%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU759^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:10 AM UTC 2026
% Result : Theorem 2.11s 0.64s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 21 unt; 0 typ; 6 def)
% Number of atoms : 4561 (1206 equ; 0 cnn)
% Maximal formula atoms : 280 ( 74 avg)
% Number of connectives : 2384 ( 70 ~; 62 |; 849 &; 271 @)
% ( 10 <=>;1122 =>; 0 <=; 0 <~>)
% Maximal formula depth : 289 ( 36 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 : 507 ( 504 usr; 312 con; 0-4 aty)
% Number of variables : 87 ( 0 sgn 69 !; 18 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_279,type,
contrasubsetT1: $o ).
thf(func_def_280,type,
contrasubsetT2: $o ).
thf(func_def_281,type,
contrasubsetT3: $o ).
thf(func_def_282,type,
doubleComplementI1: $o ).
thf(func_def_283,type,
doubleComplementE1: $o ).
thf(func_def_284,type,
doubleComplementSub1: $o ).
thf(func_def_285,type,
doubleComplementSub2: $o ).
thf(func_def_286,type,
doubleComplementEq: $o ).
thf(func_def_287,type,
complementTnotintersectT: $o ).
thf(func_def_288,type,
complementImpComplementIntersect: $o ).
thf(func_def_289,type,
complementSubsetComplementIntersect: $o ).
thf(func_def_290,type,
complementInPowersetComplementIntersect: $o ).
thf(func_def_291,type,
contraSubsetComplement: $o ).
thf(func_def_292,type,
complementTcontraSubset: $o ).
thf(func_def_293,type,
binunionTILcontra: $o ).
thf(func_def_294,type,
binunionTIRcontra: $o ).
thf(func_def_295,type,
inIntersectImpInUnion: $o ).
thf(func_def_296,type,
inIntersectImpInUnion2: $o ).
thf(func_def_297,type,
inIntersectImpInIntersectUnions: $o ).
thf(func_def_298,type,
intersectInPowersetIntersectUnions: $o ).
thf(func_def_299,type,
inComplementUnionImpNotIn1: $o ).
thf(func_def_300,type,
inComplementUnionImpInComplement1: $o ).
thf(func_def_301,type,
binunionTE: $o ).
thf(func_def_302,type,
binunionTEcontra: $o ).
thf(func_def_303,type,
demorgan2a1: $o ).
thf(func_def_304,type,
complementUnionInPowersetComplement: $o ).
thf(func_def_305,type,
demorgan2a2: $o ).
thf(func_def_306,type,
demorgan1a: $o ).
thf(func_def_307,type,
demorgan1b: $o ).
thf(func_def_308,type,
demorgan1: $o ).
thf(func_def_309,type,
demorgan2a: $o ).
thf(func_def_310,type,
demorgan2b2: $o ).
thf(func_def_311,type,
demorgan2b: $o ).
thf(func_def_312,type,
demorgan2: $o ).
thf(func_def_313,type,
woz13rule0: $o ).
thf(func_def_316,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_317,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_318,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_319,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_320,type,
vOR: $o > $o > $o ).
thf(func_def_321,type,
vAND: $o > $o > $o ).
thf(func_def_322,type,
vNOT: $o > $o ).
thf(func_def_323,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_324,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_325,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_326,type,
vIMP: $o > $o > $o ).
thf(func_def_327,type,
sP0: $i > $i > $o ).
thf(func_def_328,type,
sP1: $i > $o ).
thf(func_def_329,type,
sP2: $o ).
thf(func_def_330,type,
sP3: $o ).
thf(func_def_353,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_354,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_355,type,
sK28: $i > $o ).
thf(func_def_367,type,
sK40: $i > ( $i > $o ) > $i ).
thf(func_def_368,type,
sK41: $i > $o ).
thf(func_def_377,type,
sK50: $o ).
thf(func_def_390,type,
sK63: $i > $o ).
thf(func_def_391,type,
sK64: $i > $o ).
thf(func_def_392,type,
sK65: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_393,type,
sK66: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_394,type,
sK67: $i > $i > $i > $i > $i ).
thf(func_def_395,type,
sK68: $i > $i > $i > $i > $i ).
thf(func_def_400,type,
sK73: $i > $o ).
thf(func_def_401,type,
sK74: $i > $o ).
thf(func_def_402,type,
sK75: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_403,type,
sK76: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_408,type,
sK81: $i > $o ).
thf(func_def_413,type,
sK86: $i > $o ).
thf(func_def_446,type,
sK119: ( $i > $i ) > $i > $i > $i ).
thf(func_def_449,type,
sK122: $i > $i ).
thf(func_def_450,type,
sK123: $i > $i > $i > $i ).
thf(func_def_463,type,
sK136: $i > $i > $o ).
thf(func_def_467,type,
sK140: $i > $i > $i ).
thf(func_def_475,type,
sK148: $i > $i > $i ).
thf(func_def_478,type,
sK151: $i > $o ).
thf(func_def_482,type,
sK155: $i > $i > $o ).
thf(func_def_490,type,
sK163: $i > $i ).
thf(func_def_492,type,
sK165: $i > $i ).
thf(func_def_506,type,
sK179: ( $i > $o ) > $i ).
thf(func_def_507,type,
sK180: $i > $o ).
thf(func_def_508,type,
sK181: $i > $i ).
thf(func_def_516,type,
sK189: $i > $i > $i ).
thf(func_def_528,type,
sK201: $i > $i > $i > $i > $i ).
thf(func_def_564,type,
sK237: $i > $i ).
thf(func_def_567,type,
sK240: $i > $i > ( $i > $i ) > $i ).
thf(func_def_575,type,
sK248: $i > $i ).
thf(func_def_605,type,
sK278: $i > $o ).
thf(func_def_607,type,
sK280: ( $i > $o ) > $i ).
thf(func_def_608,type,
sK281: ( $i > $o ) > $i ).
thf(func_def_611,type,
sK284: $o ).
thf(func_def_615,type,
sK288: $i > $i ).
thf(func_def_619,type,
sK292: $i > $i > ( $i > $i ) > $i ).
thf(func_def_622,type,
sK295: $i > $i ).
thf(func_def_624,type,
sK297: $i > $o ).
thf(func_def_635,type,
sK308: $o ).
thf(func_def_644,type,
sK317: $i > $i > $i ).
thf(func_def_660,type,
sK333: $i > $i > $o ).
thf(func_def_666,type,
sK339: ( $i > $o ) > $i > $i ).
thf(func_def_668,type,
sK341: $i > $o ).
thf(func_def_674,type,
sK347: $i > $i ).
thf(func_def_678,type,
sK351: $o ).
thf(func_def_694,type,
sK367: ( $i > $o ) > $i > $i ).
thf(func_def_696,type,
sK369: $i > $o ).
thf(func_def_698,type,
sK371: $i > $i > $i > $i > $i ).
thf(func_def_722,type,
sK395: $i > $o ).
thf(func_def_724,type,
sK397: $i > ( $i > $o ) > $i > $i ).
thf(func_def_725,type,
sK398: $i > $o ).
thf(func_def_728,type,
sK401: $o ).
thf(func_def_735,type,
sK408: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_736,type,
sK409: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_739,type,
sK412: $i > $o ).
thf(func_def_740,type,
sK413: $i > $o ).
thf(func_def_741,type,
sK414: $i > $i > $i > $i > $i ).
thf(func_def_749,type,
sK422: $i > $i > $o ).
thf(func_def_751,type,
sK424: $i > $o ).
thf(func_def_757,type,
sK430: $i > $o ).
thf(func_def_759,type,
sK432: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_760,type,
sK433: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_780,type,
sK453: $o ).
thf(func_def_787,type,
sK460: $i > $o ).
thf(func_def_794,type,
sK467: ( $i > $o ) > $i > $i ).
thf(func_def_796,type,
sK469: $i > $o ).
thf(func_def_801,type,
sK474: $i > $i > $o ).
thf(func_def_807,type,
sK480: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_808,type,
sK481: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_812,type,
sK485: $i > $o ).
thf(func_def_818,type,
sK491: $i > $i ).
thf(func_def_819,type,
sK492: $i > $i ).
thf(func_def_820,type,
sK493: $i > $i ).
thf(func_def_821,type,
sK494: $i > $i ).
thf(func_def_822,type,
sK495: $i > $i ).
thf(func_def_823,type,
sK496: $i > $i > $i > $i ).
thf(func_def_824,type,
sK497: $i > $i ).
thf(func_def_825,type,
sK498: $i > $i ).
thf(func_def_826,type,
sK499: $i > $i ).
thf(func_def_827,type,
sK500: $i > $i ).
thf(func_def_828,type,
sK501: $i > $i > $i ).
thf(func_def_829,type,
sK502: $i > $i > $i ).
thf(func_def_830,type,
sK503: $i > $i > $i > $i ).
thf(func_def_831,type,
sK504: $i > $i > $i > $i ).
thf(func_def_832,type,
sK505: $i > $i > $i > $i ).
thf(func_def_833,type,
sK506: $i > $i > $i ).
thf(func_def_834,type,
sK507: $i > $i > $i ).
thf(func_def_835,type,
sK508: $i > $i > $i ).
thf(func_def_841,type,
sK514: $i > $i ).
thf(func_def_844,type,
sK517: $i > $o ).
thf(func_def_845,type,
sK518: ( $i > $o ) > $i ).
thf(func_def_848,type,
sK521: $i > ( $i > $o ) > $i ).
thf(func_def_849,type,
sK522: $i > $o ).
thf(func_def_864,type,
sK537: $o ).
thf(func_def_874,type,
sK547: $i > $i > $i ).
thf(func_def_878,type,
sK551: $o ).
thf(func_def_880,type,
sK553: $i > $o ).
thf(func_def_889,type,
sK562: $i > $i > ( $i > $i ) > $i ).
thf(func_def_890,type,
sK563: $i > $i ).
thf(func_def_898,type,
sK571: $i > $o ).
thf(func_def_906,type,
sK579: $i > $o ).
thf(func_def_908,type,
sK581: $i > ( $i > $o ) > $i ).
thf(func_def_909,type,
sK582: $i > $i > $i ).
thf(func_def_913,type,
sK586: $i > $o ).
thf(func_def_915,type,
sK588: ( $i > $o ) > $i ).
thf(func_def_916,type,
sK589: $i > $o ).
thf(func_def_917,type,
sK590: $i > $i ).
thf(func_def_922,type,
sK595: $o ).
thf(func_def_930,type,
sK603: $i > $i > $i > $i ).
thf(func_def_950,type,
sK623: $o ).
thf(func_def_951,type,
sK624: $i > $i > $o ).
thf(func_def_954,type,
sK627: $i > $i > $i ).
thf(func_def_957,type,
sK630: $i > $i > $i > $i ).
thf(func_def_958,type,
sK631: $i > $i > $i > $i ).
thf(func_def_981,type,
sK654: $i > ( $i > $i ) > $i > $i ).
thf(func_def_983,type,
sK656: $i > $i ).
thf(func_def_985,type,
sK658: $o ).
thf(func_def_997,type,
sK670: $i > $o ).
thf(func_def_999,type,
sK672: $i > ( $i > $o ) > $i ).
thf(func_def_1007,type,
sK680: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1010,type,
sK683: $i > $i ).
thf(func_def_1013,type,
sK686: $i > $i > $o ).
thf(func_def_1015,type,
sK688: $i > $i ).
thf(func_def_1031,type,
sK704: $o ).
thf(func_def_1032,type,
sK705: $i > $o ).
thf(func_def_1041,type,
sK714: $i > $i > $i > $i ).
thf(func_def_1042,type,
sK715: $i > $i > $i > $i ).
thf(func_def_1051,type,
sK724: $i > $o ).
thf(func_def_1052,type,
sK725: ( $i > $o ) > $i > $i ).
thf(func_def_1057,type,
sK730: $i > $o ).
thf(func_def_1073,type,
sK746: $o ).
thf(func_def_1079,type,
sK752: ( $i > $i > $o ) > $i > $i ).
thf(func_def_1080,type,
sK753: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1081,type,
sK754: ( $i > $i > $o ) > $i > $i ).
thf(func_def_1083,type,
sK756: $i > $i > $o ).
thf(func_def_1084,type,
sK757: $i > $i ).
thf(func_def_1085,type,
sK758: $i > $i ).
thf(func_def_1087,type,
sK760: $o ).
thf(func_def_1105,type,
sK778: $i > $i > $i ).
thf(func_def_1115,type,
sK788: $i > $i > $i > $i > $i ).
thf(func_def_1116,type,
sK789: $i > $i > $i > $i > $i ).
thf(func_def_1117,type,
sK790: $i > $i > $i > $i > $i ).
thf(func_def_1118,type,
sK791: $i > $i > $i > $i > $i ).
thf(func_def_1120,type,
sK793: $o ).
thf(func_def_1132,type,
sK805: $o ).
thf(func_def_1133,type,
sK806: $o > $i > $i > $i ).
thf(func_def_1138,type,
sK811: $i > ( $i > $o ) > $i ).
thf(func_def_1139,type,
sK812: $i > $o ).
thf(func_def_1161,type,
sK834: $o ).
thf(func_def_1167,type,
sK840: $o ).
thf(func_def_1192,type,
sK865: ( $i > $o ) > $i > $i ).
thf(func_def_1193,type,
sK866: ( $i > $o ) > $i > $i ).
thf(func_def_1195,type,
sK868: $i > $o ).
thf(func_def_1197,type,
sK870: $i > $i > $i ).
thf(func_def_1198,type,
sK871: $i > $i > $i ).
thf(func_def_1207,type,
sK880: $i > $o ).
thf(f89,axiom,
( subsetTrans
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(f111,axiom,
( binintersectLsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(f280,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule1) ).
thf(f281,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f280]) ).
thf(f565,plain,
( subsetTrans
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f89]) ).
thf(f566,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
=> ( ( ( subset @ X2 @ X0 )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f565]) ).
thf(f655,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f281]) ).
thf(f656,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ X1 @ X3 )
= $true )
=> ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f655]) ).
thf(f740,plain,
( binintersectLsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
inference(rectify,[],[f111]) ).
thf(f741,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
<=> ( binintersectLsub = $true ) ),
inference(fool_elimination,[],[f740]) ).
thf(f946,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X1 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f656]) ).
thf(f947,plain,
( ( symdiffIneg2 = $true )
& ( binintersectSubset2 = $true )
& ( notsubsetI = $true )
& ( iftrueProp1 = $true )
& ( upairsetIR = $true )
& ( eta1 = $true )
& ( setunionE2 = $true )
& ( complementTI1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( binunionEcases = $true )
& ( lam2p = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrI = $true )
& ( emptyE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( setukpairinjL1 = $true )
& ( subsetE2 = $true )
& ( emptyinPowerset = $true )
& ( setminusELneg = $true )
& ( vacuousDall = $true )
& ( brelnall2 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( upairset2E = $true )
& ( noeltsimpempty = $true )
& ( setunionsingleton2 = $true )
& ( dpsetconstrSub = $true )
& ( disjointsetsI1 = $true )
& ( setminusERneg = $true )
& ( demorgan1b = $true )
& ( setminusIRneg = $true )
& ( nonemptyI = $true )
& ( emptysetimpfalse = $true )
& ( setminusILneg = $true )
& ( funcGraphProp3 = $true )
& ( setadjoinSub = $true )
& ( setukpairinjR11 = $true )
& ( upairequniteq = $true )
& ( setukpairinjL2 = $true )
& ( singletonsswitch = $true )
& ( theeq = $true )
& ( descrp = $true )
& ( notinemptyset = $true )
& ( doubleComplementI1 = $true )
& ( setunionAx = $true )
& ( demorgan2a = $true )
& ( exuE3u = $true )
& ( setextAx = $true )
& ( contrasubsetT = $true )
& ( ex1E2 = $true )
& ( ksndsingleton = $true )
& ( dpsetconstrER = $true )
& ( prop2set2propI = $true )
& ( setadjoinAx = $true )
& ( doubleComplementSub1 = $true )
& ( prop2setE = $true )
& ( setminusSubset1 = $true )
& ( binunionT_lem = $true )
& ( binunionTIRcontra = $true )
& ( descr__Cong = $true )
& ( binintersectLsub = $true )
& ( lam2lamEq = $true )
& ( omega__Cong = $true )
& ( demorgan2 = $true )
& ( inIntersectImpInUnion = $true )
& ( singletonsubset = $true )
& ( binintersectI = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( symdiffI2 = $true )
& ( subsetTrans = $true )
& ( demorgan2b2 = $true )
& ( binunionTILcontra = $true )
& ( powersetE1 = $true )
& ( ap2apEq1 = $true )
& ( complementTnotintersectT = $true )
& ( complementTE1 = $true )
& ( subsetI2 = $true )
& ( setminusEL = $true )
& ( exuI1 = $true )
& ( prop2setI = $true )
& ( cartprodmempair = $true )
& ( eqbreln = $true )
& ( setukpairinjR12 = $true )
& ( funcext = $true )
& ( iffalse = $true )
& ( complementSubsetComplementIntersect = $true )
& ( ex1I2 = $true )
& ( singletonsuniq = $true )
& ( setextsub = $true )
& ( dsetconstr__Cong = $true )
& ( setminusI = $true )
& ( binunionRsub = $true )
& ( setunionsingleton1 = $true )
& ( binintersectRsub = $true )
& ( singletoninpowunion = $true )
& ( beta1 = $true )
& ( demorgan1 = $true )
& ( inCongP = $true )
& ( sepSubset = $true )
& ( exuE1 = $true )
& ( ifSingleton = $true )
& ( cartprodpairsurjEq = $true )
& ( binunionTEcontra = $true )
& ( funcGraphProp1 = $true )
& ( beta2 = $true )
& ( subbreln = $true )
& ( setminusT_lem = $true )
& ( subPowSU = $true )
& ( binintersectER = $true )
& ( powersetsubset = $true )
& ( cartprodmempair1 = $true )
& ( omegaSAx = $true )
& ( brelnall1 = $true )
& ( setext = $true )
& ( ubforcartprodlem1 = $true )
& ( setukpairIL = $true )
& ( setoftrueEq = $true )
& ( ex1E1 = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoin__Cong = $true )
& ( emptyI = $true )
& ( binunionIR = $true )
& ( demorgan1a = $true )
& ( symdiffIneg1 = $true )
& ( setukpairinjR2 = $true )
& ( in__Cong = $true )
& ( contraSubsetComplement = $true )
& ( doubleComplementE1 = $true )
& ( nonemptyImpWitness = $true )
& ( theprop = $true )
& ( doubleComplementSub2 = $true )
& ( apProp = $true )
& ( powersetAx = $true )
& ( iftrueorfalse = $true )
& ( binunionLsub = $true )
& ( ap2apEq2 = $true )
& ( binintersectSubset5 = $true )
& ( omegaIndAx = $true )
& ( binintersectEL = $true )
& ( notequalI1 = $true )
& ( emptysetsubset = $true )
& ( cartprodsndpairEq = $true )
& ( ubforcartprodlem3 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( subsetE = $true )
& ( emptyset__Cong = $true )
& ( ap2p = $true )
& ( kpairiskpair = $true )
& ( exuE2 = $true )
& ( nonemptyE1 = $true )
& ( cartprodsndin = $true )
& ( setunionI = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X3 )
= $true )
& ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( lamProp = $true )
& ( cartprodfstin = $true )
& ( iffalseProp1 = $true )
& ( setOfPairsIsBReln = $true )
& ( funcext2 = $true )
& ( powersetI1 = $true )
& ( eta2 = $true )
& ( setbeta = $true )
& ( setunionsingleton = $true )
& ( funcGraphProp2 = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( exu__Cong = $true )
& ( replAx = $true )
& ( binunionTE = $true )
& ( subsetTI = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR = $true )
& ( notinsingleton = $true )
& ( kpairp = $true )
& ( binintersectTERcontra = $true )
& ( setadjoinOr = $true )
& ( notdexE = $true )
& ( notequalI2 = $true )
& ( eqinunit = $true )
& ( demorgan2b = $true )
& ( omega0Ax = $true )
& ( powerset__Cong = $true )
& ( setukpairinjL = $true )
& ( iffalseProp2 = $true )
& ( setadjoinIL = $true )
& ( subsetemptysetimpeq = $true )
& ( exuI2 = $true )
& ( setadjoinSub2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( complementT_lem = $true )
& ( upairinpowunion = $true )
& ( kpairsurjEq = $true )
& ( contrasubsetT3 = $true )
& ( cartprodpairmemEL = $true )
& ( powersetT_lem = $true )
& ( subset2powerset = $true )
& ( setadjoinE = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( contrasubsetT1 = $true )
& ( notdallE = $true )
& ( exuE3e = $true )
& ( binunionE = $true )
& ( setextT = $true )
& ( secondinupair = $true )
& ( binintersectSubset3 = $true )
& ( eqimpsubset2 = $true )
& ( upairsetE = $true )
& ( contrasubsetT2 = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( cartprodpairmemER = $true )
& ( ex1I = $true )
& ( cartprodpairin = $true )
& ( emptyInPowerset = $true )
& ( emptysetE = $true )
& ( woz13rule0 = $true )
& ( funcinfuncset = $true )
& ( upairsubunion = $true )
& ( setminusSubset2 = $true )
& ( doubleComplementEq = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR1 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrI = $true )
& ( complementUnionInPowersetComplement = $true )
& ( bs114d = $true )
& ( lamp = $true )
& ( complementTcontraSubset = $true )
& ( setunion__Cong = $true )
& ( funcImageSingleton = $true )
& ( subsetRefl = $true )
& ( ksndpairEq = $true )
& ( symdiffE = $true )
& ( setukpairIR = $true )
& ( binintersectSubset4 = $true )
& ( powersetTI1 = $true )
& ( emptysetAx = $true )
& ( setunionE = $true )
& ( setadjoinIR = $true )
& ( iftrueProp2 = $true )
& ( inPowerset = $true )
& ( ifp = $true )
& ( iftrue = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( powersetE = $true )
& ( setminusLsub = $true )
& ( emptyinunitempty = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( exuEu = $true )
& ( upairsetIL = $true )
& ( symdiffI1 = $true )
& ( setminusER = $true )
& ( funcextLem = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( quantDeMorgan3 = $true )
& ( foundationAx = $true )
& ( kfstpairEq = $true )
& ( dpsetconstrERa = $true )
& ( sepInPowerset = $true )
& ( singletonprop = $true )
& ( binintersectSubset1 = $true )
& ( demorgan2a1 = $true )
& ( complementImpComplementIntersect = $true )
& ( infuncsetfunc = $true )
& ( dsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( kfstsingleton = $true )
& ( app = $true )
& ( powersetTE1 = $true )
& ( uniqinunit = $true )
& ( demorgan2a2 = $true )
& ( binintersectT_lem = $true )
& ( binintersectTELcontra = $true ) ),
inference(flattening,[],[f946]) ).
thf(f1101,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true )
| ( ( subset @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f566]) ).
thf(f1102,plain,
( ( subsetTrans = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f1101]) ).
thf(f1618,plain,
( ( ( subsetTrans = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true )
& ( ( subset @ X2 @ X0 )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(nnf_transformation,[],[f1102]) ).
thf(f1619,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X0 @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
| ( $true
= ( subset @ X3 @ X5 ) )
| ( $true
!= ( subset @ X4 @ X5 ) ) )
| ( subsetTrans != $true ) ) ),
inference(rectify,[],[f1618]) ).
thf(f1620,plain,
( ( ( subsetTrans = $true )
| ( ( $true
= ( subset @ sK437 @ sK438 ) )
& ( ( subset @ sK437 @ sK439 )
!= $true )
& ( $true
= ( subset @ sK438 @ sK439 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
| ( $true
= ( subset @ X3 @ X5 ) )
| ( $true
!= ( subset @ X4 @ X5 ) ) )
| ( subsetTrans != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK437,sK438,sK439]),skolemize(X0,sK437),skolemize(X1,sK438),skolemize(X2,sK439)],[f1619]) ).
thf(f1636,plain,
( ( symdiffIneg2 = $true )
& ( binintersectSubset2 = $true )
& ( notsubsetI = $true )
& ( iftrueProp1 = $true )
& ( upairsetIR = $true )
& ( eta1 = $true )
& ( setunionE2 = $true )
& ( complementTI1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( binunionEcases = $true )
& ( lam2p = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrI = $true )
& ( emptyE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( setukpairinjL1 = $true )
& ( subsetE2 = $true )
& ( emptyinPowerset = $true )
& ( setminusELneg = $true )
& ( vacuousDall = $true )
& ( brelnall2 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( upairset2E = $true )
& ( noeltsimpempty = $true )
& ( setunionsingleton2 = $true )
& ( dpsetconstrSub = $true )
& ( disjointsetsI1 = $true )
& ( setminusERneg = $true )
& ( demorgan1b = $true )
& ( setminusIRneg = $true )
& ( nonemptyI = $true )
& ( emptysetimpfalse = $true )
& ( setminusILneg = $true )
& ( funcGraphProp3 = $true )
& ( setadjoinSub = $true )
& ( setukpairinjR11 = $true )
& ( upairequniteq = $true )
& ( setukpairinjL2 = $true )
& ( singletonsswitch = $true )
& ( theeq = $true )
& ( descrp = $true )
& ( notinemptyset = $true )
& ( doubleComplementI1 = $true )
& ( setunionAx = $true )
& ( demorgan2a = $true )
& ( exuE3u = $true )
& ( setextAx = $true )
& ( contrasubsetT = $true )
& ( ex1E2 = $true )
& ( ksndsingleton = $true )
& ( dpsetconstrER = $true )
& ( prop2set2propI = $true )
& ( setadjoinAx = $true )
& ( doubleComplementSub1 = $true )
& ( prop2setE = $true )
& ( setminusSubset1 = $true )
& ( binunionT_lem = $true )
& ( binunionTIRcontra = $true )
& ( descr__Cong = $true )
& ( binintersectLsub = $true )
& ( lam2lamEq = $true )
& ( omega__Cong = $true )
& ( demorgan2 = $true )
& ( inIntersectImpInUnion = $true )
& ( singletonsubset = $true )
& ( binintersectI = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( symdiffI2 = $true )
& ( subsetTrans = $true )
& ( demorgan2b2 = $true )
& ( binunionTILcontra = $true )
& ( powersetE1 = $true )
& ( ap2apEq1 = $true )
& ( complementTnotintersectT = $true )
& ( complementTE1 = $true )
& ( subsetI2 = $true )
& ( setminusEL = $true )
& ( exuI1 = $true )
& ( prop2setI = $true )
& ( cartprodmempair = $true )
& ( eqbreln = $true )
& ( setukpairinjR12 = $true )
& ( funcext = $true )
& ( iffalse = $true )
& ( complementSubsetComplementIntersect = $true )
& ( ex1I2 = $true )
& ( singletonsuniq = $true )
& ( setextsub = $true )
& ( dsetconstr__Cong = $true )
& ( setminusI = $true )
& ( binunionRsub = $true )
& ( setunionsingleton1 = $true )
& ( binintersectRsub = $true )
& ( singletoninpowunion = $true )
& ( beta1 = $true )
& ( demorgan1 = $true )
& ( inCongP = $true )
& ( sepSubset = $true )
& ( exuE1 = $true )
& ( ifSingleton = $true )
& ( cartprodpairsurjEq = $true )
& ( binunionTEcontra = $true )
& ( funcGraphProp1 = $true )
& ( beta2 = $true )
& ( subbreln = $true )
& ( setminusT_lem = $true )
& ( subPowSU = $true )
& ( binintersectER = $true )
& ( powersetsubset = $true )
& ( cartprodmempair1 = $true )
& ( omegaSAx = $true )
& ( brelnall1 = $true )
& ( setext = $true )
& ( ubforcartprodlem1 = $true )
& ( setukpairIL = $true )
& ( setoftrueEq = $true )
& ( ex1E1 = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoin__Cong = $true )
& ( emptyI = $true )
& ( binunionIR = $true )
& ( demorgan1a = $true )
& ( symdiffIneg1 = $true )
& ( setukpairinjR2 = $true )
& ( in__Cong = $true )
& ( contraSubsetComplement = $true )
& ( doubleComplementE1 = $true )
& ( nonemptyImpWitness = $true )
& ( theprop = $true )
& ( doubleComplementSub2 = $true )
& ( apProp = $true )
& ( powersetAx = $true )
& ( iftrueorfalse = $true )
& ( binunionLsub = $true )
& ( ap2apEq2 = $true )
& ( binintersectSubset5 = $true )
& ( omegaIndAx = $true )
& ( binintersectEL = $true )
& ( notequalI1 = $true )
& ( emptysetsubset = $true )
& ( cartprodsndpairEq = $true )
& ( ubforcartprodlem3 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( subsetE = $true )
& ( emptyset__Cong = $true )
& ( ap2p = $true )
& ( kpairiskpair = $true )
& ( exuE2 = $true )
& ( nonemptyE1 = $true )
& ( cartprodsndin = $true )
& ( setunionI = $true )
& ( $true
= ( in @ sK457 @ ( powerset @ sK455 ) ) )
& ( $true
= ( in @ sK458 @ ( powerset @ sK455 ) ) )
& ( $true
= ( subset @ sK456 @ sK458 ) )
& ( $true
!= ( subset @ ( binintersect @ sK456 @ sK457 ) @ sK458 ) )
& ( $true
= ( in @ sK456 @ ( powerset @ sK455 ) ) )
& ( lamProp = $true )
& ( cartprodfstin = $true )
& ( iffalseProp1 = $true )
& ( setOfPairsIsBReln = $true )
& ( funcext2 = $true )
& ( powersetI1 = $true )
& ( eta2 = $true )
& ( setbeta = $true )
& ( setunionsingleton = $true )
& ( funcGraphProp2 = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( exu__Cong = $true )
& ( replAx = $true )
& ( binunionTE = $true )
& ( subsetTI = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR = $true )
& ( notinsingleton = $true )
& ( kpairp = $true )
& ( binintersectTERcontra = $true )
& ( setadjoinOr = $true )
& ( notdexE = $true )
& ( notequalI2 = $true )
& ( eqinunit = $true )
& ( demorgan2b = $true )
& ( omega0Ax = $true )
& ( powerset__Cong = $true )
& ( setukpairinjL = $true )
& ( iffalseProp2 = $true )
& ( setadjoinIL = $true )
& ( subsetemptysetimpeq = $true )
& ( exuI2 = $true )
& ( setadjoinSub2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( complementT_lem = $true )
& ( upairinpowunion = $true )
& ( kpairsurjEq = $true )
& ( contrasubsetT3 = $true )
& ( cartprodpairmemEL = $true )
& ( powersetT_lem = $true )
& ( subset2powerset = $true )
& ( setadjoinE = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( contrasubsetT1 = $true )
& ( notdallE = $true )
& ( exuE3e = $true )
& ( binunionE = $true )
& ( setextT = $true )
& ( secondinupair = $true )
& ( binintersectSubset3 = $true )
& ( eqimpsubset2 = $true )
& ( upairsetE = $true )
& ( contrasubsetT2 = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( cartprodpairmemER = $true )
& ( ex1I = $true )
& ( cartprodpairin = $true )
& ( emptyInPowerset = $true )
& ( emptysetE = $true )
& ( woz13rule0 = $true )
& ( funcinfuncset = $true )
& ( upairsubunion = $true )
& ( setminusSubset2 = $true )
& ( doubleComplementEq = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR1 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrI = $true )
& ( complementUnionInPowersetComplement = $true )
& ( bs114d = $true )
& ( lamp = $true )
& ( complementTcontraSubset = $true )
& ( setunion__Cong = $true )
& ( funcImageSingleton = $true )
& ( subsetRefl = $true )
& ( ksndpairEq = $true )
& ( symdiffE = $true )
& ( setukpairIR = $true )
& ( binintersectSubset4 = $true )
& ( powersetTI1 = $true )
& ( emptysetAx = $true )
& ( setunionE = $true )
& ( setadjoinIR = $true )
& ( iftrueProp2 = $true )
& ( inPowerset = $true )
& ( ifp = $true )
& ( iftrue = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( powersetE = $true )
& ( setminusLsub = $true )
& ( emptyinunitempty = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( exuEu = $true )
& ( upairsetIL = $true )
& ( symdiffI1 = $true )
& ( setminusER = $true )
& ( funcextLem = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( quantDeMorgan3 = $true )
& ( foundationAx = $true )
& ( kfstpairEq = $true )
& ( dpsetconstrERa = $true )
& ( sepInPowerset = $true )
& ( singletonprop = $true )
& ( binintersectSubset1 = $true )
& ( demorgan2a1 = $true )
& ( complementImpComplementIntersect = $true )
& ( infuncsetfunc = $true )
& ( dsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( kfstsingleton = $true )
& ( app = $true )
& ( powersetTE1 = $true )
& ( uniqinunit = $true )
& ( demorgan2a2 = $true )
& ( binintersectT_lem = $true )
& ( binintersectTELcontra = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK455,sK456,sK457,sK458]),skolemize(X0,sK455),skolemize(X1,sK456),skolemize(X2,sK457),skolemize(X3,sK458)],[f947]) ).
thf(f1935,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[],[f741]) ).
thf(f1936,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X2 @ X3 ) @ X2 ) ) ) ),
inference(rectify,[],[f1935]) ).
thf(f1937,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ( $true
!= ( subset @ ( binintersect @ sK774 @ sK775 ) @ sK774 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK774,sK775]),skolemize(X2,sK774),skolemize(X3,sK775)],[f1936]) ).
thf(f2605,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
| ( $true
!= ( subset @ X4 @ X5 ) )
| ( subsetTrans != $true )
| ( $true
= ( subset @ X3 @ X5 ) ) ),
inference(cnf_transformation,[],[f1620]) ).
thf(f2757,plain,
( $true
!= ( subset @ ( binintersect @ sK456 @ sK457 ) @ sK458 ) ),
inference(cnf_transformation,[],[f1636]) ).
thf(f2758,plain,
( $true
= ( subset @ sK456 @ sK458 ) ),
inference(cnf_transformation,[],[f1636]) ).
thf(f2843,plain,
subsetTrans = $true,
inference(cnf_transformation,[],[f1636]) ).
thf(f2853,plain,
binintersectLsub = $true,
inference(cnf_transformation,[],[f1636]) ).
thf(f3364,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) ),
inference(cnf_transformation,[],[f1937]) ).
thf(f4950,definition,
( spl883_272
<=> ( $true
= ( subset @ ( binintersect @ sK456 @ sK457 ) @ sK458 ) ) ),
introduced(definition,[new_symbols(definition,[spl883_272])],[avatar_definition]) ).
thf(f4952,plain,
( ( $true
!= ( subset @ ( binintersect @ sK456 @ sK457 ) @ sK458 ) )
| spl883_272 ),
inference(avatar_component_clause,[],[f4950]) ).
thf(f4953,plain,
~ spl883_272,
inference(avatar_split_clause,[],[f2757,f4950]) ).
thf(f6487,definition,
( spl883_605
<=> ( $true
= ( subset @ sK456 @ sK458 ) ) ),
introduced(definition,[new_symbols(definition,[spl883_605])],[avatar_definition]) ).
thf(f6489,plain,
( ( $true
= ( subset @ sK456 @ sK458 ) )
| ~ spl883_605 ),
inference(avatar_component_clause,[],[f6487]) ).
thf(f6490,plain,
spl883_605,
inference(avatar_split_clause,[],[f2758,f6487]) ).
thf(f6898,definition,
( spl883_694
<=> ( subsetTrans = $true ) ),
introduced(definition,[new_symbols(definition,[spl883_694])],[avatar_definition]) ).
thf(f7158,definition,
( spl883_751
<=> ( binintersectLsub = $true ) ),
introduced(definition,[new_symbols(definition,[spl883_751])],[avatar_definition]) ).
thf(f7161,plain,
spl883_751,
inference(avatar_split_clause,[],[f2853,f7158]) ).
thf(f8276,plain,
spl883_694,
inference(avatar_split_clause,[],[f2843,f6898]) ).
thf(f9111,definition,
( spl883_1149
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
| ( $true
= ( subset @ X3 @ X5 ) )
| ( $true
!= ( subset @ X4 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl883_1149])],[avatar_definition]) ).
thf(f9112,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X3 @ X5 ) )
| ( ( subset @ X3 @ X4 )
!= $true )
| ( $true
!= ( subset @ X4 @ X5 ) ) )
| ~ spl883_1149 ),
inference(avatar_component_clause,[],[f9111]) ).
thf(f9113,plain,
( spl883_1149
| ~ spl883_694 ),
inference(avatar_split_clause,[],[f2605,f6898,f9111]) ).
thf(f10324,definition,
( spl883_1396
<=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl883_1396])],[avatar_definition]) ).
thf(f10325,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ~ spl883_1396 ),
inference(avatar_component_clause,[],[f10324]) ).
thf(f10326,plain,
( spl883_1396
| ~ spl883_751 ),
inference(avatar_split_clause,[],[f3364,f7158,f10324]) ).
thf(f11918,plain,
( ! [X0: $i] :
( ( $true
!= ( subset @ X0 @ sK458 ) )
| ( $true
!= ( subset @ ( binintersect @ sK456 @ sK457 ) @ X0 ) )
| ( $true != $true ) )
| spl883_272
| ~ spl883_1149 ),
inference(superposition,[],[f4952,f9112]) ).
thf(f11924,plain,
( ! [X0: $i] :
( ( $true
!= ( subset @ ( binintersect @ sK456 @ sK457 ) @ X0 ) )
| ( $true
!= ( subset @ X0 @ sK458 ) ) )
| spl883_272
| ~ spl883_1149 ),
inference(trivial_inequality_removal,[],[f11918]) ).
thf(f12219,plain,
( ( $true != $true )
| ( $true
!= ( subset @ sK456 @ sK458 ) )
| spl883_272
| ~ spl883_1149
| ~ spl883_1396 ),
inference(superposition,[],[f11924,f10325]) ).
thf(f12247,plain,
( ( $true
!= ( subset @ sK456 @ sK458 ) )
| spl883_272
| ~ spl883_1149
| ~ spl883_1396 ),
inference(trivial_inequality_removal,[],[f12219]) ).
thf(f12276,plain,
( $false
| spl883_272
| ~ spl883_605
| ~ spl883_1149
| ~ spl883_1396 ),
inference(forward_subsumption_resolution,[],[f12247,f6489]) ).
thf(f12277,plain,
( spl883_272
| ~ spl883_605
| ~ spl883_1149
| ~ spl883_1396 ),
inference(avatar_contradiction_clause,[],[f12276]) ).
cnf(s171,plain,
~ spl883_272,
inference(sat_conversion,[],[f4953]) ).
cnf(s471,plain,
spl883_605,
inference(sat_conversion,[],[f6490]) ).
cnf(s604,plain,
spl883_751,
inference(sat_conversion,[],[f7161]) ).
cnf(s875,plain,
spl883_694,
inference(sat_conversion,[],[f8276]) ).
cnf(s1093,plain,
( ~ spl883_694
| spl883_1149 ),
inference(sat_conversion,[],[f9113]) ).
cnf(s1416,plain,
( ~ spl883_751
| spl883_1396 ),
inference(sat_conversion,[],[f10326]) ).
cnf(s1512,plain,
( spl883_272
| ~ spl883_605
| ~ spl883_1149
| ~ spl883_1396 ),
inference(sat_conversion,[],[f12277]) ).
cnf(s1585,plain,
spl883_1149,
inference(rat,[],[s1093,s875]) ).
cnf(s1645,plain,
spl883_1396,
inference(rat,[],[s1416,s604]) ).
cnf(s1679,plain,
spl883_272,
inference(rat,[],[s1512,s1645,s1585,s471]) ).
cnf(s1794,plain,
$false,
inference(rat,[],[s171,s1679]) ).
thf(f12278,plain,
$false,
inference(avatar_sat_refutation,[],[s1794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU759^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:24:56 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.19/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.28/0.44 % (151866)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.44 % (151872)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1402739267:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.28/0.44 % (151879)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.28/0.44 % (151879)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
% 0.28/0.44 % (151873)lrs+10_16_si=on:nwc=1.5:random_seed=1490368032:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.28/0.44 % (151874)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3506512193:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.28/0.44 % (151876)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=269029275:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.28/0.44 % (151875)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=3951466264: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)
% 0.28/0.44 % (151879)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=1069485952:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.28/0.44 % (151878)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1316088507:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.28/0.44 % (151874)Instruction limit reached!
% 0.28/0.44 % (151874)------------------------------
% 0.28/0.44 % (151874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (151874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.44 % (151874)CaDiCaL version: 2.1.3
% 0.28/0.44 % (151874)Termination reason: Instruction limit
% 0.28/0.44 % (151874)Termination phase: shuffling
% 0.28/0.44 % (151874)Time elapsed: 0.002 s
% 0.28/0.44 % (151874)Peak memory usage: 10 MB
% 0.28/0.44 % (151874)Instructions burned: 3 (million)
% 0.28/0.44 % (151873)Instruction limit reached!
% 0.28/0.44 % (151873)------------------------------
% 0.28/0.44 % (151873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (151873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.44 % (151873)CaDiCaL version: 2.1.3
% 0.28/0.44 % (151873)Termination reason: Instruction limit
% 0.28/0.44 % (151873)Termination phase: shuffling
% 0.28/0.44 % (151873)Time elapsed: 0.009 s
% 0.28/0.44 % (151873)Peak memory usage: 10 MB
% 0.28/0.44 % (151873)Instructions burned: 19 (million)
% 0.28/0.44 % (151876)Instruction limit reached!
% 0.28/0.44 % (151876)------------------------------
% 0.28/0.44 % (151876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (151876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.44 % (151876)CaDiCaL version: 2.1.3
% 0.28/0.44 % (151876)Termination reason: Instruction limit
% 0.28/0.44 % (151876)Termination phase: shuffling
% 0.28/0.44 % (151876)Time elapsed: 0.012 s
% 0.28/0.44 % (151876)Peak memory usage: 10 MB
% 0.28/0.44 % (151876)Instructions burned: 26 (million)
% 0.28/0.44 % (151872)Instruction limit reached!
% 0.28/0.44 % (151872)------------------------------
% 0.28/0.44 % (151872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (151872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.44 % (151872)CaDiCaL version: 2.1.3
% 0.28/0.44 % (151872)Termination reason: Instruction limit
% 0.28/0.44 % (151872)Termination phase: Preprocessing 3
% 0.28/0.44 % (151872)Time elapsed: 0.022 s
% 0.28/0.44 % (151872)Peak memory usage: 12 MB
% 0.28/0.44 % (151872)Instructions burned: 91 (million)
% 0.28/0.44 % (151895)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=251117510:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.28/0.44 % (151895)Instruction limit reached!
% 0.28/0.44 % (151895)------------------------------
% 0.28/0.44 % (151895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (151895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (151895)CaDiCaL version: 2.1.3
% 1.05/0.48 % (151895)Termination reason: Instruction limit
% 1.05/0.48 % (151895)Termination phase: shuffling
% 1.05/0.48 % (151895)Time elapsed: 0.002 s
% 1.05/0.48 % (151895)Peak memory usage: 10 MB
% 1.05/0.48 % (151895)Instructions burned: 3 (million)
% 1.05/0.48 % (151904)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1573492214:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.05/0.48 % (151902)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.05/0.48 % (151899)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3510344500:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.05/0.48 % (151904)Instruction limit reached!
% 1.05/0.48 % (151904)------------------------------
% 1.05/0.48 % (151904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.48 % (151904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (151904)CaDiCaL version: 2.1.3
% 1.05/0.48 % (151904)Termination reason: Instruction limit
% 1.05/0.48 % (151904)Termination phase: shuffling
% 1.05/0.48 % (151904)Time elapsed: 0.003 s
% 1.05/0.48 % (151904)Peak memory usage: 10 MB
% 1.05/0.48 % (151904)Instructions burned: 12 (million)
% 1.05/0.48 % (151899)Instruction limit reached!
% 1.05/0.48 % (151899)------------------------------
% 1.05/0.48 % (151899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.48 % (151899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (151899)CaDiCaL version: 2.1.3
% 1.05/0.48 % (151899)Termination reason: Instruction limit
% 1.05/0.48 % (151899)Termination phase: shuffling
% 1.05/0.48 % (151899)Time elapsed: 0.003 s
% 1.05/0.48 % (151899)Peak memory usage: 10 MB
% 1.05/0.48 % (151899)Instructions burned: 6 (million)
% 1.05/0.48 % (151902)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3497175655:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.05/0.48 % (151878)Instruction limit reached!
% 1.05/0.48 % (151878)------------------------------
% 1.05/0.48 % (151878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.48 % (151878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (151878)CaDiCaL version: 2.1.3
% 1.05/0.48 % (151878)Termination reason: Instruction limit
% 1.05/0.48 % (151878)Termination phase: Preprocessing 3
% 1.05/0.48 % (151878)Time elapsed: 0.034 s
% 1.05/0.48 % (151878)Peak memory usage: 12 MB
% 1.05/0.48 % (151878)Instructions burned: 76 (million)
% 1.05/0.48 % (151902)Instruction limit reached!
% 1.05/0.48 % (151902)------------------------------
% 1.05/0.48 % (151902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.48 % (151902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.48 % (151902)CaDiCaL version: 2.1.3
% 1.05/0.48 % (151902)Termination reason: Instruction limit
% 1.05/0.48 % (151902)Termination phase: shuffling
% 1.05/0.48 % (151902)Time elapsed: 0.004 s
% 1.05/0.48 % (151902)Peak memory usage: 10 MB
% 1.05/0.48 % (151902)Instructions burned: 8 (million)
% 1.05/0.48 % (151915)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=3664203393:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.05/0.48 % (151911)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.05/0.48 % (151911)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.05/0.48 % (151911)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4272302434:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.05/0.48 % (151918)lrs+10_1_si=on:cs=on:random_seed=410229343:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.05/0.48 % (151920)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.05/0.51 % (151920)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=1551752188:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.05/0.51 % (151918)Instruction limit reached!
% 1.05/0.51 % (151918)------------------------------
% 1.05/0.51 % (151918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.51 % (151918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.51 % (151918)CaDiCaL version: 2.1.3
% 1.05/0.51 % (151918)Termination reason: Instruction limit
% 1.05/0.51 % (151918)Termination phase: shuffling
% 1.05/0.51 % (151918)Time elapsed: 0.004 s
% 1.05/0.51 % (151918)Peak memory usage: 10 MB
% 1.05/0.51 % (151918)Instructions burned: 8 (million)
% 1.05/0.51 % (151921)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1871280804:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.05/0.51 % (151920)Instruction limit reached!
% 1.05/0.51 % (151920)------------------------------
% 1.05/0.51 % (151920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.51 % (151920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.51 % (151920)CaDiCaL version: 2.1.3
% 1.05/0.51 % (151920)Termination reason: Instruction limit
% 1.05/0.51 % (151920)Termination phase: shuffling
% 1.05/0.51 % (151920)Time elapsed: 0.002 s
% 1.05/0.51 % (151920)Peak memory usage: 10 MB
% 1.05/0.51 % (151920)Instructions burned: 4 (million)
% 1.05/0.51 % (151911)Instruction limit reached!
% 1.05/0.51 % (151911)------------------------------
% 1.05/0.51 % (151911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.51 % (151911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.51 % (151911)CaDiCaL version: 2.1.3
% 1.05/0.51 % (151911)Termination reason: Instruction limit
% 1.05/0.51 % (151911)Termination phase: shuffling
% 1.05/0.51 % (151911)Time elapsed: 0.013 s
% 1.05/0.51 % (151911)Peak memory usage: 10 MB
% 1.05/0.51 % (151911)Instructions burned: 29 (million)
% 1.05/0.51 % (151915)Instruction limit reached!
% 1.05/0.51 % (151915)------------------------------
% 1.05/0.51 % (151915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.51 % (151915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.51 % (151915)CaDiCaL version: 2.1.3
% 1.05/0.51 % (151915)Termination reason: Instruction limit
% 1.05/0.51 % (151915)Termination phase: Property scanning
% 1.05/0.51 % (151915)Time elapsed: 0.019 s
% 1.05/0.51 % (151915)Peak memory usage: 11 MB
% 1.05/0.51 % (151915)Instructions burned: 89 (million)
% 1.05/0.51 % (151879)Instruction limit reached!
% 1.05/0.51 % (151879)------------------------------
% 1.05/0.51 % (151879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.51 % (151879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.51 % (151879)CaDiCaL version: 2.1.3
% 1.05/0.51 % (151879)Termination reason: Instruction limit
% 1.05/0.51 % (151879)Termination phase: Property scanning
% 1.05/0.51 % (151879)Time elapsed: 0.067 s
% 1.05/0.51 % (151879)Peak memory usage: 13 MB
% 1.05/0.51 % (151879)Instructions burned: 159 (million)
% 1.05/0.51 % (151942)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2029101158:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.05/0.51 % (151921)Instruction limit reached!
% 1.05/0.51 % (151921)------------------------------
% 1.05/0.51 % (151921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.51 % (151921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.51 % (151921)CaDiCaL version: 2.1.3
% 1.05/0.51 % (151921)Termination reason: Instruction limit
% 1.05/0.51 % (151921)Termination phase: Property scanning
% 1.05/0.51 % (151921)Time elapsed: 0.017 s
% 1.05/0.51 % (151921)Peak memory usage: 11 MB
% 1.05/0.51 % (151921)Instructions burned: 40 (million)
% 1.05/0.51 % (151937)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=469555642:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.05/0.51 % (151940)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2126999006:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.05/0.51 % (151941)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1909327814:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.05/0.56 % (151941)Instruction limit reached!
% 1.05/0.56 % (151941)------------------------------
% 1.05/0.56 % (151941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151941)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151941)Termination reason: Instruction limit
% 1.05/0.56 % (151941)Termination phase: shuffling
% 1.05/0.56 % (151941)Time elapsed: 0.007 s
% 1.05/0.56 % (151941)Peak memory usage: 10 MB
% 1.05/0.56 % (151941)Instructions burned: 15 (million)
% 1.05/0.56 % (151946)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2092966788:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.05/0.56 % (151940)Instruction limit reached!
% 1.05/0.56 % (151940)------------------------------
% 1.05/0.56 % (151940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151940)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151940)Termination reason: Instruction limit
% 1.05/0.56 % (151940)Termination phase: shuffling
% 1.05/0.56 % (151940)Time elapsed: 0.012 s
% 1.05/0.56 % (151940)Peak memory usage: 10 MB
% 1.05/0.56 % (151940)Instructions burned: 26 (million)
% 1.05/0.56 % (151949)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3382746243:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.05/0.56 % (151946)Instruction limit reached!
% 1.05/0.56 % (151946)------------------------------
% 1.05/0.56 % (151946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151946)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151946)Termination reason: Instruction limit
% 1.05/0.56 % (151946)Termination phase: shuffling
% 1.05/0.56 % (151946)Time elapsed: 0.007 s
% 1.05/0.56 % (151946)Peak memory usage: 10 MB
% 1.05/0.56 % (151949)Instruction limit reached!
% 1.05/0.56 % (151949)------------------------------
% 1.05/0.56 % (151949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151946)Instructions burned: 19 (million)
% 1.05/0.56 % (151949)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151949)Termination reason: Instruction limit
% 1.05/0.56 % (151949)Termination phase: shuffling
% 1.05/0.56 % (151949)Time elapsed: 0.003 s
% 1.05/0.56 % (151949)Peak memory usage: 10 MB
% 1.05/0.56 % (151949)Instructions burned: 6 (million)
% 1.05/0.56 % (151958)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=256451521:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.05/0.56 % (151961)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=307034918:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.05/0.56 % (151968)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.05/0.56 % (151968)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.05/0.56 % (151967)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2622086229:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.05/0.56 % (151968)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=3852805319:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.05/0.56 % (151958)Instruction limit reached!
% 1.05/0.56 % (151958)------------------------------
% 1.05/0.56 % (151958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.56 % (151958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.56 % (151958)CaDiCaL version: 2.1.3
% 1.05/0.56 % (151958)Termination reason: Instruction limit
% 1.05/0.56 % (151958)Termination phase: shuffling
% 1.05/0.56 % (151958)Time elapsed: 0.011 s
% 1.05/0.56 % (151958)Peak memory usage: 11 MB
% 1.05/0.56 % (151958)Instructions burned: 26 (million)
% 1.72/0.62 % (151961)Instruction limit reached!
% 1.72/0.62 % (151961)------------------------------
% 1.72/0.62 % (151961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.62 % (151961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.62 % (151961)CaDiCaL version: 2.1.3
% 1.72/0.62 % (151961)Termination reason: Instruction limit
% 1.72/0.62 % (151961)Termination phase: shuffling
% 1.72/0.62 % (151961)Time elapsed: 0.010 s
% 1.72/0.62 % (151961)Peak memory usage: 11 MB
% 1.72/0.62 % (151961)Instructions burned: 23 (million)
% 1.72/0.62 % (151968)Instruction limit reached!
% 1.72/0.62 % (151968)------------------------------
% 1.72/0.62 % (151968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.62 % (151968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.62 % (151968)CaDiCaL version: 2.1.3
% 1.72/0.62 % (151968)Termination reason: Instruction limit
% 1.72/0.62 % (151968)Termination phase: shuffling
% 1.72/0.62 % (151968)Time elapsed: 0.006 s
% 1.72/0.62 % (151968)Peak memory usage: 10 MB
% 1.72/0.62 % (151968)Instructions burned: 14 (million)
% 1.72/0.62 % (151983)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.72/0.62 % (151983)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=2396139951:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.72/0.62 % (151986)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=1473734444:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.72/0.62 % (151983)Instruction limit reached!
% 1.72/0.62 % (151983)------------------------------
% 1.72/0.62 % (151983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.62 % (151983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.62 % (151983)CaDiCaL version: 2.1.3
% 1.72/0.62 % (151983)Termination reason: Instruction limit
% 1.72/0.62 % (151983)Termination phase: shuffling
% 1.72/0.62 % (151983)Time elapsed: 0.004 s
% 1.72/0.62 % (151983)Peak memory usage: 10 MB
% 1.72/0.62 % (151983)Instructions burned: 8 (million)
% 1.72/0.62 % (151989)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4023635941:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.72/0.62 % (151967)Instruction limit reached!
% 1.72/0.62 % (151967)------------------------------
% 1.72/0.62 % (151967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.62 % (151967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.62 % (151967)CaDiCaL version: 2.1.3
% 1.72/0.62 % (151967)Termination reason: Instruction limit
% 1.72/0.62 % (151967)Termination phase: Preprocessing 3
% 1.72/0.62 % (151967)Time elapsed: 0.027 s
% 1.72/0.62 % (151967)Peak memory usage: 12 MB
% 1.72/0.62 % (151967)Instructions burned: 60 (million)
% 1.72/0.62 % (151989)Instruction limit reached!
% 1.72/0.62 % (151989)------------------------------
% 1.72/0.62 % (151989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.62 % (151989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.62 % (151989)CaDiCaL version: 2.1.3
% 1.72/0.62 % (151989)Termination reason: Instruction limit
% 1.72/0.62 % (151989)Termination phase: shuffling
% 1.72/0.62 % (151989)Time elapsed: 0.004 s
% 1.72/0.62 % (151989)Peak memory usage: 10 MB
% 1.72/0.62 % (151989)Instructions burned: 8 (million)
% 1.72/0.62 % (151942)Instruction limit reached!
% 1.72/0.62 % (151942)------------------------------
% 1.72/0.62 % (151942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.62 % (151942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.62 % (151942)CaDiCaL version: 2.1.3
% 1.72/0.62 % (151942)Termination reason: Instruction limit
% 1.72/0.62 % (151942)Termination phase: Saturation
% 1.72/0.62 % (151942)Time elapsed: 0.080 s
% 1.72/0.62 % (151942)Peak memory usage: 15 MB
% 1.72/0.62 % (151942)Instructions burned: 330 (million)
% 1.72/0.62 % (151986)Instruction limit reached!
% 1.72/0.62 % (151986)------------------------------
% 1.72/0.62 % (151986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.62 % (151986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (151986)CaDiCaL version: 2.1.3
% 2.11/0.64 % (151986)Termination reason: Instruction limit
% 2.11/0.64 % (151986)Termination phase: shuffling
% 2.11/0.64 % (151986)Time elapsed: 0.014 s
% 2.11/0.64 % (151986)Peak memory usage: 10 MB
% 2.11/0.64 % (151986)Instructions burned: 31 (million)
% 2.11/0.64 % (152005)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1216124777:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.11/0.64 % (151999)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2107535267:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.11/0.64 % (152001)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=194359827:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.11/0.64 % (152003)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1329895565:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.11/0.64 % (151999)Instruction limit reached!
% 2.11/0.64 % (151999)------------------------------
% 2.11/0.64 % (151999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (151999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (151999)CaDiCaL version: 2.1.3
% 2.11/0.64 % (151999)Termination reason: Instruction limit
% 2.11/0.64 % (151999)Termination phase: shuffling
% 2.11/0.64 % (151999)Time elapsed: 0.011 s
% 2.11/0.64 % (151999)Peak memory usage: 10 MB
% 2.11/0.64 % (152006)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2642209920:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.11/0.64 % (151999)Instructions burned: 25 (million)
% 2.11/0.64 % (152001)Instruction limit reached!
% 2.11/0.64 % (152001)------------------------------
% 2.11/0.64 % (152001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152001)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152001)Termination reason: Instruction limit
% 2.11/0.64 % (152001)Termination phase: shuffling
% 2.11/0.64 % (152001)Time elapsed: 0.009 s
% 2.11/0.64 % (152001)Peak memory usage: 10 MB
% 2.11/0.64 % (152001)Instructions burned: 20 (million)
% 2.11/0.64 % (151937)Instruction limit reached!
% 2.11/0.64 % (151937)------------------------------
% 2.11/0.64 % (151937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (151937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (151937)CaDiCaL version: 2.1.3
% 2.11/0.64 % (151937)Termination reason: Instruction limit
% 2.11/0.64 % (151937)Termination phase: Saturation
% 2.11/0.64 % (151937)Time elapsed: 0.108 s
% 2.11/0.64 % (151937)Peak memory usage: 15 MB
% 2.11/0.64 % (151937)Instructions burned: 250 (million)
% 2.11/0.64 % (152020)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.11/0.64 % (152019)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=948882788:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.11/0.64 % (152005)Instruction limit reached!
% 2.11/0.64 % (152005)------------------------------
% 2.11/0.64 % (152005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152005)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152005)Termination reason: Instruction limit
% 2.11/0.64 % (152005)Termination phase: Property scanning
% 2.11/0.64 % (152005)Time elapsed: 0.032 s
% 2.11/0.64 % (152005)Peak memory usage: 12 MB
% 2.11/0.64 % (152005)Instructions burned: 145 (million)
% 2.11/0.64 % (152020)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=32851098:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.11/0.64 % (152020)Instruction limit reached!
% 2.11/0.64 % (152020)------------------------------
% 2.11/0.64 % (152020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152020)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152020)Termination reason: Instruction limit
% 2.11/0.64 % (152020)Termination phase: shuffling
% 2.11/0.64 % (152020)Time elapsed: 0.004 s
% 2.11/0.64 % (152020)Peak memory usage: 10 MB
% 2.11/0.64 % (152020)Instructions burned: 7 (million)
% 2.11/0.64 % (152026)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2647524227:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.11/0.64 % (152033)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=2218664540:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.11/0.64 % (152019)Instruction limit reached!
% 2.11/0.64 % (152019)------------------------------
% 2.11/0.64 % (152019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152019)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152019)Termination reason: Instruction limit
% 2.11/0.64 % (152019)Termination phase: Property scanning
% 2.11/0.64 % (152019)Time elapsed: 0.020 s
% 2.11/0.64 % (152019)Peak memory usage: 11 MB
% 2.11/0.64 % (152019)Instructions burned: 44 (million)
% 2.11/0.64 % (152036)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.11/0.64 % (152036)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1832315455:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.11/0.64 % (152036)Instruction limit reached!
% 2.11/0.64 % (152036)------------------------------
% 2.11/0.64 % (152036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152036)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152036)Termination reason: Instruction limit
% 2.11/0.64 % (152036)Termination phase: shuffling
% 2.11/0.64 % (152036)Time elapsed: 0.003 s
% 2.11/0.64 % (152036)Peak memory usage: 10 MB
% 2.11/0.64 % (152036)Instructions burned: 6 (million)
% 2.11/0.64 % (152042)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3137781240:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.11/0.64 % (152047)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1548499247:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.11/0.64 % (152033)Instruction limit reached!
% 2.11/0.64 % (152033)------------------------------
% 2.11/0.64 % (152033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152033)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152033)Termination reason: Instruction limit
% 2.11/0.64 % (152033)Termination phase: Saturation
% 2.11/0.64 % (152033)Time elapsed: 0.037 s
% 2.11/0.64 % (152033)Peak memory usage: 12 MB
% 2.11/0.64 % (152033)Instructions burned: 170 (million)
% 2.11/0.64 % (152042)Instruction limit reached!
% 2.11/0.64 % (152042)------------------------------
% 2.11/0.64 % (152042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152042)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152042)Termination reason: Instruction limit
% 2.11/0.64 % (152042)Termination phase: shuffling
% 2.11/0.64 % (152042)Time elapsed: 0.011 s
% 2.11/0.64 % (152042)Peak memory usage: 10 MB
% 2.11/0.64 % (152042)Instructions burned: 24 (million)
% 2.11/0.64 % (152047)Instruction limit reached!
% 2.11/0.64 % (152047)------------------------------
% 2.11/0.64 % (152047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152047)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152047)Termination reason: Instruction limit
% 2.11/0.64 % (152047)Termination phase: shuffling
% 2.11/0.64 % (152047)Time elapsed: 0.008 s
% 2.11/0.64 % (152047)Peak memory usage: 10 MB
% 2.11/0.64 % (152047)Instructions burned: 19 (million)
% 2.11/0.64 % (152058)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=3040571950:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.11/0.64 % (152006)Instruction limit reached!
% 2.11/0.64 % (152006)------------------------------
% 2.11/0.64 % (152006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (152006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (152006)CaDiCaL version: 2.1.3
% 2.11/0.64 % (152006)Termination reason: Instruction limit
% 2.11/0.64 % (152006)Termination phase: Saturation
% 2.11/0.64 % (152006)Time elapsed: 0.080 s
% 2.11/0.64 % (152006)Peak memory usage: 13 MB
% 2.11/0.64 % (152006)Instructions burned: 195 (million)
% 2.11/0.64 % (152059)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=466032526:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.11/0.64 % (151875) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-151866-151875"...
% 2.11/0.64 % (152062)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=2738085648:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.11/0.64 % (151875)...printing done.
% 2.11/0.64 % (152066)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=791031490:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.11/0.64 % (151875)Refutation found. Thanks to Tanya!
% 2.11/0.64 % SZS status Theorem for theBenchmark
% 2.11/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.11/0.64 % (151875)------------------------------
% 2.11/0.64 % (151875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.64 % (151875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.64 % (151875)CaDiCaL version: 2.1.3
% 2.11/0.64 % (151875)Termination reason: Refutation
% 2.11/0.64 % (151875)Time elapsed: 0.271 s
% 2.11/0.64 % (151875)Peak memory usage: 21 MB
% 2.11/0.64 % (151875)Instructions burned: 525 (million)
% 2.11/0.64 % (151866)Success in time 0.328 s
% 2.11/0.64 % Vampire exiting
%------------------------------------------------------------------------------