%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU758^1 : 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 : n018.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 08:31:10 AM UTC 2026
% Result : Theorem 1.70s 0.61s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 31 unt; 0 typ; 11 def)
% Number of atoms : 4793 (1263 equ; 0 cnn)
% Maximal formula atoms : 278 ( 48 avg)
% Number of connectives : 2597 ( 125 ~; 107 |; 852 &; 372 @)
% ( 19 <=>;1122 =>; 0 <=; 0 <~>)
% Maximal formula depth : 286 ( 24 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 : 514 ( 511 usr; 319 con; 0-4 aty)
% Number of variables : 128 ( 0 sgn 104 !; 24 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_279,type,
contrasubsetT1: $o ).
thf(func_def_280,type,
contrasubsetT2: $o ).
thf(func_def_281,type,
contrasubsetT3: $o ).
thf(func_def_282,type,
doubleComplementI1: $o ).
thf(func_def_283,type,
doubleComplementE1: $o ).
thf(func_def_284,type,
doubleComplementSub1: $o ).
thf(func_def_285,type,
doubleComplementSub2: $o ).
thf(func_def_286,type,
doubleComplementEq: $o ).
thf(func_def_287,type,
complementTnotintersectT: $o ).
thf(func_def_288,type,
complementImpComplementIntersect: $o ).
thf(func_def_289,type,
complementSubsetComplementIntersect: $o ).
thf(func_def_290,type,
complementInPowersetComplementIntersect: $o ).
thf(func_def_291,type,
contraSubsetComplement: $o ).
thf(func_def_292,type,
complementTcontraSubset: $o ).
thf(func_def_293,type,
binunionTILcontra: $o ).
thf(func_def_294,type,
binunionTIRcontra: $o ).
thf(func_def_295,type,
inIntersectImpInUnion: $o ).
thf(func_def_296,type,
inIntersectImpInUnion2: $o ).
thf(func_def_297,type,
inIntersectImpInIntersectUnions: $o ).
thf(func_def_298,type,
intersectInPowersetIntersectUnions: $o ).
thf(func_def_299,type,
inComplementUnionImpNotIn1: $o ).
thf(func_def_300,type,
inComplementUnionImpInComplement1: $o ).
thf(func_def_301,type,
binunionTE: $o ).
thf(func_def_302,type,
binunionTEcontra: $o ).
thf(func_def_303,type,
demorgan2a1: $o ).
thf(func_def_304,type,
complementUnionInPowersetComplement: $o ).
thf(func_def_305,type,
demorgan2a2: $o ).
thf(func_def_306,type,
demorgan1a: $o ).
thf(func_def_307,type,
demorgan1b: $o ).
thf(func_def_308,type,
demorgan1: $o ).
thf(func_def_309,type,
demorgan2a: $o ).
thf(func_def_310,type,
demorgan2b2: $o ).
thf(func_def_311,type,
demorgan2b: $o ).
thf(func_def_312,type,
demorgan2: $o ).
thf(func_def_315,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_316,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_317,type,
vNOT: $o > $o ).
thf(func_def_318,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_319,type,
vOR: $o > $o > $o ).
thf(func_def_320,type,
vAND: $o > $o > $o ).
thf(func_def_321,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_322,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_323,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_324,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_325,type,
vIMP: $o > $o > $o ).
thf(func_def_326,type,
sP0: $o ).
thf(func_def_327,type,
sP1: $i > $i > $o ).
thf(func_def_328,type,
sP2: $i > $o ).
thf(func_def_329,type,
sP3: $o ).
thf(func_def_330,type,
sK4: $o ).
thf(func_def_337,type,
sK11: $o ).
thf(func_def_350,type,
sK24: $o ).
thf(func_def_352,type,
sK26: $o > $i > $i > $i ).
thf(func_def_355,type,
sK29: $o ).
thf(func_def_357,type,
sK31: $i > $o ).
thf(func_def_359,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_363,type,
sK37: $i > $o ).
thf(func_def_385,type,
sK59: $i > $i > $i > $i > $i ).
thf(func_def_386,type,
sK60: $i > $i > $i > $i > $i ).
thf(func_def_394,type,
sK68: $o ).
thf(func_def_410,type,
sK84: $i > ( $i > $i ) > $i > $i ).
thf(func_def_412,type,
sK86: $i > $i ).
thf(func_def_423,type,
sK97: $i > $i > $o ).
thf(func_def_424,type,
sK98: $o ).
thf(func_def_444,type,
sK118: $i > $i > $o ).
thf(func_def_446,type,
sK120: $i > $i > $i ).
thf(func_def_450,type,
sK124: $i > ( $i > $o ) > $i ).
thf(func_def_451,type,
sK125: $i > $o ).
thf(func_def_457,type,
sK131: $o ).
thf(func_def_483,type,
sK157: $i > $o ).
thf(func_def_489,type,
sK163: $o ).
thf(func_def_497,type,
sK171: ( $i > $o ) > $i > $i ).
thf(func_def_499,type,
sK173: $i > $o ).
thf(func_def_508,type,
sK182: $i > $o ).
thf(func_def_511,type,
sK185: $i > ( $i > $o ) > $i ).
thf(func_def_512,type,
sK186: $i > ( $i > $o ) > $i ).
thf(func_def_531,type,
sK205: $i > $i > $i ).
thf(func_def_534,type,
sK208: $o ).
thf(func_def_538,type,
sK212: $i > $i > $i ).
thf(func_def_542,type,
sK216: $i > $i ).
thf(func_def_544,type,
sK218: $i > $i ).
thf(func_def_546,type,
sK220: $i > $o ).
thf(func_def_548,type,
sK222: ( $i > $o ) > $i > $i ).
thf(func_def_574,type,
sK248: ( $i > $o ) > $i ).
thf(func_def_575,type,
sK249: $i > $o ).
thf(func_def_576,type,
sK250: $i > $i ).
thf(func_def_590,type,
sK264: $i > $i > $i > $i > $i ).
thf(func_def_600,type,
sK274: $i > $i > $o ).
thf(func_def_610,type,
sK284: $o ).
thf(func_def_617,type,
sK291: $i > $i > $i > $i ).
thf(func_def_618,type,
sK292: $i > $i > $i > $i ).
thf(func_def_637,type,
sK311: $i > $i > $i > $i ).
thf(func_def_643,type,
sK317: $i > $o ).
thf(func_def_645,type,
sK319: $i > $o ).
thf(func_def_646,type,
sK320: $i > $o ).
thf(func_def_647,type,
sK321: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_648,type,
sK322: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_654,type,
sK328: $o ).
thf(func_def_675,type,
sK349: ( $i > $i ) > $i > $i > $i ).
thf(func_def_678,type,
sK352: $i > $i ).
thf(func_def_682,type,
sK356: $i > $i > $o ).
thf(func_def_694,type,
sK368: $i > $i > $i ).
thf(func_def_698,type,
sK372: $i > $o ).
thf(func_def_700,type,
sK374: $i > ( $i > $o ) > $i ).
thf(func_def_703,type,
sK377: $i > $i ).
thf(func_def_705,type,
sK379: ( $i > $i ) > $i > $i > $i ).
thf(func_def_706,type,
sK380: $i > $o ).
thf(func_def_714,type,
sK388: $i > ( $i > $o ) > $i ).
thf(func_def_715,type,
sK389: $i > ( $i > $o ) > $i ).
thf(func_def_716,type,
sK390: $i > $o ).
thf(func_def_745,type,
sK419: $i > $i ).
thf(func_def_751,type,
sK425: $i > $i > $o ).
thf(func_def_752,type,
sK426: $i > $i ).
thf(func_def_753,type,
sK427: $i > $i ).
thf(func_def_754,type,
sK428: ( $i > $i > $o ) > $i > $i ).
thf(func_def_755,type,
sK429: ( $i > $i > $o ) > $i > $i ).
thf(func_def_756,type,
sK430: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_757,type,
sK431: $i > ( $i > $o ) > $i ).
thf(func_def_758,type,
sK432: $i > $o ).
thf(func_def_786,type,
sK460: $i > $i > $i ).
thf(func_def_787,type,
sK461: $i > $i > $i ).
thf(func_def_790,type,
sK464: $i > $o ).
thf(func_def_792,type,
sK466: ( $i > $o ) > $i ).
thf(func_def_793,type,
sK467: ( $i > $o ) > $i ).
thf(func_def_796,type,
sK470: $i > $i ).
thf(func_def_797,type,
sK471: ( $i > $i ) > $i > $i > $i ).
thf(func_def_799,type,
sK473: $i > $o ).
thf(func_def_801,type,
sK475: ( $i > $o ) > $i > $i ).
thf(func_def_805,type,
sK479: $i > $i > $i > $i ).
thf(func_def_806,type,
sK480: $i > $i > $i > $i ).
thf(func_def_815,type,
sK489: $o ).
thf(func_def_819,type,
sK493: $i > $i > $i > $i > $i ).
thf(func_def_826,type,
sK500: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_827,type,
sK501: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_830,type,
sK504: $i > $o ).
thf(func_def_831,type,
sK505: $i > $o ).
thf(func_def_833,type,
sK507: $i > $o ).
thf(func_def_837,type,
sK511: $i > $o ).
thf(func_def_839,type,
sK513: $i > ( $i > $o ) > $i ).
thf(func_def_849,type,
sK523: $i > $i > $i > $i > $i ).
thf(func_def_850,type,
sK524: $i > $i > $i > $i > $i ).
thf(func_def_851,type,
sK525: $i > $i > $i > $i > $i ).
thf(func_def_852,type,
sK526: $i > $i > $i > $i > $i ).
thf(func_def_854,type,
sK528: $o ).
thf(func_def_857,type,
sK531: ( $i > $i ) > $i > $i > $i ).
thf(func_def_860,type,
sK534: $i > $i ).
thf(func_def_868,type,
sK542: $i > $o ).
thf(func_def_869,type,
sK543: $i > $o ).
thf(func_def_870,type,
sK544: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_871,type,
sK545: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_873,type,
sK547: $i > $i ).
thf(func_def_874,type,
sK548: $i > $i ).
thf(func_def_875,type,
sK549: $i > $i ).
thf(func_def_876,type,
sK550: $i > $i ).
thf(func_def_877,type,
sK551: $i > $i ).
thf(func_def_878,type,
sK552: $i > $i > $i > $i ).
thf(func_def_879,type,
sK553: $i > $i ).
thf(func_def_880,type,
sK554: $i > $i ).
thf(func_def_881,type,
sK555: $i > $i ).
thf(func_def_882,type,
sK556: $i > $i ).
thf(func_def_883,type,
sK557: $i > $i > $i ).
thf(func_def_884,type,
sK558: $i > $i > $i ).
thf(func_def_885,type,
sK559: $i > $i > $i > $i ).
thf(func_def_886,type,
sK560: $i > $i > $i > $i ).
thf(func_def_887,type,
sK561: $i > $i > $i > $i ).
thf(func_def_888,type,
sK562: $i > $i > $i ).
thf(func_def_889,type,
sK563: $i > $i > $i ).
thf(func_def_890,type,
sK564: $i > $i > $i ).
thf(func_def_897,type,
sK571: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_898,type,
sK572: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_902,type,
sK576: $i > $o ).
thf(func_def_917,type,
sK591: $i > $i > $o ).
thf(func_def_925,type,
sK599: $i > $o ).
thf(func_def_934,type,
sK608: $o ).
thf(func_def_940,type,
sK614: $i > $i > $o ).
thf(func_def_955,type,
sK629: $i > $o ).
thf(func_def_957,type,
sK631: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_958,type,
sK632: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_977,type,
sK651: $i > $i > $i > $i ).
thf(func_def_982,type,
sK656: $i > $o ).
thf(func_def_988,type,
sK662: $o ).
thf(func_def_991,type,
sK665: $o ).
thf(func_def_993,type,
sK667: $i > $o ).
thf(func_def_1012,type,
sK686: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1015,type,
sK689: $i > $i ).
thf(func_def_1020,type,
sK694: $i > $i ).
thf(func_def_1025,type,
sK699: $i > $i ).
thf(func_def_1027,type,
sK701: $i > $i ).
thf(func_def_1044,type,
sK718: $i > $o ).
thf(func_def_1045,type,
sK719: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1048,type,
sK722: $i > $o ).
thf(func_def_1051,type,
sK725: ( $i > $o ) > $i ).
thf(func_def_1052,type,
sK726: $i > $o ).
thf(func_def_1056,type,
sK730: $i > $i > $i ).
thf(func_def_1068,type,
sK742: $i > $o ).
thf(func_def_1071,type,
sK745: $o ).
thf(func_def_1087,type,
sK761: $o ).
thf(func_def_1098,type,
sK772: $i > $o ).
thf(func_def_1105,type,
sK779: $i > $o ).
thf(func_def_1108,type,
sK782: $i > $i > $i ).
thf(func_def_1115,type,
sK789: $i > $i > $i ).
thf(func_def_1121,type,
sK795: $i > $o ).
thf(func_def_1123,type,
sK797: ( $i > $o ) > $i > $i ).
thf(func_def_1124,type,
sK798: ( $i > $o ) > $i ).
thf(func_def_1125,type,
sK799: $i > $o ).
thf(func_def_1126,type,
sK800: $i > $i ).
thf(func_def_1129,type,
sK803: $i > $i > $i ).
thf(func_def_1161,type,
sK835: $i > $i > $o ).
thf(func_def_1165,type,
sK839: $i > $i ).
thf(func_def_1177,type,
sK851: $i > $i > $i > $i > $i ).
thf(func_def_1190,type,
sK864: $i > $o ).
thf(f85,axiom,
( notsubsetI
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( subset @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(f96,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(f110,axiom,
( binintersectEL
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(f279,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule0) ).
thf(f280,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f279]) ).
thf(f510,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f110]) ).
thf(f511,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
=> ( ( in @ X1 @ X2 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(fool_elimination,[],[f510]) ).
thf(f566,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f280]) ).
thf(f567,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
= $true )
=> ( ( in @ X3 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f566]) ).
thf(f640,plain,
( notsubsetI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> ~ ( subset @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f85]) ).
thf(f641,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( subset @ X0 @ X2 )
!= $true ) ) ) ),
inference(fool_elimination,[],[f640]) ).
thf(f678,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= powersetE1 ),
inference(rectify,[],[f96]) ).
thf(f679,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(fool_elimination,[],[f678]) ).
thf(f862,plain,
( ( notsubsetI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( subset @ X0 @ X2 )
!= $true ) ) ) ),
inference(flattening,[],[f641]) ).
thf(f907,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(ennf_transformation,[],[f511]) ).
thf(f922,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(ennf_transformation,[],[f679]) ).
thf(f925,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
!= $true ) ) ) )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f567]) ).
thf(f926,plain,
( ( demorgan2a1 = $true )
& ( ubforcartprodlem3 = $true )
& ( setunionI = $true )
& ( complementTcontraSubset = $true )
& ( exuE3u = $true )
& ( app = $true )
& ( nonemptyI = $true )
& ( beta2 = $true )
& ( funcGraphProp2 = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( cartprodpairsurjEq = $true )
& ( setukpairinjR2 = $true )
& ( emptyE1 = $true )
& ( doubleComplementI1 = $true )
& ( setunionsingleton2 = $true )
& ( iffalse = $true )
& ( in__Cong = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjL2 = $true )
& ( setminusSubset1 = $true )
& ( binunionTE = $true )
& ( exuI1 = $true )
& ( subsetI2 = $true )
& ( exuI2 = $true )
& ( contrasubsetT = $true )
& ( binunionIL = $true )
& ( funcGraphProp3 = $true )
& ( kfstsingleton = $true )
& ( symdiffI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionRsub = $true )
& ( binintersectSubset5 = $true )
& ( setunionE = $true )
& ( ap2p = $true )
& ( setukpairIL = $true )
& ( subsetI1 = $true )
& ( binunionIR = $true )
& ( emptysetimpfalse = $true )
& ( setunion__Cong = $true )
& ( singletonsswitch = $true )
& ( symdiffI2 = $true )
& ( setunionsingleton1 = $true )
& ( singletonsuniq = $true )
& ( contrasubsetT1 = $true )
& ( funcinfuncset = $true )
& ( demorgan2b = $true )
& ( binintersectTELcontra = $true )
& ( exuE3e = $true )
& ( nonemptyImpWitness = $true )
& ( kpairsurjEq = $true )
& ( iftrueorfalse = $true )
& ( inPowerset = $true )
& ( setukpairinjR1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binunionTILcontra = $true )
& ( dpsetconstrEL1 = $true )
& ( cartprodmempaircEq = $true )
& ( setunionE2 = $true )
& ( contrasubsetT3 = $true )
& ( inCongP = $true )
& ( upairset2IR = $true )
& ( complementT_lem = $true )
& ( eqimpsubset1 = $true )
& ( iffalseProp2 = $true )
& ( kpairiskpair = $true )
& ( binintersectT_lem = $true )
& ( upairequniteq = $true )
& ( foundationAx = $true )
& ( notdexE = $true )
& ( lam2p = $true )
& ( eqinunit = $true )
& ( iftrue = $true )
& ( notdallE = $true )
& ( ubforcartprodlem2 = $true )
& ( disjointsetsI1 = $true )
& ( subPowSU = $true )
& ( vacuousDall = $true )
& ( notequalI2 = $true )
& ( setminusLsub = $true )
& ( bs114d = $true )
& ( setadjoinIR = $true )
& ( binunionTEcontra = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( complementImpComplementIntersect = $true )
& ( funcextLem = $true )
& ( complementSubsetComplementIntersect = $true )
& ( eta2 = $true )
& ( setadjoinSub2 = $true )
& ( binunionEcases = $true )
& ( ex1E2 = $true )
& ( subsetE2 = $true )
& ( omega0Ax = $true )
& ( symdiffIneg1 = $true )
& ( setminusELneg = $true )
& ( omegaIndAx = $true )
& ( binintersectSubset2 = $true )
& ( setextT = $true )
& ( powersetI = $true )
& ( singletonsubset = $true )
& ( powersetTI1 = $true )
& ( ap2apEq2 = $true )
& ( symdiffE = $true )
& ( dpsetconstrERa = $true )
& ( binintersectLsub = $true )
& ( secondinupair = $true )
& ( upairsubunion = $true )
& ( binintersectSubset3 = $true )
& ( doubleComplementSub2 = $true )
& ( setext = $true )
& ( cartprodfstpairEq = $true )
& ( ex1I2 = $true )
& ( brelnall1 = $true )
& ( demorgan1 = $true )
& ( powersetI1 = $true )
& ( ksndpairEq = $true )
& ( notinsingleton = $true )
& ( funcext = $true )
& ( dpsetconstrEL2 = $true )
& ( emptysetE = $true )
& ( binunionT_lem = $true )
& ( beta1 = $true )
& ( setukpairinjR = $true )
& ( emptyset__Cong = $true )
& ( infuncsetfunc = $true )
& ( notinemptyset = $true )
& ( setminusERneg = $true )
& ( binintersectTERcontra = $true )
& ( dsetconstrEL = $true )
& ( dpsetconstrSub = $true )
& ( binintersectI = $true )
& ( funcext2 = $true )
& ( powersetE1 = $true )
& ( demorgan2a2 = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
!= $true ) ) ) )
& ( sepInPowerset = $true )
& ( subsetTrans = $true )
& ( doubleComplementE1 = $true )
& ( cartprodsndin = $true )
& ( singletonprop = $true )
& ( ifp = $true )
& ( emptyinunitempty = $true )
& ( demorgan1b = $true )
& ( powersetT_lem = $true )
& ( apProp = $true )
& ( complementTnotintersectT = $true )
& ( dsetconstrER = $true )
& ( setbeta = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( setminusIRneg = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjL = $true )
& ( binintersectEL = $true )
& ( quantDeMorgan2 = $true )
& ( theprop = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairIR = $true )
& ( emptysetAx = $true )
& ( setminusT_lem = $true )
& ( demorgan2b2 = $true )
& ( nonemptyI1 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan3 = $true )
& ( exu__Cong = $true )
& ( lam2lamEq = $true )
& ( dpsetconstrER = $true )
& ( binintersectSubset4 = $true )
& ( funcGraphProp1 = $true )
& ( eqbreln = $true )
& ( subsetTI = $true )
& ( setukpairinjL1 = $true )
& ( binintersectER = $true )
& ( exuE1 = $true )
& ( exuEu = $true )
& ( uniqinunit = $true )
& ( emptyinPowerset = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setunionsingleton = $true )
& ( complementTE1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( demorgan2a = $true )
& ( lamProp = $true )
& ( cartprodsndpairEq = $true )
& ( doubleComplementEq = $true )
& ( ex1E1 = $true )
& ( ubforcartprodlem1 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodpairmemEL = $true )
& ( emptyInPowerset = $true )
& ( doubleComplementSub1 = $true )
& ( subbreln = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( dsetconstr__Cong = $true )
& ( ex1I = $true )
& ( cartprodpairin = $true )
& ( demorgan2 = $true )
& ( upairsetIL = $true )
& ( iffalseProp1 = $true )
& ( noeltsimpempty = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( setadjoinOr = $true )
& ( binunionLsub = $true )
& ( setukpairinjR11 = $true )
& ( kfstpairEq = $true )
& ( setminusEL = $true )
& ( iftrueProp2 = $true )
& ( cartprodpairmemER = $true )
& ( setukpairinjR12 = $true )
& ( funcImageSingleton = $true )
& ( cartprodmempair1 = $true )
& ( binintersectRsub = $true )
& ( quantDeMorgan1 = $true )
& ( brelnall2 = $true )
& ( setminusILneg = $true )
& ( setadjoinSub = $true )
& ( powerset__Cong = $true )
& ( upairinpowunion = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( setadjoinAx = $true )
& ( upairsetIR = $true )
& ( theeq = $true )
& ( contrasubsetT2 = $true )
& ( kpairp = $true )
& ( subset2powerset = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetRefl = $true )
& ( prop2setI = $true )
& ( setadjoinIL = $true )
& ( powersetTE1 = $true )
& ( setextAx = $true )
& ( cartprodmempair = $true )
& ( singletoninpowunion = $true )
& ( binunionTIRcontra = $true )
& ( setadjoin__Cong = $true )
& ( demorgan1a = $true )
& ( replAx = $true )
& ( omega__Cong = $true )
& ( ap2apEq1 = $true )
& ( notsubsetI = $true )
& ( iftrueProp1 = $true )
& ( symdiffIneg2 = $true )
& ( upairsetE = $true )
& ( contraSubsetComplement = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrI = $true )
& ( exuI3 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( prop2set2propI = $true )
& ( eta1 = $true )
& ( complementTI1 = $true )
& ( ifSingleton = $true )
& ( subsetE = $true )
& ( descrp = $true )
& ( emptyI = $true )
& ( descr__Cong = $true )
& ( powersetsubset = $true )
& ( powersetE = $true )
& ( ksndsingleton = $true )
& ( exuE2 = $true )
& ( setminusSubset2 = $true )
& ( wellorderingAx = $true )
& ( cartprodfstin = $true )
& ( binunionE = $true )
& ( eqimpsubset2 = $true )
& ( emptysetsubset = $true )
& ( dsetconstrI = $true )
& ( setoftrueEq = $true )
& ( sepSubset = $true )
& ( binintersectSubset1 = $true )
& ( upairset2E = $true )
& ( lamp = $true )
& ( inIntersectImpInUnion = $true ) ),
inference(flattening,[],[f925]) ).
thf(f1061,plain,
( ( notsubsetI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f862]) ).
thf(f1062,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) )
<=> ( notsubsetI = $true ) ),
inference(flattening,[],[f1061]) ).
thf(f1451,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
!= $true )
& ( ( subset @ X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f1062]) ).
thf(f1452,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( $true
!= ( in @ X3 @ X4 ) )
& ( $true
= ( subset @ X5 @ X4 ) ) ) ) ),
inference(rectify,[],[f1451]) ).
thf(f1453,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ( ( $true
= ( in @ sK253 @ sK255 ) )
& ( ( in @ sK253 @ sK254 )
!= $true )
& ( ( subset @ sK255 @ sK254 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK253,sK254,sK255]),skolemize(X3,sK253),skolemize(X4,sK254),skolemize(X5,sK255)],[f1452]) ).
thf(f1795,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f907]) ).
thf(f1796,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binintersect @ X5 @ X3 ) )
= $true )
& ( ( in @ X4 @ X5 )
!= $true ) ) ) ),
inference(rectify,[],[f1795]) ).
thf(f1797,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ( ( $true
= ( in @ sK636 @ ( binintersect @ sK637 @ sK635 ) ) )
& ( $true
!= ( in @ sK636 @ sK637 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK635,sK636,sK637]),skolemize(X3,sK635),skolemize(X4,sK636),skolemize(X5,sK637)],[f1796]) ).
thf(f1834,plain,
( ( demorgan2a1 = $true )
& ( ubforcartprodlem3 = $true )
& ( setunionI = $true )
& ( complementTcontraSubset = $true )
& ( exuE3u = $true )
& ( app = $true )
& ( nonemptyI = $true )
& ( beta2 = $true )
& ( funcGraphProp2 = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( cartprodpairsurjEq = $true )
& ( setukpairinjR2 = $true )
& ( emptyE1 = $true )
& ( doubleComplementI1 = $true )
& ( setunionsingleton2 = $true )
& ( iffalse = $true )
& ( in__Cong = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjL2 = $true )
& ( setminusSubset1 = $true )
& ( binunionTE = $true )
& ( exuI1 = $true )
& ( subsetI2 = $true )
& ( exuI2 = $true )
& ( contrasubsetT = $true )
& ( binunionIL = $true )
& ( funcGraphProp3 = $true )
& ( kfstsingleton = $true )
& ( symdiffI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionRsub = $true )
& ( binintersectSubset5 = $true )
& ( setunionE = $true )
& ( ap2p = $true )
& ( setukpairIL = $true )
& ( subsetI1 = $true )
& ( binunionIR = $true )
& ( emptysetimpfalse = $true )
& ( setunion__Cong = $true )
& ( singletonsswitch = $true )
& ( symdiffI2 = $true )
& ( setunionsingleton1 = $true )
& ( singletonsuniq = $true )
& ( contrasubsetT1 = $true )
& ( funcinfuncset = $true )
& ( demorgan2b = $true )
& ( binintersectTELcontra = $true )
& ( exuE3e = $true )
& ( nonemptyImpWitness = $true )
& ( kpairsurjEq = $true )
& ( iftrueorfalse = $true )
& ( inPowerset = $true )
& ( setukpairinjR1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binunionTILcontra = $true )
& ( dpsetconstrEL1 = $true )
& ( cartprodmempaircEq = $true )
& ( setunionE2 = $true )
& ( contrasubsetT3 = $true )
& ( inCongP = $true )
& ( upairset2IR = $true )
& ( complementT_lem = $true )
& ( eqimpsubset1 = $true )
& ( iffalseProp2 = $true )
& ( kpairiskpair = $true )
& ( binintersectT_lem = $true )
& ( upairequniteq = $true )
& ( foundationAx = $true )
& ( notdexE = $true )
& ( lam2p = $true )
& ( eqinunit = $true )
& ( iftrue = $true )
& ( notdallE = $true )
& ( ubforcartprodlem2 = $true )
& ( disjointsetsI1 = $true )
& ( subPowSU = $true )
& ( vacuousDall = $true )
& ( notequalI2 = $true )
& ( setminusLsub = $true )
& ( bs114d = $true )
& ( setadjoinIR = $true )
& ( binunionTEcontra = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( complementImpComplementIntersect = $true )
& ( funcextLem = $true )
& ( complementSubsetComplementIntersect = $true )
& ( eta2 = $true )
& ( setadjoinSub2 = $true )
& ( binunionEcases = $true )
& ( ex1E2 = $true )
& ( subsetE2 = $true )
& ( omega0Ax = $true )
& ( symdiffIneg1 = $true )
& ( setminusELneg = $true )
& ( omegaIndAx = $true )
& ( binintersectSubset2 = $true )
& ( setextT = $true )
& ( powersetI = $true )
& ( singletonsubset = $true )
& ( powersetTI1 = $true )
& ( ap2apEq2 = $true )
& ( symdiffE = $true )
& ( dpsetconstrERa = $true )
& ( binintersectLsub = $true )
& ( secondinupair = $true )
& ( upairsubunion = $true )
& ( binintersectSubset3 = $true )
& ( doubleComplementSub2 = $true )
& ( setext = $true )
& ( cartprodfstpairEq = $true )
& ( ex1I2 = $true )
& ( brelnall1 = $true )
& ( demorgan1 = $true )
& ( powersetI1 = $true )
& ( ksndpairEq = $true )
& ( notinsingleton = $true )
& ( funcext = $true )
& ( dpsetconstrEL2 = $true )
& ( emptysetE = $true )
& ( binunionT_lem = $true )
& ( beta1 = $true )
& ( setukpairinjR = $true )
& ( emptyset__Cong = $true )
& ( infuncsetfunc = $true )
& ( notinemptyset = $true )
& ( setminusERneg = $true )
& ( binintersectTERcontra = $true )
& ( dsetconstrEL = $true )
& ( dpsetconstrSub = $true )
& ( binintersectI = $true )
& ( funcext2 = $true )
& ( powersetE1 = $true )
& ( demorgan2a2 = $true )
& ( $true
= ( in @ sK672 @ ( powerset @ sK673 ) ) )
& ( $true
= ( in @ sK674 @ ( powerset @ sK673 ) ) )
& ( ( in @ sK675 @ ( binintersect @ sK672 @ sK674 ) )
= $true )
& ( $true
!= ( in @ sK675 @ sK673 ) )
& ( sepInPowerset = $true )
& ( subsetTrans = $true )
& ( doubleComplementE1 = $true )
& ( cartprodsndin = $true )
& ( singletonprop = $true )
& ( ifp = $true )
& ( emptyinunitempty = $true )
& ( demorgan1b = $true )
& ( powersetT_lem = $true )
& ( apProp = $true )
& ( complementTnotintersectT = $true )
& ( dsetconstrER = $true )
& ( setbeta = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( setminusIRneg = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjL = $true )
& ( binintersectEL = $true )
& ( quantDeMorgan2 = $true )
& ( theprop = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairIR = $true )
& ( emptysetAx = $true )
& ( setminusT_lem = $true )
& ( demorgan2b2 = $true )
& ( nonemptyI1 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan3 = $true )
& ( exu__Cong = $true )
& ( lam2lamEq = $true )
& ( dpsetconstrER = $true )
& ( binintersectSubset4 = $true )
& ( funcGraphProp1 = $true )
& ( eqbreln = $true )
& ( subsetTI = $true )
& ( setukpairinjL1 = $true )
& ( binintersectER = $true )
& ( exuE1 = $true )
& ( exuEu = $true )
& ( uniqinunit = $true )
& ( emptyinPowerset = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setunionsingleton = $true )
& ( complementTE1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( demorgan2a = $true )
& ( lamProp = $true )
& ( cartprodsndpairEq = $true )
& ( doubleComplementEq = $true )
& ( ex1E1 = $true )
& ( ubforcartprodlem1 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodpairmemEL = $true )
& ( emptyInPowerset = $true )
& ( doubleComplementSub1 = $true )
& ( subbreln = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( dsetconstr__Cong = $true )
& ( ex1I = $true )
& ( cartprodpairin = $true )
& ( demorgan2 = $true )
& ( upairsetIL = $true )
& ( iffalseProp1 = $true )
& ( noeltsimpempty = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( setadjoinOr = $true )
& ( binunionLsub = $true )
& ( setukpairinjR11 = $true )
& ( kfstpairEq = $true )
& ( setminusEL = $true )
& ( iftrueProp2 = $true )
& ( cartprodpairmemER = $true )
& ( setukpairinjR12 = $true )
& ( funcImageSingleton = $true )
& ( cartprodmempair1 = $true )
& ( binintersectRsub = $true )
& ( quantDeMorgan1 = $true )
& ( brelnall2 = $true )
& ( setminusILneg = $true )
& ( setadjoinSub = $true )
& ( powerset__Cong = $true )
& ( upairinpowunion = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( setadjoinAx = $true )
& ( upairsetIR = $true )
& ( theeq = $true )
& ( contrasubsetT2 = $true )
& ( kpairp = $true )
& ( subset2powerset = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetRefl = $true )
& ( prop2setI = $true )
& ( setadjoinIL = $true )
& ( powersetTE1 = $true )
& ( setextAx = $true )
& ( cartprodmempair = $true )
& ( singletoninpowunion = $true )
& ( binunionTIRcontra = $true )
& ( setadjoin__Cong = $true )
& ( demorgan1a = $true )
& ( replAx = $true )
& ( omega__Cong = $true )
& ( ap2apEq1 = $true )
& ( notsubsetI = $true )
& ( iftrueProp1 = $true )
& ( symdiffIneg2 = $true )
& ( upairsetE = $true )
& ( contraSubsetComplement = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrI = $true )
& ( exuI3 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( prop2set2propI = $true )
& ( eta1 = $true )
& ( complementTI1 = $true )
& ( ifSingleton = $true )
& ( subsetE = $true )
& ( descrp = $true )
& ( emptyI = $true )
& ( descr__Cong = $true )
& ( powersetsubset = $true )
& ( powersetE = $true )
& ( ksndsingleton = $true )
& ( exuE2 = $true )
& ( setminusSubset2 = $true )
& ( wellorderingAx = $true )
& ( cartprodfstin = $true )
& ( binunionE = $true )
& ( eqimpsubset2 = $true )
& ( emptysetsubset = $true )
& ( dsetconstrI = $true )
& ( setoftrueEq = $true )
& ( sepSubset = $true )
& ( binintersectSubset1 = $true )
& ( upairset2E = $true )
& ( lamp = $true )
& ( inIntersectImpInUnion = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK672,sK673,sK674,sK675]),skolemize(X0,sK672),skolemize(X1,sK673),skolemize(X2,sK674),skolemize(X3,sK675)],[f926]) ).
thf(f1944,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f922]) ).
thf(f1945,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) )
& ( ( subset @ X2 @ X3 )
!= $true ) ) ) ),
inference(rectify,[],[f1944]) ).
thf(f1946,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ( ( ( in @ sK785 @ ( powerset @ sK786 ) )
= $true )
& ( $true
!= ( subset @ sK785 @ sK786 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK785,sK786]),skolemize(X2,sK785),skolemize(X3,sK786)],[f1945]) ).
thf(f2372,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( notsubsetI != $true )
| ( $true
!= ( in @ X0 @ X2 ) ) ),
inference(cnf_transformation,[],[f1453]) ).
thf(f2905,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[],[f1797]) ).
thf(f2990,plain,
notsubsetI = $true,
inference(cnf_transformation,[],[f1834]) ).
thf(f3078,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f1834]) ).
thf(f3097,plain,
( $true
!= ( in @ sK675 @ sK673 ) ),
inference(cnf_transformation,[],[f1834]) ).
thf(f3098,plain,
( ( in @ sK675 @ ( binintersect @ sK672 @ sK674 ) )
= $true ),
inference(cnf_transformation,[],[f1834]) ).
thf(f3100,plain,
( $true
= ( in @ sK672 @ ( powerset @ sK673 ) ) ),
inference(cnf_transformation,[],[f1834]) ).
thf(f3102,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f1834]) ).
thf(f3390,plain,
! [X0: $i,X1: $i] :
( ( powersetE1 != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f1946]) ).
thf(f3933,definition,
( spl879_45
<=> ( binintersectEL = $true ) ),
introduced(definition,[new_symbols(definition,[spl879_45])],[avatar_definition]) ).
thf(f4791,definition,
( spl879_239
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl879_239])],[avatar_definition]) ).
thf(f4792,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X2 )
= $true ) )
| ~ spl879_239 ),
inference(avatar_component_clause,[],[f4791]) ).
thf(f4793,plain,
( ~ spl879_45
| spl879_239 ),
inference(avatar_split_clause,[],[f2905,f4791,f3933]) ).
thf(f4839,definition,
( spl879_250
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( $true
!= ( in @ X5 @ X4 ) )
| ( ( in @ X5 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl879_250])],[avatar_definition]) ).
thf(f4840,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( $true
!= ( in @ X5 @ X4 ) )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ~ spl879_250 ),
inference(avatar_component_clause,[],[f4839]) ).
thf(f6300,definition,
( spl879_567
<=> ( powersetE1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl879_567])],[avatar_definition]) ).
thf(f6304,definition,
( spl879_568
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl879_568])],[avatar_definition]) ).
thf(f6305,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ~ spl879_568 ),
inference(avatar_component_clause,[],[f6304]) ).
thf(f6306,plain,
( ~ spl879_567
| spl879_568 ),
inference(avatar_split_clause,[],[f3390,f6304,f6300]) ).
thf(f6377,definition,
( spl879_584
<=> ( notsubsetI = $true ) ),
introduced(definition,[new_symbols(definition,[spl879_584])],[avatar_definition]) ).
thf(f6380,plain,
( ~ spl879_584
| spl879_250 ),
inference(avatar_split_clause,[],[f2372,f4839,f6377]) ).
thf(f6499,plain,
spl879_567,
inference(avatar_split_clause,[],[f3102,f6300]) ).
thf(f6816,definition,
( spl879_677
<=> ( ( in @ sK675 @ ( binintersect @ sK672 @ sK674 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl879_677])],[avatar_definition]) ).
thf(f6818,plain,
( ( ( in @ sK675 @ ( binintersect @ sK672 @ sK674 ) )
= $true )
| ~ spl879_677 ),
inference(avatar_component_clause,[],[f6816]) ).
thf(f6819,plain,
spl879_677,
inference(avatar_split_clause,[],[f3098,f6816]) ).
thf(f7087,definition,
( spl879_735
<=> ( $true
= ( in @ sK675 @ sK673 ) ) ),
introduced(definition,[new_symbols(definition,[spl879_735])],[avatar_definition]) ).
thf(f7089,plain,
( ( $true
!= ( in @ sK675 @ sK673 ) )
| spl879_735 ),
inference(avatar_component_clause,[],[f7087]) ).
thf(f7090,plain,
~ spl879_735,
inference(avatar_split_clause,[],[f3097,f7087]) ).
thf(f7458,definition,
( spl879_812
<=> ( $true
= ( in @ sK672 @ ( powerset @ sK673 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl879_812])],[avatar_definition]) ).
thf(f7460,plain,
( ( $true
= ( in @ sK672 @ ( powerset @ sK673 ) ) )
| ~ spl879_812 ),
inference(avatar_component_clause,[],[f7458]) ).
thf(f7461,plain,
spl879_812,
inference(avatar_split_clause,[],[f3100,f7458]) ).
thf(f7955,plain,
spl879_45,
inference(avatar_split_clause,[],[f3078,f3933]) ).
thf(f9859,plain,
spl879_584,
inference(avatar_split_clause,[],[f2990,f6377]) ).
thf(f10846,definition,
( spl879_1423
<=> ( $true
= ( in @ sK675 @ sK672 ) ) ),
introduced(definition,[new_symbols(definition,[spl879_1423])],[avatar_definition]) ).
thf(f10848,plain,
( ( $true
= ( in @ sK675 @ sK672 ) )
| ~ spl879_1423 ),
inference(avatar_component_clause,[],[f10846]) ).
thf(f11041,plain,
( ( $true != $true )
| ( ( subset @ sK672 @ sK673 )
= $true )
| ~ spl879_568
| ~ spl879_812 ),
inference(superposition,[],[f6305,f7460]) ).
thf(f11053,plain,
( ( ( subset @ sK672 @ sK673 )
= $true )
| ~ spl879_568
| ~ spl879_812 ),
inference(trivial_inequality_removal,[],[f11041]) ).
thf(f11061,definition,
( spl879_1437
<=> ( ( subset @ sK672 @ sK673 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl879_1437])],[avatar_definition]) ).
thf(f11063,plain,
( ( ( subset @ sK672 @ sK673 )
= $true )
| ~ spl879_1437 ),
inference(avatar_component_clause,[],[f11061]) ).
thf(f11064,plain,
( spl879_1437
| ~ spl879_568
| ~ spl879_812 ),
inference(avatar_split_clause,[],[f11053,f7458,f6304,f11061]) ).
thf(f11249,plain,
( ( $true != $true )
| ( $true
= ( in @ sK675 @ sK672 ) )
| ~ spl879_239
| ~ spl879_677 ),
inference(superposition,[],[f4792,f6818]) ).
thf(f11256,plain,
( ( $true
= ( in @ sK675 @ sK672 ) )
| ~ spl879_239
| ~ spl879_677 ),
inference(trivial_inequality_removal,[],[f11249]) ).
thf(f11263,plain,
( spl879_1423
| ~ spl879_239
| ~ spl879_677 ),
inference(avatar_split_clause,[],[f11256,f6816,f4791,f10846]) ).
thf(f11607,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( subset @ X0 @ sK673 ) )
| ( ( in @ sK675 @ X0 )
!= $true ) )
| ~ spl879_250
| spl879_735 ),
inference(superposition,[],[f7089,f4840]) ).
thf(f11630,plain,
( ! [X0: $i] :
( ( $true
!= ( subset @ X0 @ sK673 ) )
| ( ( in @ sK675 @ X0 )
!= $true ) )
| ~ spl879_250
| spl879_735 ),
inference(trivial_inequality_removal,[],[f11607]) ).
thf(f11633,plain,
( ( $true
!= ( in @ sK675 @ sK672 ) )
| ( $true != $true )
| ~ spl879_250
| spl879_735
| ~ spl879_1437 ),
inference(superposition,[],[f11630,f11063]) ).
thf(f11644,plain,
( ( $true
!= ( in @ sK675 @ sK672 ) )
| ~ spl879_250
| spl879_735
| ~ spl879_1437 ),
inference(trivial_inequality_removal,[],[f11633]) ).
thf(f11655,plain,
( $false
| ~ spl879_250
| spl879_735
| ~ spl879_1423
| ~ spl879_1437 ),
inference(forward_subsumption_resolution,[],[f11644,f10848]) ).
thf(f11656,plain,
( ~ spl879_250
| spl879_735
| ~ spl879_1423
| ~ spl879_1437 ),
inference(avatar_contradiction_clause,[],[f11655]) ).
cnf(s153,plain,
( ~ spl879_45
| spl879_239 ),
inference(sat_conversion,[],[f4793]) ).
cnf(s431,plain,
( ~ spl879_567
| spl879_568 ),
inference(sat_conversion,[],[f6306]) ).
cnf(s445,plain,
( spl879_250
| ~ spl879_584 ),
inference(sat_conversion,[],[f6380]) ).
cnf(s472,plain,
spl879_567,
inference(sat_conversion,[],[f6499]) ).
cnf(s543,plain,
spl879_677,
inference(sat_conversion,[],[f6819]) ).
cnf(s603,plain,
~ spl879_735,
inference(sat_conversion,[],[f7090]) ).
cnf(s693,plain,
spl879_812,
inference(sat_conversion,[],[f7461]) ).
cnf(s811,plain,
spl879_45,
inference(sat_conversion,[],[f7955]) ).
cnf(s1295,plain,
spl879_584,
inference(sat_conversion,[],[f9859]) ).
cnf(s1464,plain,
( ~ spl879_568
| ~ spl879_812
| spl879_1437 ),
inference(sat_conversion,[],[f11064]) ).
cnf(s1475,plain,
( ~ spl879_239
| ~ spl879_677
| spl879_1423 ),
inference(sat_conversion,[],[f11263]) ).
cnf(s1485,plain,
( ~ spl879_250
| spl879_735
| ~ spl879_1423
| ~ spl879_1437 ),
inference(sat_conversion,[],[f11656]) ).
cnf(s1655,plain,
spl879_250,
inference(rat,[],[s445,s1295]) ).
cnf(s1660,plain,
spl879_568,
inference(rat,[],[s431,s472]) ).
cnf(s1662,plain,
spl879_1437,
inference(rat,[],[s1464,s693,s1660]) ).
cnf(s1663,plain,
~ spl879_1423,
inference(rat,[],[s1485,s1655,s603,s1662]) ).
cnf(s1664,plain,
~ spl879_239,
inference(rat,[],[s1475,s543,s1663]) ).
cnf(s1773,plain,
$false,
inference(rat,[],[s153,s1664,s811]) ).
thf(f11657,plain,
$false,
inference(avatar_sat_refutation,[],[s1773]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU758^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.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 14:24:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.21/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.45 % (150956)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.45 % (150961)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1762247316:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.45 % (150968)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.45 % (150968)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
% 0.30/0.45 % (150962)lrs+10_16_si=on:nwc=1.5:random_seed=4165260116:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.45 % (150963)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=120372953:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.45 % (150965)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1709772767:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.45 % (150966)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3613188240:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.45 % (150964)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=3149872458: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)
% 0.30/0.45 % (150968)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=257703191:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.45 % (150963)Instruction limit reached!
% 0.30/0.45 % (150963)------------------------------
% 0.30/0.45 % (150963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (150963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.45 % (150963)CaDiCaL version: 2.1.3
% 0.30/0.45 % (150963)Termination reason: Instruction limit
% 0.30/0.45 % (150963)Termination phase: shuffling
% 0.30/0.45 % (150963)Time elapsed: 0.003 s
% 0.30/0.45 % (150963)Peak memory usage: 10 MB
% 0.30/0.45 % (150963)Instructions burned: 5 (million)
% 0.30/0.45 % (150962)Instruction limit reached!
% 0.30/0.45 % (150962)------------------------------
% 0.30/0.45 % (150962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (150962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.45 % (150962)CaDiCaL version: 2.1.3
% 0.30/0.45 % (150962)Termination reason: Instruction limit
% 0.30/0.45 % (150962)Termination phase: shuffling
% 0.30/0.45 % (150962)Time elapsed: 0.009 s
% 0.30/0.45 % (150962)Peak memory usage: 10 MB
% 0.30/0.45 % (150962)Instructions burned: 19 (million)
% 0.30/0.45 % (150965)Instruction limit reached!
% 0.30/0.45 % (150965)------------------------------
% 0.30/0.45 % (150965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (150965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.45 % (150965)CaDiCaL version: 2.1.3
% 0.30/0.45 % (150965)Termination reason: Instruction limit
% 0.30/0.45 % (150965)Termination phase: shuffling
% 0.30/0.45 % (150965)Time elapsed: 0.012 s
% 0.30/0.45 % (150965)Peak memory usage: 10 MB
% 0.30/0.45 % (150965)Instructions burned: 26 (million)
% 0.30/0.45 % (150961)Instruction limit reached!
% 0.30/0.45 % (150961)------------------------------
% 0.30/0.45 % (150961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (150961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.45 % (150961)CaDiCaL version: 2.1.3
% 0.30/0.45 % (150961)Termination reason: Instruction limit
% 0.30/0.45 % (150961)Termination phase: Preprocessing 3
% 0.30/0.45 % (150961)Time elapsed: 0.023 s
% 0.30/0.45 % (150961)Peak memory usage: 12 MB
% 0.30/0.45 % (150961)Instructions burned: 91 (million)
% 0.30/0.45 % (150984)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=491089165:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.45 % (150984)Instruction limit reached!
% 0.30/0.45 % (150984)------------------------------
% 0.30/0.45 % (150984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (150984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (150984)CaDiCaL version: 2.1.3
% 1.05/0.48 % (150984)Termination reason: Instruction limit
% 1.05/0.48 % (150984)Termination phase: shuffling
% 1.05/0.48 % (150984)Time elapsed: 0.002 s
% 1.05/0.48 % (150984)Peak memory usage: 10 MB
% 1.05/0.48 % (150984)Instructions burned: 3 (million)
% 1.05/0.48 % (150992)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3492450601:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.05/0.48 % (150990)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.05/0.48 % (150987)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=532361618:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.05/0.48 % (150992)Instruction limit reached!
% 1.05/0.48 % (150992)------------------------------
% 1.05/0.48 % (150992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.48 % (150992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (150992)CaDiCaL version: 2.1.3
% 1.05/0.48 % (150992)Termination reason: Instruction limit
% 1.05/0.48 % (150992)Termination phase: shuffling
% 1.05/0.48 % (150992)Time elapsed: 0.003 s
% 1.05/0.48 % (150992)Peak memory usage: 10 MB
% 1.05/0.48 % (150992)Instructions burned: 12 (million)
% 1.05/0.48 % (150990)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=133262312:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.05/0.48 % (150987)Instruction limit reached!
% 1.05/0.48 % (150987)------------------------------
% 1.05/0.48 % (150987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.48 % (150987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (150987)CaDiCaL version: 2.1.3
% 1.05/0.48 % (150987)Termination reason: Instruction limit
% 1.05/0.48 % (150987)Termination phase: shuffling
% 1.05/0.48 % (150987)Time elapsed: 0.003 s
% 1.05/0.48 % (150987)Peak memory usage: 10 MB
% 1.05/0.48 % (150987)Instructions burned: 6 (million)
% 1.05/0.48 % (150966)Instruction limit reached!
% 1.05/0.48 % (150966)------------------------------
% 1.05/0.48 % (150966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.48 % (150966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (150966)CaDiCaL version: 2.1.3
% 1.05/0.48 % (150966)Termination reason: Instruction limit
% 1.05/0.48 % (150966)Termination phase: Preprocessing 3
% 1.05/0.48 % (150966)Time elapsed: 0.035 s
% 1.05/0.48 % (150966)Peak memory usage: 12 MB
% 1.05/0.48 % (150966)Instructions burned: 75 (million)
% 1.05/0.48 % (150990)Instruction limit reached!
% 1.05/0.48 % (150990)------------------------------
% 1.05/0.48 % (150990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.48 % (150990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (150990)CaDiCaL version: 2.1.3
% 1.05/0.48 % (150990)Termination reason: Instruction limit
% 1.05/0.48 % (150990)Termination phase: shuffling
% 1.05/0.48 % (150990)Time elapsed: 0.004 s
% 1.05/0.48 % (150990)Peak memory usage: 10 MB
% 1.05/0.48 % (150990)Instructions burned: 8 (million)
% 1.05/0.48 % (150999)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
% 1.05/0.48 % (150999)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.05/0.48 % (151004)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=575227213:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.05/0.48 % (150999)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2846470018:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.05/0.48 % (151009)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.05/0.48 % (151007)lrs+10_1_si=on:cs=on:random_seed=4277498155:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.05/0.52 % (151009)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=3133623213:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.05/0.52 % (151010)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2618033334:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.05/0.52 % (151007)Instruction limit reached!
% 1.05/0.52 % (151007)------------------------------
% 1.05/0.52 % (151007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.52 % (151007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.52 % (151007)CaDiCaL version: 2.1.3
% 1.05/0.52 % (151007)Termination reason: Instruction limit
% 1.05/0.52 % (151007)Termination phase: shuffling
% 1.05/0.52 % (151007)Time elapsed: 0.004 s
% 1.05/0.52 % (151007)Peak memory usage: 10 MB
% 1.05/0.52 % (151007)Instructions burned: 9 (million)
% 1.05/0.52 % (151009)Instruction limit reached!
% 1.05/0.52 % (151009)------------------------------
% 1.05/0.52 % (151009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.52 % (151009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.52 % (151009)CaDiCaL version: 2.1.3
% 1.05/0.52 % (151009)Termination reason: Instruction limit
% 1.05/0.52 % (151009)Termination phase: shuffling
% 1.05/0.52 % (151009)Time elapsed: 0.002 s
% 1.05/0.52 % (151009)Peak memory usage: 10 MB
% 1.05/0.52 % (151009)Instructions burned: 3 (million)
% 1.05/0.52 % (150999)Instruction limit reached!
% 1.05/0.52 % (150999)------------------------------
% 1.05/0.52 % (150999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.52 % (150999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.52 % (150999)CaDiCaL version: 2.1.3
% 1.05/0.52 % (150999)Termination reason: Instruction limit
% 1.05/0.52 % (150999)Termination phase: shuffling
% 1.05/0.52 % (150999)Time elapsed: 0.013 s
% 1.05/0.52 % (150999)Peak memory usage: 10 MB
% 1.05/0.52 % (150999)Instructions burned: 29 (million)
% 1.05/0.52 % (151004)Instruction limit reached!
% 1.05/0.52 % (151004)------------------------------
% 1.05/0.52 % (151004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.52 % (151004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.52 % (151004)CaDiCaL version: 2.1.3
% 1.05/0.52 % (151004)Termination reason: Instruction limit
% 1.05/0.52 % (151004)Termination phase: Property scanning
% 1.05/0.52 % (151004)Time elapsed: 0.019 s
% 1.05/0.52 % (151004)Peak memory usage: 11 MB
% 1.05/0.52 % (151004)Instructions burned: 87 (million)
% 1.05/0.52 % (150968)Instruction limit reached!
% 1.05/0.52 % (150968)------------------------------
% 1.05/0.52 % (150968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.52 % (150968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.52 % (150968)CaDiCaL version: 2.1.3
% 1.05/0.52 % (150968)Termination reason: Instruction limit
% 1.05/0.52 % (150968)Termination phase: Property scanning
% 1.05/0.52 % (150968)Time elapsed: 0.066 s
% 1.05/0.52 % (150968)Peak memory usage: 13 MB
% 1.05/0.52 % (150968)Instructions burned: 158 (million)
% 1.05/0.52 % (151033)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=46755947:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.05/0.52 % (151010)Instruction limit reached!
% 1.05/0.52 % (151010)------------------------------
% 1.05/0.52 % (151010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.52 % (151010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.52 % (151010)CaDiCaL version: 2.1.3
% 1.05/0.52 % (151010)Termination reason: Instruction limit
% 1.05/0.52 % (151010)Termination phase: Property scanning
% 1.05/0.52 % (151010)Time elapsed: 0.017 s
% 1.05/0.52 % (151010)Peak memory usage: 11 MB
% 1.05/0.52 % (151010)Instructions burned: 39 (million)
% 1.05/0.52 % (151029)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1500294204:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.05/0.52 % (151030)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3111889257:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.05/0.52 % (151028)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2003121290:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.05/0.56 % (151030)Instruction limit reached!
% 1.05/0.56 % (151030)------------------------------
% 1.05/0.56 % (151030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151030)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151030)Termination reason: Instruction limit
% 1.05/0.56 % (151030)Termination phase: shuffling
% 1.05/0.56 % (151030)Time elapsed: 0.007 s
% 1.05/0.56 % (151030)Peak memory usage: 10 MB
% 1.05/0.56 % (151030)Instructions burned: 14 (million)
% 1.05/0.56 % (151036)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1950567545:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.05/0.56 % (151029)Instruction limit reached!
% 1.05/0.56 % (151029)------------------------------
% 1.05/0.56 % (151029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151029)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151029)Termination reason: Instruction limit
% 1.05/0.56 % (151029)Termination phase: shuffling
% 1.05/0.56 % (151029)Time elapsed: 0.012 s
% 1.05/0.56 % (151029)Peak memory usage: 11 MB
% 1.05/0.56 % (151029)Instructions burned: 26 (million)
% 1.05/0.56 % (151036)Instruction limit reached!
% 1.05/0.56 % (151036)------------------------------
% 1.05/0.56 % (151036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151036)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151036)Termination reason: Instruction limit
% 1.05/0.56 % (151036)Termination phase: shuffling
% 1.05/0.56 % (151036)Time elapsed: 0.007 s
% 1.05/0.56 % (151036)Peak memory usage: 10 MB
% 1.05/0.56 % (151036)Instructions burned: 15 (million)
% 1.05/0.56 % (151040)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1282824661: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)
% 1.05/0.56 % (151040)Instruction limit reached!
% 1.05/0.56 % (151040)------------------------------
% 1.05/0.56 % (151040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151040)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151040)Termination reason: Instruction limit
% 1.05/0.56 % (151040)Termination phase: shuffling
% 1.05/0.56 % (151040)Time elapsed: 0.002 s
% 1.05/0.56 % (151040)Peak memory usage: 10 MB
% 1.05/0.56 % (151040)Instructions burned: 4 (million)
% 1.05/0.56 % (151047)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1993879612:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.05/0.56 % (151051)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=343295114:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.05/0.56 % (151055)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=874319911:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.05/0.56 % (151059)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
% 1.05/0.56 % (151059)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.05/0.56 % (151047)Instruction limit reached!
% 1.05/0.56 % (151047)------------------------------
% 1.05/0.56 % (151047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151047)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151047)Termination reason: Instruction limit
% 1.05/0.56 % (151047)Termination phase: shuffling
% 1.05/0.56 % (151047)Time elapsed: 0.012 s
% 1.05/0.56 % (151047)Peak memory usage: 10 MB
% 1.05/0.56 % (151047)Instructions burned: 26 (million)
% 1.05/0.56 % (151059)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=3376180196:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.70/0.61 % (151051)Instruction limit reached!
% 1.70/0.61 % (151051)------------------------------
% 1.70/0.61 % (151051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151051)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151051)Termination reason: Instruction limit
% 1.70/0.61 % (151051)Termination phase: shuffling
% 1.70/0.61 % (151051)Time elapsed: 0.010 s
% 1.70/0.61 % (151051)Peak memory usage: 10 MB
% 1.70/0.61 % (151051)Instructions burned: 23 (million)
% 1.70/0.61 % (151059)Instruction limit reached!
% 1.70/0.61 % (151059)------------------------------
% 1.70/0.61 % (151059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151059)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151059)Termination reason: Instruction limit
% 1.70/0.61 % (151059)Termination phase: shuffling
% 1.70/0.61 % (151059)Time elapsed: 0.007 s
% 1.70/0.61 % (151059)Peak memory usage: 10 MB
% 1.70/0.61 % (151059)Instructions burned: 15 (million)
% 1.70/0.61 % (151071)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.70/0.61 % (151071)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=3027330372:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.70/0.61 % (151075)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=2524891285:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.70/0.61 % (151071)Instruction limit reached!
% 1.70/0.61 % (151071)------------------------------
% 1.70/0.61 % (151071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151071)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151071)Termination reason: Instruction limit
% 1.70/0.61 % (151071)Termination phase: shuffling
% 1.70/0.61 % (151071)Time elapsed: 0.004 s
% 1.70/0.61 % (151071)Peak memory usage: 10 MB
% 1.70/0.61 % (151071)Instructions burned: 8 (million)
% 1.70/0.61 % (151055)Instruction limit reached!
% 1.70/0.61 % (151055)------------------------------
% 1.70/0.61 % (151055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151055)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151055)Termination reason: Instruction limit
% 1.70/0.61 % (151055)Termination phase: Preprocessing 3
% 1.70/0.61 % (151055)Time elapsed: 0.027 s
% 1.70/0.61 % (151055)Peak memory usage: 12 MB
% 1.70/0.61 % (151055)Instructions burned: 60 (million)
% 1.70/0.61 % (151081)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1142108580:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.70/0.61 % (151081)Instruction limit reached!
% 1.70/0.61 % (151081)------------------------------
% 1.70/0.61 % (151081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151081)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151081)Termination reason: Instruction limit
% 1.70/0.61 % (151081)Termination phase: shuffling
% 1.70/0.61 % (151081)Time elapsed: 0.004 s
% 1.70/0.61 % (151081)Peak memory usage: 10 MB
% 1.70/0.61 % (151081)Instructions burned: 8 (million)
% 1.70/0.61 % (151033)Instruction limit reached!
% 1.70/0.61 % (151033)------------------------------
% 1.70/0.61 % (151033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151033)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151033)Termination reason: Instruction limit
% 1.70/0.61 % (151033)Termination phase: Saturation
% 1.70/0.61 % (151033)Time elapsed: 0.079 s
% 1.70/0.61 % (151033)Peak memory usage: 15 MB
% 1.70/0.61 % (151033)Instructions burned: 329 (million)
% 1.70/0.61 % (151075)Instruction limit reached!
% 1.70/0.61 % (151075)------------------------------
% 1.70/0.61 % (151075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151075)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151075)Termination reason: Instruction limit
% 1.70/0.61 % (151075)Termination phase: shuffling
% 1.70/0.61 % (151075)Time elapsed: 0.014 s
% 1.70/0.61 % (151075)Peak memory usage: 10 MB
% 1.70/0.61 % (151075)Instructions burned: 32 (million)
% 1.70/0.61 % (151086)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2253820303:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.70/0.61 % (151089)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2121524226:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.70/0.61 % (151095)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2406865412:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.70/0.61 % (151094)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2375924678:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.70/0.61 % (151086)Instruction limit reached!
% 1.70/0.61 % (151086)------------------------------
% 1.70/0.61 % (151086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151086)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151086)Termination reason: Instruction limit
% 1.70/0.61 % (151086)Termination phase: shuffling
% 1.70/0.61 % (151086)Time elapsed: 0.012 s
% 1.70/0.61 % (151086)Peak memory usage: 10 MB
% 1.70/0.61 % (151086)Instructions burned: 26 (million)
% 1.70/0.61 % (151089)Instruction limit reached!
% 1.70/0.61 % (151089)------------------------------
% 1.70/0.61 % (151089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151089)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151089)Termination reason: Instruction limit
% 1.70/0.61 % (151089)Termination phase: shuffling
% 1.70/0.61 % (151089)Time elapsed: 0.010 s
% 1.70/0.61 % (151089)Peak memory usage: 10 MB
% 1.70/0.61 % (151089)Instructions burned: 23 (million)
% 1.70/0.61 % (151096)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=543528616:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.70/0.61 % (151108)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.70/0.61 % (151028)Instruction limit reached!
% 1.70/0.61 % (151028)------------------------------
% 1.70/0.61 % (151028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151028)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151028)Termination reason: Instruction limit
% 1.70/0.61 % (151028)Termination phase: Saturation
% 1.70/0.61 % (151028)Time elapsed: 0.111 s
% 1.70/0.61 % (151028)Peak memory usage: 15 MB
% 1.70/0.61 % (151028)Instructions burned: 250 (million)
% 1.70/0.61 % (151108)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1442162930:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.70/0.61 % (151107)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3914710516:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.70/0.61 % (151095)Instruction limit reached!
% 1.70/0.61 % (151095)------------------------------
% 1.70/0.61 % (151095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151095)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151095)Termination reason: Instruction limit
% 1.70/0.61 % (151095)Termination phase: Property scanning
% 1.70/0.61 % (151095)Time elapsed: 0.032 s
% 1.70/0.61 % (151095)Peak memory usage: 12 MB
% 1.70/0.61 % (151095)Instructions burned: 148 (million)
% 1.70/0.61 % (151108)Instruction limit reached!
% 1.70/0.61 % (151108)------------------------------
% 1.70/0.61 % (151108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151108)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151108)Termination reason: Instruction limit
% 1.70/0.61 % (151108)Termination phase: shuffling
% 1.70/0.61 % (151108)Time elapsed: 0.004 s
% 1.70/0.61 % (151108)Peak memory usage: 10 MB
% 1.70/0.61 % (151108)Instructions burned: 8 (million)
% 1.70/0.61 % (151124)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=3610839374:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.70/0.61 % (151120)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=4203805388:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.70/0.61 % (151107)Instruction limit reached!
% 1.70/0.61 % (151107)------------------------------
% 1.70/0.61 % (151107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151125)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.70/0.61 % (151107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151107)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151107)Termination reason: Instruction limit
% 1.70/0.61 % (151107)Termination phase: Property scanning
% 1.70/0.61 % (151107)Time elapsed: 0.020 s
% 1.70/0.61 % (151107)Peak memory usage: 11 MB
% 1.70/0.61 % (151107)Instructions burned: 44 (million)
% 1.70/0.61 % (151125)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1677959613:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.70/0.61 % (151125)Instruction limit reached!
% 1.70/0.61 % (151125)------------------------------
% 1.70/0.61 % (151125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (151125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (151125)CaDiCaL version: 2.1.3
% 1.70/0.61 % (151125)Termination reason: Instruction limit
% 1.70/0.61 % (151125)Termination phase: shuffling
% 1.70/0.61 % (151125)Time elapsed: 0.003 s
% 1.70/0.61 % (151125)Peak memory usage: 10 MB
% 1.70/0.61 % (151125)Instructions burned: 6 (million)
% 1.70/0.61 % (151132)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2752897186:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.70/0.61 % (150964) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-150956-150964"...
% 1.70/0.61 % (151134)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=15246407:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 1.70/0.61 % (150964)...printing done.
% 1.70/0.61 % (150964)Refutation found. Thanks to Tanya!
% 1.70/0.61 % SZS status Theorem for theBenchmark
% 1.70/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.70/0.61 % (150964)------------------------------
% 1.70/0.61 % (150964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.61 % (150964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.61 % (150964)CaDiCaL version: 2.1.3
% 1.70/0.61 % (150964)Termination reason: Refutation
% 1.70/0.61 % (150964)Time elapsed: 0.237 s
% 1.70/0.61 % (150964)Peak memory usage: 21 MB
% 1.70/0.61 % (150964)Instructions burned: 464 (million)
% 1.70/0.61 % (150956)Success in time 0.3 s
% 1.70/0.61 % Vampire exiting
%------------------------------------------------------------------------------