%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU714^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:30:55 AM UTC 2026
% Result : Theorem 0.30s 0.44s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 18 unt; 0 typ; 5 def)
% Number of atoms : 4435 (1223 equ; 0 cnn)
% Maximal formula atoms : 232 ( 82 avg)
% Number of connectives : 2157 ( 49 ~; 40 |; 933 &; 200 @)
% ( 8 <=>; 927 =>; 0 <=; 0 <~>)
% Maximal formula depth : 239 ( 38 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 : 453 ( 450 usr; 262 con; 0-4 aty)
% Number of variables : 60 ( 0 sgn 46 !; 14 ?; 60 :)
% 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_271,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_272,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_273,type,
vOR: $o > $o > $o ).
thf(func_def_274,type,
vAND: $o > $o > $o ).
thf(func_def_275,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_276,type,
vNOT: $o > $o ).
thf(func_def_277,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_278,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_279,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_280,type,
vIMP: $o > $o > $o ).
thf(func_def_281,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_282,type,
sP0: $i > $i > $o ).
thf(func_def_283,type,
sP1: $i > $o ).
thf(func_def_284,type,
sP2: $o ).
thf(func_def_285,type,
sP3: $o ).
thf(func_def_296,type,
sK14: $i > $i ).
thf(func_def_300,type,
sK18: $o ).
thf(func_def_301,type,
sK19: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_302,type,
sK20: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_306,type,
sK24: $i > $o ).
thf(func_def_309,type,
sK27: $i > $i ).
thf(func_def_311,type,
sK29: $i > ( $i > $i ) > $i > $i ).
thf(func_def_322,type,
sK40: $o ).
thf(func_def_324,type,
sK42: $i > $o ).
thf(func_def_325,type,
sK43: $i > $i ).
thf(func_def_326,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_342,type,
sK60: $i > $o ).
thf(func_def_350,type,
sK68: $o ).
thf(func_def_357,type,
sK75: $i > $i > $o ).
thf(func_def_361,type,
sK79: ( $i > $o ) > $i > $i ).
thf(func_def_363,type,
sK81: $i > $o ).
thf(func_def_368,type,
sK86: $i > $i > $i > $i > $i ).
thf(func_def_375,type,
sK93: $i > $i > $i ).
thf(func_def_376,type,
sK94: $i > $i > $i ).
thf(func_def_377,type,
sK95: $i > $i > $i ).
thf(func_def_382,type,
sK100: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_383,type,
sK101: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_384,type,
sK102: $i > $o ).
thf(func_def_385,type,
sK103: $i > $o ).
thf(func_def_398,type,
sK116: ( $i > $o ) > $i ).
thf(func_def_399,type,
sK117: ( $i > $o ) > $i ).
thf(func_def_400,type,
sK118: $i > $o ).
thf(func_def_410,type,
sK128: $i > $o ).
thf(func_def_432,type,
sK150: $i > $i ).
thf(func_def_443,type,
sK161: $i > $i ).
thf(func_def_447,type,
sK165: $i > $i > ( $i > $i ) > $i ).
thf(func_def_449,type,
sK167: $i > $o ).
thf(func_def_452,type,
sK170: $i > ( $i > $o ) > $i ).
thf(func_def_455,type,
sK173: $i > $i > $i ).
thf(func_def_462,type,
sK180: $i > $o ).
thf(func_def_465,type,
sK183: $i > ( $i > $o ) > $i ).
thf(func_def_466,type,
sK184: $i > $o ).
thf(func_def_467,type,
sK185: $i > $o ).
thf(func_def_468,type,
sK186: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_469,type,
sK187: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_472,type,
sK190: ( $i > $o ) > $i > $i ).
thf(func_def_474,type,
sK192: $i > $o ).
thf(func_def_479,type,
sK197: $i > $i ).
thf(func_def_482,type,
sK200: $i > $i > ( $i > $i ) > $i ).
thf(func_def_484,type,
sK202: ( $i > $o ) > $i ).
thf(func_def_485,type,
sK203: $i > $o ).
thf(func_def_494,type,
sK212: $i > $i ).
thf(func_def_495,type,
sK213: $i > $i ).
thf(func_def_496,type,
sK214: $i > $i ).
thf(func_def_497,type,
sK215: $i > $i ).
thf(func_def_498,type,
sK216: $i > $i ).
thf(func_def_499,type,
sK217: $i > $i > $i > $i ).
thf(func_def_500,type,
sK218: $i > $i ).
thf(func_def_501,type,
sK219: $i > $i ).
thf(func_def_502,type,
sK220: $i > $i ).
thf(func_def_503,type,
sK221: $i > $i ).
thf(func_def_504,type,
sK222: $i > $i > $i ).
thf(func_def_505,type,
sK223: $i > $i > $i ).
thf(func_def_506,type,
sK224: $i > $i > $i > $i ).
thf(func_def_507,type,
sK225: $i > $i > $i > $i ).
thf(func_def_508,type,
sK226: $i > $i > $i > $i ).
thf(func_def_509,type,
sK227: $i > $i > $i ).
thf(func_def_510,type,
sK228: $i > $i > $i ).
thf(func_def_511,type,
sK229: $i > $i > $i ).
thf(func_def_512,type,
sK230: $i > ( $i > $i ) > $i > $i ).
thf(func_def_514,type,
sK232: $i > $i ).
thf(func_def_519,type,
sK237: $o ).
thf(func_def_533,type,
sK251: $o ).
thf(func_def_536,type,
sK254: $i > $o ).
thf(func_def_537,type,
sK255: $i > $o ).
thf(func_def_538,type,
sK256: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_539,type,
sK257: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_548,type,
sK266: $o ).
thf(func_def_559,type,
sK277: $o ).
thf(func_def_560,type,
sK278: $o > $i > $i > $i ).
thf(func_def_561,type,
sK279: $o ).
thf(func_def_562,type,
sK280: $i > $o ).
thf(func_def_565,type,
sK283: $i > $o ).
thf(func_def_579,type,
sK297: $o ).
thf(func_def_584,type,
sK302: $o ).
thf(func_def_588,type,
sK306: $i > $i > $o ).
thf(func_def_611,type,
sK329: $i > $o ).
thf(func_def_616,type,
sK334: $i > $i ).
thf(func_def_620,type,
sK338: $i > $o ).
thf(func_def_635,type,
sK353: $i > $i > $i > $i > $i ).
thf(func_def_639,type,
sK357: $i > $i ).
thf(func_def_641,type,
sK359: $i > ( $i > $i ) > $i > $i ).
thf(func_def_642,type,
sK360: $i > ( $i > $o ) > $i ).
thf(func_def_643,type,
sK361: $i > $o ).
thf(func_def_667,type,
sK385: $i > $o ).
thf(func_def_668,type,
sK386: $i > $i ).
thf(func_def_669,type,
sK387: ( $i > $o ) > $i ).
thf(func_def_670,type,
sK388: $i > $i > $i > $i > $i ).
thf(func_def_682,type,
sK400: $i > $o ).
thf(func_def_684,type,
sK402: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_685,type,
sK403: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_690,type,
sK408: $i > $i ).
thf(func_def_691,type,
sK409: $i > $i ).
thf(func_def_700,type,
sK418: ( $i > $o ) > $i > $i ).
thf(func_def_702,type,
sK420: $i > $o ).
thf(func_def_708,type,
sK426: $o ).
thf(func_def_711,type,
sK429: ( $i > $i > $o ) > $i > $i ).
thf(func_def_712,type,
sK430: ( $i > $i > $o ) > $i > $i ).
thf(func_def_713,type,
sK431: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_715,type,
sK433: $i > $i > $o ).
thf(func_def_716,type,
sK434: $i > $i ).
thf(func_def_717,type,
sK435: $i > $i ).
thf(func_def_723,type,
sK441: $i > $o ).
thf(func_def_728,type,
sK446: $i > $o ).
thf(func_def_733,type,
sK451: $o ).
thf(func_def_741,type,
sK459: $i > $i > $o ).
thf(func_def_746,type,
sK464: $o ).
thf(func_def_753,type,
sK471: $i > $i > $o ).
thf(func_def_764,type,
sK482: $o ).
thf(func_def_773,type,
sK491: $o ).
thf(func_def_794,type,
sK512: $o ).
thf(func_def_798,type,
sK516: $i > $i ).
thf(func_def_803,type,
sK521: $i > $o ).
thf(func_def_808,type,
sK526: $i > $i > $i ).
thf(func_def_819,type,
sK537: $o ).
thf(func_def_833,type,
sK551: $i > $o ).
thf(func_def_835,type,
sK553: $i > $i > $i > $i > $i ).
thf(func_def_836,type,
sK554: $i > $i > $i > $i > $i ).
thf(func_def_841,type,
sK559: $i > $i > $i > $i ).
thf(func_def_842,type,
sK560: $i > $i > $i > $i ).
thf(func_def_859,type,
sK577: $i > $i ).
thf(func_def_862,type,
sK580: $i > ( $i > $i ) > $i > $i ).
thf(func_def_863,type,
sK581: $i > $i > $o ).
thf(func_def_868,type,
sK586: $i > $o ).
thf(func_def_874,type,
sK592: $i > ( $i > $o ) > $i ).
thf(func_def_875,type,
sK593: $i > $o ).
thf(func_def_881,type,
sK599: $i > $i > $o ).
thf(func_def_888,type,
sK606: $i > $i > $i > $i > $i ).
thf(func_def_889,type,
sK607: $i > $i > $i > $i > $i ).
thf(func_def_890,type,
sK608: $i > $i > $i > $i > $i ).
thf(func_def_891,type,
sK609: $i > $i > $i > $i > $i ).
thf(func_def_894,type,
sK612: $i > $i > $i ).
thf(func_def_901,type,
sK619: $i > $i > $o ).
thf(func_def_907,type,
sK625: $i > ( $i > $o ) > $i ).
thf(func_def_908,type,
sK626: $i > ( $i > $o ) > $i ).
thf(func_def_909,type,
sK627: $i > $o ).
thf(func_def_914,type,
sK632: $i > $o ).
thf(func_def_917,type,
sK635: $i > $o ).
thf(func_def_928,type,
sK646: $i > $i > $i ).
thf(func_def_934,type,
sK652: $i > $i > $i ).
thf(func_def_935,type,
sK653: $i > $o ).
thf(func_def_938,type,
sK656: $i > ( $i > $o ) > $i ).
thf(func_def_939,type,
sK657: $i > ( $i > $o ) > $i ).
thf(func_def_948,type,
sK666: $i > $o ).
thf(func_def_951,type,
sK669: $i > ( $i > $o ) > $i ).
thf(func_def_955,type,
sK673: $i > $i > $i ).
thf(func_def_959,type,
sK677: $i > $i ).
thf(func_def_969,type,
sK687: $i > ( $i > $o ) > $i > $i ).
thf(func_def_971,type,
sK689: $i > $o ).
thf(func_def_979,type,
sK697: $i > $i > $i ).
thf(func_def_988,type,
sK706: $i > $o ).
thf(func_def_990,type,
sK708: ( $i > $o ) > $i > $i ).
thf(f92,axiom,
! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= subset2powerset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(f128,axiom,
! [X0: $i,X1: $i] :
( ( subset @ ( setminus @ X0 @ X1 ) @ X0 )
= setminusLsub ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(f235,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(f236,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f235]) ).
thf(f370,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( setminus @ X0 @ X1 ) @ X0 )
= setminusLsub ),
inference(rectify,[],[f128]) ).
thf(f371,plain,
( ( setminusLsub = $true )
<=> ! [X1: $i,X0: $i] :
( ( subset @ ( setminus @ X0 @ X1 ) @ X0 )
= $true ) ),
inference(fool_elimination,[],[f370]) ).
thf(f418,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= subset2powerset ),
inference(rectify,[],[f92]) ).
thf(f419,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( subset2powerset = $true ) ),
inference(fool_elimination,[],[f418]) ).
thf(f632,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f236]) ).
thf(f633,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f632]) ).
thf(f793,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $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,[],[f633]) ).
thf(f794,plain,
( ( funcinfuncset = $true )
& ( singletoninpowerset = $true )
& ( lam2p = $true )
& ( ap2apEq2 = $true )
& ( binintersectI = $true )
& ( eqbreln = $true )
& ( setukpairinjL = $true )
& ( setunionE2 = $true )
& ( exuI1 = $true )
& ( cartprodpairmemER = $true )
& ( ex1I2 = $true )
& ( brelnall2 = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( powersetE = $true )
& ( binintersectSubset2 = $true )
& ( dpsetconstrEL1 = $true )
& ( notsubsetI = $true )
& ( setunionsingleton1 = $true )
& ( foundationAx = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetsubset = $true )
& ( emptysetE = $true )
& ( subPowSU = $true )
& ( kfstsingleton = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( powersetAx = $true )
& ( powersetI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( exuI2 = $true )
& ( singletonsuniq = $true )
& ( setminusLsub = $true )
& ( omega__Cong = $true )
& ( subsetRefl = $true )
& ( iffalseProp2 = $true )
& ( setunionAx = $true )
& ( ubforcartprodlem3 = $true )
& ( descrp = $true )
& ( cartprodpairmemEL = $true )
& ( exuE3e = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrER = $true )
& ( subsetI1 = $true )
& ( lamp = $true )
& ( notequalI2 = $true )
& ( cartprodpairsurjEq = $true )
& ( vacuousDall = $true )
& ( cartprodfstpairEq = $true )
& ( subsetemptysetimpeq = $true )
& ( descr__Cong = $true )
& ( setadjoinIL = $true )
& ( funcImageSingleton = $true )
& ( binintersectLsub = $true )
& ( upairset2E = $true )
& ( kfstpairEq = $true )
& ( upairinpowunion = $true )
& ( notequalI1 = $true )
& ( eta2 = $true )
& ( powersetT_lem = $true )
& ( binunionE = $true )
& ( lamProp = $true )
& ( binunionIL = $true )
& ( binunionIR = $true )
& ( setminusI = $true )
& ( setukpairIL = $true )
& ( setoftrueEq = $true )
& ( subsetE = $true )
& ( upairsetIR = $true )
& ( sepInPowerset = $true )
& ( dpsetconstrER = $true )
& ( brelnall1 = $true )
& ( symdiffIneg2 = $true )
& ( iffalse = $true )
& ( emptyinPowerset = $true )
& ( funcext2 = $true )
& ( setextAx = $true )
& ( symdiffI1 = $true )
& ( upairsubunion = $true )
& ( setukpairinjL1 = $true )
& ( setbeta = $true )
& ( beta1 = $true )
& ( iftrueProp1 = $true )
& ( setminusIRneg = $true )
& ( setminusELneg = $true )
& ( kpairp = $true )
& ( setunionE = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( exuE2 = $true )
& ( binintersectEL = $true )
& ( symdiffE = $true )
& ( setminusSubset2 = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( iffalseProp1 = $true )
& ( dpsetconstrEL2 = $true )
& ( app = $true )
& ( binintersectT_lem = $true )
& ( disjointsetsI1 = $true )
& ( exuI3 = $true )
& ( emptyI = $true )
& ( binunionT_lem = $true )
& ( cartprodpairin = $true )
& ( ksndsingleton = $true )
& ( funcext = $true )
& ( setukpairinjL2 = $true )
& ( inPowerset = $true )
& ( funcGraphProp4 = $true )
& ( quantDeMorgan3 = $true )
& ( singletoninpowunion = $true )
& ( ifp = $true )
& ( setukpairinjR = $true )
& ( ex1I = $true )
& ( symdiffIneg1 = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyE1 = $true )
& ( eqimpsubset2 = $true )
& ( lam2lamEq = $true )
& ( binintersectSubset3 = $true )
& ( setukpairIR = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan2 = $true )
& ( setunion__Cong = $true )
& ( iftrue = $true )
& ( exuE3u = $true )
& ( upairset2IR = $true )
& ( ifSingleton = $true )
& ( upairsetE = $true )
& ( eqimpsubset1 = $true )
& ( secondinupair = $true )
& ( theeq = $true )
& ( iftrueProp2 = $true )
& ( omegaIndAx = $true )
& ( notdallE = $true )
& ( setminusER = $true )
& ( powersetI = $true )
& ( setadjoinSub2 = $true )
& ( emptyinunitempty = $true )
& ( uniqinunit = $true )
& ( notinsingleton = $true )
& ( emptyset__Cong = $true )
& ( emptysetAx = $true )
& ( binunionRsub = $true )
& ( exuE1 = $true )
& ( theprop = $true )
& ( prop2setE = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrI = $true )
& ( notinemptyset = $true )
& ( nonemptyI = $true )
& ( ap2p = $true )
& ( funcGraphProp1 = $true )
& ( setminusEL = $true )
& ( cartprodmempaircEq = $true )
& ( setunionI = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectER = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem2 = $true )
& ( quantDeMorgan4 = $true )
& ( powersetE1 = $true )
& ( setukpairinjR1 = $true )
& ( inCongP = $true )
& ( setadjoinIR = $true )
& ( iftrueorfalse = $true )
& ( cartprodmempair = $true )
& ( emptysetimpfalse = $true )
& ( binintersectRsub = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( emptyE1 = $true )
& ( ex1E1 = $true )
& ( subsetI2 = $true )
& ( eta1 = $true )
& ( setukpairinjR11 = $true )
& ( bs114d = $true )
& ( prop2set2propI = $true )
& ( upairequniteq = $true )
& ( subsetE2 = $true )
& ( dpsetconstrSub = $true )
& ( sepSubset = $true )
& ( singletonprop = $true )
& ( setextsub = $true )
& ( setext = $true )
& ( binunionEcases = $true )
& ( setunionsingleton2 = $true )
& ( setminusSubset1 = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ( ksndpairEq = $true )
& ( setminusILneg = $true )
& ( cartprodfstin = $true )
& ( infuncsetfunc = $true )
& ( dpsetconstrERa = $true )
& ( setminusERneg = $true )
& ( symdiffI2 = $true )
& ( setminusT_lem = $true )
& ( beta2 = $true )
& ( kpairiskpair = $true )
& ( dpsetconstrI = $true )
& ( cartprodsndpairEq = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( upairsetIL = $true )
& ( emptyInPowerset = $true )
& ( nonemptyI1 = $true )
& ( exu__Cong = $true )
& ( cartprodmempair1 = $true )
& ( powerset__Cong = $true )
& ( kpairsurjEq = $true )
& ( singletonsubset = $true )
& ( cartprodsndin = $true )
& ( setunionsingleton = $true )
& ( dsetconstrEL = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( notdexE = $true )
& ( replAx = $true )
& ( subbreln = $true )
& ( ap2apEq1 = $true )
& ( setukpairinjR2 = $true )
& ( setadjoinSub = $true )
& ( funcGraphProp3 = $true )
& ( eqinunit = $true )
& ( setadjoinE = $true )
& ( ex1E2 = $true )
& ( singletonsswitch = $true )
& ( setukpairinjR12 = $true )
& ( subsetTrans = $true ) ),
inference(flattening,[],[f793]) ).
thf(f924,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
<=> ( subset2powerset = $true ) ),
inference(ennf_transformation,[],[f419]) ).
thf(f1266,plain,
( ( funcinfuncset = $true )
& ( singletoninpowerset = $true )
& ( lam2p = $true )
& ( ap2apEq2 = $true )
& ( binintersectI = $true )
& ( eqbreln = $true )
& ( setukpairinjL = $true )
& ( setunionE2 = $true )
& ( exuI1 = $true )
& ( cartprodpairmemER = $true )
& ( ex1I2 = $true )
& ( brelnall2 = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( powersetE = $true )
& ( binintersectSubset2 = $true )
& ( dpsetconstrEL1 = $true )
& ( notsubsetI = $true )
& ( setunionsingleton1 = $true )
& ( foundationAx = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetsubset = $true )
& ( emptysetE = $true )
& ( subPowSU = $true )
& ( kfstsingleton = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( powersetAx = $true )
& ( powersetI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( exuI2 = $true )
& ( singletonsuniq = $true )
& ( setminusLsub = $true )
& ( omega__Cong = $true )
& ( subsetRefl = $true )
& ( iffalseProp2 = $true )
& ( setunionAx = $true )
& ( ubforcartprodlem3 = $true )
& ( descrp = $true )
& ( cartprodpairmemEL = $true )
& ( exuE3e = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrER = $true )
& ( subsetI1 = $true )
& ( lamp = $true )
& ( notequalI2 = $true )
& ( cartprodpairsurjEq = $true )
& ( vacuousDall = $true )
& ( cartprodfstpairEq = $true )
& ( subsetemptysetimpeq = $true )
& ( descr__Cong = $true )
& ( setadjoinIL = $true )
& ( funcImageSingleton = $true )
& ( binintersectLsub = $true )
& ( upairset2E = $true )
& ( kfstpairEq = $true )
& ( upairinpowunion = $true )
& ( notequalI1 = $true )
& ( eta2 = $true )
& ( powersetT_lem = $true )
& ( binunionE = $true )
& ( lamProp = $true )
& ( binunionIL = $true )
& ( binunionIR = $true )
& ( setminusI = $true )
& ( setukpairIL = $true )
& ( setoftrueEq = $true )
& ( subsetE = $true )
& ( upairsetIR = $true )
& ( sepInPowerset = $true )
& ( dpsetconstrER = $true )
& ( brelnall1 = $true )
& ( symdiffIneg2 = $true )
& ( iffalse = $true )
& ( emptyinPowerset = $true )
& ( funcext2 = $true )
& ( setextAx = $true )
& ( symdiffI1 = $true )
& ( upairsubunion = $true )
& ( setukpairinjL1 = $true )
& ( setbeta = $true )
& ( beta1 = $true )
& ( iftrueProp1 = $true )
& ( setminusIRneg = $true )
& ( setminusELneg = $true )
& ( kpairp = $true )
& ( setunionE = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( exuE2 = $true )
& ( binintersectEL = $true )
& ( symdiffE = $true )
& ( setminusSubset2 = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
!= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( iffalseProp1 = $true )
& ( dpsetconstrEL2 = $true )
& ( app = $true )
& ( binintersectT_lem = $true )
& ( disjointsetsI1 = $true )
& ( exuI3 = $true )
& ( emptyI = $true )
& ( binunionT_lem = $true )
& ( cartprodpairin = $true )
& ( ksndsingleton = $true )
& ( funcext = $true )
& ( setukpairinjL2 = $true )
& ( inPowerset = $true )
& ( funcGraphProp4 = $true )
& ( quantDeMorgan3 = $true )
& ( singletoninpowunion = $true )
& ( ifp = $true )
& ( setukpairinjR = $true )
& ( ex1I = $true )
& ( symdiffIneg1 = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyE1 = $true )
& ( eqimpsubset2 = $true )
& ( lam2lamEq = $true )
& ( binintersectSubset3 = $true )
& ( setukpairIR = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan2 = $true )
& ( setunion__Cong = $true )
& ( iftrue = $true )
& ( exuE3u = $true )
& ( upairset2IR = $true )
& ( ifSingleton = $true )
& ( upairsetE = $true )
& ( eqimpsubset1 = $true )
& ( secondinupair = $true )
& ( theeq = $true )
& ( iftrueProp2 = $true )
& ( omegaIndAx = $true )
& ( notdallE = $true )
& ( setminusER = $true )
& ( powersetI = $true )
& ( setadjoinSub2 = $true )
& ( emptyinunitempty = $true )
& ( uniqinunit = $true )
& ( notinsingleton = $true )
& ( emptyset__Cong = $true )
& ( emptysetAx = $true )
& ( binunionRsub = $true )
& ( exuE1 = $true )
& ( theprop = $true )
& ( prop2setE = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrI = $true )
& ( notinemptyset = $true )
& ( nonemptyI = $true )
& ( ap2p = $true )
& ( funcGraphProp1 = $true )
& ( setminusEL = $true )
& ( cartprodmempaircEq = $true )
& ( setunionI = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectER = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem2 = $true )
& ( quantDeMorgan4 = $true )
& ( powersetE1 = $true )
& ( setukpairinjR1 = $true )
& ( inCongP = $true )
& ( setadjoinIR = $true )
& ( iftrueorfalse = $true )
& ( cartprodmempair = $true )
& ( emptysetimpfalse = $true )
& ( binintersectRsub = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( emptyE1 = $true )
& ( ex1E1 = $true )
& ( subsetI2 = $true )
& ( eta1 = $true )
& ( setukpairinjR11 = $true )
& ( bs114d = $true )
& ( prop2set2propI = $true )
& ( upairequniteq = $true )
& ( subsetE2 = $true )
& ( dpsetconstrSub = $true )
& ( sepSubset = $true )
& ( singletonprop = $true )
& ( setextsub = $true )
& ( setext = $true )
& ( binunionEcases = $true )
& ( setunionsingleton2 = $true )
& ( setminusSubset1 = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ( ksndpairEq = $true )
& ( setminusILneg = $true )
& ( cartprodfstin = $true )
& ( infuncsetfunc = $true )
& ( dpsetconstrERa = $true )
& ( setminusERneg = $true )
& ( symdiffI2 = $true )
& ( setminusT_lem = $true )
& ( beta2 = $true )
& ( kpairiskpair = $true )
& ( dpsetconstrI = $true )
& ( cartprodsndpairEq = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( upairsetIL = $true )
& ( emptyInPowerset = $true )
& ( nonemptyI1 = $true )
& ( exu__Cong = $true )
& ( cartprodmempair1 = $true )
& ( powerset__Cong = $true )
& ( kpairsurjEq = $true )
& ( singletonsubset = $true )
& ( cartprodsndin = $true )
& ( setunionsingleton = $true )
& ( dsetconstrEL = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( notdexE = $true )
& ( replAx = $true )
& ( subbreln = $true )
& ( ap2apEq1 = $true )
& ( setukpairinjR2 = $true )
& ( setadjoinSub = $true )
& ( funcGraphProp3 = $true )
& ( eqinunit = $true )
& ( setadjoinE = $true )
& ( ex1E2 = $true )
& ( singletonsswitch = $true )
& ( setukpairinjR12 = $true )
& ( subsetTrans = $true ) ),
inference(rectify,[],[f794]) ).
thf(f1267,plain,
( ( funcinfuncset = $true )
& ( singletoninpowerset = $true )
& ( lam2p = $true )
& ( ap2apEq2 = $true )
& ( binintersectI = $true )
& ( eqbreln = $true )
& ( setukpairinjL = $true )
& ( setunionE2 = $true )
& ( exuI1 = $true )
& ( cartprodpairmemER = $true )
& ( ex1I2 = $true )
& ( brelnall2 = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( powersetE = $true )
& ( binintersectSubset2 = $true )
& ( dpsetconstrEL1 = $true )
& ( notsubsetI = $true )
& ( setunionsingleton1 = $true )
& ( foundationAx = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetsubset = $true )
& ( emptysetE = $true )
& ( subPowSU = $true )
& ( kfstsingleton = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( powersetAx = $true )
& ( powersetI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( exuI2 = $true )
& ( singletonsuniq = $true )
& ( setminusLsub = $true )
& ( omega__Cong = $true )
& ( subsetRefl = $true )
& ( iffalseProp2 = $true )
& ( setunionAx = $true )
& ( ubforcartprodlem3 = $true )
& ( descrp = $true )
& ( cartprodpairmemEL = $true )
& ( exuE3e = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrER = $true )
& ( subsetI1 = $true )
& ( lamp = $true )
& ( notequalI2 = $true )
& ( cartprodpairsurjEq = $true )
& ( vacuousDall = $true )
& ( cartprodfstpairEq = $true )
& ( subsetemptysetimpeq = $true )
& ( descr__Cong = $true )
& ( setadjoinIL = $true )
& ( funcImageSingleton = $true )
& ( binintersectLsub = $true )
& ( upairset2E = $true )
& ( kfstpairEq = $true )
& ( upairinpowunion = $true )
& ( notequalI1 = $true )
& ( eta2 = $true )
& ( powersetT_lem = $true )
& ( binunionE = $true )
& ( lamProp = $true )
& ( binunionIL = $true )
& ( binunionIR = $true )
& ( setminusI = $true )
& ( setukpairIL = $true )
& ( setoftrueEq = $true )
& ( subsetE = $true )
& ( upairsetIR = $true )
& ( sepInPowerset = $true )
& ( dpsetconstrER = $true )
& ( brelnall1 = $true )
& ( symdiffIneg2 = $true )
& ( iffalse = $true )
& ( emptyinPowerset = $true )
& ( funcext2 = $true )
& ( setextAx = $true )
& ( symdiffI1 = $true )
& ( upairsubunion = $true )
& ( setukpairinjL1 = $true )
& ( setbeta = $true )
& ( beta1 = $true )
& ( iftrueProp1 = $true )
& ( setminusIRneg = $true )
& ( setminusELneg = $true )
& ( kpairp = $true )
& ( setunionE = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( exuE2 = $true )
& ( binintersectEL = $true )
& ( symdiffE = $true )
& ( setminusSubset2 = $true )
& ( ( in @ ( setminus @ sK282 @ sK281 ) @ ( powerset @ sK282 ) )
!= $true )
& ( ( in @ sK281 @ ( powerset @ sK282 ) )
= $true )
& ( iffalseProp1 = $true )
& ( dpsetconstrEL2 = $true )
& ( app = $true )
& ( binintersectT_lem = $true )
& ( disjointsetsI1 = $true )
& ( exuI3 = $true )
& ( emptyI = $true )
& ( binunionT_lem = $true )
& ( cartprodpairin = $true )
& ( ksndsingleton = $true )
& ( funcext = $true )
& ( setukpairinjL2 = $true )
& ( inPowerset = $true )
& ( funcGraphProp4 = $true )
& ( quantDeMorgan3 = $true )
& ( singletoninpowunion = $true )
& ( ifp = $true )
& ( setukpairinjR = $true )
& ( ex1I = $true )
& ( symdiffIneg1 = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyE1 = $true )
& ( eqimpsubset2 = $true )
& ( lam2lamEq = $true )
& ( binintersectSubset3 = $true )
& ( setukpairIR = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan2 = $true )
& ( setunion__Cong = $true )
& ( iftrue = $true )
& ( exuE3u = $true )
& ( upairset2IR = $true )
& ( ifSingleton = $true )
& ( upairsetE = $true )
& ( eqimpsubset1 = $true )
& ( secondinupair = $true )
& ( theeq = $true )
& ( iftrueProp2 = $true )
& ( omegaIndAx = $true )
& ( notdallE = $true )
& ( setminusER = $true )
& ( powersetI = $true )
& ( setadjoinSub2 = $true )
& ( emptyinunitempty = $true )
& ( uniqinunit = $true )
& ( notinsingleton = $true )
& ( emptyset__Cong = $true )
& ( emptysetAx = $true )
& ( binunionRsub = $true )
& ( exuE1 = $true )
& ( theprop = $true )
& ( prop2setE = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrI = $true )
& ( notinemptyset = $true )
& ( nonemptyI = $true )
& ( ap2p = $true )
& ( funcGraphProp1 = $true )
& ( setminusEL = $true )
& ( cartprodmempaircEq = $true )
& ( setunionI = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectER = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem2 = $true )
& ( quantDeMorgan4 = $true )
& ( powersetE1 = $true )
& ( setukpairinjR1 = $true )
& ( inCongP = $true )
& ( setadjoinIR = $true )
& ( iftrueorfalse = $true )
& ( cartprodmempair = $true )
& ( emptysetimpfalse = $true )
& ( binintersectRsub = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( emptyE1 = $true )
& ( ex1E1 = $true )
& ( subsetI2 = $true )
& ( eta1 = $true )
& ( setukpairinjR11 = $true )
& ( bs114d = $true )
& ( prop2set2propI = $true )
& ( upairequniteq = $true )
& ( subsetE2 = $true )
& ( dpsetconstrSub = $true )
& ( sepSubset = $true )
& ( singletonprop = $true )
& ( setextsub = $true )
& ( setext = $true )
& ( binunionEcases = $true )
& ( setunionsingleton2 = $true )
& ( setminusSubset1 = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ( ksndpairEq = $true )
& ( setminusILneg = $true )
& ( cartprodfstin = $true )
& ( infuncsetfunc = $true )
& ( dpsetconstrERa = $true )
& ( setminusERneg = $true )
& ( symdiffI2 = $true )
& ( setminusT_lem = $true )
& ( beta2 = $true )
& ( kpairiskpair = $true )
& ( dpsetconstrI = $true )
& ( cartprodsndpairEq = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( upairsetIL = $true )
& ( emptyInPowerset = $true )
& ( nonemptyI1 = $true )
& ( exu__Cong = $true )
& ( cartprodmempair1 = $true )
& ( powerset__Cong = $true )
& ( kpairsurjEq = $true )
& ( singletonsubset = $true )
& ( cartprodsndin = $true )
& ( setunionsingleton = $true )
& ( dsetconstrEL = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( notdexE = $true )
& ( replAx = $true )
& ( subbreln = $true )
& ( ap2apEq1 = $true )
& ( setukpairinjR2 = $true )
& ( setadjoinSub = $true )
& ( funcGraphProp3 = $true )
& ( eqinunit = $true )
& ( setadjoinE = $true )
& ( ex1E2 = $true )
& ( singletonsswitch = $true )
& ( setukpairinjR12 = $true )
& ( subsetTrans = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281,sK282]),skolemize(X0,sK281),skolemize(X1,sK282)],[f1266]) ).
thf(f1466,plain,
( ( ( setminusLsub = $true )
| ? [X1: $i,X0: $i] :
( ( subset @ ( setminus @ X0 @ X1 ) @ X0 )
!= $true ) )
& ( ! [X1: $i,X0: $i] :
( ( subset @ ( setminus @ X0 @ X1 ) @ X0 )
= $true )
| ( setminusLsub != $true ) ) ),
inference(nnf_transformation,[],[f371]) ).
thf(f1467,plain,
( ( ( setminusLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( setminus @ X1 @ X0 ) @ X1 )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( subset @ ( setminus @ X3 @ X2 ) @ X3 )
= $true )
| ( setminusLsub != $true ) ) ),
inference(rectify,[],[f1466]) ).
thf(f1468,plain,
( ( ( setminusLsub = $true )
| ( ( subset @ ( setminus @ sK495 @ sK494 ) @ sK495 )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( subset @ ( setminus @ X3 @ X2 ) @ X3 )
= $true )
| ( setminusLsub != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK494,sK495]),skolemize(X0,sK494),skolemize(X1,sK495)],[f1467]) ).
thf(f1542,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( subset2powerset != $true ) )
& ( ( subset2powerset = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f924]) ).
thf(f1543,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( subset2powerset != $true ) )
& ( ( subset2powerset = $true )
| ? [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X3 ) ) )
& ( ( subset @ X2 @ X3 )
= $true ) ) ) ),
inference(rectify,[],[f1542]) ).
thf(f1544,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( subset2powerset != $true ) )
& ( ( subset2powerset = $true )
| ( ( ( in @ sK566 @ ( powerset @ sK567 ) )
!= $true )
& ( ( subset @ sK566 @ sK567 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK566,sK567]),skolemize(X2,sK566),skolemize(X3,sK567)],[f1543]) ).
thf(f2145,plain,
subset2powerset = $true,
inference(cnf_transformation,[],[f1267]) ).
thf(f2210,plain,
( ( in @ ( setminus @ sK282 @ sK281 ) @ ( powerset @ sK282 ) )
!= $true ),
inference(cnf_transformation,[],[f1267]) ).
thf(f2271,plain,
setminusLsub = $true,
inference(cnf_transformation,[],[f1267]) ).
thf(f2564,plain,
! [X2: $i,X3: $i] :
( ( setminusLsub != $true )
| ( ( subset @ ( setminus @ X3 @ X2 ) @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f1468]) ).
thf(f2656,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( subset2powerset != $true ) ),
inference(cnf_transformation,[],[f1544]) ).
thf(f4059,definition,
( spl716_220
<=> ( ( in @ ( setminus @ sK282 @ sK281 ) @ ( powerset @ sK282 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl716_220])],[avatar_definition]) ).
thf(f4061,plain,
( ( ( in @ ( setminus @ sK282 @ sK281 ) @ ( powerset @ sK282 ) )
!= $true )
| spl716_220 ),
inference(avatar_component_clause,[],[f4059]) ).
thf(f4062,plain,
~ spl716_220,
inference(avatar_split_clause,[],[f2210,f4059]) ).
thf(f6150,definition,
( spl716_673
<=> ( setminusLsub = $true ) ),
introduced(definition,[new_symbols(definition,[spl716_673])],[avatar_definition]) ).
thf(f6153,plain,
spl716_673,
inference(avatar_split_clause,[],[f2271,f6150]) ).
thf(f6309,definition,
( spl716_706
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl716_706])],[avatar_definition]) ).
thf(f6310,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ~ spl716_706 ),
inference(avatar_component_clause,[],[f6309]) ).
thf(f6332,definition,
( spl716_711
<=> ( subset2powerset = $true ) ),
introduced(definition,[new_symbols(definition,[spl716_711])],[avatar_definition]) ).
thf(f7359,definition,
( spl716_923
<=> ! [X2: $i,X3: $i] :
( ( subset @ ( setminus @ X3 @ X2 ) @ X3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl716_923])],[avatar_definition]) ).
thf(f7360,plain,
( ! [X2: $i,X3: $i] :
( ( subset @ ( setminus @ X3 @ X2 ) @ X3 )
= $true )
| ~ spl716_923 ),
inference(avatar_component_clause,[],[f7359]) ).
thf(f7361,plain,
( spl716_923
| ~ spl716_673 ),
inference(avatar_split_clause,[],[f2564,f6150,f7359]) ).
thf(f7426,plain,
spl716_711,
inference(avatar_split_clause,[],[f2145,f6332]) ).
thf(f8159,plain,
( ~ spl716_711
| spl716_706 ),
inference(avatar_split_clause,[],[f2656,f6309,f6332]) ).
thf(f8820,plain,
( ( $true != $true )
| ( ( subset @ ( setminus @ sK282 @ sK281 ) @ sK282 )
!= $true )
| spl716_220
| ~ spl716_706 ),
inference(superposition,[],[f4061,f6310]) ).
thf(f8824,plain,
( ( ( subset @ ( setminus @ sK282 @ sK281 ) @ sK282 )
!= $true )
| spl716_220
| ~ spl716_706 ),
inference(trivial_inequality_removal,[],[f8820]) ).
thf(f8830,plain,
( $false
| spl716_220
| ~ spl716_706
| ~ spl716_923 ),
inference(forward_subsumption_resolution,[],[f8824,f7360]) ).
thf(f8831,plain,
( spl716_220
| ~ spl716_706
| ~ spl716_923 ),
inference(avatar_contradiction_clause,[],[f8830]) ).
cnf(s141,plain,
~ spl716_220,
inference(sat_conversion,[],[f4062]) ).
cnf(s585,plain,
spl716_673,
inference(sat_conversion,[],[f6153]) ).
cnf(s888,plain,
( ~ spl716_673
| spl716_923 ),
inference(sat_conversion,[],[f7361]) ).
cnf(s911,plain,
spl716_711,
inference(sat_conversion,[],[f7426]) ).
cnf(s1105,plain,
( spl716_706
| ~ spl716_711 ),
inference(sat_conversion,[],[f8159]) ).
cnf(s1154,plain,
( spl716_220
| ~ spl716_706
| ~ spl716_923 ),
inference(sat_conversion,[],[f8831]) ).
cnf(s1166,plain,
spl716_706,
inference(rat,[],[s1105,s911]) ).
cnf(s1221,plain,
spl716_923,
inference(rat,[],[s888,s585]) ).
cnf(s1222,plain,
spl716_220,
inference(rat,[],[s1154,s1166,s1221]) ).
cnf(s1370,plain,
$false,
inference(rat,[],[s141,s1222]) ).
thf(f8832,plain,
$false,
inference(avatar_sat_refutation,[],[s1370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU714^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n010.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:14:18 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.22/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.44 % (2919807)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.44 % (2919815)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=332993471:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.30/0.44 % (2919812)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2169704338:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.44 % (2919816)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3179331235:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.44 % (2919813)lrs+10_16_si=on:nwc=1.5:random_seed=2098630034:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.44 % (2919818)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.44 % (2919818)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.30/0.44 % (2919814)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1951053174:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.44 % (2919818)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=205004824:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.44 % (2919813)Instruction limit reached!
% 0.30/0.44 % (2919813)------------------------------
% 0.30/0.44 % (2919813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919813)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919813)Termination reason: Instruction limit
% 0.30/0.44 % (2919813)Termination phase: shuffling
% 0.30/0.44 % (2919813)Time elapsed: 0.009 s
% 0.30/0.44 % (2919813)Peak memory usage: 10 MB
% 0.30/0.44 % (2919813)Instructions burned: 20 (million)
% 0.30/0.44 % (2919814)Instruction limit reached!
% 0.30/0.44 % (2919814)------------------------------
% 0.30/0.44 % (2919814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919814)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919814)Termination reason: Instruction limit
% 0.30/0.44 % (2919814)Termination phase: shuffling
% 0.30/0.44 % (2919814)Time elapsed: 0.006 s
% 0.30/0.44 % (2919814)Peak memory usage: 10 MB
% 0.30/0.44 % (2919814)Instructions burned: 3 (million)
% 0.30/0.44 % (2919816)Instruction limit reached!
% 0.30/0.44 % (2919816)------------------------------
% 0.30/0.44 % (2919816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919816)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919816)Termination reason: Instruction limit
% 0.30/0.44 % (2919816)Termination phase: Property scanning
% 0.30/0.44 % (2919816)Time elapsed: 0.012 s
% 0.30/0.44 % (2919816)Peak memory usage: 10 MB
% 0.30/0.44 % (2919816)Instructions burned: 26 (million)
% 0.30/0.44 % (2919817)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=746698467:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.44 % (2919825)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2068663226:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.44 % (2919826)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=28382804:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.30/0.44 % (2919827)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.44 % (2919825)Instruction limit reached!
% 0.30/0.44 % (2919825)------------------------------
% 0.30/0.44 % (2919825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919825)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919825)Termination reason: Instruction limit
% 0.30/0.44 % (2919825)Termination phase: shuffling
% 0.30/0.44 % (2919825)Time elapsed: 0.002 s
% 0.30/0.44 % (2919825)Peak memory usage: 10 MB
% 0.30/0.44 % (2919825)Instructions burned: 3 (million)
% 0.30/0.44 % (2919826)Instruction limit reached!
% 0.30/0.44 % (2919826)------------------------------
% 0.30/0.44 % (2919826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919826)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919826)Termination reason: Instruction limit
% 0.30/0.44 % (2919826)Termination phase: shuffling
% 0.30/0.44 % (2919826)Time elapsed: 0.003 s
% 0.30/0.44 % (2919826)Peak memory usage: 10 MB
% 0.30/0.44 % (2919826)Instructions burned: 5 (million)
% 0.30/0.44 % (2919827)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2248004082:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.30/0.44 % (2919827)Instruction limit reached!
% 0.30/0.44 % (2919827)------------------------------
% 0.30/0.44 % (2919827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919827)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919827)Termination reason: Instruction limit
% 0.30/0.44 % (2919827)Termination phase: shuffling
% 0.30/0.44 % (2919827)Time elapsed: 0.004 s
% 0.30/0.44 % (2919827)Peak memory usage: 10 MB
% 0.30/0.44 % (2919827)Instructions burned: 8 (million)
% 0.30/0.44 % (2919812)Instruction limit reached!
% 0.30/0.44 % (2919812)------------------------------
% 0.30/0.44 % (2919812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919812)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919812)Termination reason: Instruction limit
% 0.30/0.44 % (2919812)Termination phase: Preprocessing 3
% 0.30/0.44 % (2919812)Time elapsed: 0.041 s
% 0.30/0.44 % (2919812)Peak memory usage: 13 MB
% 0.30/0.44 % (2919812)Instructions burned: 89 (million)
% 0.30/0.44 % (2919832)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.30/0.44 % (2919832)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.44 % (2919831)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1382184591:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.30/0.44 % (2919817)Instruction limit reached!
% 0.30/0.44 % (2919817)------------------------------
% 0.30/0.44 % (2919817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919817)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919817)Termination reason: Instruction limit
% 0.30/0.44 % (2919817)Termination phase: Preprocessing 3
% 0.30/0.44 % (2919817)Time elapsed: 0.035 s
% 0.30/0.44 % (2919817)Peak memory usage: 12 MB
% 0.30/0.44 % (2919817)Instructions burned: 76 (million)
% 0.30/0.44 % (2919832)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1440331454:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.30/0.44 % (2919834)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=2915654079:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.30/0.44 % (2919831)Instruction limit reached!
% 0.30/0.44 % (2919831)------------------------------
% 0.30/0.44 % (2919831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919831)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919831)Termination reason: Instruction limit
% 0.30/0.44 % (2919831)Termination phase: shuffling
% 0.30/0.44 % (2919831)Time elapsed: 0.006 s
% 0.30/0.44 % (2919831)Peak memory usage: 10 MB
% 0.30/0.44 % (2919831)Instructions burned: 13 (million)
% 0.30/0.44 % (2919835)lrs+10_1_si=on:cs=on:random_seed=1510016565:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.30/0.44 % (2919835)Instruction limit reached!
% 0.30/0.44 % (2919835)------------------------------
% 0.30/0.44 % (2919835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919835)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919835)Termination reason: Instruction limit
% 0.30/0.44 % (2919835)Termination phase: shuffling
% 0.30/0.44 % (2919835)Time elapsed: 0.004 s
% 0.30/0.44 % (2919835)Peak memory usage: 10 MB
% 0.30/0.44 % (2919835)Instructions burned: 9 (million)
% 0.30/0.44 % (2919832)Instruction limit reached!
% 0.30/0.44 % (2919832)------------------------------
% 0.30/0.44 % (2919832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919832)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919832)Termination reason: Instruction limit
% 0.30/0.44 % (2919832)Termination phase: shuffling
% 0.30/0.44 % (2919832)Time elapsed: 0.013 s
% 0.30/0.44 % (2919832)Peak memory usage: 10 MB
% 0.30/0.44 % (2919832)Instructions burned: 30 (million)
% 0.30/0.44 % (2919838)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.30/0.44 % (2919838)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=2439337345:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.30/0.44 % (2919818)Instruction limit reached!
% 0.30/0.44 % (2919818)------------------------------
% 0.30/0.44 % (2919818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919818)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919818)Termination reason: Instruction limit
% 0.30/0.44 % (2919818)Termination phase: Saturation
% 0.30/0.44 % (2919818)Time elapsed: 0.066 s
% 0.30/0.44 % (2919818)Peak memory usage: 14 MB
% 0.30/0.44 % (2919818)Instructions burned: 157 (million)
% 0.30/0.44 % (2919815) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2919807-2919815"...
% 0.30/0.44 % (2919838)Instruction limit reached!
% 0.30/0.44 % (2919838)------------------------------
% 0.30/0.44 % (2919838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919838)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919838)Termination reason: Instruction limit
% 0.30/0.44 % (2919838)Termination phase: shuffling
% 0.30/0.44 % (2919838)Time elapsed: 0.002 s
% 0.30/0.44 % (2919838)Peak memory usage: 10 MB
% 0.30/0.44 % (2919838)Instructions burned: 4 (million)
% 0.30/0.44 % (2919840)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=565561524:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.30/0.44 % (2919815)...printing done.
% 0.30/0.44 % (2919815)Refutation found. Thanks to Tanya!
% 0.30/0.44 % SZS status Theorem for theBenchmark
% 0.30/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.44 % (2919815)------------------------------
% 0.30/0.44 % (2919815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.44 % (2919815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.44 % (2919815)CaDiCaL version: 2.1.3
% 0.30/0.44 % (2919815)Termination reason: Refutation
% 0.30/0.44 % (2919815)Time elapsed: 0.084 s
% 0.30/0.44 % (2919815)Peak memory usage: 19 MB
% 0.30/0.44 % (2919815)Instructions burned: 316 (million)
% 0.30/0.44 % (2919807)Success in time 0.133 s
% 0.30/0.44 % Vampire exiting
%------------------------------------------------------------------------------