%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU724^1 : 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 : n012.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 08:30:58 AM UTC 2026
% Result : Theorem 0.50s 0.29s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 18 unt; 0 typ; 5 def)
% Number of atoms : 4737 (1301 equ; 0 cnn)
% Maximal formula atoms : 246 ( 91 avg)
% Number of connectives : 2351 ( 80 ~; 53 |; 744 &; 232 @)
% ( 9 <=>;1233 =>; 0 <=; 0 <~>)
% Maximal formula depth : 254 ( 42 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 : 468 ( 465 usr; 273 con; 0-4 aty)
% Number of variables : 72 ( 0 sgn 58 !; 14 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_281,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_282,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_283,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_284,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_285,type,
vOR: $o > $o > $o ).
thf(func_def_286,type,
vAND: $o > $o > $o ).
thf(func_def_287,type,
vNOT: $o > $o ).
thf(func_def_288,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_289,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_290,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_291,type,
vIMP: $o > $o > $o ).
thf(func_def_292,type,
sP0: $i > $i > $o ).
thf(func_def_293,type,
sP1: $i > $o ).
thf(func_def_294,type,
sP2: $o ).
thf(func_def_295,type,
sP3: $o ).
thf(func_def_309,type,
sK17: $i > ( $i > $i ) > $i > $i ).
thf(func_def_311,type,
sK19: $i > $i ).
thf(func_def_315,type,
sK23: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_316,type,
sK24: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_317,type,
sK25: $i > $o ).
thf(func_def_318,type,
sK26: $i > $o ).
thf(func_def_319,type,
sK27: $i > $i > ( $i > $i ) > $i ).
thf(func_def_320,type,
sK28: $i > $i ).
thf(func_def_330,type,
sK38: $o ).
thf(func_def_331,type,
sK39: $i > ( $i > $o ) > $i ).
thf(func_def_332,type,
sK40: $i > $o ).
thf(func_def_346,type,
sK54: $i > $i > $i > $i ).
thf(func_def_357,type,
sK65: $i > $i > $o ).
thf(func_def_371,type,
sK79: $i > ( $i > $o ) > $i ).
thf(func_def_372,type,
sK80: $i > $o ).
thf(func_def_383,type,
sK91: $o ).
thf(func_def_388,type,
sK96: $i > $o ).
thf(func_def_389,type,
sK97: $i > $i ).
thf(func_def_390,type,
sK98: ( $i > $o ) > $i ).
thf(func_def_402,type,
sK110: $o ).
thf(func_def_405,type,
sK113: $o ).
thf(func_def_406,type,
sK114: ( $i > $o ) > $i > $i ).
thf(func_def_407,type,
sK115: ( $i > $o ) > $i > $i ).
thf(func_def_409,type,
sK117: $i > $o ).
thf(func_def_420,type,
sK128: $i > $i > $i > $i > $i ).
thf(func_def_421,type,
sK129: $i > $i > $i > $i > $i ).
thf(func_def_427,type,
sK135: $i > $o ).
thf(func_def_433,type,
sK141: $i > $i > $i > $i ).
thf(func_def_434,type,
sK142: $i > $i > $i > $i ).
thf(func_def_441,type,
sK149: $i > ( $i > $o ) > $i ).
thf(func_def_442,type,
sK150: $i > $o ).
thf(func_def_445,type,
sK153: $i > $i > $i > $i > $i ).
thf(func_def_452,type,
sK160: $i > $i ).
thf(func_def_458,type,
sK166: $i > $i ).
thf(func_def_460,type,
sK168: ( $i > $i ) > $i > $i > $i ).
thf(func_def_462,type,
sK170: $i > $o ).
thf(func_def_465,type,
sK173: $i > $o ).
thf(func_def_470,type,
sK178: $i > $i ).
thf(func_def_472,type,
sK180: $i > $o ).
thf(func_def_496,type,
sK204: $i > $o ).
thf(func_def_503,type,
sK211: $o ).
thf(func_def_507,type,
sK215: $o ).
thf(func_def_516,type,
sK224: $i > $i > $o ).
thf(func_def_517,type,
sK225: $i > $i ).
thf(func_def_518,type,
sK226: $i > $i ).
thf(func_def_519,type,
sK227: ( $i > $i > $o ) > $i > $i ).
thf(func_def_520,type,
sK228: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_521,type,
sK229: ( $i > $i > $o ) > $i > $i ).
thf(func_def_540,type,
sK248: $o ).
thf(func_def_557,type,
sK265: $i > $i > $o ).
thf(func_def_566,type,
sK274: $o ).
thf(func_def_567,type,
sK275: $o > $i > $i > $i ).
thf(func_def_571,type,
sK279: $i > $o ).
thf(func_def_574,type,
sK282: $i > ( $i > $o ) > $i ).
thf(func_def_590,type,
sK298: $i > $i ).
thf(func_def_591,type,
sK299: $i > $i ).
thf(func_def_592,type,
sK300: $i > $i ).
thf(func_def_593,type,
sK301: $i > $i ).
thf(func_def_594,type,
sK302: $i > $i ).
thf(func_def_595,type,
sK303: $i > $i > $i > $i ).
thf(func_def_596,type,
sK304: $i > $i ).
thf(func_def_597,type,
sK305: $i > $i ).
thf(func_def_598,type,
sK306: $i > $i ).
thf(func_def_599,type,
sK307: $i > $i ).
thf(func_def_600,type,
sK308: $i > $i > $i ).
thf(func_def_601,type,
sK309: $i > $i > $i > $i ).
thf(func_def_602,type,
sK310: $i > $i > $i > $i ).
thf(func_def_603,type,
sK311: $i > $i > $i > $i ).
thf(func_def_604,type,
sK312: $i > $i > $i ).
thf(func_def_605,type,
sK313: $i > $i > $i ).
thf(func_def_606,type,
sK314: $i > $i > $i ).
thf(func_def_607,type,
sK315: $i > $i > $i ).
thf(func_def_616,type,
sK324: $i > $i > $i ).
thf(func_def_617,type,
sK325: $i > ( $i > $o ) > $i ).
thf(func_def_618,type,
sK326: $i > $o ).
thf(func_def_627,type,
sK335: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_628,type,
sK336: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_631,type,
sK339: $i > $o ).
thf(func_def_632,type,
sK340: $i > $o ).
thf(func_def_638,type,
sK346: $i > $o ).
thf(func_def_640,type,
sK348: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_641,type,
sK349: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_648,type,
sK356: $o ).
thf(func_def_656,type,
sK364: $i > $o ).
thf(func_def_662,type,
sK370: $i > $i > $o ).
thf(func_def_669,type,
sK377: $i > $i ).
thf(func_def_673,type,
sK381: $i > $o ).
thf(func_def_687,type,
sK395: $i > $i > $i ).
thf(func_def_688,type,
sK396: $i > $o ).
thf(func_def_689,type,
sK397: $i > $i ).
thf(func_def_691,type,
sK399: $i > $i ).
thf(func_def_693,type,
sK401: $i > $o ).
thf(func_def_696,type,
sK404: $i > $o ).
thf(func_def_703,type,
sK411: $i > $o ).
thf(func_def_710,type,
sK418: $i > $o ).
thf(func_def_711,type,
sK419: ( $i > $o ) > $i > $i ).
thf(func_def_713,type,
sK421: $i > $o ).
thf(func_def_715,type,
sK423: ( $i > $o ) > $i > $i ).
thf(func_def_718,type,
sK426: $o ).
thf(func_def_721,type,
sK429: $o ).
thf(func_def_733,type,
sK441: $o ).
thf(func_def_745,type,
sK453: $i > $i > $i > $i > $i ).
thf(func_def_750,type,
sK458: $i > $i > $i ).
thf(func_def_753,type,
sK461: $i > $i > $o ).
thf(func_def_774,type,
sK482: $i > $i > $o ).
thf(func_def_778,type,
sK486: $i > $o ).
thf(func_def_780,type,
sK488: ( $i > $o ) > $i > $i ).
thf(func_def_781,type,
sK489: ( $i > $o ) > $i > $i ).
thf(func_def_793,type,
sK501: ( $i > $o ) > $i > $i ).
thf(func_def_795,type,
sK503: $i > $o ).
thf(func_def_797,type,
sK505: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_798,type,
sK506: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_802,type,
sK510: $i > $o ).
thf(func_def_819,type,
sK527: $o ).
thf(func_def_825,type,
sK533: $o ).
thf(func_def_841,type,
sK549: $i > $i ).
thf(func_def_847,type,
sK555: $i > ( $i > $i ) > $i > $i ).
thf(func_def_849,type,
sK557: $i > $i ).
thf(func_def_865,type,
sK573: $i > $o ).
thf(func_def_867,type,
sK575: $i > ( $i > $o ) > $i ).
thf(func_def_868,type,
sK576: $i > $o ).
thf(func_def_875,type,
sK583: $i > $i > $i ).
thf(func_def_882,type,
sK590: $i > $i > $i > $i ).
thf(func_def_888,type,
sK596: $o ).
thf(func_def_890,type,
sK598: $i > $i ).
thf(func_def_893,type,
sK601: $i > $i > ( $i > $i ) > $i ).
thf(func_def_895,type,
sK603: $i > $i > $o ).
thf(func_def_899,type,
sK607: ( $i > $o ) > $i > $i > $i ).
thf(func_def_902,type,
sK610: $i > $o ).
thf(func_def_917,type,
sK625: $i > $i > $i ).
thf(func_def_921,type,
sK629: $i > $i > $i ).
thf(func_def_927,type,
sK635: $i > $i > ( $i > $i ) > $i ).
thf(func_def_928,type,
sK636: $i > $i ).
thf(func_def_931,type,
sK639: $o ).
thf(func_def_935,type,
sK643: $i > $i > $i ).
thf(func_def_936,type,
sK644: $i > $i > $i ).
thf(func_def_954,type,
sK662: $i > $i > $i > $i ).
thf(func_def_955,type,
sK663: $i > $i > $i > $i ).
thf(func_def_966,type,
sK674: $o ).
thf(func_def_975,type,
sK683: $i > $i ).
thf(func_def_980,type,
sK688: $i > $i > $i ).
thf(func_def_987,type,
sK695: ( $i > $o ) > $i ).
thf(func_def_988,type,
sK696: $i > $o ).
thf(func_def_991,type,
sK699: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_992,type,
sK700: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_993,type,
sK701: $i > $o ).
thf(func_def_994,type,
sK702: $i > $o ).
thf(func_def_995,type,
sK703: $i > $o ).
thf(func_def_996,type,
sK704: $i > $i ).
thf(func_def_997,type,
sK705: ( $i > $o ) > $i ).
thf(func_def_1002,type,
sK710: $i > $o ).
thf(func_def_1003,type,
sK711: ( $i > $o ) > $i ).
thf(func_def_1004,type,
sK712: ( $i > $o ) > $i ).
thf(func_def_1005,type,
sK713: $i > $o ).
thf(func_def_1014,type,
sK722: $i > $i > $i > $i > $i ).
thf(func_def_1027,type,
sK735: $i > $i > $i ).
thf(func_def_1028,type,
sK736: $i > $i > $o ).
thf(func_def_1040,type,
sK748: $i > $i > $i > $i > $i ).
thf(func_def_1041,type,
sK749: $i > $i > $i > $i > $i ).
thf(func_def_1042,type,
sK750: $i > $i > $i > $i > $i ).
thf(func_def_1043,type,
sK751: $i > $i > $i > $i > $i ).
thf(f85,axiom,
( notsubsetI
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( subset @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(f245,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ X2 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(f246,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ X2 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f245]) ).
thf(f313,plain,
( notsubsetI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> ~ ( subset @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f85]) ).
thf(f314,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( subset @ X0 @ X2 )
!= $true ) ) ) ),
inference(fool_elimination,[],[f313]) ).
thf(f714,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ X2 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f246]) ).
thf(f715,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ X2 )
= $true )
=> ( ( ( in @ X3 @ X2 )
!= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f714]) ).
thf(f732,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( subset @ X0 @ X2 )
!= $true ) ) )
<=> ( notsubsetI = $true ) ),
inference(flattening,[],[f314]) ).
thf(f770,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ X2 )
= $true )
=> ( ( ( in @ X3 @ X2 )
!= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f715]) ).
thf(f779,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( notsubsetI = $true ) ),
inference(ennf_transformation,[],[f732]) ).
thf(f780,plain,
( ( notsubsetI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f779]) ).
thf(f1038,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f770]) ).
thf(f1039,plain,
( ( setadjoinIL = $true )
& ( subsetI1 = $true )
& ( setukpairIR = $true )
& ( iftrueProp1 = $true )
& ( exuE3u = $true )
& ( setunionsingleton1 = $true )
& ( binintersectI = $true )
& ( kfstsingleton = $true )
& ( omega__Cong = $true )
& ( binunionE = $true )
& ( upairsetE = $true )
& ( funcextLem = $true )
& ( theeq = $true )
& ( singletonprop = $true )
& ( emptyE1 = $true )
& ( setminusELneg = $true )
& ( subbreln = $true )
& ( powersetE = $true )
& ( setadjoinSub2 = $true )
& ( upairsubunion = $true )
& ( funcext = $true )
& ( setadjoin__Cong = $true )
& ( exuI1 = $true )
& ( vacuousDall = $true )
& ( setunionsingleton2 = $true )
& ( foundationAx = $true )
& ( subsetI2 = $true )
& ( singletonsubset = $true )
& ( upairset2IR = $true )
& ( setminusERneg = $true )
& ( dsetconstrI = $true )
& ( ifSingleton = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( ifp = $true )
& ( app = $true )
& ( iftrueProp2 = $true )
& ( emptyI = $true )
& ( dpsetconstrEL2 = $true )
& ( funcGraphProp2 = $true )
& ( eqbreln = $true )
& ( replAx = $true )
& ( setminusLsub = $true )
& ( lam2lamEq = $true )
& ( singletonsuniq = $true )
& ( setminusIRneg = $true )
& ( notinsingleton = $true )
& ( prop2setE = $true )
& ( binintersectSubset2 = $true )
& ( beta2 = $true )
& ( exuE2 = $true )
& ( noeltsimpempty = $true )
& ( setukpairinjR = $true )
& ( iftrue = $true )
& ( eqimpsubset1 = $true )
& ( setbeta = $true )
& ( setukpairinjL2 = $true )
& ( setextsub = $true )
& ( kpairiskpair = $true )
& ( eta1 = $true )
& ( upairequniteq = $true )
& ( exuI2 = $true )
& ( bs114d = $true )
& ( subsetTrans = $true )
& ( cartprodsndpairEq = $true )
& ( powersetT_lem = $true )
& ( ubforcartprodlem2 = $true )
& ( powersetAx = $true )
& ( setminusER = $true )
& ( quantDeMorgan4 = $true )
& ( cartprodsndin = $true )
& ( funcImageSingleton = $true )
& ( notequalI1 = $true )
& ( singletoninpowerset = $true )
& ( kpairp = $true )
& ( subsetE2 = $true )
& ( ex1I2 = $true )
& ( setadjoinAx = $true )
& ( setukpairIL = $true )
& ( emptysetimpfalse = $true )
& ( inCongP = $true )
& ( infuncsetfunc = $true )
& ( dpsetconstrEL1 = $true )
& ( theprop = $true )
& ( funcext2 = $true )
& ( setadjoinIR = $true )
& ( emptysetAx = $true )
& ( binunionIL = $true )
& ( nonemptyI = $true )
& ( setminusSubset2 = $true )
& ( nonemptyImpWitness = $true )
& ( subset2powerset = $true )
& ( binintersectSubset3 = $true )
& ( ap2apEq2 = $true )
& ( iffalse = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( descrp = $true )
& ( upairset2E = $true )
& ( descr__Cong = $true )
& ( binintersectSubset4 = $true )
& ( symdiffI1 = $true )
& ( cartprodpairmemEL = $true )
& ( setadjoinOr = $true )
& ( binintersectTELcontra = $true )
& ( setminusSubset1 = $true )
& ( setadjoinE = $true )
& ( funcGraphProp1 = $true )
& ( dsetconstrER = $true )
& ( powersetsubset = $true )
& ( dpsetconstrSub = $true )
& ( complementT_lem = $true )
& ( binintersectEL = $true )
& ( setukpairinjR2 = $true )
& ( exuE3e = $true )
& ( subsetE = $true )
& ( dsetconstr__Cong = $true )
& ( setextT = $true )
& ( iffalseProp1 = $true )
& ( setOfPairsIsBReln = $true )
& ( nonemptyE1 = $true )
& ( funcGraphProp3 = $true )
& ( eta2 = $true )
& ( omegaSAx = $true )
& ( apProp = $true )
& ( ksndsingleton = $true )
& ( upairsetIR = $true )
& ( subsetRefl = $true )
& ( setminusI = $true )
& ( symdiffI2 = $true )
& ( wellorderingAx = $true )
& ( setunionAx = $true )
& ( uniqinunit = $true )
& ( nonemptyI1 = $true )
& ( eqinunit = $true )
& ( ksndpairEq = $true )
& ( contrasubsetT = $true )
& ( prop2setI = $true )
& ( secondinupair = $true )
& ( disjointsetsI1 = $true )
& ( emptysetE = $true )
& ( sepSubset = $true )
& ( dsetconstrEL = $true )
& ( ap2apEq1 = $true )
& ( funcGraphProp4 = $true )
& ( subPowSU = $true )
& ( setukpairinjL = $true )
& ( ex1E2 = $true )
& ( setunionI = $true )
& ( in__Cong = $true )
& ( setukpairinjR11 = $true )
& ( subsetTI = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectER = $true )
& ( notsubsetI = $true )
& ( powerset__Cong = $true )
& ( setadjoinSub = $true )
& ( setoftrueEq = $true )
& ( cartprodpairmemER = $true )
& ( notequalI2 = $true )
& ( notdallE = $true )
& ( emptyset__Cong = $true )
& ( cartprodmempaircEq = $true )
& ( ap2p = $true )
& ( setunionE2 = $true )
& ( binintersectTERcontra = $true )
& ( lamp = $true )
& ( exuE1 = $true )
& ( setukpairinjR1 = $true )
& ( powersetTE1 = $true )
& ( beta1 = $true )
& ( lamProp = $true )
& ( binunionIR = $true )
& ( complementTE1 = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempair = $true )
& ( exuI3 = $true )
& ( cartprodmempair1 = $true )
& ( quantDeMorgan2 = $true )
& ( singletonsswitch = $true )
& ( emptyInPowerset = $true )
& ( setminusT_lem = $true )
& ( exu__Cong = $true )
& ( eqimpsubset2 = $true )
& ( setminusEL = $true )
& ( binunionEcases = $true )
& ( binintersectSubset1 = $true )
& ( exuEu = $true )
& ( symdiffE = $true )
& ( setminusILneg = $true )
& ( kfstpairEq = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( setunion__Cong = $true )
& ( sepInPowerset = $true )
& ( iftrueorfalse = $true )
& ( binintersectSubset5 = $true )
& ( powersetI1 = $true )
& ( binintersectT_lem = $true )
& ( notinemptyset = $true )
& ( emptyinPowerset = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodfstin = $true )
& ( binunionT_lem = $true )
& ( prop2set2propI = $true )
& ( ubforcartprodlem3 = $true )
& ( powersetTI1 = $true )
& ( binintersectRsub = $true )
& ( brelnall2 = $true )
& ( binunionLsub = $true )
& ( lam2p = $true )
& ( brelnall1 = $true )
& ( ex1I = $true )
& ( dpsetconstrER = $true )
& ( setext = $true )
& ( kpairsurjEq = $true )
& ( emptyinunitempty = $true )
& ( setextAx = $true )
& ( dpsetconstrI = $true )
& ( binintersectLsub = $true )
& ( binunionRsub = $true )
& ( upairinpowunion = $true )
& ( ex1E1 = $true )
& ( dpsetconstrERa = $true )
& ( omegaIndAx = $true )
& ( setukpairinjR12 = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( setunionE = $true )
& ( setunionsingleton = $true )
& ( symdiffIneg2 = $true )
& ( powersetI = $true )
& ( emptysetsubset = $true )
& ( cartprodpairin = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( subset @ X1 @ X2 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) ) )
& ( iffalseProp2 = $true )
& ( funcinfuncset = $true )
& ( notdexE = $true )
& ( complementTI1 = $true )
& ( singletoninpowunion = $true )
& ( symdiffIneg1 = $true ) ),
inference(flattening,[],[f1038]) ).
thf(f1674,plain,
( ( setadjoinIL = $true )
& ( subsetI1 = $true )
& ( setukpairIR = $true )
& ( iftrueProp1 = $true )
& ( exuE3u = $true )
& ( setunionsingleton1 = $true )
& ( binintersectI = $true )
& ( kfstsingleton = $true )
& ( omega__Cong = $true )
& ( binunionE = $true )
& ( upairsetE = $true )
& ( funcextLem = $true )
& ( theeq = $true )
& ( singletonprop = $true )
& ( emptyE1 = $true )
& ( setminusELneg = $true )
& ( subbreln = $true )
& ( powersetE = $true )
& ( setadjoinSub2 = $true )
& ( upairsubunion = $true )
& ( funcext = $true )
& ( setadjoin__Cong = $true )
& ( exuI1 = $true )
& ( vacuousDall = $true )
& ( setunionsingleton2 = $true )
& ( foundationAx = $true )
& ( subsetI2 = $true )
& ( singletonsubset = $true )
& ( upairset2IR = $true )
& ( setminusERneg = $true )
& ( dsetconstrI = $true )
& ( ifSingleton = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( ifp = $true )
& ( app = $true )
& ( iftrueProp2 = $true )
& ( emptyI = $true )
& ( dpsetconstrEL2 = $true )
& ( funcGraphProp2 = $true )
& ( eqbreln = $true )
& ( replAx = $true )
& ( setminusLsub = $true )
& ( lam2lamEq = $true )
& ( singletonsuniq = $true )
& ( setminusIRneg = $true )
& ( notinsingleton = $true )
& ( prop2setE = $true )
& ( binintersectSubset2 = $true )
& ( beta2 = $true )
& ( exuE2 = $true )
& ( noeltsimpempty = $true )
& ( setukpairinjR = $true )
& ( iftrue = $true )
& ( eqimpsubset1 = $true )
& ( setbeta = $true )
& ( setukpairinjL2 = $true )
& ( setextsub = $true )
& ( kpairiskpair = $true )
& ( eta1 = $true )
& ( upairequniteq = $true )
& ( exuI2 = $true )
& ( bs114d = $true )
& ( subsetTrans = $true )
& ( cartprodsndpairEq = $true )
& ( powersetT_lem = $true )
& ( ubforcartprodlem2 = $true )
& ( powersetAx = $true )
& ( setminusER = $true )
& ( quantDeMorgan4 = $true )
& ( cartprodsndin = $true )
& ( funcImageSingleton = $true )
& ( notequalI1 = $true )
& ( singletoninpowerset = $true )
& ( kpairp = $true )
& ( subsetE2 = $true )
& ( ex1I2 = $true )
& ( setadjoinAx = $true )
& ( setukpairIL = $true )
& ( emptysetimpfalse = $true )
& ( inCongP = $true )
& ( infuncsetfunc = $true )
& ( dpsetconstrEL1 = $true )
& ( theprop = $true )
& ( funcext2 = $true )
& ( setadjoinIR = $true )
& ( emptysetAx = $true )
& ( binunionIL = $true )
& ( nonemptyI = $true )
& ( setminusSubset2 = $true )
& ( nonemptyImpWitness = $true )
& ( subset2powerset = $true )
& ( binintersectSubset3 = $true )
& ( ap2apEq2 = $true )
& ( iffalse = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( descrp = $true )
& ( upairset2E = $true )
& ( descr__Cong = $true )
& ( binintersectSubset4 = $true )
& ( symdiffI1 = $true )
& ( cartprodpairmemEL = $true )
& ( setadjoinOr = $true )
& ( binintersectTELcontra = $true )
& ( setminusSubset1 = $true )
& ( setadjoinE = $true )
& ( funcGraphProp1 = $true )
& ( dsetconstrER = $true )
& ( powersetsubset = $true )
& ( dpsetconstrSub = $true )
& ( complementT_lem = $true )
& ( binintersectEL = $true )
& ( setukpairinjR2 = $true )
& ( exuE3e = $true )
& ( subsetE = $true )
& ( dsetconstr__Cong = $true )
& ( setextT = $true )
& ( iffalseProp1 = $true )
& ( setOfPairsIsBReln = $true )
& ( nonemptyE1 = $true )
& ( funcGraphProp3 = $true )
& ( eta2 = $true )
& ( omegaSAx = $true )
& ( apProp = $true )
& ( ksndsingleton = $true )
& ( upairsetIR = $true )
& ( subsetRefl = $true )
& ( setminusI = $true )
& ( symdiffI2 = $true )
& ( wellorderingAx = $true )
& ( setunionAx = $true )
& ( uniqinunit = $true )
& ( nonemptyI1 = $true )
& ( eqinunit = $true )
& ( ksndpairEq = $true )
& ( contrasubsetT = $true )
& ( prop2setI = $true )
& ( secondinupair = $true )
& ( disjointsetsI1 = $true )
& ( emptysetE = $true )
& ( sepSubset = $true )
& ( dsetconstrEL = $true )
& ( ap2apEq1 = $true )
& ( funcGraphProp4 = $true )
& ( subPowSU = $true )
& ( setukpairinjL = $true )
& ( ex1E2 = $true )
& ( setunionI = $true )
& ( in__Cong = $true )
& ( setukpairinjR11 = $true )
& ( subsetTI = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectER = $true )
& ( notsubsetI = $true )
& ( powerset__Cong = $true )
& ( setadjoinSub = $true )
& ( setoftrueEq = $true )
& ( cartprodpairmemER = $true )
& ( notequalI2 = $true )
& ( notdallE = $true )
& ( emptyset__Cong = $true )
& ( cartprodmempaircEq = $true )
& ( ap2p = $true )
& ( setunionE2 = $true )
& ( binintersectTERcontra = $true )
& ( lamp = $true )
& ( exuE1 = $true )
& ( setukpairinjR1 = $true )
& ( powersetTE1 = $true )
& ( beta1 = $true )
& ( lamProp = $true )
& ( binunionIR = $true )
& ( complementTE1 = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempair = $true )
& ( exuI3 = $true )
& ( cartprodmempair1 = $true )
& ( quantDeMorgan2 = $true )
& ( singletonsswitch = $true )
& ( emptyInPowerset = $true )
& ( setminusT_lem = $true )
& ( exu__Cong = $true )
& ( eqimpsubset2 = $true )
& ( setminusEL = $true )
& ( binunionEcases = $true )
& ( binintersectSubset1 = $true )
& ( exuEu = $true )
& ( symdiffE = $true )
& ( setminusILneg = $true )
& ( kfstpairEq = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( setunion__Cong = $true )
& ( sepInPowerset = $true )
& ( iftrueorfalse = $true )
& ( binintersectSubset5 = $true )
& ( powersetI1 = $true )
& ( binintersectT_lem = $true )
& ( notinemptyset = $true )
& ( emptyinPowerset = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodfstin = $true )
& ( binunionT_lem = $true )
& ( prop2set2propI = $true )
& ( ubforcartprodlem3 = $true )
& ( powersetTI1 = $true )
& ( binintersectRsub = $true )
& ( brelnall2 = $true )
& ( binunionLsub = $true )
& ( lam2p = $true )
& ( brelnall1 = $true )
& ( ex1I = $true )
& ( dpsetconstrER = $true )
& ( setext = $true )
& ( kpairsurjEq = $true )
& ( emptyinunitempty = $true )
& ( setextAx = $true )
& ( dpsetconstrI = $true )
& ( binintersectLsub = $true )
& ( binunionRsub = $true )
& ( upairinpowunion = $true )
& ( ex1E1 = $true )
& ( dpsetconstrERa = $true )
& ( omegaIndAx = $true )
& ( setukpairinjR12 = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( setunionE = $true )
& ( setunionsingleton = $true )
& ( symdiffIneg2 = $true )
& ( powersetI = $true )
& ( emptysetsubset = $true )
& ( cartprodpairin = $true )
& ( ( in @ sK668 @ ( powerset @ sK667 ) )
= $true )
& ( ( in @ sK669 @ ( powerset @ sK667 ) )
= $true )
& ( ( in @ sK670 @ sK669 )
!= $true )
& ( $true
= ( in @ sK670 @ sK667 ) )
& ( ( subset @ sK668 @ sK669 )
= $true )
& ( ( in @ sK670 @ sK668 )
= $true )
& ( iffalseProp2 = $true )
& ( funcinfuncset = $true )
& ( notdexE = $true )
& ( complementTI1 = $true )
& ( singletoninpowunion = $true )
& ( symdiffIneg1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK667,sK668,sK669,sK670]),skolemize(X0,sK667),skolemize(X1,sK668),skolemize(X2,sK669),skolemize(X3,sK670)],[f1039]) ).
thf(f1744,plain,
( ( ( notsubsetI = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true )
& ( ( subset @ X0 @ X2 )
= $true ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) )
| ( notsubsetI != $true ) ) ),
inference(nnf_transformation,[],[f780]) ).
thf(f1745,plain,
( ( ( notsubsetI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( notsubsetI != $true ) ) ),
inference(rectify,[],[f1744]) ).
thf(f1746,plain,
( ( ( notsubsetI = $true )
| ( ( ( in @ sK730 @ sK728 )
!= $true )
& ( ( in @ sK730 @ sK729 )
= $true )
& ( ( subset @ sK729 @ sK728 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( notsubsetI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK728,sK729,sK730]),skolemize(X0,sK728),skolemize(X1,sK729),skolemize(X2,sK730)],[f1745]) ).
thf(f2653,plain,
( ( in @ sK670 @ sK668 )
= $true ),
inference(cnf_transformation,[],[f1674]) ).
thf(f2654,plain,
( ( subset @ sK668 @ sK669 )
= $true ),
inference(cnf_transformation,[],[f1674]) ).
thf(f2656,plain,
( ( in @ sK670 @ sK669 )
!= $true ),
inference(cnf_transformation,[],[f1674]) ).
thf(f2738,plain,
notsubsetI = $true,
inference(cnf_transformation,[],[f1674]) ).
thf(f2973,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( notsubsetI != $true ) ),
inference(cnf_transformation,[],[f1746]) ).
thf(f4236,definition,
( spl755_225
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( subset @ X5 @ X4 )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl755_225])],[avatar_definition]) ).
thf(f4237,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
!= $true )
| ( ( subset @ X5 @ X4 )
!= $true ) )
| ~ spl755_225 ),
inference(avatar_component_clause,[],[f4236]) ).
thf(f4492,definition,
( spl755_281
<=> ( ( in @ sK670 @ sK669 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl755_281])],[avatar_definition]) ).
thf(f4494,plain,
( ( ( in @ sK670 @ sK669 )
!= $true )
| spl755_281 ),
inference(avatar_component_clause,[],[f4492]) ).
thf(f4495,plain,
~ spl755_281,
inference(avatar_split_clause,[],[f2656,f4492]) ).
thf(f5638,definition,
( spl755_531
<=> ( notsubsetI = $true ) ),
introduced(definition,[new_symbols(definition,[spl755_531])],[avatar_definition]) ).
thf(f6925,definition,
( spl755_800
<=> ( ( subset @ sK668 @ sK669 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl755_800])],[avatar_definition]) ).
thf(f6927,plain,
( ( ( subset @ sK668 @ sK669 )
= $true )
| ~ spl755_800 ),
inference(avatar_component_clause,[],[f6925]) ).
thf(f6928,plain,
spl755_800,
inference(avatar_split_clause,[],[f2654,f6925]) ).
thf(f6944,definition,
( spl755_804
<=> ( ( in @ sK670 @ sK668 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl755_804])],[avatar_definition]) ).
thf(f6946,plain,
( ( ( in @ sK670 @ sK668 )
= $true )
| ~ spl755_804 ),
inference(avatar_component_clause,[],[f6944]) ).
thf(f6947,plain,
spl755_804,
inference(avatar_split_clause,[],[f2653,f6944]) ).
thf(f8093,plain,
spl755_531,
inference(avatar_split_clause,[],[f2738,f5638]) ).
thf(f8142,plain,
( ~ spl755_531
| spl755_225 ),
inference(avatar_split_clause,[],[f2973,f4236,f5638]) ).
thf(f9866,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ sK669 )
!= $true )
| ( $true != $true )
| ( ( in @ sK670 @ X0 )
!= $true ) )
| ~ spl755_225
| spl755_281 ),
inference(superposition,[],[f4494,f4237]) ).
thf(f9867,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ sK669 )
!= $true )
| ( ( in @ sK670 @ X0 )
!= $true ) )
| ~ spl755_225
| spl755_281 ),
inference(trivial_inequality_removal,[],[f9866]) ).
thf(f10050,plain,
( ( ( in @ sK670 @ sK668 )
!= $true )
| ( $true != $true )
| ~ spl755_225
| spl755_281
| ~ spl755_800 ),
inference(superposition,[],[f9867,f6927]) ).
thf(f10054,plain,
( ( ( in @ sK670 @ sK668 )
!= $true )
| ~ spl755_225
| spl755_281
| ~ spl755_800 ),
inference(trivial_inequality_removal,[],[f10050]) ).
thf(f10063,plain,
( $false
| ~ spl755_225
| spl755_281
| ~ spl755_800
| ~ spl755_804 ),
inference(forward_subsumption_resolution,[],[f10054,f6946]) ).
thf(f10064,plain,
( ~ spl755_225
| spl755_281
| ~ spl755_800
| ~ spl755_804 ),
inference(avatar_contradiction_clause,[],[f10063]) ).
cnf(s190,plain,
~ spl755_281,
inference(sat_conversion,[],[f4495]) ).
cnf(s724,plain,
spl755_800,
inference(sat_conversion,[],[f6928]) ).
cnf(s728,plain,
spl755_804,
inference(sat_conversion,[],[f6947]) ).
cnf(s1022,plain,
spl755_531,
inference(sat_conversion,[],[f8093]) ).
cnf(s1036,plain,
( spl755_225
| ~ spl755_531 ),
inference(sat_conversion,[],[f8142]) ).
cnf(s1253,plain,
( ~ spl755_225
| spl755_281
| ~ spl755_800
| ~ spl755_804 ),
inference(sat_conversion,[],[f10064]) ).
cnf(s1261,plain,
spl755_225,
inference(rat,[],[s1036,s1022]) ).
cnf(s1303,plain,
spl755_281,
inference(rat,[],[s1253,s728,s1261,s724]) ).
cnf(s1475,plain,
$false,
inference(rat,[],[s190,s1303]) ).
thf(f10065,plain,
$false,
inference(avatar_sat_refutation,[],[s1475]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU724^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:16:34 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.14 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
% 0.08/0.23 % (168603)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.23 % (168614)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.23 % (168614)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
% 0.08/0.23 % (168609)lrs+10_16_si=on:nwc=1.5:random_seed=2100703933:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.23 % (168608)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3147040573:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.23 % (168610)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=727509920:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.23 % (168611)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=4184774271: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)
% 0.08/0.23 % (168613)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1487533491:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.23 % (168614)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=3279730606:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.23 % (168610)Instruction limit reached!
% 0.08/0.23 % (168610)------------------------------
% 0.08/0.23 % (168610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.23 % (168610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.23 % (168610)CaDiCaL version: 2.1.3
% 0.08/0.23 % (168610)Termination reason: Instruction limit
% 0.08/0.23 % (168610)Termination phase: shuffling
% 0.08/0.23 % (168610)Time elapsed: 0.002 s
% 0.08/0.23 % (168610)Peak memory usage: 10 MB
% 0.08/0.23 % (168610)Instructions burned: 7 (million)
% 0.08/0.23 % (168612)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1300314034:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.23 % (168609)Instruction limit reached!
% 0.08/0.23 % (168609)------------------------------
% 0.08/0.23 % (168609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.23 % (168609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.23 % (168609)CaDiCaL version: 2.1.3
% 0.08/0.23 % (168609)Termination reason: Instruction limit
% 0.08/0.23 % (168609)Termination phase: shuffling
% 0.08/0.23 % (168609)Time elapsed: 0.005 s
% 0.08/0.23 % (168609)Peak memory usage: 10 MB
% 0.08/0.23 % (168609)Instructions burned: 21 (million)
% 0.08/0.23 % (168612)Instruction limit reached!
% 0.08/0.23 % (168612)------------------------------
% 0.08/0.23 % (168612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.23 % (168612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.23 % (168612)CaDiCaL version: 2.1.3
% 0.08/0.23 % (168612)Termination reason: Instruction limit
% 0.08/0.23 % (168612)Termination phase: Property scanning
% 0.08/0.23 % (168612)Time elapsed: 0.006 s
% 0.08/0.23 % (168612)Peak memory usage: 10 MB
% 0.08/0.23 % (168612)Instructions burned: 26 (million)
% 0.08/0.23 % (168621)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2419465469:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.08/0.23 % (168621)Instruction limit reached!
% 0.08/0.23 % (168621)------------------------------
% 0.08/0.23 % (168621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.23 % (168621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.23 % (168621)CaDiCaL version: 2.1.3
% 0.08/0.23 % (168621)Termination reason: Instruction limit
% 0.08/0.23 % (168621)Termination phase: shuffling
% 0.08/0.23 % (168621)Time elapsed: 0.001 s
% 0.08/0.23 % (168621)Peak memory usage: 10 MB
% 0.08/0.23 % (168621)Instructions burned: 3 (million)
% 0.08/0.23 % (168623)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1119928127:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.08/0.23 % (168624)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.25 % (168623)Instruction limit reached!
% 0.50/0.25 % (168623)------------------------------
% 0.50/0.25 % (168623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.25 % (168623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.25 % (168623)CaDiCaL version: 2.1.3
% 0.50/0.25 % (168623)Termination reason: Instruction limit
% 0.50/0.25 % (168623)Termination phase: shuffling
% 0.50/0.25 % (168623)Time elapsed: 0.002 s
% 0.50/0.25 % (168623)Peak memory usage: 10 MB
% 0.50/0.25 % (168623)Instructions burned: 8 (million)
% 0.50/0.25 % (168613)Instruction limit reached!
% 0.50/0.25 % (168613)------------------------------
% 0.50/0.25 % (168613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.25 % (168613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.25 % (168613)CaDiCaL version: 2.1.3
% 0.50/0.25 % (168613)Termination reason: Instruction limit
% 0.50/0.25 % (168613)Termination phase: Preprocessing 3
% 0.50/0.25 % (168613)Time elapsed: 0.019 s
% 0.50/0.25 % (168613)Peak memory usage: 12 MB
% 0.50/0.25 % (168613)Instructions burned: 76 (million)
% 0.50/0.25 % (168624)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=46728777:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.50/0.25 % (168624)Instruction limit reached!
% 0.50/0.25 % (168624)------------------------------
% 0.50/0.25 % (168624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.25 % (168624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.25 % (168624)CaDiCaL version: 2.1.3
% 0.50/0.25 % (168624)Termination reason: Instruction limit
% 0.50/0.25 % (168624)Termination phase: shuffling
% 0.50/0.25 % (168624)Time elapsed: 0.002 s
% 0.50/0.25 % (168624)Peak memory usage: 10 MB
% 0.50/0.25 % (168624)Instructions burned: 8 (million)
% 0.50/0.25 % (168608)Instruction limit reached!
% 0.50/0.25 % (168608)------------------------------
% 0.50/0.25 % (168608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.25 % (168608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.25 % (168608)CaDiCaL version: 2.1.3
% 0.50/0.25 % (168608)Termination reason: Instruction limit
% 0.50/0.25 % (168608)Termination phase: Preprocessing 3
% 0.50/0.25 % (168608)Time elapsed: 0.022 s
% 0.50/0.25 % (168608)Peak memory usage: 13 MB
% 0.50/0.25 % (168608)Instructions burned: 90 (million)
% 0.50/0.25 % (168626)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1089292063:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.50/0.25 % (168628)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
% 0.50/0.25 % (168628)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.25 % (168626)Instruction limit reached!
% 0.50/0.25 % (168626)------------------------------
% 0.50/0.25 % (168626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.25 % (168626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.25 % (168626)CaDiCaL version: 2.1.3
% 0.50/0.25 % (168626)Termination reason: Instruction limit
% 0.50/0.25 % (168626)Termination phase: shuffling
% 0.50/0.25 % (168626)Time elapsed: 0.003 s
% 0.50/0.25 % (168626)Peak memory usage: 10 MB
% 0.50/0.25 % (168626)Instructions burned: 12 (million)
% 0.50/0.25 % (168628)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1686801437:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.50/0.25 % (168630)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=2556030798:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.50/0.25 % (168632)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.50/0.25 % (168631)lrs+10_1_si=on:cs=on:random_seed=843518258:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.50/0.27 % (168632)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=1900558499:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.27 % (168632)Instruction limit reached!
% 0.50/0.27 % (168632)------------------------------
% 0.50/0.27 % (168632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.27 % (168632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.27 % (168632)CaDiCaL version: 2.1.3
% 0.50/0.27 % (168632)Termination reason: Instruction limit
% 0.50/0.27 % (168632)Termination phase: shuffling
% 0.50/0.27 % (168632)Time elapsed: 0.001 s
% 0.50/0.27 % (168632)Peak memory usage: 10 MB
% 0.50/0.27 % (168632)Instructions burned: 3 (million)
% 0.50/0.27 % (168631)Instruction limit reached!
% 0.50/0.27 % (168631)------------------------------
% 0.50/0.27 % (168631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.27 % (168631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.27 % (168631)CaDiCaL version: 2.1.3
% 0.50/0.27 % (168631)Termination reason: Instruction limit
% 0.50/0.27 % (168631)Termination phase: shuffling
% 0.50/0.27 % (168631)Time elapsed: 0.003 s
% 0.50/0.27 % (168631)Peak memory usage: 10 MB
% 0.50/0.27 % (168631)Instructions burned: 12 (million)
% 0.50/0.27 % (168628)Instruction limit reached!
% 0.50/0.27 % (168628)------------------------------
% 0.50/0.27 % (168628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.27 % (168628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.27 % (168628)CaDiCaL version: 2.1.3
% 0.50/0.27 % (168628)Termination reason: Instruction limit
% 0.50/0.27 % (168628)Termination phase: shuffling
% 0.50/0.27 % (168628)Time elapsed: 0.007 s
% 0.50/0.27 % (168628)Peak memory usage: 10 MB
% 0.50/0.27 % (168628)Instructions burned: 30 (million)
% 0.50/0.27 % (168614)Instruction limit reached!
% 0.50/0.27 % (168614)------------------------------
% 0.50/0.27 % (168614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.27 % (168614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.27 % (168614)CaDiCaL version: 2.1.3
% 0.50/0.27 % (168614)Termination reason: Instruction limit
% 0.50/0.27 % (168614)Termination phase: Saturation
% 0.50/0.27 % (168614)Time elapsed: 0.036 s
% 0.50/0.27 % (168614)Peak memory usage: 13 MB
% 0.50/0.27 % (168614)Instructions burned: 161 (million)
% 0.50/0.27 % (168634)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=652796027:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.50/0.27 % (168639)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3984711540:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.50/0.27 % (168640)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3446414860:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.50/0.27 % (168641)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=427540042:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.50/0.27 % (168634)Instruction limit reached!
% 0.50/0.27 % (168634)------------------------------
% 0.50/0.27 % (168634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.27 % (168642)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3747667244:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.50/0.27 % (168634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.27 % (168634)CaDiCaL version: 2.1.3
% 0.50/0.27 % (168634)Termination reason: Instruction limit
% 0.50/0.27 % (168634)Termination phase: SInE selection
% 0.50/0.27 % (168634)Time elapsed: 0.009 s
% 0.50/0.27 % (168634)Peak memory usage: 11 MB
% 0.50/0.27 % (168634)Instructions burned: 38 (million)
% 0.50/0.27 % (168630)Instruction limit reached!
% 0.50/0.27 % (168630)------------------------------
% 0.50/0.27 % (168630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.27 % (168630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.27 % (168630)CaDiCaL version: 2.1.3
% 0.50/0.27 % (168630)Termination reason: Instruction limit
% 0.50/0.27 % (168630)Termination phase: Property scanning
% 0.50/0.27 % (168630)Time elapsed: 0.019 s
% 0.50/0.29 % (168630)Peak memory usage: 11 MB
% 0.50/0.29 % (168630)Instructions burned: 90 (million)
% 0.50/0.29 % (168641)Instruction limit reached!
% 0.50/0.29 % (168641)------------------------------
% 0.50/0.29 % (168641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168641)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168641)Termination reason: Instruction limit
% 0.50/0.29 % (168641)Termination phase: shuffling
% 0.50/0.29 % (168641)Time elapsed: 0.004 s
% 0.50/0.29 % (168641)Peak memory usage: 11 MB
% 0.50/0.29 % (168641)Instructions burned: 17 (million)
% 0.50/0.29 % (168640)Instruction limit reached!
% 0.50/0.29 % (168640)------------------------------
% 0.50/0.29 % (168640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168640)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168640)Termination reason: Instruction limit
% 0.50/0.29 % (168640)Termination phase: SInE selection
% 0.50/0.29 % (168640)Time elapsed: 0.009 s
% 0.50/0.29 % (168640)Peak memory usage: 11 MB
% 0.50/0.29 % (168640)Instructions burned: 38 (million)
% 0.50/0.29 % (168648)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=834835856:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.50/0.29 % (168649)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1041905679:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.29 % (168649)Instruction limit reached!
% 0.50/0.29 % (168649)------------------------------
% 0.50/0.29 % (168649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168649)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168649)Termination reason: Instruction limit
% 0.50/0.29 % (168649)Termination phase: shuffling
% 0.50/0.29 % (168649)Time elapsed: 0.001 s
% 0.50/0.29 % (168649)Peak memory usage: 10 MB
% 0.50/0.29 % (168649)Instructions burned: 3 (million)
% 0.50/0.29 % (168650)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3839587894:i=26:ep=R:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/26Mi)
% 0.50/0.29 % (168648)Instruction limit reached!
% 0.50/0.29 % (168648)------------------------------
% 0.50/0.29 % (168648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168648)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168648)Termination reason: Instruction limit
% 0.50/0.29 % (168648)Termination phase: shuffling
% 0.50/0.29 % (168648)Time elapsed: 0.004 s
% 0.50/0.29 % (168648)Peak memory usage: 10 MB
% 0.50/0.29 % (168648)Instructions burned: 16 (million)
% 0.50/0.29 % (168651)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3830418238:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/23Mi)
% 0.50/0.29 % (168650)Instruction limit reached!
% 0.50/0.29 % (168650)------------------------------
% 0.50/0.29 % (168650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168650)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168650)Termination reason: Instruction limit
% 0.50/0.29 % (168650)Termination phase: shuffling
% 0.50/0.29 % (168650)Time elapsed: 0.007 s
% 0.50/0.29 % (168650)Peak memory usage: 10 MB
% 0.50/0.29 % (168650)Instructions burned: 30 (million)
% 0.50/0.29 % (168651)Instruction limit reached!
% 0.50/0.29 % (168651)------------------------------
% 0.50/0.29 % (168651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168651)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168651)Termination reason: Instruction limit
% 0.50/0.29 % (168651)Termination phase: shuffling
% 0.50/0.29 % (168651)Time elapsed: 0.006 s
% 0.50/0.29 % (168651)Peak memory usage: 10 MB
% 0.50/0.29 % (168651)Instructions burned: 24 (million)
% 0.50/0.29 % (168656)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
% 0.50/0.29 % (168656)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.50/0.29 % (168655)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3554400609:cond=on:i=60:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/60Mi)
% 0.50/0.29 % (168656)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=4112810139:i=14:add=off:nm=40:rtra=on:rawr=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.50/0.29 % (168658)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.50/0.29 % (168656)Instruction limit reached!
% 0.50/0.29 % (168656)------------------------------
% 0.50/0.29 % (168656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168656)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168656)Termination reason: Instruction limit
% 0.50/0.29 % (168656)Termination phase: shuffling
% 0.50/0.29 % (168656)Time elapsed: 0.004 s
% 0.50/0.29 % (168656)Peak memory usage: 10 MB
% 0.50/0.29 % (168656)Instructions burned: 17 (million)
% 0.50/0.29 % (168658)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=3946509605:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.50/0.29 % (168659)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=4094490669:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2999 on theBenchmark for (2999ds/31Mi)
% 0.50/0.29 % (168658)Instruction limit reached!
% 0.50/0.29 % (168658)------------------------------
% 0.50/0.29 % (168658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168658)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168658)Termination reason: Instruction limit
% 0.50/0.29 % (168658)Termination phase: shuffling
% 0.50/0.29 % (168658)Time elapsed: 0.003 s
% 0.50/0.29 % (168658)Peak memory usage: 10 MB
% 0.50/0.29 % (168658)Instructions burned: 12 (million)
% 0.50/0.29 % (168655)Instruction limit reached!
% 0.50/0.29 % (168655)------------------------------
% 0.50/0.29 % (168655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168655)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168655)Termination reason: Instruction limit
% 0.50/0.29 % (168655)Termination phase: Preprocessing 3
% 0.50/0.29 % (168655)Time elapsed: 0.015 s
% 0.50/0.29 % (168655)Peak memory usage: 12 MB
% 0.50/0.29 % (168655)Instructions burned: 60 (million)
% 0.50/0.29 % (168662)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1991784971:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.50/0.29 % (168659)Instruction limit reached!
% 0.50/0.29 % (168659)------------------------------
% 0.50/0.29 % (168659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168659)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168659)Termination reason: Instruction limit
% 0.50/0.29 % (168659)Termination phase: shuffling
% 0.50/0.29 % (168659)Time elapsed: 0.008 s
% 0.50/0.29 % (168659)Peak memory usage: 11 MB
% 0.50/0.29 % (168659)Instructions burned: 34 (million)
% 0.50/0.29 % (168662)Instruction limit reached!
% 0.50/0.29 % (168662)------------------------------
% 0.50/0.29 % (168662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168662)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168662)Termination reason: Instruction limit
% 0.50/0.29 % (168662)Termination phase: shuffling
% 0.50/0.29 % (168662)Time elapsed: 0.002 s
% 0.50/0.29 % (168662)Peak memory usage: 10 MB
% 0.50/0.29 % (168662)Instructions burned: 8 (million)
% 0.50/0.29 % (168665)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3046854900:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.50/0.29 % (168666)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3747707925:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 0.50/0.29 % (168665)Instruction limit reached!
% 0.50/0.29 % (168665)------------------------------
% 0.50/0.29 % (168665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168665)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168665)Termination reason: Instruction limit
% 0.50/0.29 % (168665)Termination phase: shuffling
% 0.50/0.29 % (168665)Time elapsed: 0.006 s
% 0.50/0.29 % (168665)Peak memory usage: 10 MB
% 0.50/0.29 % (168665)Instructions burned: 26 (million)
% 0.50/0.29 % (168668)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=932097169:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 0.50/0.29 % (168669)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3519871837:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 0.50/0.29 % (168666)Instruction limit reached!
% 0.50/0.29 % (168666)------------------------------
% 0.50/0.29 % (168666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168666)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168666)Termination reason: Instruction limit
% 0.50/0.29 % (168666)Termination phase: shuffling
% 0.50/0.29 % (168666)Time elapsed: 0.005 s
% 0.50/0.29 % (168666)Peak memory usage: 10 MB
% 0.50/0.29 % (168666)Instructions burned: 23 (million)
% 0.50/0.29 % (168639)Instruction limit reached!
% 0.50/0.29 % (168639)------------------------------
% 0.50/0.29 % (168639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168639)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168639)Termination reason: Instruction limit
% 0.50/0.29 % (168639)Termination phase: Saturation
% 0.50/0.29 % (168639)Time elapsed: 0.060 s
% 0.50/0.29 % (168639)Peak memory usage: 15 MB
% 0.50/0.29 % (168639)Instructions burned: 251 (million)
% 0.50/0.29 % (168611) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-168603-168611"...
% 0.50/0.29 % (168611)...printing done.
% 0.50/0.29 % (168611)Refutation found. Thanks to Tanya!
% 0.50/0.29 % SZS status Theorem for theBenchmark
% 0.50/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.50/0.29 % (168611)------------------------------
% 0.50/0.29 % (168611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.29 % (168611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.29 % (168611)CaDiCaL version: 2.1.3
% 0.50/0.29 % (168611)Termination reason: Refutation
% 0.50/0.29 % (168611)Time elapsed: 0.109 s
% 0.50/0.29 % (168611)Peak memory usage: 20 MB
% 0.50/0.29 % (168611)Instructions burned: 398 (million)
% 0.50/0.29 % (168603)Success in time 0.14 s
% 0.50/0.29 % Vampire exiting
%------------------------------------------------------------------------------