%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU732^1 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:01 AM UTC 2026
% Result : Theorem 2.51s 0.72s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 22 unt; 0 typ; 7 def)
% Number of atoms : 4929 (1352 equ; 0 cnn)
% Maximal formula atoms : 253 ( 72 avg)
% Number of connectives : 2512 ( 81 ~; 58 |; 768 &; 326 @)
% ( 12 <=>;1267 =>; 0 <=; 0 <~>)
% Maximal formula depth : 262 ( 34 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 : 481 ( 478 usr; 286 con; 0-4 aty)
% Number of variables : 103 ( 0 sgn 83 !; 20 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_279,type,
contrasubsetT1: $o ).
thf(func_def_280,type,
contrasubsetT2: $o ).
thf(func_def_281,type,
contrasubsetT3: $o ).
thf(func_def_282,type,
doubleComplementI1: $o ).
thf(func_def_283,type,
doubleComplementE1: $o ).
thf(func_def_284,type,
doubleComplementSub1: $o ).
thf(func_def_285,type,
doubleComplementSub2: $o ).
thf(func_def_286,type,
doubleComplementEq: $o ).
thf(func_def_289,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_290,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_291,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_292,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_293,type,
vNOT: $o > $o ).
thf(func_def_294,type,
vOR: $o > $o > $o ).
thf(func_def_295,type,
vAND: $o > $o > $o ).
thf(func_def_296,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_297,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_298,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_299,type,
vIMP: $o > $o > $o ).
thf(func_def_300,type,
sP0: $o ).
thf(func_def_301,type,
sP1: $i > $i > $o ).
thf(func_def_302,type,
sP2: $i > $o ).
thf(func_def_303,type,
sP3: $o ).
thf(func_def_304,type,
sK4: $i > $i ).
thf(func_def_307,type,
sK7: $i > $i > ( $i > $i ) > $i ).
thf(func_def_310,type,
sK10: $i > $i > $i ).
thf(func_def_313,type,
sK13: $i > $o ).
thf(func_def_326,type,
sK26: $o ).
thf(func_def_330,type,
sK30: $i > $i > $i ).
thf(func_def_335,type,
sK35: $o ).
thf(func_def_342,type,
sK42: $i > $o ).
thf(func_def_344,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_352,type,
sK52: $i > ( $i > $o ) > $i ).
thf(func_def_353,type,
sK53: $i > $o ).
thf(func_def_359,type,
sK59: $o ).
thf(func_def_362,type,
sK62: $o ).
thf(func_def_368,type,
sK68: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_369,type,
sK69: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_370,type,
sK70: $i > $o ).
thf(func_def_371,type,
sK71: $i > $o ).
thf(func_def_389,type,
sK89: $i > $i > $o ).
thf(func_def_393,type,
sK93: $i > $o ).
thf(func_def_396,type,
sK96: $i > ( $i > $o ) > $i ).
thf(func_def_399,type,
sK99: $i > $o ).
thf(func_def_401,type,
sK101: ( $i > $o ) > $i > $i ).
thf(func_def_402,type,
sK102: ( $i > $o ) > $i > $i ).
thf(func_def_407,type,
sK107: $i > $o ).
thf(func_def_415,type,
sK115: $o ).
thf(func_def_418,type,
sK118: $o ).
thf(func_def_422,type,
sK122: $o ).
thf(func_def_438,type,
sK138: $i > $o ).
thf(func_def_440,type,
sK140: ( $i > $o ) > $i > $i ).
thf(func_def_455,type,
sK155: $i > $i > ( $i > $i ) > $i ).
thf(func_def_456,type,
sK156: $i > $i ).
thf(func_def_459,type,
sK159: $i > $i ).
thf(func_def_467,type,
sK167: $i > $o ).
thf(func_def_469,type,
sK169: ( $i > $o ) > $i ).
thf(func_def_470,type,
sK170: ( $i > $o ) > $i ).
thf(func_def_476,type,
sK176: $i > $o ).
thf(func_def_477,type,
sK177: ( $i > $o ) > $i ).
thf(func_def_494,type,
sK194: $i > $i > $i ).
thf(func_def_505,type,
sK205: $i > $o ).
thf(func_def_506,type,
sK206: $i > $i ).
thf(func_def_507,type,
sK207: ( $i > $o ) > $i ).
thf(func_def_509,type,
sK209: $i > $o ).
thf(func_def_519,type,
sK219: $i > $o ).
thf(func_def_520,type,
sK220: $i > $o ).
thf(func_def_521,type,
sK221: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_522,type,
sK222: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_530,type,
sK230: $i > $i ).
thf(func_def_534,type,
sK234: $i > $i > ( $i > $i ) > $i ).
thf(func_def_536,type,
sK236: $o ).
thf(func_def_546,type,
sK246: $i > $i > $o ).
thf(func_def_548,type,
sK248: $o > $i > $i > $i ).
thf(func_def_551,type,
sK251: $o ).
thf(func_def_554,type,
sK254: ( $i > $o ) > $i ).
thf(func_def_555,type,
sK255: $i > $o ).
thf(func_def_556,type,
sK256: $i > $i ).
thf(func_def_561,type,
sK261: $i > $o ).
thf(func_def_563,type,
sK263: ( $i > $o ) > $i > $i ).
thf(func_def_567,type,
sK267: $i > $i ).
thf(func_def_569,type,
sK269: $i > ( $i > $i ) > $i > $i ).
thf(func_def_576,type,
sK276: $o ).
thf(func_def_577,type,
sK277: $i > $i ).
thf(func_def_584,type,
sK284: $i > $i > $i ).
thf(func_def_585,type,
sK285: $i > $i > $i ).
thf(func_def_591,type,
sK291: $i > $o ).
thf(func_def_597,type,
sK297: $i > $i > $o ).
thf(func_def_600,type,
sK300: $i > $o ).
thf(func_def_604,type,
sK304: $i > $o ).
thf(func_def_612,type,
sK312: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_613,type,
sK313: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_617,type,
sK317: $i > $o ).
thf(func_def_630,type,
sK330: $i > $i > $i > $i ).
thf(func_def_631,type,
sK331: $i > $i > $i > $i ).
thf(func_def_635,type,
sK335: $i > $i > $i ).
thf(func_def_641,type,
sK341: $i > ( $i > $o ) > $i ).
thf(func_def_642,type,
sK342: $i > $o ).
thf(func_def_666,type,
sK366: $i > $i > $i > $i > $i ).
thf(func_def_682,type,
sK382: $o ).
thf(func_def_690,type,
sK390: $i > $o ).
thf(func_def_692,type,
sK392: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_693,type,
sK393: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_698,type,
sK398: $i > $i > $i > $i ).
thf(func_def_699,type,
sK399: $i > $i > $i > $i ).
thf(func_def_705,type,
sK405: $o ).
thf(func_def_716,type,
sK416: $i > $i > $o ).
thf(func_def_723,type,
sK423: $i > $o ).
thf(func_def_724,type,
sK424: $i > $o ).
thf(func_def_725,type,
sK425: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_726,type,
sK426: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_728,type,
sK428: $i > $i ).
thf(func_def_732,type,
sK432: $i > $i > ( $i > $i ) > $i ).
thf(func_def_749,type,
sK449: ( $i > $i > $o ) > $i > $i ).
thf(func_def_750,type,
sK450: ( $i > $i > $o ) > $i > $i ).
thf(func_def_751,type,
sK451: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_753,type,
sK453: $i > $i > $o ).
thf(func_def_754,type,
sK454: $i > $i ).
thf(func_def_755,type,
sK455: $i > $i ).
thf(func_def_763,type,
sK463: $i > $i > $o ).
thf(func_def_767,type,
sK467: $i > $i > $i ).
thf(func_def_773,type,
sK473: $i > $i > $i > $i > $i ).
thf(func_def_774,type,
sK474: $i > $i > $i > $i > $i ).
thf(func_def_786,type,
sK486: $i > $i > $o ).
thf(func_def_795,type,
sK495: $i > $i > $i > $i > $i ).
thf(func_def_812,type,
sK512: $i > $i > $i > $i ).
thf(func_def_820,type,
sK520: $i > $i > $i ).
thf(func_def_821,type,
sK521: $i > $i > $i ).
thf(func_def_828,type,
sK528: $i > $o ).
thf(func_def_829,type,
sK529: ( $i > $o ) > $i > $i ).
thf(func_def_830,type,
sK530: $i > $i > $i ).
thf(func_def_843,type,
sK543: $i > $i ).
thf(func_def_845,type,
sK545: $i > $i ).
thf(func_def_847,type,
sK547: $i > $i > $o ).
thf(func_def_856,type,
sK556: $i > $o ).
thf(func_def_871,type,
sK571: $i > $i > $i > $i ).
thf(func_def_883,type,
sK583: $i > $o ).
thf(func_def_886,type,
sK586: $i > ( $i > $o ) > $i ).
thf(func_def_895,type,
sK595: $i > $o ).
thf(func_def_898,type,
sK598: $o ).
thf(func_def_901,type,
sK601: $o ).
thf(func_def_905,type,
sK605: $i > $i > $i > $i > $i ).
thf(func_def_912,type,
sK612: $i > ( $i > $i ) > $i > $i ).
thf(func_def_914,type,
sK614: $i > $i ).
thf(func_def_921,type,
sK621: $i > $i ).
thf(func_def_923,type,
sK623: $o ).
thf(func_def_937,type,
sK637: $o ).
thf(func_def_940,type,
sK640: $i > $o ).
thf(func_def_944,type,
sK644: $i > $o ).
thf(func_def_950,type,
sK650: ( $i > $o ) > $i > $i > $i ).
thf(func_def_953,type,
sK653: $i > $o ).
thf(func_def_978,type,
sK678: $i > $o ).
thf(func_def_980,type,
sK680: ( $i > $o ) > $i > $i ).
thf(func_def_981,type,
sK681: ( $i > $o ) > $i > $i ).
thf(func_def_990,type,
sK690: $i > $o ).
thf(func_def_991,type,
sK691: $i > $o ).
thf(func_def_1006,type,
sK706: $i > ( $i > $o ) > $i ).
thf(func_def_1007,type,
sK707: $i > $o ).
thf(func_def_1010,type,
sK710: $i > $i ).
thf(func_def_1020,type,
sK720: $o ).
thf(func_def_1028,type,
sK728: $i > $i > $i > $i > $i ).
thf(func_def_1029,type,
sK729: $i > $i > $i > $i > $i ).
thf(func_def_1030,type,
sK730: $i > $i > $i > $i > $i ).
thf(func_def_1031,type,
sK731: $i > $i > $i > $i > $i ).
thf(func_def_1035,type,
sK735: $i > $i ).
thf(func_def_1043,type,
sK743: $i > $o ).
thf(func_def_1045,type,
sK745: $i > $i ).
thf(func_def_1046,type,
sK746: $i > $i ).
thf(func_def_1047,type,
sK747: $i > $i ).
thf(func_def_1048,type,
sK748: $i > $i ).
thf(func_def_1049,type,
sK749: $i > $i ).
thf(func_def_1050,type,
sK750: $i > $i > $i > $i ).
thf(func_def_1051,type,
sK751: $i > $i ).
thf(func_def_1052,type,
sK752: $i > $i ).
thf(func_def_1053,type,
sK753: $i > $i ).
thf(func_def_1054,type,
sK754: $i > $i ).
thf(func_def_1055,type,
sK755: $i > $i > $i ).
thf(func_def_1056,type,
sK756: $i > $i > $i ).
thf(func_def_1057,type,
sK757: $i > $i > $i > $i ).
thf(func_def_1058,type,
sK758: $i > $i > $i > $i ).
thf(func_def_1059,type,
sK759: $i > $i > $i > $i ).
thf(func_def_1060,type,
sK760: $i > $i > $i ).
thf(func_def_1061,type,
sK761: $i > $i > $i ).
thf(func_def_1062,type,
sK762: $i > $i > $i ).
thf(f110,axiom,
( binintersectEL
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(f122,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f253,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(f254,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f253]) ).
thf(f279,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f110]) ).
thf(f280,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) )
=> ( ( in @ X2 @ X1 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(fool_elimination,[],[f279]) ).
thf(f512,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f254]) ).
thf(f513,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f512]) ).
thf(f572,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) )
= setminusER ),
inference(rectify,[],[f122]) ).
thf(f573,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[],[f572]) ).
thf(f771,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f513]) ).
thf(f779,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f573]) ).
thf(f816,plain,
( ( binintersectEL = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[],[f280]) ).
thf(f824,plain,
( ( setminusER = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f779]) ).
thf(f1067,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f771]) ).
thf(f1068,plain,
( ( subset2powerset = $true )
& ( dsetconstr__Cong = $true )
& ( setminusIRneg = $true )
& ( iffalseProp2 = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( powersetI1 = $true )
& ( setminusELneg = $true )
& ( cartprodpairin = $true )
& ( cartprodpairmemEL = $true )
& ( bs114d = $true )
& ( setextsub = $true )
& ( subsetTI = $true )
& ( exuE3u = $true )
& ( contrasubsetT2 = $true )
& ( kfstsingleton = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( cartprodfstpairEq = $true )
& ( symdiffI1 = $true )
& ( iftrueProp2 = $true )
& ( emptysetsubset = $true )
& ( setukpairIL = $true )
& ( setukpairinjR2 = $true )
& ( upairset2IR = $true )
& ( prop2setE = $true )
& ( setminusERneg = $true )
& ( setadjoin__Cong = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR11 = $true )
& ( binintersectSubset2 = $true )
& ( funcGraphProp2 = $true )
& ( exuE1 = $true )
& ( subbreln = $true )
& ( descrp = $true )
& ( iffalseProp1 = $true )
& ( symdiffIneg1 = $true )
& ( setukpairinjR1 = $true )
& ( omega__Cong = $true )
& ( complementT_lem = $true )
& ( exuI2 = $true )
& ( exuE3e = $true )
& ( eqinunit = $true )
& ( upairsubunion = $true )
& ( nonemptyI1 = $true )
& ( ksndpairEq = $true )
& ( emptyInPowerset = $true )
& ( upairequniteq = $true )
& ( exuEu = $true )
& ( binintersectLsub = $true )
& ( funcGraphProp4 = $true )
& ( kpairp = $true )
& ( powersetI = $true )
& ( brelnall2 = $true )
& ( notsubsetI = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIL = $true )
& ( lamProp = $true )
& ( sepInPowerset = $true )
& ( setminusT_lem = $true )
& ( ubforcartprodlem3 = $true )
& ( binintersectSubset1 = $true )
& ( upairset2E = $true )
& ( powersetAx = $true )
& ( binintersectSubset5 = $true )
& ( symdiffI2 = $true )
& ( kfstpairEq = $true )
& ( complementTI1 = $true )
& ( cartprodfstin = $true )
& ( prop2setI = $true )
& ( complementTE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( powerset__Cong = $true )
& ( theeq = $true )
& ( quantDeMorgan3 = $true )
& ( exuI1 = $true )
& ( notequalI2 = $true )
& ( binintersectRsub = $true )
& ( ap2apEq1 = $true )
& ( exuE2 = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectTELcontra = $true )
& ( inCongP = $true )
& ( binunionLsub = $true )
& ( contrasubsetT1 = $true )
& ( nonemptyImpWitness = $true )
& ( funcGraphProp3 = $true )
& ( ifSingleton = $true )
& ( notinemptyset = $true )
& ( cartprodsndpairEq = $true )
& ( upairinpowunion = $true )
& ( singletonprop = $true )
& ( dsetconstrI = $true )
& ( prop2set2propI = $true )
& ( funcGraphProp1 = $true )
& ( binintersectER = $true )
& ( setminusER = $true )
& ( kpairiskpair = $true )
& ( quantDeMorgan4 = $true )
& ( powersetE1 = $true )
& ( emptysetimpfalse = $true )
& ( setukpairinjR12 = $true )
& ( beta1 = $true )
& ( doubleComplementSub1 = $true )
& ( setadjoinAx = $true )
& ( symdiffE = $true )
& ( nonemptyE1 = $true )
& ( iftrueorfalse = $true )
& ( upairsetIL = $true )
& ( uniqinunit = $true )
& ( symdiffIneg2 = $true )
& ( dpsetconstrEL1 = $true )
& ( notequalI1 = $true )
& ( eqimpsubset2 = $true )
& ( dpsetconstrER = $true )
& ( setadjoinOr = $true )
& ( setminusSubset2 = $true )
& ( funcextLem = $true )
& ( singletoninpowunion = $true )
& ( binunionEcases = $true )
& ( theprop = $true )
& ( setminusILneg = $true )
& ( doubleComplementEq = $true )
& ( iffalse = $true )
& ( descr__Cong = $true )
& ( replAx = $true )
& ( lam2p = $true )
& ( emptysetE = $true )
& ( exu__Cong = $true )
& ( subsetRefl = $true )
& ( kpairsurjEq = $true )
& ( setbeta = $true )
& ( powersetTE1 = $true )
& ( setminusSubset1 = $true )
& ( setukpairinjL1 = $true )
& ( omegaIndAx = $true )
& ( ex1I2 = $true )
& ( ex1E1 = $true )
& ( omegaSAx = $true )
& ( cartprodmempaircEq = $true )
& ( setunionI = $true )
& ( setextAx = $true )
& ( ap2apEq2 = $true )
& ( ap2p = $true )
& ( cartprodsndin = $true )
& ( subsetemptysetimpeq = $true )
& ( dpsetconstrERa = $true )
& ( binintersectI = $true )
& ( setukpairinjL2 = $true )
& ( eqbreln = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectSubset4 = $true )
& ( setext = $true )
& ( funcinfuncset = $true )
& ( apProp = $true )
& ( vacuousDall = $true )
& ( setextT = $true )
& ( binintersectTERcontra = $true )
& ( singletonsuniq = $true )
& ( iftrueProp1 = $true )
& ( setadjoinIR = $true )
& ( app = $true )
& ( subsetI2 = $true )
& ( infuncsetfunc = $true )
& ( setukpairIR = $true )
& ( setunionsingleton2 = $true )
& ( dsetconstrEL = $true )
& ( lamp = $true )
& ( subsetE = $true )
& ( emptysetAx = $true )
& ( contrasubsetT3 = $true )
& ( dsetconstrER = $true )
& ( binunionE = $true )
& ( eta2 = $true )
& ( notdallE = $true )
& ( setunion__Cong = $true )
& ( setukpairinjL = $true )
& ( eqimpsubset1 = $true )
& ( binintersectT_lem = $true )
& ( ex1I = $true )
& ( dpsetconstrSub = $true )
& ( ifp = $true )
& ( subsetI1 = $true )
& ( cartprodmempair1 = $true )
& ( inPowerset = $true )
& ( singletonsubset = $true )
& ( setunionE2 = $true )
& ( setminusLsub = $true )
& ( setunionAx = $true )
& ( doubleComplementSub2 = $true )
& ( notinsingleton = $true )
& ( upairsetE = $true )
& ( lam2lamEq = $true )
& ( contrasubsetT = $true )
& ( singletonsswitch = $true )
& ( ex1E2 = $true )
& ( setminusI = $true )
& ( powersetTI1 = $true )
& ( exuI3 = $true )
& ( powersetT_lem = $true )
& ( foundationAx = $true )
& ( subsetE2 = $true )
& ( setukpairinjR = $true )
& ( sepSubset = $true )
& ( singletoninpowerset = $true )
& ( eta1 = $true )
& ( doubleComplementE1 = $true )
& ( binunionIR = $true )
& ( ubforcartprodlem1 = $true )
& ( disjointsetsI1 = $true )
& ( powersetsubset = $true )
& ( setOfPairsIsBReln = $true )
& ( binunionT_lem = $true )
& ( noeltsimpempty = $true )
& ( subsetTrans = $true )
& ( omega0Ax = $true )
& ( binunionRsub = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( cartprodpairmemER = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( brelnall1 = $true )
& ( powersetE = $true )
& ( beta2 = $true )
& ( dpsetconstrI = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodpairsurjEq = $true )
& ( funcext2 = $true )
& ( setunionsingleton1 = $true )
& ( doubleComplementI1 = $true )
& ( setunionE = $true )
& ( nonemptyI = $true )
& ( setminusEL = $true )
& ( setunionsingleton = $true )
& ( binintersectSubset3 = $true )
& ( emptyinunitempty = $true )
& ( upairsetIR = $true )
& ( binunionIL = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( in__Cong = $true )
& ( cartprodmempair = $true )
& ( notdexE = $true )
& ( funcext = $true )
& ( iftrue = $true ) ),
inference(flattening,[],[f1067]) ).
thf(f1153,plain,
( ( ( binintersectEL = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[],[f816]) ).
thf(f1154,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[],[f1153]) ).
thf(f1155,plain,
( ( ( binintersectEL = $true )
| ( ( ( in @ sK65 @ ( binintersect @ sK66 @ sK67 ) )
= $true )
& ( ( in @ sK65 @ sK66 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65,sK66,sK67]),skolemize(X0,sK65),skolemize(X1,sK66),skolemize(X2,sK67)],[f1154]) ).
thf(f1406,plain,
( ( ( setminusER = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[],[f824]) ).
thf(f1407,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(rectify,[],[f1406]) ).
thf(f1408,plain,
( ( ( setminusER = $true )
| ( ( ( in @ sK328 @ sK327 )
= $true )
& ( ( in @ sK328 @ ( setminus @ sK329 @ sK327 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK327,sK328,sK329]),skolemize(X0,sK327),skolemize(X1,sK328),skolemize(X2,sK329)],[f1407]) ).
thf(f1551,plain,
( ( subset2powerset = $true )
& ( dsetconstr__Cong = $true )
& ( setminusIRneg = $true )
& ( iffalseProp2 = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( powersetI1 = $true )
& ( setminusELneg = $true )
& ( cartprodpairin = $true )
& ( cartprodpairmemEL = $true )
& ( bs114d = $true )
& ( setextsub = $true )
& ( subsetTI = $true )
& ( exuE3u = $true )
& ( contrasubsetT2 = $true )
& ( kfstsingleton = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( cartprodfstpairEq = $true )
& ( symdiffI1 = $true )
& ( iftrueProp2 = $true )
& ( emptysetsubset = $true )
& ( setukpairIL = $true )
& ( setukpairinjR2 = $true )
& ( upairset2IR = $true )
& ( prop2setE = $true )
& ( setminusERneg = $true )
& ( setadjoin__Cong = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR11 = $true )
& ( binintersectSubset2 = $true )
& ( funcGraphProp2 = $true )
& ( exuE1 = $true )
& ( subbreln = $true )
& ( descrp = $true )
& ( iffalseProp1 = $true )
& ( symdiffIneg1 = $true )
& ( setukpairinjR1 = $true )
& ( omega__Cong = $true )
& ( complementT_lem = $true )
& ( exuI2 = $true )
& ( exuE3e = $true )
& ( eqinunit = $true )
& ( upairsubunion = $true )
& ( nonemptyI1 = $true )
& ( ksndpairEq = $true )
& ( emptyInPowerset = $true )
& ( upairequniteq = $true )
& ( exuEu = $true )
& ( binintersectLsub = $true )
& ( funcGraphProp4 = $true )
& ( kpairp = $true )
& ( powersetI = $true )
& ( brelnall2 = $true )
& ( notsubsetI = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIL = $true )
& ( lamProp = $true )
& ( sepInPowerset = $true )
& ( setminusT_lem = $true )
& ( ubforcartprodlem3 = $true )
& ( binintersectSubset1 = $true )
& ( upairset2E = $true )
& ( powersetAx = $true )
& ( binintersectSubset5 = $true )
& ( symdiffI2 = $true )
& ( kfstpairEq = $true )
& ( complementTI1 = $true )
& ( cartprodfstin = $true )
& ( prop2setI = $true )
& ( complementTE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( powerset__Cong = $true )
& ( theeq = $true )
& ( quantDeMorgan3 = $true )
& ( exuI1 = $true )
& ( notequalI2 = $true )
& ( binintersectRsub = $true )
& ( ap2apEq1 = $true )
& ( exuE2 = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectTELcontra = $true )
& ( inCongP = $true )
& ( binunionLsub = $true )
& ( contrasubsetT1 = $true )
& ( nonemptyImpWitness = $true )
& ( funcGraphProp3 = $true )
& ( ifSingleton = $true )
& ( notinemptyset = $true )
& ( cartprodsndpairEq = $true )
& ( upairinpowunion = $true )
& ( singletonprop = $true )
& ( dsetconstrI = $true )
& ( prop2set2propI = $true )
& ( funcGraphProp1 = $true )
& ( binintersectER = $true )
& ( setminusER = $true )
& ( kpairiskpair = $true )
& ( quantDeMorgan4 = $true )
& ( powersetE1 = $true )
& ( emptysetimpfalse = $true )
& ( setukpairinjR12 = $true )
& ( beta1 = $true )
& ( doubleComplementSub1 = $true )
& ( setadjoinAx = $true )
& ( symdiffE = $true )
& ( nonemptyE1 = $true )
& ( iftrueorfalse = $true )
& ( upairsetIL = $true )
& ( uniqinunit = $true )
& ( symdiffIneg2 = $true )
& ( dpsetconstrEL1 = $true )
& ( notequalI1 = $true )
& ( eqimpsubset2 = $true )
& ( dpsetconstrER = $true )
& ( setadjoinOr = $true )
& ( setminusSubset2 = $true )
& ( funcextLem = $true )
& ( singletoninpowunion = $true )
& ( binunionEcases = $true )
& ( theprop = $true )
& ( setminusILneg = $true )
& ( doubleComplementEq = $true )
& ( iffalse = $true )
& ( descr__Cong = $true )
& ( replAx = $true )
& ( lam2p = $true )
& ( emptysetE = $true )
& ( exu__Cong = $true )
& ( subsetRefl = $true )
& ( kpairsurjEq = $true )
& ( setbeta = $true )
& ( powersetTE1 = $true )
& ( setminusSubset1 = $true )
& ( setukpairinjL1 = $true )
& ( omegaIndAx = $true )
& ( ex1I2 = $true )
& ( ex1E1 = $true )
& ( omegaSAx = $true )
& ( cartprodmempaircEq = $true )
& ( setunionI = $true )
& ( setextAx = $true )
& ( ap2apEq2 = $true )
& ( ap2p = $true )
& ( cartprodsndin = $true )
& ( subsetemptysetimpeq = $true )
& ( dpsetconstrERa = $true )
& ( binintersectI = $true )
& ( setukpairinjL2 = $true )
& ( eqbreln = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectSubset4 = $true )
& ( setext = $true )
& ( funcinfuncset = $true )
& ( apProp = $true )
& ( vacuousDall = $true )
& ( setextT = $true )
& ( binintersectTERcontra = $true )
& ( singletonsuniq = $true )
& ( iftrueProp1 = $true )
& ( setadjoinIR = $true )
& ( app = $true )
& ( subsetI2 = $true )
& ( infuncsetfunc = $true )
& ( setukpairIR = $true )
& ( setunionsingleton2 = $true )
& ( dsetconstrEL = $true )
& ( lamp = $true )
& ( subsetE = $true )
& ( emptysetAx = $true )
& ( contrasubsetT3 = $true )
& ( dsetconstrER = $true )
& ( binunionE = $true )
& ( eta2 = $true )
& ( notdallE = $true )
& ( setunion__Cong = $true )
& ( setukpairinjL = $true )
& ( eqimpsubset1 = $true )
& ( binintersectT_lem = $true )
& ( ex1I = $true )
& ( dpsetconstrSub = $true )
& ( ifp = $true )
& ( subsetI1 = $true )
& ( cartprodmempair1 = $true )
& ( inPowerset = $true )
& ( singletonsubset = $true )
& ( setunionE2 = $true )
& ( setminusLsub = $true )
& ( setunionAx = $true )
& ( doubleComplementSub2 = $true )
& ( notinsingleton = $true )
& ( upairsetE = $true )
& ( lam2lamEq = $true )
& ( contrasubsetT = $true )
& ( singletonsswitch = $true )
& ( ex1E2 = $true )
& ( setminusI = $true )
& ( powersetTI1 = $true )
& ( exuI3 = $true )
& ( powersetT_lem = $true )
& ( foundationAx = $true )
& ( subsetE2 = $true )
& ( setukpairinjR = $true )
& ( sepSubset = $true )
& ( singletoninpowerset = $true )
& ( eta1 = $true )
& ( doubleComplementE1 = $true )
& ( binunionIR = $true )
& ( ubforcartprodlem1 = $true )
& ( disjointsetsI1 = $true )
& ( powersetsubset = $true )
& ( setOfPairsIsBReln = $true )
& ( binunionT_lem = $true )
& ( noeltsimpempty = $true )
& ( subsetTrans = $true )
& ( omega0Ax = $true )
& ( binunionRsub = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( cartprodpairmemER = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( brelnall1 = $true )
& ( powersetE = $true )
& ( beta2 = $true )
& ( dpsetconstrI = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodpairsurjEq = $true )
& ( funcext2 = $true )
& ( setunionsingleton1 = $true )
& ( doubleComplementI1 = $true )
& ( setunionE = $true )
& ( nonemptyI = $true )
& ( setminusEL = $true )
& ( setunionsingleton = $true )
& ( binintersectSubset3 = $true )
& ( emptyinunitempty = $true )
& ( upairsetIR = $true )
& ( binunionIL = $true )
& ( $true
= ( in @ sK493 @ ( powerset @ sK492 ) ) )
& ( ( in @ sK494 @ ( binintersect @ sK491 @ sK493 ) )
= $true )
& ( ( in @ sK494 @ ( setminus @ sK492 @ sK491 ) )
= $true )
& ( ( in @ sK494 @ sK492 )
= $true )
& ( ( in @ sK491 @ ( powerset @ sK492 ) )
= $true )
& ( in__Cong = $true )
& ( cartprodmempair = $true )
& ( notdexE = $true )
& ( funcext = $true )
& ( iftrue = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK491,sK492,sK493,sK494]),skolemize(X0,sK491),skolemize(X1,sK492),skolemize(X2,sK493),skolemize(X3,sK494)],[f1068]) ).
thf(f1908,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( binintersectEL != $true )
| ( ( in @ X3 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f1155]) ).
thf(f2253,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( setminusER != $true )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true ) ),
inference(cnf_transformation,[],[f1408]) ).
thf(f2475,plain,
( ( in @ sK494 @ ( setminus @ sK492 @ sK491 ) )
= $true ),
inference(cnf_transformation,[],[f1551]) ).
thf(f2476,plain,
( ( in @ sK494 @ ( binintersect @ sK491 @ sK493 ) )
= $true ),
inference(cnf_transformation,[],[f1551]) ).
thf(f2622,plain,
setminusER = $true,
inference(cnf_transformation,[],[f1551]) ).
thf(f2648,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f1551]) ).
thf(f3348,definition,
( spl777_1
<=> ( binintersectEL = $true ) ),
introduced(definition,[new_symbols(definition,[spl777_1])],[avatar_definition]) ).
thf(f3351,plain,
spl777_1,
inference(avatar_split_clause,[],[f2648,f3348]) ).
thf(f4114,definition,
( spl777_175
<=> ( setminusER = $true ) ),
introduced(definition,[new_symbols(definition,[spl777_175])],[avatar_definition]) ).
thf(f4995,definition,
( spl777_367
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl777_367])],[avatar_definition]) ).
thf(f4996,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ~ spl777_367 ),
inference(avatar_component_clause,[],[f4995]) ).
thf(f6466,plain,
( spl777_367
| ~ spl777_175 ),
inference(avatar_split_clause,[],[f2253,f4114,f4995]) ).
thf(f7478,definition,
( spl777_896
<=> ( ( in @ sK494 @ ( binintersect @ sK491 @ sK493 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl777_896])],[avatar_definition]) ).
thf(f7480,plain,
( ( ( in @ sK494 @ ( binintersect @ sK491 @ sK493 ) )
= $true )
| ~ spl777_896 ),
inference(avatar_component_clause,[],[f7478]) ).
thf(f7481,plain,
spl777_896,
inference(avatar_split_clause,[],[f2476,f7478]) ).
thf(f7504,plain,
spl777_175,
inference(avatar_split_clause,[],[f2622,f4114]) ).
thf(f8623,definition,
( spl777_1131
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl777_1131])],[avatar_definition]) ).
thf(f8624,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) )
| ~ spl777_1131 ),
inference(avatar_component_clause,[],[f8623]) ).
thf(f8625,plain,
( spl777_1131
| ~ spl777_1 ),
inference(avatar_split_clause,[],[f1908,f3348,f8623]) ).
thf(f8809,definition,
( spl777_1168
<=> ( ( in @ sK494 @ ( setminus @ sK492 @ sK491 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl777_1168])],[avatar_definition]) ).
thf(f8811,plain,
( ( ( in @ sK494 @ ( setminus @ sK492 @ sK491 ) )
= $true )
| ~ spl777_1168 ),
inference(avatar_component_clause,[],[f8809]) ).
thf(f8812,plain,
spl777_1168,
inference(avatar_split_clause,[],[f2475,f8809]) ).
thf(f9208,plain,
( ( $true != $true )
| ( ( in @ sK494 @ sK491 )
!= $true )
| ~ spl777_367
| ~ spl777_1168 ),
inference(superposition,[],[f4996,f8811]) ).
thf(f9209,plain,
( ( ( in @ sK494 @ sK491 )
!= $true )
| ~ spl777_367
| ~ spl777_1168 ),
inference(trivial_inequality_removal,[],[f9208]) ).
thf(f9211,definition,
( spl777_1238
<=> ( ( in @ sK494 @ sK491 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl777_1238])],[avatar_definition]) ).
thf(f9213,plain,
( ( ( in @ sK494 @ sK491 )
!= $true )
| spl777_1238 ),
inference(avatar_component_clause,[],[f9211]) ).
thf(f9214,plain,
( ~ spl777_1238
| ~ spl777_367
| ~ spl777_1168 ),
inference(avatar_split_clause,[],[f9209,f8809,f4995,f9211]) ).
thf(f10092,plain,
( ( ( in @ sK494 @ sK491 )
= $true )
| ( $true != $true )
| ~ spl777_896
| ~ spl777_1131 ),
inference(superposition,[],[f8624,f7480]) ).
thf(f10102,plain,
( ( ( in @ sK494 @ sK491 )
= $true )
| ~ spl777_896
| ~ spl777_1131 ),
inference(trivial_inequality_removal,[],[f10092]) ).
thf(f10104,plain,
( $false
| ~ spl777_896
| ~ spl777_1131
| spl777_1238 ),
inference(forward_subsumption_resolution,[],[f10102,f9213]) ).
thf(f10105,plain,
( ~ spl777_896
| ~ spl777_1131
| spl777_1238 ),
inference(avatar_contradiction_clause,[],[f10104]) ).
cnf(s1,plain,
spl777_1,
inference(sat_conversion,[],[f3351]) ).
cnf(s571,plain,
( ~ spl777_175
| spl777_367 ),
inference(sat_conversion,[],[f6466]) ).
cnf(s819,plain,
spl777_896,
inference(sat_conversion,[],[f7481]) ).
cnf(s825,plain,
spl777_175,
inference(sat_conversion,[],[f7504]) ).
cnf(s1115,plain,
( ~ spl777_1
| spl777_1131 ),
inference(sat_conversion,[],[f8625]) ).
cnf(s1169,plain,
spl777_1168,
inference(sat_conversion,[],[f8812]) ).
cnf(s1263,plain,
( ~ spl777_367
| ~ spl777_1168
| ~ spl777_1238 ),
inference(sat_conversion,[],[f9214]) ).
cnf(s1299,plain,
( ~ spl777_896
| ~ spl777_1131
| spl777_1238 ),
inference(sat_conversion,[],[f10105]) ).
cnf(s1397,plain,
spl777_367,
inference(rat,[],[s571,s825]) ).
cnf(s1398,plain,
~ spl777_1238,
inference(rat,[],[s1263,s1169,s1397]) ).
cnf(s1399,plain,
~ spl777_1131,
inference(rat,[],[s1299,s819,s1398]) ).
cnf(s1400,plain,
~ spl777_1,
inference(rat,[],[s1115,s1399]) ).
cnf(s1643,plain,
$false,
inference(rat,[],[s1,s1400]) ).
thf(f10107,plain,
$false,
inference(avatar_sat_refutation,[],[s1643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU732^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:17:48 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.23/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.06/0.51 % (842238)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.06/0.51 % (842258)lrs+10_16_si=on:nwc=1.5:random_seed=3057359386:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.06/0.51 % (842263)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.06/0.51 % (842263)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.06/0.51 % (842258)Instruction limit reached!
% 1.06/0.51 % (842258)------------------------------
% 1.06/0.51 % (842258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (842258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.51 % (842258)CaDiCaL version: 2.1.3
% 1.06/0.51 % (842258)Termination reason: Instruction limit
% 1.06/0.51 % (842258)Termination phase: shuffling
% 1.06/0.51 % (842258)Time elapsed: 0.010 s
% 1.06/0.51 % (842258)Peak memory usage: 10 MB
% 1.06/0.51 % (842258)Instructions burned: 20 (million)
% 1.06/0.51 % (842262)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=397235658:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.06/0.51 % (842257)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2295927433:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.06/0.51 % (842261)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3256334052:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.06/0.51 % (842260)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=134655049: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)
% 1.06/0.51 % (842263)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=231284914:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.06/0.51 % (842259)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3938496641:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.06/0.51 % (842259)Instruction limit reached!
% 1.06/0.51 % (842259)------------------------------
% 1.06/0.51 % (842259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (842259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.51 % (842259)CaDiCaL version: 2.1.3
% 1.06/0.51 % (842259)Termination reason: Instruction limit
% 1.06/0.51 % (842259)Termination phase: shuffling
% 1.06/0.51 % (842259)Time elapsed: 0.005 s
% 1.06/0.51 % (842259)Peak memory usage: 10 MB
% 1.06/0.51 % (842259)Instructions burned: 5 (million)
% 1.06/0.51 % (842261)Instruction limit reached!
% 1.06/0.51 % (842261)------------------------------
% 1.06/0.51 % (842261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (842261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.51 % (842261)CaDiCaL version: 2.1.3
% 1.06/0.51 % (842261)Termination reason: Instruction limit
% 1.06/0.51 % (842261)Termination phase: Property scanning
% 1.06/0.51 % (842261)Time elapsed: 0.021 s
% 1.06/0.51 % (842261)Peak memory usage: 11 MB
% 1.06/0.51 % (842261)Instructions burned: 24 (million)
% 1.06/0.51 % (842279)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1425105281:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.06/0.51 % (842279)Instruction limit reached!
% 1.06/0.51 % (842279)------------------------------
% 1.06/0.51 % (842279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (842279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.51 % (842279)CaDiCaL version: 2.1.3
% 1.06/0.51 % (842279)Termination reason: Instruction limit
% 1.06/0.51 % (842279)Termination phase: shuffling
% 1.06/0.51 % (842279)Time elapsed: 0.002 s
% 1.06/0.51 % (842279)Peak memory usage: 10 MB
% 1.06/0.51 % (842279)Instructions burned: 4 (million)
% 1.06/0.51 % (842281)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=386002356:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.06/0.51 % (842281)Instruction limit reached!
% 1.06/0.58 % (842281)------------------------------
% 1.06/0.58 % (842281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.58 % (842281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.58 % (842281)CaDiCaL version: 2.1.3
% 1.06/0.58 % (842281)Termination reason: Instruction limit
% 1.06/0.58 % (842281)Termination phase: shuffling
% 1.06/0.58 % (842281)Time elapsed: 0.004 s
% 1.06/0.58 % (842281)Peak memory usage: 10 MB
% 1.06/0.58 % (842281)Instructions burned: 6 (million)
% 1.06/0.58 % (842286)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=548731783:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.06/0.58 % (842285)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.06/0.58 % (842286)Instruction limit reached!
% 1.06/0.58 % (842286)------------------------------
% 1.06/0.58 % (842286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.58 % (842286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.58 % (842286)CaDiCaL version: 2.1.3
% 1.06/0.58 % (842286)Termination reason: Instruction limit
% 1.06/0.58 % (842286)Termination phase: shuffling
% 1.06/0.58 % (842286)Time elapsed: 0.006 s
% 1.06/0.58 % (842286)Peak memory usage: 10 MB
% 1.06/0.58 % (842286)Instructions burned: 13 (million)
% 1.06/0.58 % (842285)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4110799245:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.06/0.58 % (842288)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.06/0.58 % (842288)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.06/0.58 % (842262)Instruction limit reached!
% 1.06/0.58 % (842262)------------------------------
% 1.06/0.58 % (842262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.58 % (842262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.58 % (842262)CaDiCaL version: 2.1.3
% 1.06/0.58 % (842262)Termination reason: Instruction limit
% 1.06/0.58 % (842262)Termination phase: Preprocessing 3
% 1.06/0.58 % (842262)Time elapsed: 0.062 s
% 1.06/0.58 % (842262)Peak memory usage: 12 MB
% 1.06/0.58 % (842262)Instructions burned: 76 (million)
% 1.06/0.58 % (842285)Instruction limit reached!
% 1.06/0.58 % (842285)------------------------------
% 1.06/0.58 % (842285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.58 % (842285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.58 % (842285)CaDiCaL version: 2.1.3
% 1.06/0.58 % (842285)Termination reason: Instruction limit
% 1.06/0.58 % (842285)Termination phase: shuffling
% 1.06/0.58 % (842285)Time elapsed: 0.006 s
% 1.06/0.58 % (842285)Peak memory usage: 10 MB
% 1.06/0.58 % (842285)Instructions burned: 7 (million)
% 1.06/0.58 % (842288)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1033888307:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.06/0.58 % (842291)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=785245973:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.06/0.58 % (842257)Instruction limit reached!
% 1.06/0.58 % (842257)------------------------------
% 1.06/0.58 % (842257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.58 % (842257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.58 % (842257)CaDiCaL version: 2.1.3
% 1.06/0.58 % (842257)Termination reason: Instruction limit
% 1.06/0.58 % (842257)Termination phase: Preprocessing 3
% 1.06/0.58 % (842257)Time elapsed: 0.075 s
% 1.06/0.58 % (842257)Peak memory usage: 13 MB
% 1.06/0.58 % (842257)Instructions burned: 87 (million)
% 1.06/0.58 % (842294)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.06/0.58 % (842294)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=3993827590:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.05/0.63 % (842293)lrs+10_1_si=on:cs=on:random_seed=4058991964:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.05/0.63 % (842294)Instruction limit reached!
% 2.05/0.63 % (842294)------------------------------
% 2.05/0.63 % (842294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.05/0.63 % (842294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.63 % (842294)CaDiCaL version: 2.1.3
% 2.05/0.63 % (842294)Termination reason: Instruction limit
% 2.05/0.63 % (842294)Termination phase: shuffling
% 2.05/0.63 % (842294)Time elapsed: 0.003 s
% 2.05/0.63 % (842294)Peak memory usage: 10 MB
% 2.05/0.63 % (842294)Instructions burned: 3 (million)
% 2.05/0.63 % (842288)Instruction limit reached!
% 2.05/0.63 % (842288)------------------------------
% 2.05/0.63 % (842288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.05/0.63 % (842288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.63 % (842288)CaDiCaL version: 2.1.3
% 2.05/0.63 % (842288)Termination reason: Instruction limit
% 2.05/0.63 % (842288)Termination phase: shuffling
% 2.05/0.63 % (842288)Time elapsed: 0.039 s
% 2.05/0.63 % (842288)Peak memory usage: 11 MB
% 2.05/0.63 % (842288)Instructions burned: 28 (million)
% 2.05/0.63 % (842293)Instruction limit reached!
% 2.05/0.63 % (842293)------------------------------
% 2.05/0.63 % (842293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.05/0.63 % (842293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.63 % (842293)CaDiCaL version: 2.1.3
% 2.05/0.63 % (842293)Termination reason: Instruction limit
% 2.05/0.63 % (842293)Termination phase: shuffling
% 2.05/0.63 % (842293)Time elapsed: 0.008 s
% 2.05/0.63 % (842293)Peak memory usage: 10 MB
% 2.05/0.63 % (842293)Instructions burned: 8 (million)
% 2.05/0.63 % (842291)Instruction limit reached!
% 2.05/0.63 % (842291)------------------------------
% 2.05/0.63 % (842291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.05/0.63 % (842291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.63 % (842291)CaDiCaL version: 2.1.3
% 2.05/0.63 % (842291)Termination reason: Instruction limit
% 2.05/0.63 % (842291)Termination phase: Property scanning
% 2.05/0.63 % (842291)Time elapsed: 0.035 s
% 2.05/0.63 % (842291)Peak memory usage: 11 MB
% 2.05/0.63 % (842291)Instructions burned: 88 (million)
% 2.05/0.63 % (842299)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1873956901:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 2.05/0.63 % (842306)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2128928437:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 2.05/0.63 % (842263)Instruction limit reached!
% 2.05/0.63 % (842263)------------------------------
% 2.05/0.63 % (842263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.05/0.63 % (842263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.63 % (842263)CaDiCaL version: 2.1.3
% 2.05/0.63 % (842263)Termination reason: Instruction limit
% 2.05/0.63 % (842263)Termination phase: Saturation
% 2.05/0.63 % (842263)Time elapsed: 0.124 s
% 2.05/0.63 % (842263)Peak memory usage: 13 MB
% 2.05/0.63 % (842263)Instructions burned: 157 (million)
% 2.05/0.63 % (842308)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2328030469:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 2.05/0.63 % (842309)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=84940993:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.05/0.63 % (842310)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=290529694:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.05/0.63 % (842299)Instruction limit reached!
% 2.05/0.63 % (842299)------------------------------
% 2.05/0.63 % (842299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.05/0.63 % (842299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.63 % (842299)CaDiCaL version: 2.1.3
% 2.05/0.63 % (842299)Termination reason: Instruction limit
% 2.05/0.63 % (842299)Termination phase: SInE selection
% 2.05/0.63 % (842299)Time elapsed: 0.031 s
% 2.51/0.72 % (842299)Peak memory usage: 11 MB
% 2.51/0.72 % (842299)Instructions burned: 39 (million)
% 2.51/0.72 % (842309)Instruction limit reached!
% 2.51/0.72 % (842309)------------------------------
% 2.51/0.72 % (842309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842309)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842309)Termination reason: Instruction limit
% 2.51/0.72 % (842309)Termination phase: shuffling
% 2.51/0.72 % (842309)Time elapsed: 0.013 s
% 2.51/0.72 % (842309)Peak memory usage: 10 MB
% 2.51/0.72 % (842309)Instructions burned: 14 (million)
% 2.51/0.72 % (842308)Instruction limit reached!
% 2.51/0.72 % (842308)------------------------------
% 2.51/0.72 % (842308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842308)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842308)Termination reason: Instruction limit
% 2.51/0.72 % (842308)Termination phase: Property scanning
% 2.51/0.72 % (842308)Time elapsed: 0.022 s
% 2.51/0.72 % (842308)Peak memory usage: 10 MB
% 2.51/0.72 % (842308)Instructions burned: 26 (million)
% 2.51/0.72 % (842315)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=291797040:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.51/0.72 % (842319)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1949689124:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 2.51/0.72 % (842315)Instruction limit reached!
% 2.51/0.72 % (842315)------------------------------
% 2.51/0.72 % (842315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842315)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842315)Termination reason: Instruction limit
% 2.51/0.72 % (842315)Termination phase: shuffling
% 2.51/0.72 % (842315)Time elapsed: 0.012 s
% 2.51/0.72 % (842315)Peak memory usage: 10 MB
% 2.51/0.72 % (842315)Instructions burned: 14 (million)
% 2.51/0.72 % (842322)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=868861843:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.51/0.72 % (842319)Instruction limit reached!
% 2.51/0.72 % (842319)------------------------------
% 2.51/0.72 % (842319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842319)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842319)Termination reason: Instruction limit
% 2.51/0.72 % (842319)Termination phase: shuffling
% 2.51/0.72 % (842319)Time elapsed: 0.003 s
% 2.51/0.72 % (842319)Peak memory usage: 10 MB
% 2.51/0.72 % (842319)Instructions burned: 3 (million)
% 2.51/0.72 % (842324)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4285896037:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.51/0.72 % (842322)Instruction limit reached!
% 2.51/0.72 % (842322)------------------------------
% 2.51/0.72 % (842322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842322)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842322)Termination reason: Instruction limit
% 2.51/0.72 % (842322)Termination phase: shuffling
% 2.51/0.72 % (842322)Time elapsed: 0.024 s
% 2.51/0.72 % (842322)Peak memory usage: 10 MB
% 2.51/0.72 % (842322)Instructions burned: 26 (million)
% 2.51/0.72 % (842328)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.51/0.72 % (842328)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.51/0.72 % (842326)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=95828781:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.51/0.72 % (842328)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=710028124:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.51/0.72 % (842324)Instruction limit reached!
% 2.51/0.72 % (842324)------------------------------
% 2.51/0.72 % (842324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842324)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842324)Termination reason: Instruction limit
% 2.51/0.72 % (842324)Termination phase: shuffling
% 2.51/0.72 % (842324)Time elapsed: 0.021 s
% 2.51/0.72 % (842324)Peak memory usage: 10 MB
% 2.51/0.72 % (842324)Instructions burned: 23 (million)
% 2.51/0.72 % (842328)Instruction limit reached!
% 2.51/0.72 % (842328)------------------------------
% 2.51/0.72 % (842328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842328)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842328)Termination reason: Instruction limit
% 2.51/0.72 % (842328)Termination phase: shuffling
% 2.51/0.72 % (842328)Time elapsed: 0.013 s
% 2.51/0.72 % (842328)Peak memory usage: 10 MB
% 2.51/0.72 % (842328)Instructions burned: 14 (million)
% 2.51/0.72 % (842306)Instruction limit reached!
% 2.51/0.72 % (842306)------------------------------
% 2.51/0.72 % (842306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842306)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842306)Termination reason: Instruction limit
% 2.51/0.72 % (842306)Termination phase: Saturation
% 2.51/0.72 % (842306)Time elapsed: 0.108 s
% 2.51/0.72 % (842306)Peak memory usage: 15 MB
% 2.51/0.72 % (842306)Instructions burned: 251 (million)
% 2.51/0.72 % (842331)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.51/0.72 % (842331)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=4000047348:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.51/0.72 % (842337)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3229593440:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.51/0.72 % (842331)Instruction limit reached!
% 2.51/0.72 % (842331)------------------------------
% 2.51/0.72 % (842331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842331)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842331)Termination reason: Instruction limit
% 2.51/0.72 % (842331)Termination phase: shuffling
% 2.51/0.72 % (842331)Time elapsed: 0.008 s
% 2.51/0.72 % (842331)Peak memory usage: 10 MB
% 2.51/0.72 % (842331)Instructions burned: 8 (million)
% 2.51/0.72 % (842334)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=137230566:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.51/0.72 % (842336)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1709869133:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.51/0.72 % (842337)Instruction limit reached!
% 2.51/0.72 % (842337)------------------------------
% 2.51/0.72 % (842337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842337)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842337)Termination reason: Instruction limit
% 2.51/0.72 % (842337)Termination phase: shuffling
% 2.51/0.72 % (842337)Time elapsed: 0.011 s
% 2.51/0.72 % (842337)Peak memory usage: 11 MB
% 2.51/0.72 % (842337)Instructions burned: 24 (million)
% 2.51/0.72 % (842326)Instruction limit reached!
% 2.51/0.72 % (842326)------------------------------
% 2.51/0.72 % (842326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842326)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842326)Termination reason: Instruction limit
% 2.51/0.72 % (842326)Termination phase: Preprocessing 3
% 2.51/0.72 % (842326)Time elapsed: 0.053 s
% 2.51/0.72 % (842326)Peak memory usage: 12 MB
% 2.51/0.72 % (842326)Instructions burned: 60 (million)
% 2.51/0.72 % (842336)Instruction limit reached!
% 2.51/0.72 % (842336)------------------------------
% 2.51/0.72 % (842336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842336)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842336)Termination reason: Instruction limit
% 2.51/0.72 % (842336)Termination phase: shuffling
% 2.51/0.72 % (842336)Time elapsed: 0.007 s
% 2.51/0.72 % (842336)Peak memory usage: 10 MB
% 2.51/0.72 % (842336)Instructions burned: 7 (million)
% 2.51/0.72 % (842340)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3827270475:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/20Mi)
% 2.51/0.72 % (842334)Instruction limit reached!
% 2.51/0.72 % (842334)------------------------------
% 2.51/0.72 % (842334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842334)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842334)Termination reason: Instruction limit
% 2.51/0.72 % (842334)Termination phase: shuffling
% 2.51/0.72 % (842334)Time elapsed: 0.027 s
% 2.51/0.72 % (842334)Peak memory usage: 11 MB
% 2.51/0.72 % (842334)Instructions burned: 31 (million)
% 2.51/0.72 % (842344)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1468149303:i=1240:rtra=on:ixr=off_2996 on theBenchmark for (2996ds/1240Mi)
% 2.51/0.72 % (842340)Instruction limit reached!
% 2.51/0.72 % (842340)------------------------------
% 2.51/0.72 % (842340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842340)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842340)Termination reason: Instruction limit
% 2.51/0.72 % (842340)Termination phase: shuffling
% 2.51/0.72 % (842340)Time elapsed: 0.020 s
% 2.51/0.72 % (842340)Peak memory usage: 11 MB
% 2.51/0.72 % (842340)Instructions burned: 22 (million)
% 2.51/0.72 % (842345)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=874759203:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2996 on theBenchmark for (2996ds/143Mi)
% 2.51/0.72 % (842346)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2975599871:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/193Mi)
% 2.51/0.72 % (842349)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3259594466:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 2.51/0.72 % (842350)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.51/0.72 % (842350)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2258185391:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 2.51/0.72 % (842350)Instruction limit reached!
% 2.51/0.72 % (842350)------------------------------
% 2.51/0.72 % (842350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842350)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842350)Termination reason: Instruction limit
% 2.51/0.72 % (842350)Termination phase: shuffling
% 2.51/0.72 % (842350)Time elapsed: 0.007 s
% 2.51/0.72 % (842350)Peak memory usage: 10 MB
% 2.51/0.72 % (842350)Instructions burned: 8 (million)
% 2.51/0.72 % (842260) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-842238-842260"...
% 2.51/0.72 % (842349)Instruction limit reached!
% 2.51/0.72 % (842349)------------------------------
% 2.51/0.72 % (842349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.72 % (842349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.72 % (842349)CaDiCaL version: 2.1.3
% 2.51/0.72 % (842349)Termination reason: Instruction limit
% 2.51/0.72 % (842349)Termination phase: Property scanning
% 2.51/0.72 % (842349)Time elapsed: 0.036 s
% 2.51/0.72 % (842349)Peak memory usage: 11 MB
% 2.51/0.72 % (842349)Instructions burned: 42 (million)
% 2.51/0.72 % (842260)...printing done.
% 2.51/0.72 % (842260)Refutation found. Thanks to Tanya!
% 2.51/0.72 % SZS status Theorem for theBenchmark
% 2.51/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/0.73 % (842260)------------------------------
% 2.51/0.73 % (842260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.73 % (842260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.73 % (842260)CaDiCaL version: 2.1.3
% 2.51/0.73 % (842260)Termination reason: Refutation
% 2.51/0.73 % (842260)Time elapsed: 0.347 s
% 2.51/0.73 % (842260)Peak memory usage: 20 MB
% 2.51/0.73 % (842260)Instructions burned: 389 (million)
% 2.51/0.73 % (842238)Success in time 0.422 s
% 2.51/0.73 % Vampire exiting
%------------------------------------------------------------------------------