847047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.66 % (847047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.66 % (847047)CaDiCaL version: 2.1.3
% 2.15/0.66 % (847053)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1300586227:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.15/0.66 % (847047)Termination reason: Instruction limit
% 2.15/0.66 % (847047)Termination phase: shuffling
% 2.15/0.66 % (847047)Time elapsed: 0.014 s
% 2.15/0.66 % (847047)Peak memory usage: 11 MB
% 2.15/0.67 % (847047)Instructions burned: 31 (million)
% 2.15/0.67 % (847058)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2673728479:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.15/0.67 % (847057)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2330180644:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.15/0.67 % (847053)Instruction limit reached!
% 2.15/0.67 % (847053)------------------------------
% 2.15/0.67 % (847053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847053)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847053)Termination reason: Instruction limit
% 2.15/0.67 % (847053)Termination phase: shuffling
% 2.15/0.67 % (847053)Time elapsed: 0.009 s
% 2.15/0.67 % (847053)Peak memory usage: 10 MB
% 2.15/0.67 % (847053)Instructions burned: 21 (million)
% 2.15/0.67 % (847059)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1868931904:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.15/0.67 % (847061)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1723591224:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.15/0.67 % (847064)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.15/0.67 % (847064)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=418688769:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.15/0.67 % (847064)Instruction limit reached!
% 2.15/0.67 % (847064)------------------------------
% 2.15/0.67 % (847064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847064)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847064)Termination reason: Instruction limit
% 2.15/0.67 % (847064)Termination phase: shuffling
% 2.15/0.67 % (847064)Time elapsed: 0.003 s
% 2.15/0.67 % (847064)Peak memory usage: 10 MB
% 2.15/0.67 % (847064)Instructions burned: 7 (million)
% 2.15/0.67 % (847058)Instruction limit reached!
% 2.15/0.67 % (847058)------------------------------
% 2.15/0.67 % (847058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847058)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847058)Termination reason: Instruction limit
% 2.15/0.67 % (847058)Termination phase: Property scanning
% 2.15/0.67 % (847058)Time elapsed: 0.031 s
% 2.15/0.67 % (847058)Peak memory usage: 12 MB
% 2.15/0.67 % (847058)Instructions burned: 143 (million)
% 2.15/0.67 % (847061)Instruction limit reached!
% 2.15/0.67 % (847061)------------------------------
% 2.15/0.67 % (847061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847061)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847061)Termination reason: Instruction limit
% 2.15/0.67 % (847061)Termination phase: Property scanning
% 2.15/0.67 % (847061)Time elapsed: 0.019 s
% 2.15/0.67 % (847061)Peak memory usage: 11 MB
% 2.15/0.67 % (847061)Instructions burned: 44 (million)
% 2.15/0.67 % (847069)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=1011438061:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.15/0.67 % (847068)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1331641426:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.15/0.67 % (847070)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.15/0.67 % (847070)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3084434628:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.15/0.67 % (847070)Instruction limit reached!
% 2.15/0.67 % (847070)------------------------------
% 2.15/0.67 % (847070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847070)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847070)Termination reason: Instruction limit
% 2.15/0.67 % (847070)Termination phase: shuffling
% 2.15/0.67 % (847070)Time elapsed: 0.004 s
% 2.15/0.67 % (847070)Peak memory usage: 10 MB
% 2.15/0.67 % (847070)Instructions burned: 8 (million)
% 2.15/0.67 % (847074)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1044971964:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.15/0.67 % (847032)Instruction limit reached!
% 2.15/0.67 % (847032)------------------------------
% 2.15/0.67 % (847032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847032)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847032)Termination reason: Instruction limit
% 2.15/0.67 % (847032)Termination phase: Saturation
% 2.15/0.67 % (847032)Time elapsed: 0.148 s
% 2.15/0.67 % (847032)Peak memory usage: 15 MB
% 2.15/0.67 % (847032)Instructions burned: 327 (million)
% 2.15/0.67 % (847069)Instruction limit reached!
% 2.15/0.67 % (847069)------------------------------
% 2.15/0.67 % (847069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847069)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847069)Termination reason: Instruction limit
% 2.15/0.67 % (847069)Termination phase: Saturation
% 2.15/0.67 % (847069)Time elapsed: 0.038 s
% 2.15/0.67 % (847069)Peak memory usage: 13 MB
% 2.15/0.67 % (847069)Instructions burned: 174 (million)
% 2.15/0.67 % (847074)Instruction limit reached!
% 2.15/0.67 % (847074)------------------------------
% 2.15/0.67 % (847074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847074)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847074)Termination reason: Instruction limit
% 2.15/0.67 % (847074)Termination phase: shuffling
% 2.15/0.67 % (847074)Time elapsed: 0.010 s
% 2.15/0.67 % (847074)Peak memory usage: 10 MB
% 2.15/0.67 % (847074)Instructions burned: 23 (million)
% 2.15/0.67 % (847076)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=477919444:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.15/0.67 % (847076)Instruction limit reached!
% 2.15/0.67 % (847076)------------------------------
% 2.15/0.67 % (847076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847076)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847076)Termination reason: Instruction limit
% 2.15/0.67 % (847076)Termination phase: shuffling
% 2.15/0.67 % (847076)Time elapsed: 0.005 s
% 2.15/0.67 % (847076)Peak memory usage: 10 MB
% 2.15/0.67 % (847076)Instructions burned: 22 (million)
% 2.15/0.67 % (847059)Instruction limit reached!
% 2.15/0.67 % (847059)------------------------------
% 2.15/0.67 % (847059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847059)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847059)Termination reason: Instruction limit
% 2.15/0.67 % (847059)Termination phase: Saturation
% 2.15/0.67 % (847059)Time elapsed: 0.083 s
% 2.15/0.67 % (847059)Peak memory usage: 13 MB
% 2.15/0.67 % (847059)Instructions burned: 194 (million)
% 2.15/0.67 % (847077)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=320947559:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.15/0.67 % (847080)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=152432064:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.15/0.67 % (847078)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=3112913066:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.15/0.67 % (847081)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1798529789:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.15/0.67 % (847080)Instruction limit reached!
% 2.15/0.67 % (847080)------------------------------
% 2.15/0.67 % (847080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847080)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847080)Termination reason: Instruction limit
% 2.15/0.67 % (847080)Termination phase: Property scanning
% 2.15/0.67 % (847080)Time elapsed: 0.011 s
% 2.15/0.67 % (847080)Peak memory usage: 11 MB
% 2.15/0.67 % (847080)Instructions burned: 47 (million)
% 2.15/0.67 % (847068)Instruction limit reached!
% 2.15/0.67 % (847068)------------------------------
% 2.15/0.67 % (847068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847068)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847068)Termination reason: Instruction limit
% 2.15/0.67 % (847068)Termination phase: Saturation
% 2.15/0.67 % (847068)Time elapsed: 0.076 s
% 2.15/0.67 % (847068)Peak memory usage: 14 MB
% 2.15/0.67 % (847068)Instructions burned: 182 (million)
% 2.15/0.67 % (847086)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=427577396:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.15/0.67 % (847086)Instruction limit reached!
% 2.15/0.67 % (847086)------------------------------
% 2.15/0.67 % (847086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847086)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847086)Termination reason: Instruction limit
% 2.15/0.67 % (847086)Termination phase: shuffling
% 2.15/0.67 % (847086)Time elapsed: 0.005 s
% 2.15/0.67 % (847086)Peak memory usage: 10 MB
% 2.15/0.67 % (847086)Instructions burned: 23 (million)
% 2.15/0.67 % (847087)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.15/0.67 % (846999) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-846991-846999"...
% 2.15/0.67 % (847089)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1581392029:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.15/0.67 % (847087)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3900285549:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.15/0.67 % (847089)Instruction limit reached!
% 2.15/0.67 % (847089)------------------------------
% 2.15/0.67 % (847089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (847089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (847089)CaDiCaL version: 2.1.3
% 2.15/0.67 % (847089)Termination reason: Instruction limit
% 2.15/0.67 % (847089)Termination phase: shuffling
% 2.15/0.67 % (847089)Time elapsed: 0.004 s
% 2.15/0.67 % (847089)Peak memory usage: 10 MB
% 2.15/0.67 % (847089)Instructions burned: 17 (million)
% 2.15/0.67 % (846999)...printing done.
% 2.15/0.67 % (846999)Refutation found. Thanks to Tanya!
% 2.15/0.67 % SZS status Theorem for theBenchmark
% 2.15/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 2.15/0.67 % (846999)------------------------------
% 2.15/0.67 % (846999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (846999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (846999)CaDiCaL version: 2.1.3
% 2.15/0.67 % (846999)Termination reason: Refutation
% 2.15/0.67 % (846999)Time elapsed: 0.307 s
% 2.15/0.67 % (846999)Peak memory usage: 22 MB
% 2.15/0.67 % (846999)Instructions burned: 596 (million)
% 2.15/0.67 % (846991)Success in time 0.366 s
% 2.15/0.67 % Vampire exiting
%------------------------------------------------------------------------------