%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU706^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:30:52 AM UTC 2026
% Result : Theorem 1.16s 0.57s
% Output : Refutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 40 unt; 0 typ; 1 def)
% Number of atoms : 3599 ( 978 equ; 0 cnn)
% Maximal formula atoms : 225 ( 64 avg)
% Number of connectives : 1820 ( 32 ~; 8 |; 680 &; 179 @)
% ( 1 <=>; 905 =>; 0 <=; 0 <~>)
% Maximal formula depth : 230 ( 30 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 : 402 ( 397 usr; 231 con; 0-4 aty)
% ( 11 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 0 sgn 31 !; 6 ?; 61 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_262,type,
vIMP: $o > $o > $o ).
thf(func_def_263,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_264,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_265,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_266,type,
vIFF: $o > $o > $o ).
thf(func_def_267,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_268,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_269,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_270,type,
vOR: $o > $o > $o ).
thf(func_def_271,type,
vNOT: $o > $o ).
thf(func_def_272,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_273,type,
vAND: $o > $o > $o ).
thf(func_def_274,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_275,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_278,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_281,type,
sK2: $i > ( $i > $i ) > $i > $i ).
thf(func_def_282,type,
sK3: $i > $i > $i ).
thf(func_def_283,type,
sK4: $i > $i > $i ).
thf(func_def_284,type,
sK5: $i > $i ).
thf(func_def_285,type,
sK6: $i > $i > $i ).
thf(func_def_286,type,
sK7: $i > $i ).
thf(func_def_287,type,
sK8: $i > ( $i > $i ) > $i > $i ).
thf(func_def_289,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_290,type,
sK11: $i > $i ).
thf(func_def_291,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_292,type,
sK13: $i > $i ).
thf(func_def_293,type,
sK14: $o > $i > $i > $i > $i ).
thf(func_def_294,type,
sK15: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_295,type,
sK16: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_296,type,
sK17: ( $i > $o ) > $i ).
thf(func_def_297,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_298,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_299,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_300,type,
sK21: ( $i > $o ) > $i > $i ).
thf(func_def_301,type,
sK22: ( $i > $o ) > $i > $i ).
thf(func_def_302,type,
sK23: ( $i > $o ) > $i ).
thf(func_def_303,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_304,type,
sK25: ( $i > $o ) > $i > $i ).
thf(func_def_305,type,
sK26: ( $i > $o ) > $i ).
thf(func_def_306,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_307,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_308,type,
sK29: ( $i > $o ) > $i ).
thf(func_def_309,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_310,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_311,type,
sK32: ( $i > $o ) > $i ).
thf(func_def_312,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_313,type,
sK34: ( $i > $o ) > $i > $i ).
thf(func_def_314,type,
sK35: ( $i > $o ) > $i > $i ).
thf(func_def_315,type,
sK36: $i > $i > ( $i > $i ) > $i ).
thf(func_def_316,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_317,type,
sK38: $i > $i > ( $i > $i ) > $i ).
thf(func_def_318,type,
sK39: $i > ( $i > $o ) > $i ).
thf(func_def_319,type,
sK40: ( $i > $o ) > $i ).
thf(func_def_320,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_321,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_322,type,
sK43: $i > $i > $i ).
thf(func_def_323,type,
sK44: $i > $i > $i ).
thf(func_def_324,type,
sK45: $i > $i > $i > $i > $i ).
thf(func_def_325,type,
sK46: $i > ( $i > $o ) > $i ).
thf(func_def_326,type,
sK47: $i > ( $i > $o ) > $i ).
thf(func_def_327,type,
sK48: $i > ( $i > $o ) > $i ).
thf(func_def_328,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_329,type,
sK50: $i > $i > $i > $i > $i ).
thf(func_def_330,type,
sK51: $i > $i > $i > $i > $i ).
thf(func_def_331,type,
sK52: $i > $i > $i > $i > $i ).
thf(func_def_332,type,
sK53: $i > $i > $i > $i > $i ).
thf(func_def_333,type,
sK54: $i > $i > $i > $i > $i ).
thf(func_def_334,type,
sK55: $i > $i > $i > $i > $i ).
thf(func_def_335,type,
sK56: $i > $o > $i > $i ).
thf(func_def_336,type,
sK57: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_337,type,
sK58: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_338,type,
sK59: $i > $i > $i > $i > $i ).
thf(func_def_339,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_340,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_341,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_342,type,
sK63: $i > $i > $i ).
thf(func_def_343,type,
sK64: $i > $i > $i ).
thf(func_def_344,type,
sK65: $i > $i > $i > $i > $i ).
thf(func_def_345,type,
sK66: $i > $i > $i > $i > $i ).
thf(func_def_346,type,
sK67: $i > $i > $i > $i ).
thf(func_def_347,type,
sK68: $i > $i > ( $i > $o ) > $i ).
thf(func_def_348,type,
sK69: $i > ( $i > $o ) > $i ).
thf(func_def_349,type,
sK70: ( $i > $o ) > $i ).
thf(func_def_350,type,
sK71: ( $i > $o ) > $i > $i ).
thf(func_def_351,type,
sK72: ( $i > $o ) > $i ).
thf(func_def_352,type,
sK73: ( $i > $o ) > $i ).
thf(func_def_353,type,
sK74: ( $i > $o ) > $i ).
thf(func_def_354,type,
sK75: ( $i > $o ) > $i ).
thf(func_def_355,type,
sK76: $i > $i > ( $i > $i ) > $i ).
thf(func_def_356,type,
sK77: $i > $i ).
thf(func_def_357,type,
sK78: ( $i > $o ) > $i > $i ).
thf(func_def_358,type,
sK79: $i > ( $i > $o ) > $i ).
thf(func_def_359,type,
sK80: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_360,type,
sK81: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_361,type,
sK82: ( $i > $o ) > $i > $i ).
thf(func_def_362,type,
sK83: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_363,type,
sK84: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_364,type,
sK85: ( $i > $o ) > $i > $i ).
thf(func_def_365,type,
sK86: ( $i > $o ) > $i > $i ).
thf(func_def_366,type,
sK87: ( $i > $o ) > $i ).
thf(func_def_367,type,
sK88: ( $i > $o ) > $i > $i ).
thf(func_def_368,type,
sK89: ( $i > $o ) > $i > $i ).
thf(func_def_369,type,
sK90: ( $i > $o ) > $i > $i ).
thf(func_def_370,type,
sK91: $i > $i > $i > $i > $i ).
thf(func_def_371,type,
sK92: $i > ( $i > $o ) > $i ).
thf(func_def_372,type,
sK93: $i > $i ).
thf(func_def_373,type,
sK94: $i > $i > $i ).
thf(func_def_374,type,
sK95: $i > $i ).
thf(func_def_375,type,
sK96: $i > $i ).
thf(func_def_376,type,
sK97: $i > $i > $i ).
thf(func_def_377,type,
sK98: ( $i > $i > $o ) > $i > $i ).
thf(func_def_378,type,
sK99: ( $i > $i > $o ) > $i > $i ).
thf(func_def_379,type,
sK100: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_380,type,
sK101: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_381,type,
sK102: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_382,type,
sK103: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_383,type,
sK104: $i > $i > $i ).
thf(func_def_384,type,
sK105: $i > $i > ( $i > $i ) > $i ).
thf(func_def_385,type,
sK106: $i > $i > $i > $i ).
thf(func_def_386,type,
sK107: $i > $i > $i > $i ).
thf(func_def_387,type,
sK108: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_388,type,
sK109: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_389,type,
sK110: ( $i > $o ) > $i ).
thf(func_def_390,type,
sK111: ( $i > $o ) > $i > $i ).
thf(func_def_391,type,
sK112: ( $i > $o ) > $i ).
thf(func_def_392,type,
sK113: ( $i > $o ) > $i > $i ).
thf(func_def_393,type,
sK114: $i > $i ).
thf(func_def_394,type,
sK115: $i > $i > $i ).
thf(func_def_395,type,
sK116: $i > $i > $i ).
thf(func_def_396,type,
sK117: $i > $i > $i ).
thf(func_def_397,type,
sK118: $i > $i > $i ).
thf(func_def_398,type,
sK119: $i > $i > $i > $i ).
thf(f47,axiom,
! [X0: $i,X1: $i] :
( ( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= notinsingleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(f155,axiom,
! [X0: $i] :
( ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
= setunionsingleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(f156,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) )
= singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f229,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
=> ! [X0: $i] :
( ( singleton @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ( setunion @ X0 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(f230,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
=> ! [X0: $i] :
( ( singleton @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ( setunion @ X0 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f229]) ).
thf(f249,plain,
( setunionsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f155]) ).
thf(f290,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) )
= singleton ),
inference(rectify,[],[f156]) ).
thf(f291,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f290]) ).
thf(f310,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
=> ! [X0: $i] :
( ( singleton @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ( setunion @ X0 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f230]) ).
thf(f311,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 )
=> ! [X0: $i] :
( ( ( singleton @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( setunion @ X0 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f310]) ).
thf(f519,plain,
! [X0: $i,X1: $i] :
( ( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= notinsingleton ),
inference(rectify,[],[f47]) ).
thf(f520,plain,
( notinsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f519]) ).
thf(f674,plain,
( ? [X0: $i] :
( ( ( singleton @ X0 )
= $true )
& ? [X1: $i] :
( ( ( setunion @ X0 )
!= X1 )
& ( ( in @ X1 @ X0 )
= $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,[],[f311]) ).
thf(f675,plain,
( ( setminusEL = $true )
& ( eta1 = $true )
& ( binunionLsub = $true )
& ( symdiffIneg2 = $true )
& ( cartprodfstin = $true )
& ( descr__Cong = $true )
& ( emptysetE = $true )
& ( subsetTrans = $true )
& ( nonemptyI1 = $true )
& ( setminusLsub = $true )
& ( binunionIL = $true )
& ( funcextLem = $true )
& ( brelnall2 = $true )
& ( symdiffIneg1 = $true )
& ( eqimpsubset2 = $true )
& ( prop2setI = $true )
& ( dsetconstrEL = $true )
& ( omega__Cong = $true )
& ( ifSingleton = $true )
& ( powersetsubset = $true )
& ( theprop = $true )
& ( ap2apEq2 = $true )
& ( eqimpsubset1 = $true )
& ( foundationAx = $true )
& ( bs114d = $true )
& ( setunionE = $true )
& ( singletonprop = $true )
& ( funcext2 = $true )
& ( wellorderingAx = $true )
& ( singletoninpowerset = $true )
& ( dpsetconstrI = $true )
& ( setminusI = $true )
& ( powerset__Cong = $true )
& ( setukpairinjL1 = $true )
& ( omegaIndAx = $true )
& ( kfstpairEq = $true )
& ( powersetI1 = $true )
& ( funcGraphProp4 = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI1 = $true )
& ( exuE1 = $true )
& ( notequalI1 = $true )
& ( binintersectRsub = $true )
& ( binunionE = $true )
& ( setukpairinjR11 = $true )
& ( emptyinunitempty = $true )
& ( binunionEcases = $true )
& ( descrp = $true )
& ( funcImageSingleton = $true )
& ( emptysetAx = $true )
& ( emptyset__Cong = $true )
& ( brelnall1 = $true )
& ( upairinpowunion = $true )
& ( cartprodmempaircEq = $true )
& ( upairsetIL = $true )
& ( subset2powerset = $true )
& ( powersetE = $true )
& ( exuI3 = $true )
& ( notsubsetI = $true )
& ( subsetE = $true )
& ? [X0: $i] :
( ( ( singleton @ X0 )
= $true )
& ? [X1: $i] :
( ( ( setunion @ X0 )
!= X1 )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( singletonsuniq = $true )
& ( lamProp = $true )
& ( powersetI = $true )
& ( setukpairinjR2 = $true )
& ( quantDeMorgan4 = $true )
& ( inCongP = $true )
& ( vacuousDall = $true )
& ( powersetAx = $true )
& ( binintersectLsub = $true )
& ( setunionsingleton1 = $true )
& ( dsetconstrI = $true )
& ( setext = $true )
& ( binintersectI = $true )
& ( symdiffI1 = $true )
& ( setadjoinSub = $true )
& ( cartprodsndpairEq = $true )
& ( beta1 = $true )
& ( app = $true )
& ( upairequniteq = $true )
& ( exuEu = $true )
& ( symdiffI2 = $true )
& ( lam2lamEq = $true )
& ( setOfPairsIsBReln = $true )
& ( ifp = $true )
& ( setoftrueEq = $true )
& ( binintersectSubset2 = $true )
& ( setminusSubset2 = $true )
& ( setextAx = $true )
& ( setminusIRneg = $true )
& ( subbreln = $true )
& ( subsetE2 = $true )
& ( subsetI1 = $true )
& ( emptyinPowerset = $true )
& ( setbeta = $true )
& ( setadjoin__Cong = $true )
& ( exuE2 = $true )
& ( cartprodpairmemER = $true )
& ( apProp = $true )
& ( setadjoinOr = $true )
& ( notdallE = $true )
& ( setunionsingleton = $true )
& ( eta2 = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan1 = $true )
& ( kfstsingleton = $true )
& ( emptyInPowerset = $true )
& ( funcGraphProp1 = $true )
& ( cartprodmempair1 = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR1 = $true )
& ( omegaSAx = $true )
& ( lam2p = $true )
& ( setukpairinjR12 = $true )
& ( exuI2 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectSubset1 = $true )
& ( infuncsetfunc = $true )
& ( iftrueProp2 = $true )
& ( notdexE = $true )
& ( funcinfuncset = $true )
& ( subsetRefl = $true )
& ( iffalseProp1 = $true )
& ( setminusELneg = $true )
& ( subsetI2 = $true )
& ( dpsetconstrEL2 = $true )
& ( iftrueProp1 = $true )
& ( prop2set2propI = $true )
& ( upairsetE = $true )
& ( disjointsetsI1 = $true )
& ( beta2 = $true )
& ( setadjoinSub2 = $true )
& ( ubforcartprodlem1 = $true )
& ( lamp = $true )
& ( setadjoinIR = $true )
& ( binintersectER = $true )
& ( nonemptyI = $true )
& ( singletonsubset = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( ap2apEq1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( cartprodpairmemEL = $true )
& ( ubforcartprodlem2 = $true )
& ( uniqinunit = $true )
& ( setukpairinjL2 = $true )
& ( replAx = $true )
& ( binunionIR = $true )
& ( notinsingleton = $true )
& ( symdiffE = $true )
& ( dpsetconstrSub = $true )
& ( ex1E1 = $true )
& ( setunionI = $true )
& ( setukpairinjR = $true )
& ( exuE3e = $true )
& ( setminusER = $true )
& ( setunion__Cong = $true )
& ( nonemptyE1 = $true )
& ( dpsetconstrEL1 = $true )
& ( subPowSU = $true )
& ( powersetE1 = $true )
& ( emptyE1 = $true )
& ( setunionE2 = $true )
& ( setadjoinE = $true )
& ( eqbreln = $true )
& ( singletonsswitch = $true )
& ( cartprodpairsurjEq = $true )
& ( singletoninpowunion = $true )
& ( ex1E2 = $true )
& ( cartprodpairin = $true )
& ( exu__Cong = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( ex1I2 = $true )
& ( setadjoinAx = $true )
& ( binunionRsub = $true )
& ( setadjoinIL = $true )
& ( omega0Ax = $true )
& ( setukpairIL = $true )
& ( dpsetconstrERa = $true )
& ( cartprodfstpairEq = $true )
& ( setminusILneg = $true )
& ( ap2p = $true )
& ( kpairp = $true )
& ( binintersectSubset5 = $true )
& ( notinemptyset = $true )
& ( cartprodmempair = $true )
& ( ksndpairEq = $true )
& ( upairsubunion = $true )
& ( emptysetimpfalse = $true )
& ( kpairsurjEq = $true )
& ( setminusERneg = $true )
& ( ex1I = $true )
& ( funcGraphProp3 = $true )
& ( ubforcartprodlem3 = $true )
& ( sepSubset = $true )
& ( funcGraphProp2 = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( setunionAx = $true )
& ( funcext = $true )
& ( upairset2IR = $true )
& ( ksndsingleton = $true )
& ( setukpairIR = $true )
& ( kpairiskpair = $true )
& ( inPowerset = $true )
& ( prop2setE = $true )
& ( iffalseProp2 = $true )
& ( noeltsimpempty = $true )
& ( sepInPowerset = $true )
& ( in__Cong = $true )
& ( setunionsingleton2 = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodsndin = $true )
& ( setextsub = $true )
& ( setukpairinjL = $true )
& ( emptysetsubset = $true )
& ( setminusSubset1 = $true )
& ( binintersectSubset3 = $true ) ),
inference(flattening,[],[f674]) ).
thf(f676,plain,
( ( setminusEL = $true )
& ( eta1 = $true )
& ( binunionLsub = $true )
& ( symdiffIneg2 = $true )
& ( cartprodfstin = $true )
& ( descr__Cong = $true )
& ( emptysetE = $true )
& ( subsetTrans = $true )
& ( nonemptyI1 = $true )
& ( setminusLsub = $true )
& ( binunionIL = $true )
& ( funcextLem = $true )
& ( brelnall2 = $true )
& ( symdiffIneg1 = $true )
& ( eqimpsubset2 = $true )
& ( prop2setI = $true )
& ( dsetconstrEL = $true )
& ( omega__Cong = $true )
& ( ifSingleton = $true )
& ( powersetsubset = $true )
& ( theprop = $true )
& ( ap2apEq2 = $true )
& ( eqimpsubset1 = $true )
& ( foundationAx = $true )
& ( bs114d = $true )
& ( setunionE = $true )
& ( singletonprop = $true )
& ( funcext2 = $true )
& ( wellorderingAx = $true )
& ( singletoninpowerset = $true )
& ( dpsetconstrI = $true )
& ( setminusI = $true )
& ( powerset__Cong = $true )
& ( setukpairinjL1 = $true )
& ( omegaIndAx = $true )
& ( kfstpairEq = $true )
& ( powersetI1 = $true )
& ( funcGraphProp4 = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI1 = $true )
& ( exuE1 = $true )
& ( notequalI1 = $true )
& ( binintersectRsub = $true )
& ( binunionE = $true )
& ( setukpairinjR11 = $true )
& ( emptyinunitempty = $true )
& ( binunionEcases = $true )
& ( descrp = $true )
& ( funcImageSingleton = $true )
& ( emptysetAx = $true )
& ( emptyset__Cong = $true )
& ( brelnall1 = $true )
& ( upairinpowunion = $true )
& ( cartprodmempaircEq = $true )
& ( upairsetIL = $true )
& ( subset2powerset = $true )
& ( powersetE = $true )
& ( exuI3 = $true )
& ( notsubsetI = $true )
& ( subsetE = $true )
& ( ( singleton @ sK0 )
= $true )
& ( ( setunion @ sK0 )
!= sK1 )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( singletonsuniq = $true )
& ( lamProp = $true )
& ( powersetI = $true )
& ( setukpairinjR2 = $true )
& ( quantDeMorgan4 = $true )
& ( inCongP = $true )
& ( vacuousDall = $true )
& ( powersetAx = $true )
& ( binintersectLsub = $true )
& ( setunionsingleton1 = $true )
& ( dsetconstrI = $true )
& ( setext = $true )
& ( binintersectI = $true )
& ( symdiffI1 = $true )
& ( setadjoinSub = $true )
& ( cartprodsndpairEq = $true )
& ( beta1 = $true )
& ( app = $true )
& ( upairequniteq = $true )
& ( exuEu = $true )
& ( symdiffI2 = $true )
& ( lam2lamEq = $true )
& ( setOfPairsIsBReln = $true )
& ( ifp = $true )
& ( setoftrueEq = $true )
& ( binintersectSubset2 = $true )
& ( setminusSubset2 = $true )
& ( setextAx = $true )
& ( setminusIRneg = $true )
& ( subbreln = $true )
& ( subsetE2 = $true )
& ( subsetI1 = $true )
& ( emptyinPowerset = $true )
& ( setbeta = $true )
& ( setadjoin__Cong = $true )
& ( exuE2 = $true )
& ( cartprodpairmemER = $true )
& ( apProp = $true )
& ( setadjoinOr = $true )
& ( notdallE = $true )
& ( setunionsingleton = $true )
& ( eta2 = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan1 = $true )
& ( kfstsingleton = $true )
& ( emptyInPowerset = $true )
& ( funcGraphProp1 = $true )
& ( cartprodmempair1 = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR1 = $true )
& ( omegaSAx = $true )
& ( lam2p = $true )
& ( setukpairinjR12 = $true )
& ( exuI2 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectSubset1 = $true )
& ( infuncsetfunc = $true )
& ( iftrueProp2 = $true )
& ( notdexE = $true )
& ( funcinfuncset = $true )
& ( subsetRefl = $true )
& ( iffalseProp1 = $true )
& ( setminusELneg = $true )
& ( subsetI2 = $true )
& ( dpsetconstrEL2 = $true )
& ( iftrueProp1 = $true )
& ( prop2set2propI = $true )
& ( upairsetE = $true )
& ( disjointsetsI1 = $true )
& ( beta2 = $true )
& ( setadjoinSub2 = $true )
& ( ubforcartprodlem1 = $true )
& ( lamp = $true )
& ( setadjoinIR = $true )
& ( binintersectER = $true )
& ( nonemptyI = $true )
& ( singletonsubset = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( ap2apEq1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( cartprodpairmemEL = $true )
& ( ubforcartprodlem2 = $true )
& ( uniqinunit = $true )
& ( setukpairinjL2 = $true )
& ( replAx = $true )
& ( binunionIR = $true )
& ( notinsingleton = $true )
& ( symdiffE = $true )
& ( dpsetconstrSub = $true )
& ( ex1E1 = $true )
& ( setunionI = $true )
& ( setukpairinjR = $true )
& ( exuE3e = $true )
& ( setminusER = $true )
& ( setunion__Cong = $true )
& ( nonemptyE1 = $true )
& ( dpsetconstrEL1 = $true )
& ( subPowSU = $true )
& ( powersetE1 = $true )
& ( emptyE1 = $true )
& ( setunionE2 = $true )
& ( setadjoinE = $true )
& ( eqbreln = $true )
& ( singletonsswitch = $true )
& ( cartprodpairsurjEq = $true )
& ( singletoninpowunion = $true )
& ( ex1E2 = $true )
& ( cartprodpairin = $true )
& ( exu__Cong = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( ex1I2 = $true )
& ( setadjoinAx = $true )
& ( binunionRsub = $true )
& ( setadjoinIL = $true )
& ( omega0Ax = $true )
& ( setukpairIL = $true )
& ( dpsetconstrERa = $true )
& ( cartprodfstpairEq = $true )
& ( setminusILneg = $true )
& ( ap2p = $true )
& ( kpairp = $true )
& ( binintersectSubset5 = $true )
& ( notinemptyset = $true )
& ( cartprodmempair = $true )
& ( ksndpairEq = $true )
& ( upairsubunion = $true )
& ( emptysetimpfalse = $true )
& ( kpairsurjEq = $true )
& ( setminusERneg = $true )
& ( ex1I = $true )
& ( funcGraphProp3 = $true )
& ( ubforcartprodlem3 = $true )
& ( sepSubset = $true )
& ( funcGraphProp2 = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( setunionAx = $true )
& ( funcext = $true )
& ( upairset2IR = $true )
& ( ksndsingleton = $true )
& ( setukpairIR = $true )
& ( kpairiskpair = $true )
& ( inPowerset = $true )
& ( prop2setE = $true )
& ( iffalseProp2 = $true )
& ( noeltsimpempty = $true )
& ( sepInPowerset = $true )
& ( in__Cong = $true )
& ( setunionsingleton2 = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodsndin = $true )
& ( setextsub = $true )
& ( setukpairinjL = $true )
& ( emptysetsubset = $true )
& ( setminusSubset1 = $true )
& ( binintersectSubset3 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f675]) ).
thf(f681,plain,
( notinsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f520]) ).
thf(f765,plain,
notinsingleton = $true,
inference(cnf_transformation,[],[f676]) ).
thf(f814,plain,
setunionsingleton = $true,
inference(cnf_transformation,[],[f676]) ).
thf(f855,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f676]) ).
thf(f856,plain,
( ( setunion @ sK0 )
!= sK1 ),
inference(cnf_transformation,[],[f676]) ).
thf(f857,plain,
( ( singleton @ sK0 )
= $true ),
inference(cnf_transformation,[],[f676]) ).
thf(f1022,plain,
( setunionsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f249]) ).
thf(f1088,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f291]) ).
thf(f1137,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[],[f681,f765]) ).
thf(f1151,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f857,f1088]) ).
thf(f1251,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) ) ),
inference(definition_unfolding,[],[f1022,f814]) ).
thf(f1578,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ( setadjoin @ Y0 @ emptyset )
= sK0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1151]) ).
thf(f1579,plain,
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ( setadjoin @ Y0 @ emptyset )
= sK0 ) )
@ sK9 ) ),
inference(sigma_proxy_clausification,[],[f1578]) ).
thf(f1580,plain,
( $true
= ( ( in @ sK9 @ sK0 )
& ( ( setadjoin @ sK9 @ emptyset )
= sK0 ) ) ),
inference(beta-eta_normalization,[],[f1579]) ).
thf(f1581,plain,
( ( ( setadjoin @ sK9 @ emptyset )
= sK0 )
= $true ),
inference(and_proxy_clausification,[],[f1580]) ).
thf(f1583,plain,
( sK0
= ( setadjoin @ sK9 @ emptyset ) ),
inference(equality_proxy_clausification,[],[f1581]) ).
thf(f2252,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1137]) ).
thf(f2253,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f2252]) ).
thf(f2254,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( Y0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f2253]) ).
thf(f2255,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( X2 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f2254]) ).
thf(f2256,plain,
! [X2: $i,X1: $i] :
( ( ( X2 != X1 )
= $false )
| ( ( ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2255]) ).
thf(f2257,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true )
| ( $true
= ( X2 = X1 ) ) ),
inference(not_proxy_clausification,[],[f2256]) ).
thf(f2258,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= $false ) ),
inference(not_proxy_clausification,[],[f2257]) ).
thf(f2259,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f2258]) ).
thf(f3313,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1251]) ).
thf(f3314,plain,
! [X1: $i] :
( ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
= $true ),
inference(beta-eta_normalization,[],[f3313]) ).
thf(f3315,plain,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(equality_proxy_clausification,[],[f3314]) ).
thf(f3993,plain,
( sK9
= ( setunion @ sK0 ) ),
inference(superposition,[],[f3315,f1583]) ).
thf(f4005,plain,
sK9 != sK1,
inference(superposition,[],[f856,f3993]) ).
thf(f4014,definition,
( spl120_24
<=> ( sK9 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl120_24])],[avatar_definition]) ).
thf(f4016,plain,
( ( sK9 != sK1 )
| spl120_24 ),
inference(avatar_component_clause,[],[f4014]) ).
thf(f4021,plain,
~ spl120_24,
inference(avatar_split_clause,[],[f4005,f4014]) ).
thf(f4089,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK0 )
= $false )
| ( sK9 = X0 ) ),
inference(superposition,[],[f2259,f1583]) ).
thf(f4109,plain,
( ( $false = $true )
| ( sK9 = sK1 ) ),
inference(superposition,[],[f855,f4089]) ).
thf(f4119,plain,
sK9 = sK1,
inference(trivial_inequality_removal,[],[f4109]) ).
thf(f4144,plain,
( $false
| spl120_24 ),
inference(forward_subsumption_resolution,[],[f4119,f4016]) ).
thf(f4145,plain,
spl120_24,
inference(avatar_contradiction_clause,[],[f4144]) ).
cnf(s30,plain,
~ spl120_24,
inference(sat_conversion,[],[f4021]) ).
cnf(s38,plain,
spl120_24,
inference(sat_conversion,[],[f4145]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s30,s38]) ).
thf(f4148,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU706^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:14:56 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.44 % (138168)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.46/0.44 % (138184)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=975133627:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.46/0.44 % (138184)Instruction limit reached!
% 0.46/0.44 % (138184)------------------------------
% 0.46/0.44 % (138184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (138184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (138184)CaDiCaL version: 2.1.3
% 0.46/0.44 % (138184)Termination reason: Instruction limit
% 0.46/0.44 % (138184)Termination phase: shuffling
% 0.46/0.44 % (138184)Time elapsed: 0.002 s
% 0.46/0.44 % (138184)Peak memory usage: 10 MB
% 0.46/0.44 % (138184)Instructions burned: 7 (million)
% 0.46/0.44 % (138188)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.46/0.44 % (138188)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
% 0.46/0.44 % (138183)lrs+10_16_si=on:nwc=1.5:random_seed=3955357755:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.46/0.44 % (138181)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=744186052:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.46/0.44 % (138187)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=264561904:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.46/0.44 % (138188)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=920323363:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.46/0.44 % (138185)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=2826638606: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)
% 0.46/0.44 % (138193)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2450650924:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.46/0.44 % (138193)Instruction limit reached!
% 0.46/0.44 % (138193)------------------------------
% 0.46/0.44 % (138193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (138193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (138193)CaDiCaL version: 2.1.3
% 0.46/0.44 % (138193)Termination reason: Instruction limit
% 0.46/0.44 % (138193)Termination phase: shuffling
% 0.46/0.44 % (138193)Time elapsed: 0.002 s
% 0.46/0.44 % (138193)Peak memory usage: 10 MB
% 0.46/0.44 % (138193)Instructions burned: 9 (million)
% 0.46/0.44 % (138183)Instruction limit reached!
% 0.46/0.44 % (138183)------------------------------
% 0.46/0.44 % (138183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (138183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (138183)CaDiCaL version: 2.1.3
% 0.46/0.44 % (138183)Termination reason: Instruction limit
% 0.46/0.44 % (138183)Termination phase: shuffling
% 0.46/0.44 % (138183)Time elapsed: 0.010 s
% 0.46/0.44 % (138183)Peak memory usage: 10 MB
% 0.46/0.44 % (138183)Instructions burned: 18 (million)
% 0.46/0.44 % (138186)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1522188969:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.46/0.44 % (138206)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2100882766:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.46/0.44 % (138186)Instruction limit reached!
% 0.46/0.44 % (138186)------------------------------
% 0.46/0.44 % (138186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (138186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (138186)CaDiCaL version: 2.1.3
% 0.46/0.44 % (138186)Termination reason: Instruction limit
% 0.46/0.44 % (138186)Termination phase: Property scanning
% 0.46/0.44 % (138186)Time elapsed: 0.011 s
% 0.46/0.44 % (138186)Peak memory usage: 10 MB
% 0.46/0.44 % (138186)Instructions burned: 24 (million)
% 0.46/0.44 % (138206)Instruction limit reached!
% 1.16/0.48 % (138206)------------------------------
% 1.16/0.48 % (138206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.48 % (138206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.48 % (138206)CaDiCaL version: 2.1.3
% 1.16/0.48 % (138206)Termination reason: Instruction limit
% 1.16/0.48 % (138206)Termination phase: shuffling
% 1.16/0.48 % (138206)Time elapsed: 0.002 s
% 1.16/0.48 % (138206)Peak memory usage: 10 MB
% 1.16/0.48 % (138206)Instructions burned: 8 (million)
% 1.16/0.48 % (138215)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
% 1.16/0.48 % (138215)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.16/0.48 % (138215)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3941960088:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.16/0.48 % (138187)Instruction limit reached!
% 1.16/0.48 % (138187)------------------------------
% 1.16/0.48 % (138187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.48 % (138187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.48 % (138187)CaDiCaL version: 2.1.3
% 1.16/0.48 % (138187)Termination reason: Instruction limit
% 1.16/0.48 % (138187)Termination phase: Preprocessing 3
% 1.16/0.48 % (138187)Time elapsed: 0.036 s
% 1.16/0.48 % (138187)Peak memory usage: 12 MB
% 1.16/0.48 % (138187)Instructions burned: 77 (million)
% 1.16/0.48 % (138214)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=125262237:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.16/0.48 % (138207)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.16/0.48 % (138215)Instruction limit reached!
% 1.16/0.48 % (138215)------------------------------
% 1.16/0.48 % (138215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.48 % (138215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.48 % (138215)CaDiCaL version: 2.1.3
% 1.16/0.48 % (138215)Termination reason: Instruction limit
% 1.16/0.48 % (138215)Termination phase: shuffling
% 1.16/0.48 % (138215)Time elapsed: 0.007 s
% 1.16/0.48 % (138215)Peak memory usage: 10 MB
% 1.16/0.48 % (138215)Instructions burned: 30 (million)
% 1.16/0.48 % (138214)Instruction limit reached!
% 1.16/0.48 % (138214)------------------------------
% 1.16/0.48 % (138214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.48 % (138214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.48 % (138214)CaDiCaL version: 2.1.3
% 1.16/0.48 % (138214)Termination reason: Instruction limit
% 1.16/0.48 % (138214)Termination phase: shuffling
% 1.16/0.48 % (138214)Time elapsed: 0.006 s
% 1.16/0.48 % (138214)Peak memory usage: 10 MB
% 1.16/0.48 % (138214)Instructions burned: 13 (million)
% 1.16/0.48 % (138207)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1960387738:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.16/0.48 % (138220)lrs+10_1_si=on:cs=on:random_seed=555845887:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.16/0.48 % (138207)Instruction limit reached!
% 1.16/0.48 % (138207)------------------------------
% 1.16/0.48 % (138207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.48 % (138207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.48 % (138207)CaDiCaL version: 2.1.3
% 1.16/0.48 % (138207)Termination reason: Instruction limit
% 1.16/0.48 % (138207)Termination phase: shuffling
% 1.16/0.48 % (138207)Time elapsed: 0.004 s
% 1.16/0.48 % (138207)Peak memory usage: 10 MB
% 1.16/0.48 % (138207)Instructions burned: 9 (million)
% 1.16/0.48 % (138181)Instruction limit reached!
% 1.16/0.48 % (138181)------------------------------
% 1.16/0.48 % (138181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.48 % (138181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.48 % (138218)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=770369494:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.16/0.51 % (138181)CaDiCaL version: 2.1.3
% 1.16/0.51 % (138181)Termination reason: Instruction limit
% 1.16/0.51 % (138181)Termination phase: Property scanning
% 1.16/0.51 % (138181)Time elapsed: 0.056 s
% 1.16/0.51 % (138181)Peak memory usage: 13 MB
% 1.16/0.51 % (138181)Instructions burned: 88 (million)
% 1.16/0.51 % (138220)Instruction limit reached!
% 1.16/0.51 % (138220)------------------------------
% 1.16/0.51 % (138220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.51 % (138220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.51 % (138220)CaDiCaL version: 2.1.3
% 1.16/0.51 % (138220)Termination reason: Instruction limit
% 1.16/0.51 % (138220)Termination phase: shuffling
% 1.16/0.51 % (138220)Time elapsed: 0.003 s
% 1.16/0.51 % (138220)Peak memory usage: 10 MB
% 1.16/0.51 % (138220)Instructions burned: 12 (million)
% 1.16/0.51 % (138221)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.16/0.52 % (138227)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2432404367:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.16/0.52 % (138221)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=432638063:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.16/0.52 % (138221)Instruction limit reached!
% 1.16/0.52 % (138221)------------------------------
% 1.16/0.52 % (138221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.52 % (138221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.52 % (138221)CaDiCaL version: 2.1.3
% 1.16/0.52 % (138221)Termination reason: Instruction limit
% 1.16/0.52 % (138221)Termination phase: shuffling
% 1.16/0.52 % (138221)Time elapsed: 0.002 s
% 1.16/0.52 % (138221)Peak memory usage: 10 MB
% 1.16/0.52 % (138221)Instructions burned: 4 (million)
% 1.16/0.52 % (138225)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3019737563:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.16/0.52 % (138226)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3817170057:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.16/0.52 % (138227)Instruction limit reached!
% 1.16/0.52 % (138227)------------------------------
% 1.16/0.52 % (138227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.52 % (138227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.52 % (138227)CaDiCaL version: 2.1.3
% 1.16/0.52 % (138227)Termination reason: Instruction limit
% 1.16/0.52 % (138227)Termination phase: Property scanning
% 1.16/0.52 % (138227)Time elapsed: 0.007 s
% 1.16/0.52 % (138227)Peak memory usage: 10 MB
% 1.16/0.52 % (138227)Instructions burned: 28 (million)
% 1.16/0.52 % (138234)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3907015741:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.16/0.52 % (138234)Instruction limit reached!
% 1.16/0.52 % (138234)------------------------------
% 1.16/0.52 % (138234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.52 % (138234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.52 % (138234)CaDiCaL version: 2.1.3
% 1.16/0.52 % (138234)Termination reason: Instruction limit
% 1.16/0.52 % (138234)Termination phase: shuffling
% 1.16/0.52 % (138234)Time elapsed: 0.003 s
% 1.16/0.52 % (138234)Peak memory usage: 10 MB
% 1.16/0.52 % (138234)Instructions burned: 14 (million)
% 1.16/0.52 % (138218)Instruction limit reached!
% 1.16/0.52 % (138218)------------------------------
% 1.16/0.52 % (138218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.52 % (138218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.52 % (138218)CaDiCaL version: 2.1.3
% 1.16/0.52 % (138218)Termination reason: Instruction limit
% 1.16/0.52 % (138218)Termination phase: Function definition elimination
% 1.16/0.52 % (138218)Time elapsed: 0.036 s
% 1.16/0.52 % (138218)Peak memory usage: 11 MB
% 1.16/0.52 % (138218)Instructions burned: 88 (million)
% 1.16/0.52 % (138225)Instruction limit reached!
% 1.16/0.52 % (138225)------------------------------
% 1.16/0.57 % (138225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138225)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138225)Termination reason: Instruction limit
% 1.16/0.57 % (138225)Termination phase: SInE selection
% 1.16/0.57 % (138225)Time elapsed: 0.017 s
% 1.16/0.57 % (138225)Peak memory usage: 11 MB
% 1.16/0.57 % (138225)Instructions burned: 39 (million)
% 1.16/0.57 % (138239)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3986408737:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.16/0.57 % (138248)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=690527357:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.16/0.57 % (138248)Instruction limit reached!
% 1.16/0.57 % (138248)------------------------------
% 1.16/0.57 % (138248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138248)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138248)Termination reason: Instruction limit
% 1.16/0.57 % (138248)Termination phase: shuffling
% 1.16/0.57 % (138248)Time elapsed: 0.004 s
% 1.16/0.57 % (138248)Peak memory usage: 10 MB
% 1.16/0.57 % (138248)Instructions burned: 16 (million)
% 1.16/0.57 % (138188)Instruction limit reached!
% 1.16/0.57 % (138188)------------------------------
% 1.16/0.57 % (138188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138188)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138188)Termination reason: Instruction limit
% 1.16/0.57 % (138188)Termination phase: Saturation
% 1.16/0.57 % (138188)Time elapsed: 0.108 s
% 1.16/0.57 % (138188)Peak memory usage: 13 MB
% 1.16/0.57 % (138188)Instructions burned: 159 (million)
% 1.16/0.57 % (138256)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3059267397:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.16/0.57 % (138249)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1943418979: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)
% 1.16/0.57 % (138249)Instruction limit reached!
% 1.16/0.57 % (138249)------------------------------
% 1.16/0.57 % (138249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138249)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138249)Termination reason: Instruction limit
% 1.16/0.57 % (138249)Termination phase: shuffling
% 1.16/0.57 % (138249)Time elapsed: 0.004 s
% 1.16/0.57 % (138249)Peak memory usage: 10 MB
% 1.16/0.57 % (138249)Instructions burned: 7 (million)
% 1.16/0.57 % (138256)Instruction limit reached!
% 1.16/0.57 % (138256)------------------------------
% 1.16/0.57 % (138256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138256)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138256)Termination reason: Instruction limit
% 1.16/0.57 % (138256)Termination phase: shuffling
% 1.16/0.57 % (138256)Time elapsed: 0.006 s
% 1.16/0.57 % (138256)Peak memory usage: 11 MB
% 1.16/0.57 % (138256)Instructions burned: 24 (million)
% 1.16/0.57 % (138250)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1892827194:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.16/0.57 % (138265)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.16/0.57 % (138257)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1854858676:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.16/0.57 % (138265)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=3070001512:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.16/0.57 % (138265)Instruction limit reached!
% 1.16/0.57 % (138265)------------------------------
% 1.16/0.57 % (138265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138260)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
% 1.16/0.57 % (138265)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138265)Termination reason: Instruction limit
% 1.16/0.57 % (138265)Termination phase: shuffling
% 1.16/0.57 % (138265)Time elapsed: 0.002 s
% 1.16/0.57 % (138260)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.16/0.57 % (138265)Peak memory usage: 10 MB
% 1.16/0.57 % (138265)Instructions burned: 8 (million)
% 1.16/0.57 % (138260)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=2402011234:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.16/0.57 % (138250)Instruction limit reached!
% 1.16/0.57 % (138250)------------------------------
% 1.16/0.57 % (138250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138250)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138250)Termination reason: Instruction limit
% 1.16/0.57 % (138250)Termination phase: shuffling
% 1.16/0.57 % (138250)Time elapsed: 0.014 s
% 1.16/0.57 % (138250)Peak memory usage: 10 MB
% 1.16/0.57 % (138250)Instructions burned: 27 (million)
% 1.16/0.57 % (138269)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=1564988702:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.16/0.57 % (138260)Instruction limit reached!
% 1.16/0.57 % (138260)------------------------------
% 1.16/0.57 % (138260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138260)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138260)Termination reason: Instruction limit
% 1.16/0.57 % (138260)Termination phase: shuffling
% 1.16/0.57 % (138260)Time elapsed: 0.007 s
% 1.16/0.57 % (138260)Peak memory usage: 10 MB
% 1.16/0.57 % (138260)Instructions burned: 16 (million)
% 1.16/0.57 % (138269)Instruction limit reached!
% 1.16/0.57 % (138269)------------------------------
% 1.16/0.57 % (138269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138269)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138269)Termination reason: Instruction limit
% 1.16/0.57 % (138269)Termination phase: Property scanning
% 1.16/0.57 % (138269)Time elapsed: 0.007 s
% 1.16/0.57 % (138269)Peak memory usage: 11 MB
% 1.16/0.57 % (138269)Instructions burned: 32 (million)
% 1.16/0.57 % (138271)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=950302245:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.16/0.57 % (138257)Instruction limit reached!
% 1.16/0.57 % (138257)------------------------------
% 1.16/0.57 % (138257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138257)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138257)Termination reason: Instruction limit
% 1.16/0.57 % (138257)Termination phase: Preprocessing 3
% 1.16/0.57 % (138257)Time elapsed: 0.029 s
% 1.16/0.57 % (138257)Peak memory usage: 12 MB
% 1.16/0.57 % (138257)Instructions burned: 60 (million)
% 1.16/0.57 % (138278)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=927072517:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.16/0.57 % (138271)Instruction limit reached!
% 1.16/0.57 % (138271)------------------------------
% 1.16/0.57 % (138271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138271)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138271)Termination reason: Instruction limit
% 1.16/0.57 % (138271)Termination phase: shuffling
% 1.16/0.57 % (138271)Time elapsed: 0.003 s
% 1.16/0.57 % (138271)Peak memory usage: 10 MB
% 1.16/0.57 % (138271)Instructions burned: 7 (million)
% 1.16/0.57 % (138275)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3482278571:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.16/0.57 % (138278)Instruction limit reached!
% 1.16/0.57 % (138278)------------------------------
% 1.16/0.57 % (138278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138278)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138278)Termination reason: Instruction limit
% 1.16/0.57 % (138278)Termination phase: shuffling
% 1.16/0.57 % (138278)Time elapsed: 0.006 s
% 1.16/0.57 % (138278)Peak memory usage: 10 MB
% 1.16/0.57 % (138278)Instructions burned: 25 (million)
% 1.16/0.57 % (138275)Instruction limit reached!
% 1.16/0.57 % (138275)------------------------------
% 1.16/0.57 % (138275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138275)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138275)Termination reason: Instruction limit
% 1.16/0.57 % (138275)Termination phase: shuffling
% 1.16/0.57 % (138275)Time elapsed: 0.011 s
% 1.16/0.57 % (138275)Peak memory usage: 10 MB
% 1.16/0.57 % (138275)Instructions burned: 25 (million)
% 1.16/0.57 % (138282)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4164607648:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.16/0.57 % (138287)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3916938952:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.16/0.57 % (138284)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4086744443:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.16/0.57 % (138226)Instruction limit reached!
% 1.16/0.57 % (138226)------------------------------
% 1.16/0.57 % (138226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138226)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138226)Termination reason: Instruction limit
% 1.16/0.57 % (138226)Termination phase: Saturation
% 1.16/0.57 % (138226)Time elapsed: 0.115 s
% 1.16/0.57 % (138226)Peak memory usage: 15 MB
% 1.16/0.57 % (138226)Instructions burned: 250 (million)
% 1.16/0.57 % (138290)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3713550474:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.16/0.57 % (138239) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-138168-138239"...
% 1.16/0.57 % (138297)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.16/0.57 % (138297)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3725837233:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.16/0.57 % (138239)...printing done.
% 1.16/0.57 % (138239)Refutation found. Thanks to Tanya!
% 1.16/0.57 % SZS status Theorem for theBenchmark
% 1.16/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.16/0.57 % (138239)------------------------------
% 1.16/0.57 % (138239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.57 % (138239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.57 % (138239)CaDiCaL version: 2.1.3
% 1.16/0.57 % (138239)Termination reason: Refutation
% 1.16/0.57 % (138239)Time elapsed: 0.115 s
% 1.16/0.57 % (138239)Peak memory usage: 15 MB
% 1.16/0.57 % (138239)Instructions burned: 251 (million)
% 1.16/0.57 % (138168)Success in time 0.268 s
% 1.16/0.57 % Vampire exiting
%------------------------------------------------------------------------------