%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU755^1 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:09 AM UTC 2026
% Result : Theorem 3.30s 0.96s
% Output : Refutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 113 ( 36 unt; 0 typ; 13 def)
% Number of atoms : 4928 (1286 equ; 0 cnn)
% Maximal formula atoms : 277 ( 43 avg)
% Number of connectives : 2834 ( 139 ~; 133 |; 852 &; 568 @)
% ( 23 <=>;1119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 286 ( 21 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 : 144 ( 0 sgn 118 !; 26 ?; 144 :)
% 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_312,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_313,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_314,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_315,type,
vOR: $o > $o > $o ).
thf(func_def_316,type,
vAND: $o > $o > $o ).
thf(func_def_317,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_318,type,
vNOT: $o > $o ).
thf(func_def_319,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_320,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_321,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_322,type,
vIMP: $o > $o > $o ).
thf(func_def_323,type,
sP0: $o ).
thf(func_def_324,type,
sP1: $i > $i > $o ).
thf(func_def_325,type,
sP2: $i > $o ).
thf(func_def_326,type,
sP3: $o ).
thf(func_def_327,type,
sK4: $i > $i ).
thf(func_def_330,type,
sK7: $o ).
thf(func_def_341,type,
sK18: $i > $i > $o ).
thf(func_def_344,type,
sK21: ( $i > $i ) > $i > $i > $i ).
thf(func_def_347,type,
sK24: $i > $i ).
thf(func_def_353,type,
sK30: $o ).
thf(func_def_360,type,
sK37: $i > $i ).
thf(func_def_366,type,
sK43: $i > $i ).
thf(func_def_373,type,
sK50: $o > $i > $i > $i ).
thf(func_def_376,type,
sK53: $o ).
thf(func_def_384,type,
sK61: ( $i > $o ) > $i ).
thf(func_def_385,type,
sK62: ( $i > $o ) > $i ).
thf(func_def_386,type,
sK63: $i > $o ).
thf(func_def_390,type,
sK67: $i > $o ).
thf(func_def_397,type,
sK74: $i > $o ).
thf(func_def_399,type,
sK76: $i > ( $i > $o ) > $i ).
thf(func_def_405,type,
sK82: $i > $o ).
thf(func_def_406,type,
sK83: $i > $o ).
thf(func_def_407,type,
sK84: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_408,type,
sK85: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_425,type,
sK102: $o ).
thf(func_def_434,type,
sK111: $i > $o ).
thf(func_def_447,type,
sK124: $i > $o ).
thf(func_def_449,type,
sK126: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_450,type,
sK127: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_455,type,
sK132: $i > $i > $o ).
thf(func_def_463,type,
sK140: $i > $i > $i ).
thf(func_def_471,type,
sK148: $i > $i > $i > $i > $i ).
thf(func_def_472,type,
sK149: $i > $i > $i > $i > $i ).
thf(func_def_473,type,
sK150: $i > $i > $i > $i > $i ).
thf(func_def_474,type,
sK151: $i > $i > $i > $i > $i ).
thf(func_def_492,type,
sK169: $i > $i > $i ).
thf(func_def_495,type,
sK172: $o ).
thf(func_def_519,type,
sK196: $i > $o ).
thf(func_def_522,type,
sK199: $i > $i ).
thf(func_def_525,type,
sK202: $i > $i ).
thf(func_def_526,type,
sK203: $i > $i > $i > $i ).
thf(func_def_527,type,
sK204: $i > $i > $i > $i ).
thf(func_def_539,type,
sK216: $i > $i > $o ).
thf(func_def_540,type,
sK217: $i > $i ).
thf(func_def_541,type,
sK218: $i > $i ).
thf(func_def_542,type,
sK219: ( $i > $i > $o ) > $i > $i ).
thf(func_def_543,type,
sK220: ( $i > $i > $o ) > $i > $i ).
thf(func_def_544,type,
sK221: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_545,type,
sK222: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_546,type,
sK223: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_547,type,
sK224: $i > $o ).
thf(func_def_548,type,
sK225: $i > $o ).
thf(func_def_561,type,
sK238: $i > $o ).
thf(func_def_564,type,
sK241: $i > ( $i > $o ) > $i ).
thf(func_def_565,type,
sK242: $i > ( $i > $o ) > $i ).
thf(func_def_566,type,
sK243: ( $i > $i ) > $i > $i > $i ).
thf(func_def_569,type,
sK246: $i > $i ).
thf(func_def_574,type,
sK251: $i > ( $i > $o ) > $i ).
thf(func_def_575,type,
sK252: $i > $o ).
thf(func_def_582,type,
sK259: $o ).
thf(func_def_587,type,
sK264: $i > $i > ( $i > $o ) > $i ).
thf(func_def_588,type,
sK265: $i > $o ).
thf(func_def_598,type,
sK275: $i > $i > ( $i > $i ) > $i ).
thf(func_def_599,type,
sK276: $i > $i ).
thf(func_def_612,type,
sK289: $i > $o ).
thf(func_def_619,type,
sK296: $i > $i ).
thf(func_def_620,type,
sK297: $i > $i ).
thf(func_def_621,type,
sK298: $i > $i ).
thf(func_def_622,type,
sK299: $i > $i ).
thf(func_def_623,type,
sK300: $i > $i ).
thf(func_def_624,type,
sK301: $i > $i > $i > $i ).
thf(func_def_625,type,
sK302: $i > $i ).
thf(func_def_626,type,
sK303: $i > $i ).
thf(func_def_627,type,
sK304: $i > $i ).
thf(func_def_628,type,
sK305: $i > $i ).
thf(func_def_629,type,
sK306: $i > $i > $i ).
thf(func_def_630,type,
sK307: $i > $i > $i ).
thf(func_def_631,type,
sK308: $i > $i > $i > $i ).
thf(func_def_632,type,
sK309: $i > $i > $i > $i ).
thf(func_def_633,type,
sK310: $i > $i > $i > $i ).
thf(func_def_634,type,
sK311: $i > $i > $i ).
thf(func_def_635,type,
sK312: $i > $i > $i ).
thf(func_def_636,type,
sK313: $i > $i > $i ).
thf(func_def_643,type,
sK320: $i > $i > $o ).
thf(func_def_656,type,
sK333: $o ).
thf(func_def_664,type,
sK341: $o ).
thf(func_def_671,type,
sK348: $i > $o ).
thf(func_def_673,type,
sK350: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_674,type,
sK351: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_677,type,
sK354: $o ).
thf(func_def_690,type,
sK367: $i > $i > $o ).
thf(func_def_694,type,
sK371: $i > $i > $i ).
thf(func_def_707,type,
sK384: $i > $o ).
thf(func_def_709,type,
sK386: $i > $o ).
thf(func_def_715,type,
sK392: $i > $i > $o ).
thf(func_def_731,type,
sK408: $i > ( $i > $i ) > $i > $i ).
thf(func_def_733,type,
sK410: $i > $i ).
thf(func_def_735,type,
sK412: $i > $o ).
thf(func_def_747,type,
sK424: $o ).
thf(func_def_774,type,
sK451: $i > ( $i > $o ) > $i ).
thf(func_def_775,type,
sK452: $i > ( $i > $o ) > $i ).
thf(func_def_776,type,
sK453: $i > $o ).
thf(func_def_784,type,
sK461: $o ).
thf(func_def_802,type,
sK479: $o ).
thf(func_def_810,type,
sK487: $i > $o ).
thf(func_def_811,type,
sK488: ( $i > $o ) > $i ).
thf(func_def_826,type,
sK503: $i > $i > $i ).
thf(func_def_838,type,
sK515: $i > $o ).
thf(func_def_843,type,
sK520: $i > $o ).
thf(func_def_845,type,
sK522: ( $i > $o ) > $i > $i ).
thf(func_def_856,type,
sK533: $i > $i > $i > $i ).
thf(func_def_857,type,
sK534: $i > $i > $i > $i ).
thf(func_def_863,type,
sK540: $i > $o ).
thf(func_def_867,type,
sK544: $o ).
thf(func_def_871,type,
sK548: $i > $o ).
thf(func_def_878,type,
sK555: $i > $o ).
thf(func_def_886,type,
sK563: $i > $i > $o ).
thf(func_def_894,type,
sK571: ( $i > $o ) > $i > $i ).
thf(func_def_896,type,
sK573: $i > $o ).
thf(func_def_898,type,
sK575: $o ).
thf(func_def_907,type,
sK584: $i > $i > $i > $i > $i ).
thf(func_def_918,type,
sK595: $i > $i ).
thf(func_def_925,type,
sK602: $i > $i > $i > $i > $i ).
thf(func_def_926,type,
sK603: $i > $i > $i > $i > $i ).
thf(func_def_932,type,
sK609: $i > $o ).
thf(func_def_934,type,
sK611: ( $i > $o ) > $i > $i ).
thf(func_def_952,type,
sK629: $i > $i > $i ).
thf(func_def_955,type,
sK632: $i > $i > $i ).
thf(func_def_966,type,
sK643: $o ).
thf(func_def_971,type,
sK648: $i > $i > $o ).
thf(func_def_993,type,
sK670: $i > $o ).
thf(func_def_994,type,
sK671: $i > $i ).
thf(func_def_995,type,
sK672: ( $i > $o ) > $i ).
thf(func_def_999,type,
sK676: $i > $o ).
thf(func_def_1002,type,
sK679: $i > $o ).
thf(func_def_1005,type,
sK682: $i > ( $i > $o ) > $i ).
thf(func_def_1009,type,
sK686: $i > $i > $i > $i ).
thf(func_def_1014,type,
sK691: $i > $o ).
thf(func_def_1016,type,
sK693: ( $i > $o ) > $i > $i ).
thf(func_def_1056,type,
sK733: $i > $i > $i ).
thf(func_def_1059,type,
sK736: $i > $o ).
thf(func_def_1069,type,
sK746: ( $i > $o ) > $i ).
thf(func_def_1070,type,
sK747: $i > $o ).
thf(func_def_1071,type,
sK748: $i > $i ).
thf(func_def_1082,type,
sK759: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1084,type,
sK761: $i > $i ).
thf(func_def_1092,type,
sK769: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1093,type,
sK770: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1094,type,
sK771: $i > $o ).
thf(func_def_1095,type,
sK772: $i > $o ).
thf(func_def_1100,type,
sK777: $i > $o ).
thf(func_def_1102,type,
sK779: $i > ( $i > $o ) > $i ).
thf(func_def_1105,type,
sK782: $o ).
thf(func_def_1113,type,
sK790: $i > $i > $i > $i > $i ).
thf(func_def_1114,type,
sK791: $i > $i ).
thf(func_def_1116,type,
sK793: $i > $i ).
thf(func_def_1119,type,
sK796: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1123,type,
sK800: $i > $i > $i ).
thf(func_def_1129,type,
sK806: $i > $i > $i > $i ).
thf(func_def_1133,type,
sK810: $i > ( $i > $o ) > $i ).
thf(func_def_1134,type,
sK811: $i > $o ).
thf(func_def_1159,type,
sK836: $o ).
thf(func_def_1164,type,
sK841: $o ).
thf(func_def_1172,type,
sK849: $i > $i > $i > $i > $i ).
thf(func_def_1184,type,
sK861: $i > $i > $i ).
thf(func_def_1185,type,
sK862: $i > $i > $i ).
thf(f105,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) )
= binunionE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(f122,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(f124,axiom,
( setminusERneg
= ( ! [X1: $i,X0: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(f276,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2) ).
thf(f277,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f276]) ).
thf(f480,plain,
( setminusERneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X1 @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f124]) ).
thf(f481,plain,
( ( setminusERneg = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f480]) ).
thf(f565,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) )
= binunionE ),
inference(rectify,[],[f105]) ).
thf(f566,plain,
( ( binunionE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
=> ( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f565]) ).
thf(f580,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ~ ( in @ X1 @ X0 ) )
= setminusER ),
inference(rectify,[],[f122]) ).
thf(f581,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[],[f580]) ).
thf(f805,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f277]) ).
thf(f806,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f805]) ).
thf(f839,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( setminusERneg = $true ) ),
inference(flattening,[],[f481]) ).
thf(f848,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[],[f581]) ).
thf(f868,plain,
( ( binunionE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(ennf_transformation,[],[f566]) ).
thf(f869,plain,
( ( binunionE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(flattening,[],[f868]) ).
thf(f942,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) )
<=> ( setminusERneg = $true ) ),
inference(ennf_transformation,[],[f839]) ).
thf(f943,plain,
( ( setminusERneg = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) ) ),
inference(flattening,[],[f942]) ).
thf(f1051,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $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,[],[f806]) ).
thf(f1052,plain,
( ( notequalI1 = $true )
& ( cartprodmempair = $true )
& ( binintersectSubset1 = $true )
& ( subsetI2 = $true )
& ( emptyinPowerset = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( in__Cong = $true )
& ( funcGraphProp4 = $true )
& ( powersetAx = $true )
& ( wellorderingAx = $true )
& ( binunionIR = $true )
& ( iftrueorfalse = $true )
& ( inIntersectImpInUnion = $true )
& ( ap2apEq1 = $true )
& ( setukpairinjR11 = $true )
& ( subset2powerset = $true )
& ( upairsetE = $true )
& ( doubleComplementI1 = $true )
& ( upairsetIL = $true )
& ( demorgan2a1 = $true )
& ( disjointsetsI1 = $true )
& ( theeq = $true )
& ( binunionTEcontra = $true )
& ( binunionT_lem = $true )
& ( emptysetimpfalse = $true )
& ( binintersectI = $true )
& ( ifp = $true )
& ( noeltsimpempty = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( powersetE = $true )
& ( ex1I2 = $true )
& ( brelnall1 = $true )
& ( cartprodsndpairEq = $true )
& ( singletonsswitch = $true )
& ( lamProp = $true )
& ( lamp = $true )
& ( doubleComplementE1 = $true )
& ( funcGraphProp2 = $true )
& ( doubleComplementSub2 = $true )
& ( replAx = $true )
& ( powersetI = $true )
& ( demorgan1 = $true )
& ( setukpairinjR = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinIL = $true )
& ( emptysetsubset = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( prop2set2propI = $true )
& ( demorgan2a = $true )
& ( setukpairIL = $true )
& ( exu__Cong = $true )
& ( setukpairinjL2 = $true )
& ( setunion__Cong = $true )
& ( funcextLem = $true )
& ( symdiffI2 = $true )
& ( binintersectTERcontra = $true )
& ( setadjoinSub2 = $true )
& ( singletonprop = $true )
& ( quantDeMorgan1 = $true )
& ( contraSubsetComplement = $true )
& ( sepSubset = $true )
& ( ubforcartprodlem2 = $true )
& ( contrasubsetT3 = $true )
& ( eta1 = $true )
& ( ex1I = $true )
& ( setminusSubset2 = $true )
& ( prop2setE = $true )
& ( notdallE = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan2 = $true )
& ( funcinfuncset = $true )
& ( setminusSubset1 = $true )
& ( binunionRsub = $true )
& ( eqimpsubset1 = $true )
& ( exuI1 = $true )
& ( cartprodpairmemEL = $true )
& ( kfstpairEq = $true )
& ( exuE3e = $true )
& ( exuE1 = $true )
& ( funcext = $true )
& ( setminusLsub = $true )
& ( exuI2 = $true )
& ( brelnall2 = $true )
& ( iffalseProp1 = $true )
& ( singletonsubset = $true )
& ( theprop = $true )
& ( setadjoinIR = $true )
& ( setunionsingleton2 = $true )
& ( singletonsuniq = $true )
& ( setukpairinjR12 = $true )
& ( inPowerset = $true )
& ( notinsingleton = $true )
& ( kfstsingleton = $true )
& ( binunionTE = $true )
& ( binintersectEL = $true )
& ( subsetTrans = $true )
& ( contrasubsetT2 = $true )
& ( descrp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrEL1 = $true )
& ( eta2 = $true )
& ( cartprodpairin = $true )
& ( kpairsurjEq = $true )
& ( bs114d = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( binintersectRsub = $true )
& ( singletoninpowunion = $true )
& ( setukpairinjL = $true )
& ( setminusI = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinE = $true )
& ( subsetemptysetimpeq = $true )
& ( eqinunit = $true )
& ( nonemptyI = $true )
& ( subsetTI = $true )
& ( binunionEcases = $true )
& ( upairset2IR = $true )
& ( upairsubunion = $true )
& ( setminusILneg = $true )
& ( upairequniteq = $true )
& ( upairsetIR = $true )
& ( iffalse = $true )
& ( foundationAx = $true )
& ( powersetTI1 = $true )
& ( cartprodmempair1 = $true )
& ( kpairp = $true )
& ( beta1 = $true )
& ( funcGraphProp3 = $true )
& ( setunionAx = $true )
& ( complementSubsetComplementIntersect = $true )
& ( cartprodmempaircEq = $true )
& ( subsetI1 = $true )
& ( subbreln = $true )
& ( exuEu = $true )
& ( upairset2E = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( setminusERneg = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( setunionE2 = $true )
& ( subsetE2 = $true )
& ( upairinpowunion = $true )
& ( ubforcartprodlem1 = $true )
& ( singletoninpowerset = $true )
& ( beta2 = $true )
& ( powersetsubset = $true )
& ( powersetTE1 = $true )
& ( eqbreln = $true )
& ( dpsetconstrERa = $true )
& ( omega0Ax = $true )
& ( binunionIL = $true )
& ( complementTE1 = $true )
& ( ksndpairEq = $true )
& ( setextT = $true )
& ( dsetconstrER = $true )
& ( setunionE = $true )
& ( app = $true )
& ( doubleComplementSub1 = $true )
& ( funcGraphProp1 = $true )
& ( binintersectLsub = $true )
& ( notinemptyset = $true )
& ( binintersectT_lem = $true )
& ( setminusIRneg = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( setukpairinjL1 = $true )
& ( symdiffIneg2 = $true )
& ( iftrue = $true )
& ( setminusELneg = $true )
& ( dsetconstr__Cong = $true )
& ( inCongP = $true )
& ( uniqinunit = $true )
& ( demorgan1b = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodfstpairEq = $true )
& ( exuI3 = $true )
& ( infuncsetfunc = $true )
& ( emptysetE = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetRefl = $true )
& ( symdiffE = $true )
& ( inIntersectImpInUnion2 = $true )
& ( binunionLsub = $true )
& ( demorgan2a2 = $true )
& ( emptyI = $true )
& ( setukpairinjR1 = $true )
& ( descr__Cong = $true )
& ( lam2lamEq = $true )
& ( ex1E1 = $true )
& ( demorgan1a = $true )
& ( setminusEL = $true )
& ( prop2setI = $true )
& ( setunionI = $true )
& ( iftrueProp1 = $true )
& ( binintersectSubset2 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( symdiffIneg1 = $true )
& ( setadjoin__Cong = $true )
& ( exuE3u = $true )
& ( nonemptyE1 = $true )
& ( powersetE1 = $true )
& ( setextAx = $true )
& ( binintersectSubset5 = $true )
& ( notdexE = $true )
& ( setunionsingleton1 = $true )
& ( binunionTIRcontra = $true )
& ( symdiffI1 = $true )
& ( funcext2 = $true )
& ( setukpairinjR2 = $true )
& ( binintersectSubset4 = $true )
& ( eqimpsubset2 = $true )
& ( setunionsingleton = $true )
& ( binunionTILcontra = $true )
& ( subsetE = $true )
& ( ap2p = $true )
& ( complementTI1 = $true )
& ( apProp = $true )
& ( ap2apEq2 = $true )
& ( setminusT_lem = $true )
& ( emptyset__Cong = $true )
& ( emptyE1 = $true )
& ( setadjoinAx = $true )
& ( setext = $true )
& ( omegaSAx = $true )
& ( cartprodsndin = $true )
& ( binintersectSubset3 = $true )
& ( complementT_lem = $true )
& ( ubforcartprodlem3 = $true )
& ( complementTcontraSubset = $true )
& ( iftrueProp2 = $true )
& ( setbeta = $true )
& ( ex1E2 = $true )
& ( cartprodfstin = $true )
& ( setukpairIR = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( ifSingleton = $true )
& ( kpairiskpair = $true )
& ( secondinupair = $true )
& ( iffalseProp2 = $true )
& ( setminusER = $true )
& ( emptyInPowerset = $true )
& ( ksndsingleton = $true )
& ( notequalI2 = $true )
& ( subPowSU = $true )
& ( powersetI1 = $true )
& ( complementImpComplementIntersect = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( setOfPairsIsBReln = $true )
& ( lam2p = $true )
& ( binintersectER = $true )
& ( quantDeMorgan4 = $true )
& ( sepInPowerset = $true )
& ( complementTnotintersectT = $true )
& ( emptyinunitempty = $true )
& ( notsubsetI = $true )
& ( setadjoinSub = $true )
& ( omega__Cong = $true )
& ( setextsub = $true )
& ( powersetT_lem = $true )
& ( emptysetAx = $true )
& ( binintersectTELcontra = $true )
& ( dpsetconstrER = $true )
& ( doubleComplementEq = $true )
& ( nonemptyI1 = $true )
& ( setoftrueEq = $true )
& ( dpsetconstrEL2 = $true )
& ( exuE2 = $true )
& ( omegaIndAx = $true ) ),
inference(flattening,[],[f1051]) ).
thf(f1059,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[],[f848]) ).
thf(f1372,plain,
( ( ( setminusERneg = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) )
| ( setminusERneg != $true ) ) ),
inference(nnf_transformation,[],[f943]) ).
thf(f1373,plain,
( ( ( setminusERneg = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( $true
!= ( in @ X3 @ X4 ) )
| ( $true
= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) ) )
| ( setminusERneg != $true ) ) ),
inference(rectify,[],[f1372]) ).
thf(f1374,plain,
( ( ( setminusERneg = $true )
| ( ( ( in @ sK193 @ sK195 )
!= $true )
& ( $true
= ( in @ sK193 @ sK194 ) )
& ( $true
!= ( in @ sK193 @ ( setminus @ sK194 @ sK195 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( $true
!= ( in @ X3 @ X4 ) )
| ( $true
= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) ) )
| ( setminusERneg != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193,sK194,sK195]),skolemize(X0,sK193),skolemize(X1,sK194),skolemize(X2,sK195)],[f1373]) ).
thf(f1533,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f1059]) ).
thf(f1534,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) )
& ( $true
= ( in @ X5 @ X3 ) ) ) ) ),
inference(rectify,[],[f1533]) ).
thf(f1535,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( $true
= ( in @ sK380 @ ( setminus @ sK379 @ sK378 ) ) )
& ( $true
= ( in @ sK380 @ sK378 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK378,sK379,sK380]),skolemize(X3,sK378),skolemize(X4,sK379),skolemize(X5,sK380)],[f1534]) ).
thf(f1895,plain,
( ( notequalI1 = $true )
& ( cartprodmempair = $true )
& ( binintersectSubset1 = $true )
& ( subsetI2 = $true )
& ( emptyinPowerset = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( in__Cong = $true )
& ( funcGraphProp4 = $true )
& ( powersetAx = $true )
& ( wellorderingAx = $true )
& ( binunionIR = $true )
& ( iftrueorfalse = $true )
& ( inIntersectImpInUnion = $true )
& ( ap2apEq1 = $true )
& ( setukpairinjR11 = $true )
& ( subset2powerset = $true )
& ( upairsetE = $true )
& ( doubleComplementI1 = $true )
& ( upairsetIL = $true )
& ( demorgan2a1 = $true )
& ( disjointsetsI1 = $true )
& ( theeq = $true )
& ( binunionTEcontra = $true )
& ( binunionT_lem = $true )
& ( emptysetimpfalse = $true )
& ( binintersectI = $true )
& ( ifp = $true )
& ( noeltsimpempty = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( powersetE = $true )
& ( ex1I2 = $true )
& ( brelnall1 = $true )
& ( cartprodsndpairEq = $true )
& ( singletonsswitch = $true )
& ( lamProp = $true )
& ( lamp = $true )
& ( doubleComplementE1 = $true )
& ( funcGraphProp2 = $true )
& ( doubleComplementSub2 = $true )
& ( replAx = $true )
& ( powersetI = $true )
& ( demorgan1 = $true )
& ( setukpairinjR = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinIL = $true )
& ( emptysetsubset = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( prop2set2propI = $true )
& ( demorgan2a = $true )
& ( setukpairIL = $true )
& ( exu__Cong = $true )
& ( setukpairinjL2 = $true )
& ( setunion__Cong = $true )
& ( funcextLem = $true )
& ( symdiffI2 = $true )
& ( binintersectTERcontra = $true )
& ( setadjoinSub2 = $true )
& ( singletonprop = $true )
& ( quantDeMorgan1 = $true )
& ( contraSubsetComplement = $true )
& ( sepSubset = $true )
& ( ubforcartprodlem2 = $true )
& ( contrasubsetT3 = $true )
& ( eta1 = $true )
& ( ex1I = $true )
& ( setminusSubset2 = $true )
& ( prop2setE = $true )
& ( notdallE = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan2 = $true )
& ( funcinfuncset = $true )
& ( setminusSubset1 = $true )
& ( binunionRsub = $true )
& ( eqimpsubset1 = $true )
& ( exuI1 = $true )
& ( cartprodpairmemEL = $true )
& ( kfstpairEq = $true )
& ( exuE3e = $true )
& ( exuE1 = $true )
& ( funcext = $true )
& ( setminusLsub = $true )
& ( exuI2 = $true )
& ( brelnall2 = $true )
& ( iffalseProp1 = $true )
& ( singletonsubset = $true )
& ( theprop = $true )
& ( setadjoinIR = $true )
& ( setunionsingleton2 = $true )
& ( singletonsuniq = $true )
& ( setukpairinjR12 = $true )
& ( inPowerset = $true )
& ( notinsingleton = $true )
& ( kfstsingleton = $true )
& ( binunionTE = $true )
& ( binintersectEL = $true )
& ( subsetTrans = $true )
& ( contrasubsetT2 = $true )
& ( descrp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrEL1 = $true )
& ( eta2 = $true )
& ( cartprodpairin = $true )
& ( kpairsurjEq = $true )
& ( bs114d = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( binintersectRsub = $true )
& ( singletoninpowunion = $true )
& ( setukpairinjL = $true )
& ( setminusI = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinE = $true )
& ( subsetemptysetimpeq = $true )
& ( eqinunit = $true )
& ( nonemptyI = $true )
& ( subsetTI = $true )
& ( binunionEcases = $true )
& ( upairset2IR = $true )
& ( upairsubunion = $true )
& ( setminusILneg = $true )
& ( upairequniteq = $true )
& ( upairsetIR = $true )
& ( iffalse = $true )
& ( foundationAx = $true )
& ( powersetTI1 = $true )
& ( cartprodmempair1 = $true )
& ( kpairp = $true )
& ( beta1 = $true )
& ( funcGraphProp3 = $true )
& ( setunionAx = $true )
& ( complementSubsetComplementIntersect = $true )
& ( cartprodmempaircEq = $true )
& ( subsetI1 = $true )
& ( subbreln = $true )
& ( exuEu = $true )
& ( upairset2E = $true )
& ( ( in @ sK745 @ ( setminus @ sK742 @ sK744 ) )
= $true )
& ( $true
= ( in @ sK745 @ ( setminus @ sK742 @ sK743 ) ) )
& ( $true
= ( in @ sK745 @ sK742 ) )
& ( ( in @ sK745 @ ( setminus @ sK742 @ ( binunion @ sK743 @ sK744 ) ) )
!= $true )
& ( $true
= ( in @ sK744 @ ( powerset @ sK742 ) ) )
& ( ( in @ sK743 @ ( powerset @ sK742 ) )
= $true )
& ( setminusERneg = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( setunionE2 = $true )
& ( subsetE2 = $true )
& ( upairinpowunion = $true )
& ( ubforcartprodlem1 = $true )
& ( singletoninpowerset = $true )
& ( beta2 = $true )
& ( powersetsubset = $true )
& ( powersetTE1 = $true )
& ( eqbreln = $true )
& ( dpsetconstrERa = $true )
& ( omega0Ax = $true )
& ( binunionIL = $true )
& ( complementTE1 = $true )
& ( ksndpairEq = $true )
& ( setextT = $true )
& ( dsetconstrER = $true )
& ( setunionE = $true )
& ( app = $true )
& ( doubleComplementSub1 = $true )
& ( funcGraphProp1 = $true )
& ( binintersectLsub = $true )
& ( notinemptyset = $true )
& ( binintersectT_lem = $true )
& ( setminusIRneg = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( setukpairinjL1 = $true )
& ( symdiffIneg2 = $true )
& ( iftrue = $true )
& ( setminusELneg = $true )
& ( dsetconstr__Cong = $true )
& ( inCongP = $true )
& ( uniqinunit = $true )
& ( demorgan1b = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodfstpairEq = $true )
& ( exuI3 = $true )
& ( infuncsetfunc = $true )
& ( emptysetE = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetRefl = $true )
& ( symdiffE = $true )
& ( inIntersectImpInUnion2 = $true )
& ( binunionLsub = $true )
& ( demorgan2a2 = $true )
& ( emptyI = $true )
& ( setukpairinjR1 = $true )
& ( descr__Cong = $true )
& ( lam2lamEq = $true )
& ( ex1E1 = $true )
& ( demorgan1a = $true )
& ( setminusEL = $true )
& ( prop2setI = $true )
& ( setunionI = $true )
& ( iftrueProp1 = $true )
& ( binintersectSubset2 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( symdiffIneg1 = $true )
& ( setadjoin__Cong = $true )
& ( exuE3u = $true )
& ( nonemptyE1 = $true )
& ( powersetE1 = $true )
& ( setextAx = $true )
& ( binintersectSubset5 = $true )
& ( notdexE = $true )
& ( setunionsingleton1 = $true )
& ( binunionTIRcontra = $true )
& ( symdiffI1 = $true )
& ( funcext2 = $true )
& ( setukpairinjR2 = $true )
& ( binintersectSubset4 = $true )
& ( eqimpsubset2 = $true )
& ( setunionsingleton = $true )
& ( binunionTILcontra = $true )
& ( subsetE = $true )
& ( ap2p = $true )
& ( complementTI1 = $true )
& ( apProp = $true )
& ( ap2apEq2 = $true )
& ( setminusT_lem = $true )
& ( emptyset__Cong = $true )
& ( emptyE1 = $true )
& ( setadjoinAx = $true )
& ( setext = $true )
& ( omegaSAx = $true )
& ( cartprodsndin = $true )
& ( binintersectSubset3 = $true )
& ( complementT_lem = $true )
& ( ubforcartprodlem3 = $true )
& ( complementTcontraSubset = $true )
& ( iftrueProp2 = $true )
& ( setbeta = $true )
& ( ex1E2 = $true )
& ( cartprodfstin = $true )
& ( setukpairIR = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( ifSingleton = $true )
& ( kpairiskpair = $true )
& ( secondinupair = $true )
& ( iffalseProp2 = $true )
& ( setminusER = $true )
& ( emptyInPowerset = $true )
& ( ksndsingleton = $true )
& ( notequalI2 = $true )
& ( subPowSU = $true )
& ( powersetI1 = $true )
& ( complementImpComplementIntersect = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( setOfPairsIsBReln = $true )
& ( lam2p = $true )
& ( binintersectER = $true )
& ( quantDeMorgan4 = $true )
& ( sepInPowerset = $true )
& ( complementTnotintersectT = $true )
& ( emptyinunitempty = $true )
& ( notsubsetI = $true )
& ( setadjoinSub = $true )
& ( omega__Cong = $true )
& ( setextsub = $true )
& ( powersetT_lem = $true )
& ( emptysetAx = $true )
& ( binintersectTELcontra = $true )
& ( dpsetconstrER = $true )
& ( doubleComplementEq = $true )
& ( nonemptyI1 = $true )
& ( setoftrueEq = $true )
& ( dpsetconstrEL2 = $true )
& ( exuE2 = $true )
& ( omegaIndAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK742,sK743,sK744,sK745]),skolemize(X0,sK742),skolemize(X1,sK743),skolemize(X2,sK744),skolemize(X3,sK745)],[f1052]) ).
thf(f1989,plain,
( ( ( binunionE = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( binunionE != $true ) ) ),
inference(nnf_transformation,[],[f869]) ).
thf(f1990,plain,
( ( ( binunionE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
& ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
= $true )
| ( $true
= ( in @ X3 @ X4 ) ) )
| ( binunionE != $true ) ) ),
inference(rectify,[],[f1989]) ).
thf(f1991,plain,
( ( ( binunionE = $true )
| ( ( $true
= ( in @ sK842 @ ( binunion @ sK844 @ sK843 ) ) )
& ( $true
!= ( in @ sK842 @ sK844 ) )
& ( $true
!= ( in @ sK842 @ sK843 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
= $true )
| ( $true
= ( in @ X3 @ X4 ) ) )
| ( binunionE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK842,sK843,sK844]),skolemize(X0,sK842),skolemize(X1,sK843),skolemize(X2,sK844)],[f1990]) ).
thf(f2263,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X4 ) )
| ( ( in @ X3 @ X5 )
= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( setminusERneg != $true ) ),
inference(cnf_transformation,[],[f1374]) ).
thf(f2523,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( setminusER != $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f1535]) ).
thf(f3043,plain,
setminusER = $true,
inference(cnf_transformation,[],[f1895]) ).
thf(f3145,plain,
setminusERneg = $true,
inference(cnf_transformation,[],[f1895]) ).
thf(f3148,plain,
( ( in @ sK745 @ ( setminus @ sK742 @ ( binunion @ sK743 @ sK744 ) ) )
!= $true ),
inference(cnf_transformation,[],[f1895]) ).
thf(f3149,plain,
( $true
= ( in @ sK745 @ sK742 ) ),
inference(cnf_transformation,[],[f1895]) ).
thf(f3150,plain,
( $true
= ( in @ sK745 @ ( setminus @ sK742 @ sK743 ) ) ),
inference(cnf_transformation,[],[f1895]) ).
thf(f3151,plain,
( ( in @ sK745 @ ( setminus @ sK742 @ sK744 ) )
= $true ),
inference(cnf_transformation,[],[f1895]) ).
thf(f3284,plain,
binunionE = $true,
inference(cnf_transformation,[],[f1895]) ).
thf(f3430,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( binunionE != $true )
| ( $true
= ( in @ X3 @ X4 ) )
| ( $true
!= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f1991]) ).
thf(f3988,definition,
( spl868_68
<=> ( binunionE = $true ) ),
introduced(definition,[new_symbols(definition,[spl868_68])],[avatar_definition]) ).
thf(f4103,definition,
( spl868_93
<=> ( setminusERneg = $true ) ),
introduced(definition,[new_symbols(definition,[spl868_93])],[avatar_definition]) ).
thf(f4436,definition,
( spl868_168
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl868_168])],[avatar_definition]) ).
thf(f4437,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ~ spl868_168 ),
inference(avatar_component_clause,[],[f4436]) ).
thf(f4571,definition,
( spl868_198
<=> ( setminusER = $true ) ),
introduced(definition,[new_symbols(definition,[spl868_198])],[avatar_definition]) ).
thf(f4743,definition,
( spl868_236
<=> ( $true
= ( in @ sK745 @ ( setminus @ sK742 @ sK743 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl868_236])],[avatar_definition]) ).
thf(f4745,plain,
( ( $true
= ( in @ sK745 @ ( setminus @ sK742 @ sK743 ) ) )
| ~ spl868_236 ),
inference(avatar_component_clause,[],[f4743]) ).
thf(f4746,plain,
spl868_236,
inference(avatar_split_clause,[],[f3150,f4743]) ).
thf(f5235,definition,
( spl868_347
<=> ! [X6: $i,X4: $i,X7: $i] :
( ( $true
!= ( in @ X6 @ ( binunion @ X4 @ X7 ) ) )
| ( $true
= ( in @ X6 @ X4 ) )
| ( $true
= ( in @ X6 @ X7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl868_347])],[avatar_definition]) ).
thf(f5236,plain,
( ! [X6: $i,X7: $i,X4: $i] :
( ( $true
!= ( in @ X6 @ ( binunion @ X4 @ X7 ) ) )
| ( $true
= ( in @ X6 @ X7 ) )
| ( $true
= ( in @ X6 @ X4 ) ) )
| ~ spl868_347 ),
inference(avatar_component_clause,[],[f5235]) ).
thf(f6025,definition,
( spl868_516
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl868_516])],[avatar_definition]) ).
thf(f6026,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ~ spl868_516 ),
inference(avatar_component_clause,[],[f6025]) ).
thf(f6540,definition,
( spl868_627
<=> ( $true
= ( in @ sK745 @ sK742 ) ) ),
introduced(definition,[new_symbols(definition,[spl868_627])],[avatar_definition]) ).
thf(f6542,plain,
( ( $true
= ( in @ sK745 @ sK742 ) )
| ~ spl868_627 ),
inference(avatar_component_clause,[],[f6540]) ).
thf(f6543,plain,
spl868_627,
inference(avatar_split_clause,[],[f3149,f6540]) ).
thf(f6972,definition,
( spl868_718
<=> ( ( in @ sK745 @ ( setminus @ sK742 @ ( binunion @ sK743 @ sK744 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl868_718])],[avatar_definition]) ).
thf(f6974,plain,
( ( ( in @ sK745 @ ( setminus @ sK742 @ ( binunion @ sK743 @ sK744 ) ) )
!= $true )
| spl868_718 ),
inference(avatar_component_clause,[],[f6972]) ).
thf(f6975,plain,
~ spl868_718,
inference(avatar_split_clause,[],[f3148,f6972]) ).
thf(f7158,plain,
spl868_68,
inference(avatar_split_clause,[],[f3284,f3988]) ).
thf(f7263,plain,
spl868_93,
inference(avatar_split_clause,[],[f3145,f4103]) ).
thf(f7828,plain,
( spl868_516
| ~ spl868_93 ),
inference(avatar_split_clause,[],[f2263,f4103,f6025]) ).
thf(f7934,plain,
spl868_198,
inference(avatar_split_clause,[],[f3043,f4571]) ).
thf(f8850,plain,
( spl868_168
| ~ spl868_198 ),
inference(avatar_split_clause,[],[f2523,f4571,f4436]) ).
thf(f9723,plain,
( ~ spl868_68
| spl868_347 ),
inference(avatar_split_clause,[],[f3430,f5235,f3988]) ).
thf(f10050,definition,
( spl868_1351
<=> ( ( in @ sK745 @ ( setminus @ sK742 @ sK744 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl868_1351])],[avatar_definition]) ).
thf(f10052,plain,
( ( ( in @ sK745 @ ( setminus @ sK742 @ sK744 ) )
= $true )
| ~ spl868_1351 ),
inference(avatar_component_clause,[],[f10050]) ).
thf(f10053,plain,
spl868_1351,
inference(avatar_split_clause,[],[f3151,f10050]) ).
thf(f10330,plain,
( ( $true != $true )
| ( ( in @ sK745 @ sK743 )
!= $true )
| ~ spl868_168
| ~ spl868_236 ),
inference(superposition,[],[f4437,f4745]) ).
thf(f10331,plain,
( ( ( in @ sK745 @ sK743 )
!= $true )
| ~ spl868_168
| ~ spl868_236 ),
inference(trivial_inequality_removal,[],[f10330]) ).
thf(f10334,definition,
( spl868_1395
<=> ( ( in @ sK745 @ sK743 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl868_1395])],[avatar_definition]) ).
thf(f10336,plain,
( ( ( in @ sK745 @ sK743 )
!= $true )
| spl868_1395 ),
inference(avatar_component_clause,[],[f10334]) ).
thf(f10337,plain,
( ~ spl868_1395
| ~ spl868_168
| ~ spl868_236 ),
inference(avatar_split_clause,[],[f10331,f4743,f4436,f10334]) ).
thf(f10341,plain,
( ( ( in @ sK745 @ sK744 )
!= $true )
| ( $true != $true )
| ~ spl868_168
| ~ spl868_1351 ),
inference(superposition,[],[f4437,f10052]) ).
thf(f10343,plain,
( ( ( in @ sK745 @ sK744 )
!= $true )
| ~ spl868_168
| ~ spl868_1351 ),
inference(trivial_inequality_removal,[],[f10341]) ).
thf(f10346,definition,
( spl868_1396
<=> ( ( in @ sK745 @ sK744 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl868_1396])],[avatar_definition]) ).
thf(f10348,plain,
( ( ( in @ sK745 @ sK744 )
!= $true )
| spl868_1396 ),
inference(avatar_component_clause,[],[f10346]) ).
thf(f10349,plain,
( ~ spl868_1396
| ~ spl868_168
| ~ spl868_1351 ),
inference(avatar_split_clause,[],[f10343,f10050,f4436,f10346]) ).
thf(f12567,plain,
( ( $true
= ( in @ sK745 @ ( binunion @ sK743 @ sK744 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK745 @ sK742 ) )
| ~ spl868_516
| spl868_718 ),
inference(superposition,[],[f6974,f6026]) ).
thf(f12570,plain,
( ( $true
!= ( in @ sK745 @ sK742 ) )
| ( $true
= ( in @ sK745 @ ( binunion @ sK743 @ sK744 ) ) )
| ~ spl868_516
| spl868_718 ),
inference(trivial_inequality_removal,[],[f12567]) ).
thf(f12587,plain,
( ( $true
= ( in @ sK745 @ ( binunion @ sK743 @ sK744 ) ) )
| ~ spl868_516
| ~ spl868_627
| spl868_718 ),
inference(forward_subsumption_resolution,[],[f12570,f6542]) ).
thf(f12589,definition,
( spl868_1451
<=> ( $true
= ( in @ sK745 @ ( binunion @ sK743 @ sK744 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl868_1451])],[avatar_definition]) ).
thf(f12591,plain,
( ( $true
= ( in @ sK745 @ ( binunion @ sK743 @ sK744 ) ) )
| ~ spl868_1451 ),
inference(avatar_component_clause,[],[f12589]) ).
thf(f12592,plain,
( spl868_1451
| ~ spl868_516
| ~ spl868_627
| spl868_718 ),
inference(avatar_split_clause,[],[f12587,f6972,f6540,f6025,f12589]) ).
thf(f12593,plain,
( ( $true != $true )
| ( ( in @ sK745 @ sK744 )
= $true )
| ( ( in @ sK745 @ sK743 )
= $true )
| ~ spl868_347
| ~ spl868_1451 ),
inference(superposition,[],[f5236,f12591]) ).
thf(f12599,plain,
( ( ( in @ sK745 @ sK744 )
= $true )
| ( ( in @ sK745 @ sK743 )
= $true )
| ~ spl868_347
| ~ spl868_1451 ),
inference(trivial_inequality_removal,[],[f12593]) ).
thf(f12608,plain,
( ( ( in @ sK745 @ sK743 )
= $true )
| ~ spl868_347
| spl868_1396
| ~ spl868_1451 ),
inference(forward_subsumption_resolution,[],[f12599,f10348]) ).
thf(f12628,plain,
( $false
| ~ spl868_347
| spl868_1395
| spl868_1396
| ~ spl868_1451 ),
inference(forward_subsumption_resolution,[],[f12608,f10336]) ).
thf(f12629,plain,
( ~ spl868_347
| spl868_1395
| spl868_1396
| ~ spl868_1451 ),
inference(avatar_contradiction_clause,[],[f12628]) ).
cnf(s150,plain,
spl868_236,
inference(sat_conversion,[],[f4746]) ).
cnf(s491,plain,
spl868_627,
inference(sat_conversion,[],[f6543]) ).
cnf(s586,plain,
~ spl868_718,
inference(sat_conversion,[],[f6975]) ).
cnf(s632,plain,
spl868_68,
inference(sat_conversion,[],[f7158]) ).
cnf(s655,plain,
spl868_93,
inference(sat_conversion,[],[f7263]) ).
cnf(s800,plain,
( ~ spl868_93
| spl868_516 ),
inference(sat_conversion,[],[f7828]) ).
cnf(s826,plain,
spl868_198,
inference(sat_conversion,[],[f7934]) ).
cnf(s1044,plain,
( spl868_168
| ~ spl868_198 ),
inference(sat_conversion,[],[f8850]) ).
cnf(s1281,plain,
( ~ spl868_68
| spl868_347 ),
inference(sat_conversion,[],[f9723]) ).
cnf(s1364,plain,
spl868_1351,
inference(sat_conversion,[],[f10053]) ).
cnf(s1422,plain,
( ~ spl868_168
| ~ spl868_236
| ~ spl868_1395 ),
inference(sat_conversion,[],[f10337]) ).
cnf(s1423,plain,
( ~ spl868_168
| ~ spl868_1351
| ~ spl868_1396 ),
inference(sat_conversion,[],[f10349]) ).
cnf(s1488,plain,
( ~ spl868_516
| ~ spl868_627
| spl868_718
| spl868_1451 ),
inference(sat_conversion,[],[f12592]) ).
cnf(s1493,plain,
( ~ spl868_347
| spl868_1395
| spl868_1396
| ~ spl868_1451 ),
inference(sat_conversion,[],[f12629]) ).
cnf(s1561,plain,
spl868_168,
inference(rat,[],[s1044,s826]) ).
cnf(s1562,plain,
~ spl868_1396,
inference(rat,[],[s1423,s1364,s1561]) ).
cnf(s1597,plain,
spl868_516,
inference(rat,[],[s800,s655]) ).
cnf(s1601,plain,
spl868_347,
inference(rat,[],[s1281,s632]) ).
cnf(s1650,plain,
spl868_1451,
inference(rat,[],[s1488,s586,s1597,s491]) ).
cnf(s1655,plain,
spl868_1395,
inference(rat,[],[s1493,s1601,s1562,s1650]) ).
cnf(s1657,plain,
~ spl868_236,
inference(rat,[],[s1422,s1561,s1655]) ).
cnf(s1811,plain,
$false,
inference(rat,[],[s150,s1657]) ).
thf(f12630,plain,
$false,
inference(avatar_sat_refutation,[],[s1811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU755^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n003.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:23:43 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running higher-order theorem proving
% 0.25/0.35 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
% 0.78/0.57 % (2578976)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.78/0.57 % (2578983)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2079810195:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.78/0.57 % (2578981)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3406600122:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.78/0.57 % (2578983)Instruction limit reached!
% 0.78/0.57 % (2578983)------------------------------
% 0.78/0.57 % (2578983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.57 % (2578983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.57 % (2578983)CaDiCaL version: 2.1.3
% 0.78/0.57 % (2578983)Termination reason: Instruction limit
% 0.78/0.57 % (2578983)Termination phase: shuffling
% 0.78/0.57 % (2578983)Time elapsed: 0.002 s
% 0.78/0.57 % (2578983)Peak memory usage: 10 MB
% 0.78/0.57 % (2578983)Instructions burned: 3 (million)
% 0.78/0.57 % (2578987)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.78/0.57 % (2578987)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
% 0.78/0.57 % (2578982)lrs+10_16_si=on:nwc=1.5:random_seed=2519876214:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.78/0.57 % (2578985)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=230747874:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.78/0.57 % (2578986)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1713655144:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.78/0.57 % (2578984)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=1178128395: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)
% 0.78/0.57 % (2578987)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=289482013:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.78/0.57 % (2578990)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2644314893:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.78/0.57 % (2578990)Instruction limit reached!
% 0.78/0.57 % (2578990)------------------------------
% 0.78/0.57 % (2578990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.57 % (2578990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.57 % (2578990)CaDiCaL version: 2.1.3
% 0.78/0.57 % (2578990)Termination reason: Instruction limit
% 0.78/0.57 % (2578990)Termination phase: shuffling
% 0.78/0.57 % (2578990)Time elapsed: 0.001 s
% 0.78/0.57 % (2578990)Peak memory usage: 10 MB
% 0.78/0.57 % (2578990)Instructions burned: 2 (million)
% 0.78/0.57 % (2578982)Instruction limit reached!
% 0.78/0.57 % (2578982)------------------------------
% 0.78/0.57 % (2578982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.57 % (2578982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.57 % (2578982)CaDiCaL version: 2.1.3
% 0.78/0.57 % (2578982)Termination reason: Instruction limit
% 0.78/0.57 % (2578982)Termination phase: shuffling
% 0.78/0.57 % (2578982)Time elapsed: 0.016 s
% 0.78/0.57 % (2578982)Peak memory usage: 10 MB
% 0.78/0.57 % (2578982)Instructions burned: 18 (million)
% 0.78/0.57 % (2578985)Instruction limit reached!
% 0.78/0.57 % (2578985)------------------------------
% 0.78/0.57 % (2578985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.57 % (2578985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.57 % (2578985)CaDiCaL version: 2.1.3
% 0.78/0.57 % (2578985)Termination reason: Instruction limit
% 0.78/0.57 % (2578985)Termination phase: Property scanning
% 0.78/0.57 % (2578985)Time elapsed: 0.025 s
% 0.78/0.57 % (2578985)Peak memory usage: 10 MB
% 0.78/0.57 % (2578985)Instructions burned: 29 (million)
% 0.78/0.57 % (2578997)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=317888164:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.62/0.62 % (2578997)Instruction limit reached!
% 1.62/0.62 % (2578997)------------------------------
% 1.62/0.62 % (2578997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.62 % (2578997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.62 % (2578997)CaDiCaL version: 2.1.3
% 1.62/0.62 % (2578997)Termination reason: Instruction limit
% 1.62/0.62 % (2578997)Termination phase: shuffling
% 1.62/0.62 % (2578997)Time elapsed: 0.003 s
% 1.62/0.62 % (2578997)Peak memory usage: 10 MB
% 1.62/0.62 % (2578997)Instructions burned: 5 (million)
% 1.62/0.62 % (2579001)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
% 1.62/0.62 % (2579001)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.62/0.62 % (2578998)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.62/0.62 % (2579001)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3896708848:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.62/0.62 % (2578981)Instruction limit reached!
% 1.62/0.62 % (2578981)------------------------------
% 1.62/0.62 % (2578981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.62 % (2578981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.62 % (2578981)CaDiCaL version: 2.1.3
% 1.62/0.62 % (2578998)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2663159992:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.62/0.62 % (2578981)Termination reason: Instruction limit
% 1.62/0.62 % (2578981)Termination phase: Preprocessing 3
% 1.62/0.62 % (2578981)Time elapsed: 0.067 s
% 1.62/0.62 % (2578981)Peak memory usage: 13 MB
% 1.62/0.62 % (2578981)Instructions burned: 87 (million)
% 1.62/0.62 % (2579001)Instruction limit reached!
% 1.62/0.62 % (2579001)------------------------------
% 1.62/0.62 % (2579001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.62 % (2579001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.62 % (2579001)CaDiCaL version: 2.1.3
% 1.62/0.62 % (2579001)Termination reason: Instruction limit
% 1.62/0.62 % (2579001)Termination phase: shuffling
% 1.62/0.62 % (2579001)Time elapsed: 0.007 s
% 1.62/0.62 % (2579001)Peak memory usage: 11 MB
% 1.62/0.62 % (2579001)Instructions burned: 30 (million)
% 1.62/0.62 % (2578999)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4015506843:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.62/0.62 % (2578998)Instruction limit reached!
% 1.62/0.62 % (2578998)------------------------------
% 1.62/0.62 % (2578998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.62 % (2578998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.62 % (2578998)CaDiCaL version: 2.1.3
% 1.62/0.62 % (2578998)Termination reason: Instruction limit
% 1.62/0.62 % (2578998)Termination phase: shuffling
% 1.62/0.62 % (2578998)Time elapsed: 0.006 s
% 1.62/0.62 % (2578998)Peak memory usage: 10 MB
% 1.62/0.62 % (2578998)Instructions burned: 7 (million)
% 1.62/0.62 % (2578986)Instruction limit reached!
% 1.62/0.62 % (2578986)------------------------------
% 1.62/0.62 % (2578986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.62 % (2578986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.62 % (2578986)CaDiCaL version: 2.1.3
% 1.62/0.62 % (2578986)Termination reason: Instruction limit
% 1.62/0.62 % (2578986)Termination phase: Preprocessing 3
% 1.62/0.62 % (2578986)Time elapsed: 0.063 s
% 1.62/0.62 % (2578986)Peak memory usage: 12 MB
% 1.62/0.62 % (2578986)Instructions burned: 75 (million)
% 1.62/0.62 % (2579006)lrs+10_1_si=on:cs=on:random_seed=1544573552:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.62/0.62 % (2578999)Instruction limit reached!
% 1.62/0.62 % (2578999)------------------------------
% 1.62/0.62 % (2578999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.62 % (2578999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.65 % (2578999)CaDiCaL version: 2.1.3
% 1.62/0.65 % (2578999)Termination reason: Instruction limit
% 1.62/0.65 % (2578999)Termination phase: shuffling
% 1.62/0.65 % (2578999)Time elapsed: 0.011 s
% 1.62/0.65 % (2578999)Peak memory usage: 10 MB
% 1.62/0.65 % (2578999)Instructions burned: 12 (million)
% 1.62/0.65 % (2579006)Instruction limit reached!
% 1.62/0.65 % (2579006)------------------------------
% 1.62/0.65 % (2579006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.65 % (2579006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.65 % (2579006)CaDiCaL version: 2.1.3
% 1.62/0.65 % (2579006)Termination reason: Instruction limit
% 1.62/0.65 % (2579006)Termination phase: shuffling
% 1.62/0.65 % (2579006)Time elapsed: 0.003 s
% 1.62/0.65 % (2579006)Peak memory usage: 10 MB
% 1.62/0.65 % (2579006)Instructions burned: 12 (million)
% 1.62/0.65 % (2579011)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3837662733:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.62/0.65 % (2579005)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=213285681:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.62/0.65 % (2579008)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.62/0.65 % (2579008)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=2527905492:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.62/0.65 % (2579009)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3635892505:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.62/0.65 % (2579008)Instruction limit reached!
% 1.62/0.65 % (2579008)------------------------------
% 1.62/0.65 % (2579008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.65 % (2579008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.65 % (2579008)CaDiCaL version: 2.1.3
% 1.62/0.65 % (2579008)Termination reason: Instruction limit
% 1.62/0.65 % (2579008)Termination phase: shuffling
% 1.62/0.65 % (2579008)Time elapsed: 0.003 s
% 1.62/0.65 % (2579008)Peak memory usage: 10 MB
% 1.62/0.65 % (2579008)Instructions burned: 2 (million)
% 1.62/0.65 % (2579012)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2029858758:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.62/0.65 % (2578987)Instruction limit reached!
% 1.62/0.65 % (2578987)------------------------------
% 1.62/0.65 % (2578987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.65 % (2578987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.65 % (2578987)CaDiCaL version: 2.1.3
% 1.62/0.65 % (2578987)Termination reason: Instruction limit
% 1.62/0.65 % (2578987)Termination phase: Property scanning
% 1.62/0.65 % (2578987)Time elapsed: 0.127 s
% 1.62/0.65 % (2578987)Peak memory usage: 12 MB
% 1.62/0.65 % (2578987)Instructions burned: 158 (million)
% 1.62/0.65 % (2579009)Instruction limit reached!
% 1.62/0.65 % (2579009)------------------------------
% 1.62/0.65 % (2579009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.65 % (2579012)Instruction limit reached!
% 1.62/0.65 % (2579012)------------------------------
% 1.62/0.65 % (2579012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.65 % (2579009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.65 % (2579012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.65 % (2579012)CaDiCaL version: 2.1.3
% 1.62/0.65 % (2579009)CaDiCaL version: 2.1.3
% 1.62/0.65 % (2579009)Termination reason: Instruction limit
% 1.62/0.65 % (2579009)Termination phase: Property scanning
% 1.62/0.65 % (2579009)Time elapsed: 0.033 s
% 1.62/0.65 % (2579012)Termination reason: Instruction limit
% 1.62/0.65 % (2579012)Termination phase: shuffling
% 1.62/0.65 % (2579012)Time elapsed: 0.021 s
% 1.62/0.65 % (2579012)Peak memory usage: 10 MB
% 1.62/0.65 % (2579009)Peak memory usage: 11 MB
% 1.62/0.65 % (2579009)Instructions burned: 39 (million)
% 1.62/0.65 % (2579012)Instructions burned: 25 (million)
% 1.62/0.65 % (2579018)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2277775913:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.14/0.77 % (2579011)Instruction limit reached!
% 2.14/0.77 % (2579011)------------------------------
% 2.14/0.77 % (2579011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.77 % (2579011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.77 % (2579011)CaDiCaL version: 2.1.3
% 2.14/0.77 % (2579011)Termination reason: Instruction limit
% 2.14/0.77 % (2579011)Termination phase: Saturation
% 2.14/0.77 % (2579011)Time elapsed: 0.061 s
% 2.14/0.77 % (2579011)Peak memory usage: 15 MB
% 2.14/0.77 % (2579011)Instructions burned: 250 (million)
% 2.14/0.77 % (2579018)Instruction limit reached!
% 2.14/0.77 % (2579018)------------------------------
% 2.14/0.77 % (2579018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.77 % (2579018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.77 % (2579018)CaDiCaL version: 2.1.3
% 2.14/0.77 % (2579018)Termination reason: Instruction limit
% 2.14/0.77 % (2579018)Termination phase: shuffling
% 2.14/0.77 % (2579018)Time elapsed: 0.013 s
% 2.14/0.77 % (2579018)Peak memory usage: 10 MB
% 2.14/0.77 % (2579018)Instructions burned: 14 (million)
% 2.14/0.77 % (2579024)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1903538209:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.14/0.77 % (2579020)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2713113064:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.14/0.77 % (2579022)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3906666018:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 2.14/0.77 % (2579021)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2283722598:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/14Mi)
% 2.14/0.77 % (2579022)Instruction limit reached!
% 2.14/0.77 % (2579022)------------------------------
% 2.14/0.77 % (2579022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.77 % (2579022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.77 % (2579022)CaDiCaL version: 2.1.3
% 2.14/0.77 % (2579022)Termination reason: Instruction limit
% 2.14/0.77 % (2579022)Termination phase: shuffling
% 2.14/0.77 % (2579022)Time elapsed: 0.003 s
% 2.14/0.77 % (2579022)Peak memory usage: 10 MB
% 2.14/0.77 % (2579022)Instructions burned: 2 (million)
% 2.14/0.77 % (2579024)Instruction limit reached!
% 2.14/0.77 % (2579024)------------------------------
% 2.14/0.77 % (2579024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.77 % (2579024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.77 % (2579024)CaDiCaL version: 2.1.3
% 2.14/0.77 % (2579024)Termination reason: Instruction limit
% 2.14/0.77 % (2579024)Termination phase: shuffling
% 2.14/0.77 % (2579024)Time elapsed: 0.008 s
% 2.14/0.77 % (2579024)Peak memory usage: 11 MB
% 2.14/0.77 % (2579024)Instructions burned: 29 (million)
% 2.14/0.77 % (2579005)Instruction limit reached!
% 2.14/0.77 % (2579005)------------------------------
% 2.14/0.77 % (2579005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.77 % (2579005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.77 % (2579005)CaDiCaL version: 2.1.3
% 2.14/0.77 % (2579005)Termination reason: Instruction limit
% 2.14/0.77 % (2579005)Termination phase: Property scanning
% 2.14/0.77 % (2579005)Time elapsed: 0.086 s
% 2.14/0.77 % (2579005)Peak memory usage: 11 MB
% 2.14/0.77 % (2579005)Instructions burned: 87 (million)
% 2.14/0.77 % (2579031)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.14/0.77 % (2579031)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.14/0.77 % (2579021)Instruction limit reached!
% 2.14/0.77 % (2579021)------------------------------
% 2.14/0.77 % (2579021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.77 % (2579021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.77 % (2579021)CaDiCaL version: 2.1.3
% 2.35/0.90 % (2579021)Termination reason: Instruction limit
% 2.35/0.90 % (2579021)Termination phase: shuffling
% 2.35/0.90 % (2579021)Time elapsed: 0.014 s
% 2.35/0.90 % (2579021)Peak memory usage: 11 MB
% 2.35/0.90 % (2579021)Instructions burned: 14 (million)
% 2.35/0.90 % (2579031)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=3498395444:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.35/0.90 % (2579025)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3822379594:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.35/0.90 % (2579031)Instruction limit reached!
% 2.35/0.90 % (2579031)------------------------------
% 2.35/0.90 % (2579031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.90 % (2579031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.90 % (2579031)CaDiCaL version: 2.1.3
% 2.35/0.90 % (2579031)Termination reason: Instruction limit
% 2.35/0.90 % (2579031)Termination phase: shuffling
% 2.35/0.90 % (2579031)Time elapsed: 0.004 s
% 2.35/0.90 % (2579031)Peak memory usage: 10 MB
% 2.35/0.90 % (2579031)Instructions burned: 17 (million)
% 2.35/0.90 % (2579036)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2221310560:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.35/0.90 % (2579036)Instruction limit reached!
% 2.35/0.90 % (2579036)------------------------------
% 2.35/0.90 % (2579036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.90 % (2579036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.90 % (2579036)CaDiCaL version: 2.1.3
% 2.35/0.90 % (2579036)Termination reason: Instruction limit
% 2.35/0.90 % (2579036)Termination phase: shuffling
% 2.35/0.90 % (2579036)Time elapsed: 0.002 s
% 2.35/0.90 % (2579036)Peak memory usage: 10 MB
% 2.35/0.90 % (2579036)Instructions burned: 9 (million)
% 2.35/0.90 % (2579030)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2746754699:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.35/0.90 % (2579032)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.35/0.90 % (2579025)Instruction limit reached!
% 2.35/0.90 % (2579025)------------------------------
% 2.35/0.90 % (2579025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.90 % (2579025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.90 % (2579025)CaDiCaL version: 2.1.3
% 2.35/0.90 % (2579025)Termination reason: Instruction limit
% 2.35/0.90 % (2579025)Termination phase: shuffling
% 2.35/0.90 % (2579025)Time elapsed: 0.020 s
% 2.35/0.90 % (2579025)Peak memory usage: 10 MB
% 2.35/0.90 % (2579025)Instructions burned: 23 (million)
% 2.35/0.90 % (2579032)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=1210090236:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.35/0.90 % (2579039)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2657692150:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.35/0.90 % (2579034)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=3813852049:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.35/0.90 % (2579032)Instruction limit reached!
% 2.35/0.90 % (2579032)------------------------------
% 2.35/0.90 % (2579032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.90 % (2579032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.90 % (2579032)CaDiCaL version: 2.1.3
% 2.35/0.90 % (2579032)Termination reason: Instruction limit
% 2.35/0.90 % (2579032)Termination phase: shuffling
% 2.35/0.90 % (2579032)Time elapsed: 0.008 s
% 2.35/0.90 % (2579032)Peak memory usage: 10 MB
% 2.35/0.90 % (2579032)Instructions burned: 9 (million)
% 2.35/0.90 % (2579039)Instruction limit reached!
% 2.35/0.90 % (2579039)------------------------------
% 2.35/0.90 % (2579039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.90 % (2579039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579039)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579039)Termination reason: Instruction limit
% 3.30/0.96 % (2579039)Termination phase: shuffling
% 3.30/0.96 % (2579039)Time elapsed: 0.006 s
% 3.30/0.96 % (2579039)Peak memory usage: 10 MB
% 3.30/0.96 % (2579039)Instructions burned: 23 (million)
% 3.30/0.96 % (2579045)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4131686331:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 3.30/0.96 % (2579034)Instruction limit reached!
% 3.30/0.96 % (2579034)------------------------------
% 3.30/0.96 % (2579034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579034)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579034)Termination reason: Instruction limit
% 3.30/0.96 % (2579034)Termination phase: shuffling
% 3.30/0.96 % (2579034)Time elapsed: 0.026 s
% 3.30/0.96 % (2579034)Peak memory usage: 11 MB
% 3.30/0.96 % (2579034)Instructions burned: 31 (million)
% 3.30/0.96 % (2579041)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1283952660:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 3.30/0.96 % (2579046)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1380473276:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 3.30/0.96 % (2579030)Instruction limit reached!
% 3.30/0.96 % (2579030)------------------------------
% 3.30/0.96 % (2579030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579030)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579030)Termination reason: Instruction limit
% 3.30/0.96 % (2579030)Termination phase: Preprocessing 3
% 3.30/0.96 % (2579030)Time elapsed: 0.051 s
% 3.30/0.96 % (2579030)Peak memory usage: 12 MB
% 3.30/0.96 % (2579030)Instructions burned: 60 (million)
% 3.30/0.96 % (2579041)Instruction limit reached!
% 3.30/0.96 % (2579041)------------------------------
% 3.30/0.96 % (2579041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579041)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579041)Termination reason: Instruction limit
% 3.30/0.96 % (2579041)Termination phase: shuffling
% 3.30/0.96 % (2579041)Time elapsed: 0.017 s
% 3.30/0.96 % (2579041)Peak memory usage: 11 MB
% 3.30/0.96 % (2579041)Instructions burned: 20 (million)
% 3.30/0.96 % (2579050)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3297216459:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/193Mi)
% 3.30/0.96 % (2579052)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=808635035:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 3.30/0.96 % (2579053)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.30/0.96 % (2579053)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2830372535:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 3.30/0.96 % (2579053)Instruction limit reached!
% 3.30/0.96 % (2579053)------------------------------
% 3.30/0.96 % (2579053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579053)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579053)Termination reason: Instruction limit
% 3.30/0.96 % (2579053)Termination phase: shuffling
% 3.30/0.96 % (2579053)Time elapsed: 0.007 s
% 3.30/0.96 % (2579053)Peak memory usage: 10 MB
% 3.30/0.96 % (2579053)Instructions burned: 8 (million)
% 3.30/0.96 % (2579052)Instruction limit reached!
% 3.30/0.96 % (2579052)------------------------------
% 3.30/0.96 % (2579052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579052)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579052)Termination reason: Instruction limit
% 3.30/0.96 % (2579052)Termination phase: Property scanning
% 3.30/0.96 % (2579052)Time elapsed: 0.037 s
% 3.30/0.96 % (2579052)Peak memory usage: 11 MB
% 3.30/0.96 % (2579052)Instructions burned: 43 (million)
% 3.30/0.96 % (2579057)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2028564541:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 3.30/0.96 % (2579058)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=864337537:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 3.30/0.96 % (2579046)Instruction limit reached!
% 3.30/0.96 % (2579046)------------------------------
% 3.30/0.96 % (2579046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579046)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579046)Termination reason: Instruction limit
% 3.30/0.96 % (2579046)Termination phase: Property scanning
% 3.30/0.96 % (2579046)Time elapsed: 0.114 s
% 3.30/0.96 % (2579046)Peak memory usage: 12 MB
% 3.30/0.96 % (2579046)Instructions burned: 143 (million)
% 3.30/0.96 % (2579061)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.30/0.96 % (2579061)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3764493680:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2995 on theBenchmark for (2995ds/6Mi)
% 3.30/0.96 % (2579061)Instruction limit reached!
% 3.30/0.96 % (2579061)------------------------------
% 3.30/0.96 % (2579061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579061)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579061)Termination reason: Instruction limit
% 3.30/0.96 % (2579061)Termination phase: shuffling
% 3.30/0.96 % (2579061)Time elapsed: 0.006 s
% 3.30/0.96 % (2579061)Peak memory usage: 10 MB
% 3.30/0.96 % (2579061)Instructions burned: 7 (million)
% 3.30/0.96 % (2579050)Instruction limit reached!
% 3.30/0.96 % (2579050)------------------------------
% 3.30/0.96 % (2579050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579050)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579050)Termination reason: Instruction limit
% 3.30/0.96 % (2579050)Termination phase: Saturation
% 3.30/0.96 % (2579050)Time elapsed: 0.150 s
% 3.30/0.96 % (2579050)Peak memory usage: 13 MB
% 3.30/0.96 % (2579050)Instructions burned: 193 (million)
% 3.30/0.96 % (2579058)Instruction limit reached!
% 3.30/0.96 % (2579058)------------------------------
% 3.30/0.96 % (2579058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579058)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579058)Termination reason: Instruction limit
% 3.30/0.96 % (2579058)Termination phase: Saturation
% 3.30/0.96 % (2579058)Time elapsed: 0.079 s
% 3.30/0.96 % (2579058)Peak memory usage: 13 MB
% 3.30/0.96 % (2579058)Instructions burned: 170 (million)
% 3.30/0.96 % (2579020)Instruction limit reached!
% 3.30/0.96 % (2579020)------------------------------
% 3.30/0.96 % (2579020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579020)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579020)Termination reason: Instruction limit
% 3.30/0.96 % (2579020)Termination phase: Saturation
% 3.30/0.96 % (2579020)Time elapsed: 0.268 s
% 3.30/0.96 % (2579020)Peak memory usage: 15 MB
% 3.30/0.96 % (2579020)Instructions burned: 328 (million)
% 3.30/0.96 % (2579063)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3092235297:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2995 on theBenchmark for (2995ds/22Mi)
% 3.30/0.96 % (2579065)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1022296613:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 3.30/0.96 % (2579064)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2414994908:i=19:add=on:rtra=on_2995 on theBenchmark for (2995ds/19Mi)
% 3.30/0.96 % (2579063)Instruction limit reached!
% 3.30/0.96 % (2579063)------------------------------
% 3.30/0.96 % (2579063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579063)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579063)Termination reason: Instruction limit
% 3.30/0.96 % (2579063)Termination phase: shuffling
% 3.30/0.96 % (2579063)Time elapsed: 0.019 s
% 3.30/0.96 % (2579063)Peak memory usage: 10 MB
% 3.30/0.96 % (2579063)Instructions burned: 23 (million)
% 3.30/0.96 % (2579066)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3848186039:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2994 on theBenchmark for (2994ds/853Mi)
% 3.30/0.96 % (2579064)Instruction limit reached!
% 3.30/0.96 % (2579064)------------------------------
% 3.30/0.96 % (2579064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579064)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579064)Termination reason: Instruction limit
% 3.30/0.96 % (2579064)Termination phase: shuffling
% 3.30/0.96 % (2579064)Time elapsed: 0.017 s
% 3.30/0.96 % (2579064)Peak memory usage: 10 MB
% 3.30/0.96 % (2579064)Instructions burned: 20 (million)
% 3.30/0.96 % (2579057)Instruction limit reached!
% 3.30/0.96 % (2579057)------------------------------
% 3.30/0.96 % (2579057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.96 % (2579057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.96 % (2579057)CaDiCaL version: 2.1.3
% 3.30/0.96 % (2579057)Termination reason: Instruction limit
% 3.30/0.96 % (2579057)Termination phase: Saturation
% 3.30/0.96 % (2579057)Time elapsed: 0.144 s
% 3.30/0.96 % (2579057)Peak memory usage: 14 MB
% 3.30/0.96 % (2579057)Instructions burned: 181 (million)
% 3.30/0.96 % (2579070)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=4148159907:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2994 on theBenchmark for (2994ds/45Mi)
% 3.30/0.96 % (2578984) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2578976-2578984"...
% 3.30/0.96 % (2579072)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1012068308:i=480:rtra=on_2994 on theBenchmark for (2994ds/480Mi)
% 3.30/0.96 % (2579073)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3277849467:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2994 on theBenchmark for (2994ds/21Mi)
% 3.30/0.96 % (2578984)...printing done.
% 3.30/0.96 % (2578984)Refutation found. Thanks to Tanya!
% 3.30/0.96 % SZS status Theorem for theBenchmark
% 3.30/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 3.30/0.97 % (2578984)------------------------------
% 3.30/0.97 % (2578984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.97 % (2578984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.97 % (2578984)CaDiCaL version: 2.1.3
% 3.30/0.97 % (2578984)Termination reason: Refutation
% 3.30/0.97 % (2578984)Time elapsed: 0.511 s
% 3.30/0.97 % (2578984)Peak memory usage: 22 MB
% 3.30/0.97 % (2578984)Instructions burned: 566 (million)
% 3.30/0.97 % (2578976)Success in time 0.591 s
% 3.30/0.97 % Vampire exiting
%------------------------------------------------------------------------------