%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU731^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 08:33:09 AM UTC 2026
% Result : Theorem 6.53s 1.28s
% Output : Refutation 6.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 108 ( 55 unt; 0 typ; 8 def)
% Number of atoms : 4350 (1181 equ; 0 cnn)
% Maximal formula atoms : 249 ( 40 avg)
% Number of connectives : 2546 ( 8 ~; 56 |; 744 &; 642 @)
% ( 0 <=>;1040 =>; 0 <=; 0 <~>)
% Maximal formula depth : 254 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 934 ( 930 usr; 509 con; 0-4 aty)
% ( 56 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 144 ( 64 ^; 76 !; 4 ?; 144 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_287,type,
vAND: $o > $o > $o ).
thf(func_def_288,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_289,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_290,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_291,type,
vIMP: $o > $o > $o ).
thf(func_def_292,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_293,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_294,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_295,type,
vIFF: $o > $o > $o ).
thf(func_def_296,type,
vNOT: $o > $o ).
thf(func_def_297,type,
vOR: $o > $o > $o ).
thf(func_def_298,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_299,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_302,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_305,type,
sF2: $o ).
thf(func_def_306,type,
sF3: $o ).
thf(func_def_307,type,
sF4: $o ).
thf(func_def_308,type,
sF5: $o ).
thf(func_def_309,type,
sF6: $o ).
thf(func_def_310,type,
sF7: $o ).
thf(func_def_311,type,
sF8: $o ).
thf(func_def_312,type,
sF9: $o ).
thf(func_def_313,type,
sF10: $o ).
thf(func_def_314,type,
sF11: $o ).
thf(func_def_315,type,
sF12: $o ).
thf(func_def_316,type,
sF13: $o ).
thf(func_def_317,type,
sF14: $o ).
thf(func_def_318,type,
sF15: $o ).
thf(func_def_319,type,
sF16: $o ).
thf(func_def_320,type,
sF17: $o ).
thf(func_def_321,type,
sF18: $o ).
thf(func_def_322,type,
sF19: $o ).
thf(func_def_323,type,
sF20: $o ).
thf(func_def_324,type,
sF21: $o ).
thf(func_def_325,type,
sF22: $o ).
thf(func_def_326,type,
sF23: $o ).
thf(func_def_327,type,
sF24: $o ).
thf(func_def_328,type,
sF25: $o ).
thf(func_def_329,type,
sF26: $o ).
thf(func_def_330,type,
sF27: $o ).
thf(func_def_331,type,
sF28: $o ).
thf(func_def_332,type,
sF29: $o ).
thf(func_def_334,type,
sF31: $o ).
thf(func_def_335,type,
sF32: $o ).
thf(func_def_336,type,
sF33: $o ).
thf(func_def_337,type,
sF34: $o ).
thf(func_def_338,type,
sF35: $o ).
thf(func_def_339,type,
sF36: $o ).
thf(func_def_340,type,
sF37: $o ).
thf(func_def_341,type,
sF38: $o ).
thf(func_def_342,type,
sF39: $o ).
thf(func_def_343,type,
sF40: $o ).
thf(func_def_344,type,
sF41: $o ).
thf(func_def_345,type,
sF42: $o ).
thf(func_def_346,type,
sF43: $o ).
thf(func_def_347,type,
sF44: $o ).
thf(func_def_348,type,
sF45: $o ).
thf(func_def_349,type,
sF46: $o ).
thf(func_def_350,type,
sF47: $o ).
thf(func_def_351,type,
sF48: $o ).
thf(func_def_352,type,
sF49: $o ).
thf(func_def_353,type,
sF50: $o ).
thf(func_def_354,type,
sF51: $o ).
thf(func_def_355,type,
sF52: $o ).
thf(func_def_356,type,
sF53: $o ).
thf(func_def_357,type,
sF54: $o ).
thf(func_def_358,type,
sF55: $o ).
thf(func_def_359,type,
sF56: $o ).
thf(func_def_360,type,
sF57: $o ).
thf(func_def_361,type,
sF58: $o ).
thf(func_def_362,type,
sF59: $o ).
thf(func_def_363,type,
sF60: $o ).
thf(func_def_364,type,
sF61: $o ).
thf(func_def_365,type,
sF62: $o ).
thf(func_def_366,type,
sF63: $o ).
thf(func_def_367,type,
sF64: $o ).
thf(func_def_368,type,
sF65: $o ).
thf(func_def_369,type,
sF66: $o ).
thf(func_def_370,type,
sF67: $o ).
thf(func_def_371,type,
sF68: $o ).
thf(func_def_372,type,
sF69: $o ).
thf(func_def_373,type,
sF70: $o ).
thf(func_def_374,type,
sF71: $o ).
thf(func_def_375,type,
sF72: $o ).
thf(func_def_376,type,
sF73: $o ).
thf(func_def_377,type,
sF74: $o ).
thf(func_def_378,type,
sF75: $o ).
thf(func_def_379,type,
sF76: $o ).
thf(func_def_380,type,
sF77: $o ).
thf(func_def_381,type,
sF78: $o ).
thf(func_def_382,type,
sF79: $o ).
thf(func_def_383,type,
sF80: $o ).
thf(func_def_384,type,
sF81: $o ).
thf(func_def_385,type,
sF82: $o ).
thf(func_def_386,type,
sF83: $o ).
thf(func_def_387,type,
sF84: $o ).
thf(func_def_388,type,
sF85: $o ).
thf(func_def_389,type,
sF86: $o ).
thf(func_def_390,type,
sF87: $o ).
thf(func_def_391,type,
sF88: $o ).
thf(func_def_392,type,
sF89: $o ).
thf(func_def_393,type,
sF90: $o ).
thf(func_def_394,type,
sF91: $o ).
thf(func_def_395,type,
sF92: $o ).
thf(func_def_396,type,
sF93: $o ).
thf(func_def_397,type,
sF94: $o ).
thf(func_def_398,type,
sF95: $o ).
thf(func_def_399,type,
sF96: $o ).
thf(func_def_400,type,
sF97: $o ).
thf(func_def_401,type,
sF98: $o ).
thf(func_def_402,type,
sF99: $o ).
thf(func_def_403,type,
sF100: $o ).
thf(func_def_404,type,
sF101: $o ).
thf(func_def_405,type,
sF102: $o ).
thf(func_def_406,type,
sF103: $o ).
thf(func_def_407,type,
sF104: $o ).
thf(func_def_408,type,
sF105: $o ).
thf(func_def_409,type,
sF106: $o ).
thf(func_def_410,type,
sF107: $o ).
thf(func_def_411,type,
sF108: $o ).
thf(func_def_412,type,
sF109: $o ).
thf(func_def_413,type,
sF110: $o ).
thf(func_def_414,type,
sF111: $o ).
thf(func_def_415,type,
sF112: $o ).
thf(func_def_416,type,
sF113: $o ).
thf(func_def_417,type,
sF114: $o ).
thf(func_def_418,type,
sF115: $o ).
thf(func_def_419,type,
sF116: $o ).
thf(func_def_420,type,
sF117: $o ).
thf(func_def_421,type,
sF118: $o ).
thf(func_def_422,type,
sF119: $o ).
thf(func_def_423,type,
sF120: $o ).
thf(func_def_424,type,
sF121: $o ).
thf(func_def_425,type,
sF122: $o ).
thf(func_def_426,type,
sF123: $o ).
thf(func_def_427,type,
sF124: $o ).
thf(func_def_428,type,
sF125: $o ).
thf(func_def_429,type,
sF126: $o ).
thf(func_def_430,type,
sF127: $o ).
thf(func_def_431,type,
sF128: $o ).
thf(func_def_432,type,
sF129: $o ).
thf(func_def_433,type,
sF130: $o ).
thf(func_def_434,type,
sF131: $o ).
thf(func_def_435,type,
sF132: $o ).
thf(func_def_436,type,
sF133: $o ).
thf(func_def_437,type,
sF134: $o ).
thf(func_def_438,type,
sF135: $o ).
thf(func_def_439,type,
sF136: $o ).
thf(func_def_440,type,
sF137: $o ).
thf(func_def_441,type,
sF138: $o ).
thf(func_def_442,type,
sF139: $o ).
thf(func_def_443,type,
sF140: $o ).
thf(func_def_444,type,
sF141: $o ).
thf(func_def_445,type,
sF142: $o ).
thf(func_def_446,type,
sF143: $o ).
thf(func_def_447,type,
sF144: $o ).
thf(func_def_448,type,
sF145: $o ).
thf(func_def_449,type,
sF146: $o ).
thf(func_def_450,type,
sF147: $o ).
thf(func_def_451,type,
sF148: $o ).
thf(func_def_452,type,
sF149: $o ).
thf(func_def_453,type,
sF150: $o ).
thf(func_def_454,type,
sF151: $o ).
thf(func_def_455,type,
sF152: $o ).
thf(func_def_456,type,
sF153: $o ).
thf(func_def_457,type,
sF154: $o ).
thf(func_def_458,type,
sF155: $o ).
thf(func_def_459,type,
sF156: $o ).
thf(func_def_460,type,
sF157: $o ).
thf(func_def_461,type,
sF158: $o ).
thf(func_def_462,type,
sF159: $o ).
thf(func_def_463,type,
sF160: $o ).
thf(func_def_464,type,
sF161: $o ).
thf(func_def_465,type,
sF162: $o ).
thf(func_def_466,type,
sF163: $o ).
thf(func_def_467,type,
sF164: $o ).
thf(func_def_468,type,
sF165: $o ).
thf(func_def_469,type,
sF166: $o ).
thf(func_def_470,type,
sF167: $o ).
thf(func_def_471,type,
sF168: $o ).
thf(func_def_472,type,
sF169: $o ).
thf(func_def_473,type,
sF170: $o ).
thf(func_def_474,type,
sF171: $o ).
thf(func_def_475,type,
sF172: $o ).
thf(func_def_476,type,
sF173: $o ).
thf(func_def_477,type,
sF174: $o ).
thf(func_def_478,type,
sF175: $o ).
thf(func_def_479,type,
sF176: $o ).
thf(func_def_480,type,
sF177: $o ).
thf(func_def_481,type,
sF178: $o ).
thf(func_def_482,type,
sF179: $o ).
thf(func_def_483,type,
sF180: $o ).
thf(func_def_484,type,
sF181: $o ).
thf(func_def_485,type,
sF182: $o ).
thf(func_def_486,type,
sF183: $o ).
thf(func_def_487,type,
sF184: $o ).
thf(func_def_488,type,
sF185: $o ).
thf(func_def_489,type,
sF186: $o ).
thf(func_def_490,type,
sF187: $o ).
thf(func_def_491,type,
sF188: $o ).
thf(func_def_492,type,
sF189: $o ).
thf(func_def_493,type,
sF190: $o ).
thf(func_def_494,type,
sF191: $o ).
thf(func_def_495,type,
sF192: $o ).
thf(func_def_496,type,
sF193: $o ).
thf(func_def_497,type,
sF194: $o ).
thf(func_def_498,type,
sF195: $o ).
thf(func_def_499,type,
sF196: $o ).
thf(func_def_500,type,
sF197: $o ).
thf(func_def_501,type,
sF198: $o ).
thf(func_def_502,type,
sF199: $o ).
thf(func_def_503,type,
sF200: $o ).
thf(func_def_504,type,
sF201: $o ).
thf(func_def_505,type,
sF202: $o ).
thf(func_def_506,type,
sF203: $o ).
thf(func_def_507,type,
sF204: $o ).
thf(func_def_508,type,
sF205: $o ).
thf(func_def_509,type,
sF206: $o ).
thf(func_def_510,type,
sF207: $o ).
thf(func_def_511,type,
sF208: $o ).
thf(func_def_512,type,
sF209: $o ).
thf(func_def_513,type,
sF210: $o ).
thf(func_def_514,type,
sF211: $o ).
thf(func_def_515,type,
sF212: $o ).
thf(func_def_516,type,
sF213: $o ).
thf(func_def_517,type,
sF214: $o ).
thf(func_def_518,type,
sF215: $o ).
thf(func_def_519,type,
sF216: $o ).
thf(func_def_520,type,
sF217: $o ).
thf(func_def_521,type,
sF218: $o ).
thf(func_def_522,type,
sF219: $o ).
thf(func_def_523,type,
sF220: $o ).
thf(func_def_524,type,
sF221: $o ).
thf(func_def_525,type,
sF222: $o ).
thf(func_def_526,type,
sF223: $o ).
thf(func_def_527,type,
sF224: $o ).
thf(func_def_528,type,
sF225: $o ).
thf(func_def_529,type,
sF226: $o ).
thf(func_def_530,type,
sF227: $o ).
thf(func_def_531,type,
sF228: $o ).
thf(func_def_532,type,
sF229: $o ).
thf(func_def_533,type,
sF230: $o ).
thf(func_def_534,type,
sF231: $o ).
thf(func_def_535,type,
sF232: $o ).
thf(func_def_536,type,
sF233: $o ).
thf(func_def_537,type,
sF234: $o ).
thf(func_def_538,type,
sF235: $o ).
thf(func_def_539,type,
sF236: $o ).
thf(func_def_540,type,
sF237: $o ).
thf(func_def_541,type,
sF238: $o ).
thf(func_def_545,type,
sF242: $o ).
thf(func_def_548,type,
sK245: $i > $i > $i ).
thf(func_def_556,type,
sK253: $i > $i > $i ).
thf(func_def_560,type,
sK257: $i > $i > $i ).
thf(func_def_564,type,
sK261: $i > $i ).
thf(func_def_566,type,
sK263: $i > $i > $o ).
thf(func_def_567,type,
sK264: $i > $i ).
thf(func_def_568,type,
sK265: $i > $i ).
thf(func_def_569,type,
sK266: $i > $i ).
thf(func_def_570,type,
sK267: $i > ( $i > $i > $o ) > $i ).
thf(func_def_571,type,
sK268: $i > ( $i > $i > $o ) > $i ).
thf(func_def_572,type,
sK269: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_573,type,
sK270: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_574,type,
sK271: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_575,type,
sK272: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_578,type,
sK275: $i > $i ).
thf(func_def_579,type,
sK276: $i > $i ).
thf(func_def_581,type,
sK278: $i > $i ).
thf(func_def_582,type,
sK279: $i > $i ).
thf(func_def_583,type,
sK280: $i > $i ).
thf(func_def_584,type,
sK281: $i > $i ).
thf(func_def_585,type,
sK282: $i > $i ).
thf(func_def_586,type,
sK283: $i > $i ).
thf(func_def_587,type,
sK284: $i > $i ).
thf(func_def_588,type,
sK285: $i > $i ).
thf(func_def_589,type,
sK286: $i > $i ).
thf(func_def_590,type,
sK287: $i > $i ).
thf(func_def_591,type,
sK288: $i > $i ).
thf(func_def_592,type,
sK289: $i > $i ).
thf(func_def_593,type,
sK290: $i > $i ).
thf(func_def_594,type,
sK291: $i > $i ).
thf(func_def_595,type,
sK292: $i > $i ).
thf(func_def_596,type,
sK293: $i > $i ).
thf(func_def_597,type,
sK294: $i > $i ).
thf(func_def_598,type,
sK295: $i > $i ).
thf(func_def_599,type,
sK296: $i > $i ).
thf(func_def_600,type,
sK297: $i > $i ).
thf(func_def_601,type,
sK298: $i > $i ).
thf(func_def_602,type,
sK299: $i > $i > $i > $i ).
thf(func_def_603,type,
sK300: $i > $i > $i ).
thf(func_def_604,type,
sK301: $i > $i > $i > $i ).
thf(func_def_605,type,
sK302: $i > $i > $i > $i ).
thf(func_def_606,type,
sK303: $i > $i > $i ).
thf(func_def_607,type,
sK304: $i > $i > $i > $i ).
thf(func_def_608,type,
sK305: $i > $i > $i > $i ).
thf(func_def_609,type,
sK306: $i > $i > $i ).
thf(func_def_610,type,
sK307: $i > $i > $i > $i ).
thf(func_def_611,type,
sK308: $i > $i > $i > $i ).
thf(func_def_612,type,
sK309: $i > $i > $i ).
thf(func_def_613,type,
sK310: $i > $i > $i > $i ).
thf(func_def_614,type,
sK311: $i > $i > $i > $i ).
thf(func_def_615,type,
sK312: $i > $i > $i ).
thf(func_def_616,type,
sK313: $i > $i > $i > $i ).
thf(func_def_617,type,
sK314: $i > $i > $i > $i ).
thf(func_def_618,type,
sK315: $i > $i > $i ).
thf(func_def_619,type,
sK316: $i > $i > $i > $i ).
thf(func_def_620,type,
sK317: $i > $i > $i > $i ).
thf(func_def_621,type,
sK318: $i > $i > $i ).
thf(func_def_622,type,
sK319: $i > $i > $i > $i ).
thf(func_def_623,type,
sK320: $i > $i > $i > $i ).
thf(func_def_624,type,
sK321: $i > $i > $i ).
thf(func_def_625,type,
sK322: $i > $i > $i > $i ).
thf(func_def_626,type,
sK323: $i > $i ).
thf(func_def_627,type,
sK324: $i > $i > $i > $i ).
thf(func_def_628,type,
sK325: $i > $i > $i ).
thf(func_def_629,type,
sK326: $i > $i > $i > $i ).
thf(func_def_630,type,
sK327: $i > $i > $i ).
thf(func_def_631,type,
sK328: $i > $i > $i > $i ).
thf(func_def_632,type,
sK329: $i > $i > $i > $i ).
thf(func_def_633,type,
sK330: $i > $i > $i ).
thf(func_def_634,type,
sK331: $i > $i > $i > $i ).
thf(func_def_635,type,
sK332: $i > $i > $i ).
thf(func_def_636,type,
sK333: $i > $i > $i > $i ).
thf(func_def_637,type,
sK334: $i > $i > $i > $i ).
thf(func_def_638,type,
sK335: $i > $i > $i ).
thf(func_def_639,type,
sK336: $i > $i > $i > $i ).
thf(func_def_640,type,
sK337: $i > $i > $i ).
thf(func_def_641,type,
sK338: $i > $i > $i > $i ).
thf(func_def_642,type,
sK339: $i > $i > $i > $i ).
thf(func_def_643,type,
sK340: $i > $i > $i ).
thf(func_def_644,type,
sK341: $i > $i > $i > $i ).
thf(func_def_645,type,
sK342: $i > $i > $i ).
thf(func_def_646,type,
sK343: $i > $i > $i > $i ).
thf(func_def_647,type,
sK344: $i > $i ).
thf(func_def_648,type,
sK345: $i > $i > $i > $i ).
thf(func_def_649,type,
sK346: $i > $i > $i ).
thf(func_def_650,type,
sK347: $i > $i > $i > $i ).
thf(func_def_651,type,
sK348: $i > $i > $i ).
thf(func_def_652,type,
sK349: $i > $i > $i > $i ).
thf(func_def_653,type,
sK350: $i > $i > $i > $i ).
thf(func_def_654,type,
sK351: $i > $i > $i ).
thf(func_def_655,type,
sK352: $i > $i > $i > $i ).
thf(func_def_656,type,
sK353: $i > $i > $i ).
thf(func_def_657,type,
sK354: $i > $i > $i > $i ).
thf(func_def_658,type,
sK355: $i > $i > $i > $i ).
thf(func_def_659,type,
sK356: $i > $i > $i ).
thf(func_def_660,type,
sK357: $i > $i > $i > $i ).
thf(func_def_661,type,
sK358: $i > $i > $i ).
thf(func_def_662,type,
sK359: $i > $i > $i > $i ).
thf(func_def_663,type,
sK360: $i > $i > $i > $i ).
thf(func_def_664,type,
sK361: $i > $i > $i ).
thf(func_def_665,type,
sK362: $i > $i > $i > $i ).
thf(func_def_666,type,
sK363: $i > $i > $i ).
thf(func_def_667,type,
sK364: $i > $i > $i > $i ).
thf(func_def_668,type,
sK365: $i > $i ).
thf(func_def_669,type,
sK366: $i > $i > $i > $i ).
thf(func_def_670,type,
sK367: $i > $i > $i ).
thf(func_def_671,type,
sK368: $i > $i > $i > $i ).
thf(func_def_672,type,
sK369: $i > $i > $i > $i ).
thf(func_def_673,type,
sK370: $i > $i > $i ).
thf(func_def_674,type,
sK371: $i > $i > $i > $i ).
thf(func_def_675,type,
sK372: $i > $i > $i > $i ).
thf(func_def_676,type,
sK373: $i > $i > $i ).
thf(func_def_677,type,
sK374: $i > $i > $i > $i ).
thf(func_def_678,type,
sK375: $i > $i > $i > $i ).
thf(func_def_679,type,
sK376: $i > $i > $i ).
thf(func_def_680,type,
sK377: $i > $i > $i > $i ).
thf(func_def_681,type,
sK378: $i > $i > $i > $i ).
thf(func_def_682,type,
sK379: $i > $i > $i ).
thf(func_def_683,type,
sK380: $i > $i > $i > $i ).
thf(func_def_684,type,
sK381: $i > $i > $i > $i ).
thf(func_def_685,type,
sK382: $i > $i > $i ).
thf(func_def_686,type,
sK383: $i > $i > $i > $i ).
thf(func_def_687,type,
sK384: $i > $i > $i > $i ).
thf(func_def_688,type,
sK385: $i > $i > $i ).
thf(func_def_689,type,
sK386: $i > $i > $i > $i ).
thf(func_def_690,type,
sK387: $i > $i > $i > $i ).
thf(func_def_691,type,
sK388: $i > $i > $i ).
thf(func_def_692,type,
sK389: $i > $i > $i > $i ).
thf(func_def_693,type,
sK390: $i > $i > $i > $i ).
thf(func_def_694,type,
sK391: $i > $i > $i ).
thf(func_def_695,type,
sK392: $i > $i > $i > $i ).
thf(func_def_696,type,
sK393: $i > $i > $i > $i ).
thf(func_def_697,type,
sK394: $i > $i > $i ).
thf(func_def_698,type,
sK395: $i > $i > $i > $i ).
thf(func_def_699,type,
sK396: $i > $i > $i > $i ).
thf(func_def_700,type,
sK397: $i > $i > $i ).
thf(func_def_701,type,
sK398: $i > $i > $i > $i ).
thf(func_def_702,type,
sK399: $i > $i > $i > $i ).
thf(func_def_703,type,
sK400: $i > $i > $i ).
thf(func_def_704,type,
sK401: $i > $i > $i > $i ).
thf(func_def_705,type,
sK402: $i > $i > $i > $i ).
thf(func_def_706,type,
sK403: $i > $i > $i ).
thf(func_def_707,type,
sK404: $i > $i > $i > $i ).
thf(func_def_708,type,
sK405: $i > $i > $i > $i ).
thf(func_def_709,type,
sK406: $i > $i > $i ).
thf(func_def_710,type,
sK407: $i > $i > $i > $i ).
thf(func_def_711,type,
sK408: $i > $i > $i > $i ).
thf(func_def_712,type,
sK409: $i > $i > $i ).
thf(func_def_713,type,
sK410: $i > $i > $i > $i ).
thf(func_def_714,type,
sK411: $i > $i > $i > $i ).
thf(func_def_715,type,
sK412: $i > $i > $i ).
thf(func_def_716,type,
sK413: $i > $i > $i > $i ).
thf(func_def_717,type,
sK414: $i > $i ).
thf(func_def_718,type,
sK415: $i > $i > $i > $i ).
thf(func_def_719,type,
sK416: $i > $i > $i ).
thf(func_def_720,type,
sK417: $i > $i > $i > $i ).
thf(func_def_721,type,
sK418: $i > $i > $i ).
thf(func_def_722,type,
sK419: $i > $i > $i > $i ).
thf(func_def_723,type,
sK420: $i > $i > $i > $i ).
thf(func_def_724,type,
sK421: $i > $i > $i ).
thf(func_def_725,type,
sK422: $i > $i > $i > $i ).
thf(func_def_726,type,
sK423: $i > $i > $i ).
thf(func_def_727,type,
sK424: $i > $i > $i > $i ).
thf(func_def_728,type,
sK425: $i > $i > $i > $i ).
thf(func_def_729,type,
sK426: $i > $i > $i ).
thf(func_def_730,type,
sK427: $i > $i > $i > $i ).
thf(func_def_731,type,
sK428: $i > $i > $i ).
thf(func_def_732,type,
sK429: $i > $i > $i > $i ).
thf(func_def_733,type,
sK430: $i > $i > $i > $i ).
thf(func_def_734,type,
sK431: $i > $i > $i ).
thf(func_def_735,type,
sK432: $i > $i > $i > $i ).
thf(func_def_736,type,
sK433: $i > $i > $i ).
thf(func_def_737,type,
sK434: $i > $i > $i > $i ).
thf(func_def_738,type,
sK435: $i > $i > $i > $i ).
thf(func_def_739,type,
sK436: $i > $i > $i ).
thf(func_def_740,type,
sK437: $i > $i > $i > $i ).
thf(func_def_741,type,
sK438: $i > $i > $i ).
thf(func_def_742,type,
sK439: $i > $i > $i > $i ).
thf(func_def_743,type,
sK440: $i > $i > $i > $i ).
thf(func_def_744,type,
sK441: $i > $i > $i ).
thf(func_def_745,type,
sK442: $i > $i > $i > $i ).
thf(func_def_746,type,
sK443: $i > $i > $i ).
thf(func_def_747,type,
sK444: $i > $i > $i > $i ).
thf(func_def_748,type,
sK445: $i > $i > $i > $i ).
thf(func_def_749,type,
sK446: $i > $i > $i ).
thf(func_def_750,type,
sK447: $i > $i > $i > $i ).
thf(func_def_751,type,
sK448: $i > $i > $i ).
thf(func_def_752,type,
sK449: $i > $i > $i > $i ).
thf(func_def_753,type,
sK450: $i > $i > $i > $i ).
thf(func_def_754,type,
sK451: $i > $i > $i ).
thf(func_def_755,type,
sK452: $i > $i > $i > $i ).
thf(func_def_756,type,
sK453: $i > $i > $i ).
thf(func_def_757,type,
sK454: $i > $i > $i > $i ).
thf(func_def_758,type,
sK455: $i > $i ).
thf(func_def_759,type,
sK456: $i > $i > $i > $i ).
thf(func_def_760,type,
sK457: $i > $i > $i ).
thf(func_def_761,type,
sK458: $i > $i > $i > $i ).
thf(func_def_762,type,
sK459: $i > $i > $i ).
thf(func_def_763,type,
sK460: $i > $i > $i > $i ).
thf(func_def_764,type,
sK461: $i > $i > $i > $i ).
thf(func_def_765,type,
sK462: $i > $i > $i ).
thf(func_def_766,type,
sK463: $i > $i > $i > $i ).
thf(func_def_767,type,
sK464: $i > $i > $i ).
thf(func_def_768,type,
sK465: $i > $i > $i > $i ).
thf(func_def_769,type,
sK466: $i > $i > $i > $i ).
thf(func_def_770,type,
sK467: $i > $i > $i ).
thf(func_def_771,type,
sK468: $i > $i > $i > $i ).
thf(func_def_772,type,
sK469: $i > $i > $i ).
thf(func_def_773,type,
sK470: $i > $i > $i > $i ).
thf(func_def_774,type,
sK471: $i > $i > $i > $i ).
thf(func_def_775,type,
sK472: $i > $i > $i ).
thf(func_def_776,type,
sK473: $i > $i > $i > $i ).
thf(func_def_777,type,
sK474: $i > $i > $i ).
thf(func_def_778,type,
sK475: $i > $i > $i > $i ).
thf(func_def_779,type,
sK476: $i > $i > $i > $i ).
thf(func_def_780,type,
sK477: $i > $i > $i ).
thf(func_def_781,type,
sK478: $i > $i > $i > $i ).
thf(func_def_782,type,
sK479: $i > $i > $i ).
thf(func_def_783,type,
sK480: $i > $i > $i > $i ).
thf(func_def_784,type,
sK481: $i > $i > $i > $i ).
thf(func_def_785,type,
sK482: $i > $i > $i ).
thf(func_def_786,type,
sK483: $i > $i > $i > $i ).
thf(func_def_787,type,
sK484: $i > $i > $i ).
thf(func_def_788,type,
sK485: $i > $i > $i > $i ).
thf(func_def_789,type,
sK486: $i > $i > $i > $i ).
thf(func_def_790,type,
sK487: $i > $i > $i ).
thf(func_def_791,type,
sK488: $i > $i > $i > $i ).
thf(func_def_792,type,
sK489: $i > $i > $i ).
thf(func_def_793,type,
sK490: $i > $i > $i > $i ).
thf(func_def_794,type,
sK491: $i > $i > $i > $i ).
thf(func_def_795,type,
sK492: $i > $i > $i ).
thf(func_def_796,type,
sK493: $i > $i > $i > $i ).
thf(func_def_797,type,
sK494: $i > $i > $i ).
thf(func_def_798,type,
sK495: $i > $i > $i > $i ).
thf(func_def_799,type,
sK496: $i > $i ).
thf(func_def_800,type,
sK497: $i > $i > $i > $i ).
thf(func_def_801,type,
sK498: $i > $i > $i ).
thf(func_def_802,type,
sK499: $i > $i > $i ).
thf(func_def_803,type,
sK500: $i > $i > $i ).
thf(func_def_804,type,
sK501: $i > $o ).
thf(func_def_806,type,
sK503: ( $i > $o ) > $i > $i ).
thf(func_def_808,type,
sK505: $i > $o ).
thf(func_def_811,type,
sK508: $i > $o ).
thf(func_def_814,type,
sK511: $i > $o ).
thf(func_def_816,type,
sK513: $i > $o ).
thf(func_def_818,type,
sK515: $i > $i ).
thf(func_def_819,type,
sK516: ( $i > $o ) > $i ).
thf(func_def_820,type,
sK517: ( $i > $o ) > $i > $i ).
thf(func_def_822,type,
sK519: $o ).
thf(func_def_823,type,
sK520: $o ).
thf(func_def_826,type,
sK523: $i > $o ).
thf(func_def_828,type,
sK525: ( $i > $o ) > $i ).
thf(func_def_829,type,
sK526: ( $i > $o ) > $i > $i ).
thf(func_def_832,type,
sK529: $i > $i > $i ).
thf(func_def_833,type,
sK530: $i > $i > $i ).
thf(func_def_835,type,
sK532: $i > $i ).
thf(func_def_837,type,
sK534: $i > $o ).
thf(func_def_840,type,
sK537: $i > $i ).
thf(func_def_842,type,
sK539: $i > $o ).
thf(func_def_854,type,
sK551: $o ).
thf(func_def_861,type,
sK558: $i > $i > $i ).
thf(func_def_871,type,
sK568: $o ).
thf(func_def_872,type,
sK569: $o > $i > $i > $i ).
thf(func_def_875,type,
sK572: $i > $o ).
thf(func_def_877,type,
sK574: $i > $i ).
thf(func_def_878,type,
sK575: ( $i > $o ) > $i ).
thf(func_def_879,type,
sK576: ( $i > $o ) > $i > $i ).
thf(func_def_881,type,
sK578: $i > $i ).
thf(func_def_897,type,
sK594: $i > $o ).
thf(func_def_901,type,
sK598: $i > $o ).
thf(func_def_902,type,
sK599: $i > $o ).
thf(func_def_905,type,
sK602: ( $i > $o ) > $i > $i ).
thf(func_def_906,type,
sK603: $i > $o ).
thf(func_def_909,type,
sK606: ( $i > $o ) > $i > $i ).
thf(func_def_910,type,
sK607: $i > $o ).
thf(func_def_913,type,
sK610: ( $i > $o ) > $i > $i ).
thf(func_def_914,type,
sK611: $i > $o ).
thf(func_def_917,type,
sK614: ( $i > $o ) > $i > $i ).
thf(func_def_918,type,
sK615: $o ).
thf(func_def_919,type,
sK616: $o ).
thf(func_def_920,type,
sK617: $i > $o ).
thf(func_def_922,type,
sK619: $i > $i ).
thf(func_def_923,type,
sK620: ( $i > $o ) > $i ).
thf(func_def_924,type,
sK621: ( $i > $o ) > $i > $i ).
thf(func_def_925,type,
sK622: $i > $o ).
thf(func_def_927,type,
sK624: $i > $i ).
thf(func_def_928,type,
sK625: ( $i > $o ) > $i ).
thf(func_def_929,type,
sK626: ( $i > $o ) > $i ).
thf(func_def_930,type,
sK627: ( $i > $o ) > $i ).
thf(func_def_931,type,
sK628: $i > $o ).
thf(func_def_933,type,
sK630: $i > $i ).
thf(func_def_934,type,
sK631: ( $i > $o ) > $i ).
thf(func_def_935,type,
sK632: ( $i > $o ) > $i > $i ).
thf(func_def_944,type,
sK641: $i > $o ).
thf(func_def_948,type,
sK645: ( $i > $o ) > $i > $i ).
thf(func_def_949,type,
sK646: $i > $o ).
thf(func_def_950,type,
sK647: $i > $o ).
thf(func_def_951,type,
sK648: $i > $i ).
thf(func_def_952,type,
sK649: $i > $i ).
thf(func_def_955,type,
sK652: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_956,type,
sK653: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_957,type,
sK654: ( $i > $o ) > $i ).
thf(func_def_958,type,
sK655: $i > ( $i > $o ) > $i ).
thf(func_def_959,type,
sK656: ( $i > $o ) > $i ).
thf(func_def_960,type,
sK657: $i > ( $i > $o ) > $i ).
thf(func_def_961,type,
sK658: $i > ( $i > $o ) > $i ).
thf(func_def_962,type,
sK659: ( $i > $o ) > $i ).
thf(func_def_963,type,
sK660: $i > ( $i > $o ) > $i ).
thf(func_def_964,type,
sK661: ( $i > $o ) > $i ).
thf(func_def_965,type,
sK662: $i > ( $i > $o ) > $i ).
thf(func_def_966,type,
sK663: $i > ( $i > $o ) > $i ).
thf(func_def_967,type,
sK664: ( $i > $o ) > $i ).
thf(func_def_968,type,
sK665: $i > ( $i > $o ) > $i ).
thf(func_def_969,type,
sK666: ( $i > $o ) > $i ).
thf(func_def_970,type,
sK667: $i > ( $i > $o ) > $i ).
thf(func_def_971,type,
sK668: $i > ( $i > $o ) > $i ).
thf(func_def_980,type,
sK677: $i > $o ).
thf(func_def_981,type,
sK678: $i > $o ).
thf(func_def_984,type,
sK681: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_985,type,
sK682: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_986,type,
sK683: $i > ( $i > $o ) > $i ).
thf(func_def_987,type,
sK684: ( $i > $o ) > $i > $i ).
thf(func_def_990,type,
sK687: $i > $o ).
thf(func_def_991,type,
sK688: $i > $o ).
thf(func_def_992,type,
sK689: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_993,type,
sK690: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_996,type,
sK693: $i > $i > $i ).
thf(func_def_1037,type,
sK734: $i > $o ).
thf(func_def_1039,type,
sK736: $i > $o ).
thf(func_def_1047,type,
sK744: $o ).
thf(func_def_1078,type,
sK775: $i > $i > $i ).
thf(func_def_1118,type,
sK815: $o ).
thf(func_def_1173,type,
sK870: $i > $i > $i > $i ).
thf(func_def_1174,type,
sK871: $i > $i > $i > $i ).
thf(func_def_1180,type,
sK877: $i > $i > $i ).
thf(func_def_1184,type,
sK881: $i > $o ).
thf(func_def_1187,type,
sK884: ( $i > $o ) > $i > $i ).
thf(func_def_1188,type,
sK885: ( $i > $o ) > $i > $i ).
thf(func_def_1189,type,
sK886: $i > $o ).
thf(func_def_1191,type,
sK888: ( $i > $o ) > $i > $i ).
thf(func_def_1193,type,
sK890: $i > $o ).
thf(func_def_1195,type,
sK892: $i > ( $i > $o ) > $i > $i ).
thf(func_def_1196,type,
sK893: $i > $o ).
thf(func_def_1199,type,
sK896: ( $i > $o ) > $i > $i ).
thf(func_def_1200,type,
sK897: ( $i > $o ) > $i > $i ).
thf(func_def_1271,type,
sK968: $i > $i > $o ).
thf(func_def_1275,type,
sK972: $i > $i > $o ).
thf(func_def_1278,type,
sK975: $i > $i > $o ).
thf(func_def_1282,type,
sK979: $i > $i > $o ).
thf(func_def_1288,type,
sK985: $i > $i > $o ).
thf(func_def_1293,type,
sK990: $i > $i > $o ).
thf(func_def_1298,type,
sK995: $i > $i > $o ).
thf(func_def_1323,type,
sK1020: $i > $i ).
thf(func_def_1326,type,
sK1023: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1327,type,
sK1024: $i > $i ).
thf(func_def_1330,type,
sK1027: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1331,type,
sK1028: $i > $i ).
thf(func_def_1334,type,
sK1031: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1338,type,
sK1035: $i > $o ).
thf(func_def_1340,type,
sK1037: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_1341,type,
sK1038: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_1342,type,
sK1039: $i > $o ).
thf(func_def_1365,type,
sK1062: $i > $i > $i > $i > $i ).
thf(func_def_1375,type,
sK1072: $i > $i > $i > $i > $i ).
thf(func_def_1376,type,
sK1073: $i > $i > $i > $i > $i ).
thf(func_def_1381,type,
sK1078: $i > $i > $i > $i > $i ).
thf(func_def_1382,type,
sK1079: $i > $i > $i > $i > $i ).
thf(func_def_1383,type,
sK1080: $i > $i > $i > $i > $i ).
thf(func_def_1384,type,
sK1081: $i > $i > $i > $i > $i ).
thf(func_def_1385,type,
sK1082: $i > $i > $i > $i > $i ).
thf(func_def_1390,type,
sK1087: $i > $i > $i > $i > $i ).
thf(func_def_1395,type,
sK1092: $i > $i > $i > $i > $i ).
thf(func_def_1404,type,
sK1101: $i > $i ).
thf(func_def_1408,type,
sK1105: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1412,type,
sK1109: $i > $i ).
thf(func_def_1415,type,
sK1112: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1420,type,
sK1117: $o ).
thf(func_def_1424,type,
sK1121: $o ).
thf(func_def_1428,type,
sK1125: $o ).
thf(func_def_1432,type,
sK1129: $o ).
thf(func_def_1436,type,
sK1133: $o ).
thf(func_def_1440,type,
sK1137: $o ).
thf(func_def_1446,type,
sK1143: $o ).
thf(func_def_1450,type,
sK1147: $o ).
thf(func_def_1454,type,
sK1151: $o ).
thf(func_def_1473,type,
sK1170: $i > $i > $i > $i ).
thf(func_def_1474,type,
sK1171: $i > $i > $i > $i ).
thf(func_def_1478,type,
sK1175: $i > $i > $i > $i ).
thf(func_def_1482,type,
sK1179: $i > $i > $i > $i ).
thf(f112,axiom,
( binintersectSubset2
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(f117,axiom,
( binintersectSubset4
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(f250,axiom,
( doubleComplementSub1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(f251,axiom,
( doubleComplementSub2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(f252,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( X1
= ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(f253,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( X1
= ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f252]) ).
thf(f466,plain,
( binintersectSubset2
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ),
inference(rectify,[],[f112]) ).
thf(f467,plain,
( binintersectSubset2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f466]) ).
thf(f476,plain,
( binintersectSubset4
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ) ),
inference(rectify,[],[f117]) ).
thf(f477,plain,
( binintersectSubset4
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f476]) ).
thf(f728,plain,
( doubleComplementSub1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f250]) ).
thf(f729,plain,
( doubleComplementSub1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f728]) ).
thf(f730,plain,
( doubleComplementSub2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 ) ) ) ),
inference(rectify,[],[f251]) ).
thf(f731,plain,
( doubleComplementSub2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f730]) ).
thf(f732,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( X1
= ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f253]) ).
thf(f733,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f732]) ).
thf(f734,plain,
( ? [X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
!= X1 )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $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,[],[f733]) ).
thf(f735,plain,
( ? [X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
!= X1 )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $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(flattening,[],[f734]) ).
thf(f736,plain,
( ( sK1
!= ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f735]) ).
thf(f848,plain,
( binintersectSubset2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f467]) ).
thf(f853,plain,
( binintersectSubset4
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f477]) ).
thf(f986,plain,
( doubleComplementSub1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f729]) ).
thf(f987,plain,
( doubleComplementSub2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f731]) ).
thf(f1097,plain,
binintersectSubset2 = $true,
inference(cnf_transformation,[],[f736]) ).
thf(f1102,plain,
binintersectSubset4 = $true,
inference(cnf_transformation,[],[f736]) ).
thf(f1233,plain,
doubleComplementSub1 = $true,
inference(cnf_transformation,[],[f736]) ).
thf(f1234,plain,
doubleComplementSub2 = $true,
inference(cnf_transformation,[],[f736]) ).
thf(f1235,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f736]) ).
thf(f1236,plain,
( sK1
!= ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f736]) ).
thf(f1348,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f848,f1097]) ).
thf(f1353,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f853,f1102]) ).
thf(f1484,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f986,f1233]) ).
thf(f1485,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f987,f1234]) ).
thf(f1801,definition,
( sF105
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF105])],[function_definition]) ).
thf(f1802,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y1 ) ) ) )
= sF105 ),
inference(reorient_equations,[],[f1801]) ).
thf(f1803,plain,
$true = sF105,
inference(definition_folding,[],[f1348,f1802]) ).
thf(f1816,definition,
( sF110
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF110])],[function_definition]) ).
thf(f1817,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y0 ) ) ) )
= sF110 ),
inference(reorient_equations,[],[f1816]) ).
thf(f1818,plain,
$true = sF110,
inference(definition_folding,[],[f1353,f1817]) ).
thf(f2201,definition,
( sF237
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF237])],[function_definition]) ).
thf(f2202,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) )
= sF237 ),
inference(reorient_equations,[],[f2201]) ).
thf(f2203,plain,
$true = sF237,
inference(definition_folding,[],[f1484,f2202]) ).
thf(f2204,definition,
( sF238
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF238])],[function_definition]) ).
thf(f2205,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) @ Y0 ) ) ) )
= sF238 ),
inference(reorient_equations,[],[f2204]) ).
thf(f2206,plain,
$true = sF238,
inference(definition_folding,[],[f1485,f2205]) ).
thf(f2207,definition,
( sF239
= ( setminus @ sK0 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF239])],[function_definition]) ).
thf(f2208,plain,
( ( setminus @ sK0 @ sK1 )
= sF239 ),
inference(reorient_equations,[],[f2207]) ).
thf(f2209,definition,
( sF240
= ( setminus @ sK0 @ sF239 ) ),
introduced(definition,[new_symbols(definition,[sF240])],[function_definition]) ).
thf(f2210,plain,
( ( setminus @ sK0 @ sF239 )
= sF240 ),
inference(reorient_equations,[],[f2209]) ).
thf(f2211,plain,
sK1 != sF240,
inference(definition_folding,[],[f1236,f2210,f2208]) ).
thf(f2212,definition,
( sF241
= ( powerset @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF241])],[function_definition]) ).
thf(f2213,plain,
( ( powerset @ sK0 )
= sF241 ),
inference(reorient_equations,[],[f2212]) ).
thf(f2214,definition,
( sF242
= ( in @ sK1 @ sF241 ) ),
introduced(definition,[new_symbols(definition,[sF242])],[function_definition]) ).
thf(f2215,plain,
( ( in @ sK1 @ sF241 )
= sF242 ),
inference(reorient_equations,[],[f2214]) ).
thf(f2216,plain,
$true = sF242,
inference(definition_folding,[],[f1235,f2215,f2213]) ).
thf(f7554,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y1 ) ) ) ) )
| ( $false = sF105 ) ),
inference(iff_proxy_clausification,[],[f1802]) ).
thf(f7563,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y1 ) ) )
@ X1 ) )
| ( $false = sF105 ) ),
inference(pi_proxy_clausification,[],[f7554]) ).
thf(f7564,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( binintersect @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false = sF105 ) ),
inference(beta-eta_normalization,[],[f7563]) ).
thf(f7565,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( binintersect @ Y0 @ X1 )
= Y0 ) )
@ X2 ) )
| ( $false = sF105 ) ),
inference(pi_proxy_clausification,[],[f7564]) ).
thf(f7566,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( subset @ X2 @ X1 )
=> ( ( binintersect @ X2 @ X1 )
= X2 ) ) )
| ( $false = sF105 ) ),
inference(beta-eta_normalization,[],[f7565]) ).
thf(f7567,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( $false = sF105 )
| ( $true
= ( ( binintersect @ X2 @ X1 )
= X2 ) ) ),
inference(imp_proxy_clausification,[],[f7566]) ).
thf(f7568,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( $false = sF105 )
| ( ( binintersect @ X2 @ X1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f7567]) ).
thf(f7635,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y0 ) ) ) ) )
| ( $false = sF110 ) ),
inference(iff_proxy_clausification,[],[f1817]) ).
thf(f7644,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( binintersect @ Y1 @ Y0 )
= Y0 ) ) )
@ X1 ) )
| ( $false = sF110 ) ),
inference(pi_proxy_clausification,[],[f7635]) ).
thf(f7645,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( binintersect @ Y0 @ X1 )
= X1 ) ) ) )
| ( $false = sF110 ) ),
inference(beta-eta_normalization,[],[f7644]) ).
thf(f7646,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( binintersect @ Y0 @ X1 )
= X1 ) )
@ X2 ) )
| ( $false = sF110 ) ),
inference(pi_proxy_clausification,[],[f7645]) ).
thf(f7647,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( subset @ X1 @ X2 )
=> ( ( binintersect @ X2 @ X1 )
= X1 ) ) )
| ( $false = sF110 ) ),
inference(beta-eta_normalization,[],[f7646]) ).
thf(f7648,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $false )
| ( $false = sF110 )
| ( $true
= ( ( binintersect @ X2 @ X1 )
= X1 ) ) ),
inference(imp_proxy_clausification,[],[f7647]) ).
thf(f7649,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $false )
| ( $false = sF110 )
| ( ( binintersect @ X2 @ X1 )
= X1 ) ),
inference(equality_proxy_clausification,[],[f7648]) ).
thf(f10704,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false = sF237 ) ),
inference(iff_proxy_clausification,[],[f2202]) ).
thf(f10712,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $false = sF237 ) ),
inference(pi_proxy_clausification,[],[f10704]) ).
thf(f10713,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) ) ) ) )
| ( $false = sF237 ) ),
inference(beta-eta_normalization,[],[f10712]) ).
thf(f10714,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) ) )
@ X2 ) )
| ( $false = sF237 ) ),
inference(pi_proxy_clausification,[],[f10713]) ).
thf(f10715,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( subset @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) )
| ( $false = sF237 ) ),
inference(beta-eta_normalization,[],[f10714]) ).
thf(f10716,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false = sF237 )
| ( $true
= ( subset @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f10715]) ).
thf(f10717,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) @ Y0 ) ) ) ) )
| ( $false = sF238 ) ),
inference(iff_proxy_clausification,[],[f2205]) ).
thf(f10725,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) @ Y0 ) ) )
@ X1 ) )
| ( $false = sF238 ) ),
inference(pi_proxy_clausification,[],[f10717]) ).
thf(f10726,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) @ X1 ) ) ) )
| ( $false = sF238 ) ),
inference(beta-eta_normalization,[],[f10725]) ).
thf(f10727,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) @ X1 ) )
@ X2 ) )
| ( $false = sF238 ) ),
inference(pi_proxy_clausification,[],[f10726]) ).
thf(f10728,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) @ X1 ) ) )
| ( $false = sF238 ) ),
inference(beta-eta_normalization,[],[f10727]) ).
thf(f10729,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false = sF238 )
| ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f10728]) ).
thf(f10730,plain,
( ( $true
= ( in @ sK1 @ sF241 ) )
| ( $false = sF242 ) ),
inference(iff_proxy_clausification,[],[f2215]) ).
thf(f11130,plain,
! [X2: $i,X1: $i] :
( ( $false = $true )
| ( ( subset @ X2 @ X1 )
= $false )
| ( ( binintersect @ X2 @ X1 )
= X2 ) ),
inference(forward_demodulation,[],[f7568,f1803]) ).
thf(f11131,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( ( binintersect @ X2 @ X1 )
= X2 ) ),
inference(trivial_inequality_removal,[],[f11130]) ).
thf(f11142,plain,
! [X2: $i,X1: $i] :
( ( $false = $true )
| ( ( subset @ X1 @ X2 )
= $false )
| ( ( binintersect @ X2 @ X1 )
= X1 ) ),
inference(forward_demodulation,[],[f7649,f1818]) ).
thf(f11143,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $false )
| ( ( binintersect @ X2 @ X1 )
= X1 ) ),
inference(trivial_inequality_removal,[],[f11142]) ).
thf(f11498,plain,
! [X2: $i,X1: $i] :
( ( $false = $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( subset @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ),
inference(forward_demodulation,[],[f10716,f2203]) ).
thf(f11499,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f11498]) ).
thf(f11500,plain,
! [X2: $i,X1: $i] :
( ( $false = $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) @ X1 ) ) ),
inference(forward_demodulation,[],[f10729,f2206]) ).
thf(f11501,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) @ X1 ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f11500]) ).
thf(f11502,plain,
( ( $false = $true )
| ( $true
= ( in @ sK1 @ sF241 ) ) ),
inference(forward_demodulation,[],[f10730,f2216]) ).
thf(f11503,plain,
( $true
= ( in @ sK1 @ sF241 ) ),
inference(trivial_inequality_removal,[],[f11502]) ).
thf(f14103,plain,
( ( $true
= ( subset @ sK1 @ ( setminus @ sK0 @ sF239 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f11499,f2208]) ).
thf(f14132,plain,
( ( $true
= ( subset @ sK1 @ sF240 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
inference(forward_demodulation,[],[f14103,f2210]) ).
thf(f14138,plain,
( ( $false
= ( in @ sK1 @ sF241 ) )
| ( $true
= ( subset @ sK1 @ sF240 ) ) ),
inference(forward_demodulation,[],[f14132,f2213]) ).
thf(f14139,plain,
( ( $false = $true )
| ( $true
= ( subset @ sK1 @ sF240 ) ) ),
inference(forward_demodulation,[],[f14138,f11503]) ).
thf(f14140,plain,
( $true
= ( subset @ sK1 @ sF240 ) ),
inference(trivial_inequality_removal,[],[f14139]) ).
thf(f14148,plain,
( ( $false = $true )
| ( sK1
= ( binintersect @ sK1 @ sF240 ) ) ),
inference(constrained_superposition,[],[f11131,f14140]) ).
thf(f14153,plain,
( sK1
= ( binintersect @ sK1 @ sF240 ) ),
inference(trivial_inequality_removal,[],[f14148]) ).
thf(f14166,plain,
( ( $true
= ( subset @ ( setminus @ sK0 @ sF239 ) @ sK1 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f11501,f2208]) ).
thf(f14211,plain,
( ( $true
= ( subset @ sF240 @ sK1 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
inference(forward_demodulation,[],[f14166,f2210]) ).
thf(f14215,plain,
( ( $false
= ( in @ sK1 @ sF241 ) )
| ( $true
= ( subset @ sF240 @ sK1 ) ) ),
inference(forward_demodulation,[],[f14211,f2213]) ).
thf(f14216,plain,
( ( $false = $true )
| ( $true
= ( subset @ sF240 @ sK1 ) ) ),
inference(forward_demodulation,[],[f14215,f11503]) ).
thf(f14217,plain,
( $true
= ( subset @ sF240 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f14216]) ).
thf(f14232,plain,
( ( $false = $true )
| ( sF240
= ( binintersect @ sK1 @ sF240 ) ) ),
inference(constrained_superposition,[],[f11143,f14217]) ).
thf(f14235,plain,
( sF240
= ( binintersect @ sK1 @ sF240 ) ),
inference(trivial_inequality_removal,[],[f14232]) ).
thf(f14250,plain,
sK1 = sF240,
inference(forward_demodulation,[],[f14235,f14153]) ).
thf(f14258,plain,
$false,
inference(forward_subsumption_resolution,[],[f14250,f2211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU731^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:17:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.61/1.06 % (788813)Will run a generic schedule for satisfiability detection.
% 5.61/1.06 % (788826)% WARNING: option uhcvi not known.
% 5.61/1.06 % (788831)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=65634204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.61/1.06 % (788829)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=904074352:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.61/1.06 % (788825)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=236098953_2999 on theBenchmark for (2999ds/0Mi)
% 5.61/1.06 % (788826)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3885505040:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.61/1.06 % (788827)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3738215065:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.61/1.06 % (788830)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1954466744:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.61/1.06 % (788828)dis+10_1_sil=32000:sp=arity:random_seed=3787259432:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.61/1.06 % (788829)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.61/1.06 % (788826)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.61/1.06 % (788831)Instruction limit reached!
% 5.61/1.06 % (788831)------------------------------
% 5.61/1.06 % (788831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.61/1.06 % (788831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.06 % (788831)CaDiCaL version: 2.1.3
% 5.61/1.06 % (788831)Termination reason: Instruction limit
% 5.61/1.06 % (788831)Termination phase: Saturation
% 5.61/1.06 % (788831)Time elapsed: 0.035 s
% 5.61/1.06 % (788831)Peak memory usage: 14 MB
% 5.61/1.06 % (788831)Instructions burned: 163 (million)
% 5.61/1.06 % (788849)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=227160607:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.61/1.06 % (788829)Instruction limit reached!
% 5.61/1.06 % (788829)------------------------------
% 5.61/1.06 % (788829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.61/1.06 % (788829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.06 % (788829)CaDiCaL version: 2.1.3
% 5.61/1.06 % (788829)Termination reason: Instruction limit
% 5.61/1.06 % (788829)Termination phase: Property scanning
% 5.61/1.06 % (788829)Time elapsed: 0.048 s
% 5.61/1.06 % (788829)Peak memory usage: 11 MB
% 5.61/1.06 % (788829)Instructions burned: 118 (million)
% 5.61/1.06 % Exception at run slice level
% 5.61/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.61/1.06 % (788826)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.61/1.06 % (788830)Instruction limit reached!
% 5.61/1.06 % (788830)------------------------------
% 5.61/1.06 % (788830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.61/1.06 % (788830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.06 % (788830)CaDiCaL version: 2.1.3
% 5.61/1.06 % (788830)Termination reason: Instruction limit
% 5.61/1.06 % (788830)Termination phase: Saturation
% 5.61/1.06 % (788830)Time elapsed: 0.053 s
% 5.61/1.06 % (788830)Peak memory usage: 13 MB
% 5.61/1.06 % (788830)Instructions burned: 131 (million)
% 5.61/1.06 % (788828)Instruction limit reached!
% 5.61/1.06 % (788828)------------------------------
% 5.61/1.06 % (788828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.61/1.06 % (788828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.06 % (788828)CaDiCaL version: 2.1.3
% 5.61/1.06 % (788828)Termination reason: Instruction limit
% 5.61/1.06 % (788828)Termination phase: Property scanning
% 5.61/1.06 % (788828)Time elapsed: 0.047 s
% 5.61/1.06 % (788828)Peak memory usage: 12 MB
% 5.61/1.06 % (788828)Instructions burned: 103 (million)
% 5.61/1.06 % (788858)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=471915344:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.61/1.06 % (788856)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4108584718:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.61/1.06 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % (788859)ott-21_1_sil=16000:fs=off:random_seed=831921258:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 6.53/1.28 % (788864)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1288033356:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.53/1.28 % (788861)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2952756974:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 6.53/1.28 % (788858)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.53/1.28 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % (788873)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2024554697:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.53/1.28 % (788858)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.53/1.28 % (788856)Instruction limit reached!
% 6.53/1.28 % (788856)------------------------------
% 6.53/1.28 % (788856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788856)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788856)Termination reason: Instruction limit
% 6.53/1.28 % (788856)Termination phase: Saturation
% 6.53/1.28 % (788856)Time elapsed: 0.061 s
% 6.53/1.28 % (788856)Peak memory usage: 13 MB
% 6.53/1.28 % (788856)Instructions burned: 132 (million)
% 6.53/1.28 % (788885)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3850831033:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.53/1.28 % (788859)Instruction limit reached!
% 6.53/1.28 % (788859)------------------------------
% 6.53/1.28 % (788859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788859)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788859)Termination reason: Instruction limit
% 6.53/1.28 % (788859)Termination phase: Saturation
% 6.53/1.28 % (788859)Time elapsed: 0.080 s
% 6.53/1.28 % (788859)Peak memory usage: 13 MB
% 6.53/1.28 % (788859)Instructions burned: 180 (million)
% 6.53/1.28 % (788892)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2417933392:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 6.53/1.28 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % (788892)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.53/1.28 % (788901)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1664860439:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 6.53/1.28 % (788901)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.53/1.28 % (788861)Instruction limit reached!
% 6.53/1.28 % (788861)------------------------------
% 6.53/1.28 % (788861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788861)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788861)Termination reason: Instruction limit
% 6.53/1.28 % (788861)Termination phase: Saturation
% 6.53/1.28 % (788861)Time elapsed: 0.260 s
% 6.53/1.28 % (788861)Peak memory usage: 15 MB
% 6.53/1.28 % (788861)Instructions burned: 477 (million)
% 6.53/1.28 % (788932)fmb+10_1_sil=64000:random_seed=3543827584:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 6.53/1.28 % (788858)Instruction limit reached!
% 6.53/1.28 % (788858)------------------------------
% 6.53/1.28 % (788858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788858)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788858)Termination reason: Instruction limit
% 6.53/1.28 % (788858)Termination phase: Saturation
% 6.53/1.28 % (788858)Time elapsed: 0.335 s
% 6.53/1.28 % (788858)Peak memory usage: 16 MB
% 6.53/1.28 % (788858)Instructions burned: 686 (million)
% 6.53/1.28 % (788932)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.53/1.28 % (788938)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2780763082:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 6.53/1.28 % (788873)Instruction limit reached!
% 6.53/1.28 % (788873)------------------------------
% 6.53/1.28 % (788873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788873)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788873)Termination reason: Instruction limit
% 6.53/1.28 % (788873)Termination phase: Saturation
% 6.53/1.28 % (788873)Time elapsed: 0.302 s
% 6.53/1.28 % (788873)Peak memory usage: 20 MB
% 6.53/1.28 % (788873)Instructions burned: 1182 (million)
% 6.53/1.28 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % (788940)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=29218286:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 6.53/1.28 % (788941)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4037145994:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 6.53/1.28 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % (788944)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1700890541:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 6.53/1.28 % (788941)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.53/1.28 % (788946)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2824113069:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 6.53/1.28 % (788944)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.53/1.28 % (788944)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.53/1.28 % (788892)Instruction limit reached!
% 6.53/1.28 % (788892)------------------------------
% 6.53/1.28 % (788892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788892)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788892)Termination reason: Instruction limit
% 6.53/1.28 % (788892)Termination phase: Saturation
% 6.53/1.28 % (788892)Time elapsed: 0.338 s
% 6.53/1.28 % (788892)Peak memory usage: 17 MB
% 6.53/1.28 % (788892)Instructions burned: 692 (million)
% 6.53/1.28 % (788953)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3077844888:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 6.53/1.28 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % (788964)ott-2_1_sil=16000:newcnf=on:random_seed=585148812:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 6.53/1.28 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % (788964)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.53/1.28 % (788980)ott+10_1_sil=32000:tgt=ground:random_seed=1886403184:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.53/1.28 % (788901)Instruction limit reached!
% 6.53/1.28 % (788901)------------------------------
% 6.53/1.28 % (788901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788901)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788901)Termination reason: Instruction limit
% 6.53/1.28 % (788901)Termination phase: Saturation
% 6.53/1.28 % (788901)Time elapsed: 0.458 s
% 6.53/1.28 % (788901)Peak memory usage: 18 MB
% 6.53/1.28 % (788901)Instructions burned: 880 (million)
% 6.53/1.28 % (789026)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3975323326:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 6.53/1.28 % Exception at run slice level
% 6.53/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.53/1.28 % (789047)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3510675017:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 6.53/1.28 % (788944)Instruction limit reached!
% 6.53/1.28 % (788944)------------------------------
% 6.53/1.28 % (788944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788944)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788944)Termination reason: Instruction limit
% 6.53/1.28 % (788944)Termination phase: Saturation
% 6.53/1.28 % (788944)Time elapsed: 0.353 s
% 6.53/1.28 % (788944)Peak memory usage: 26 MB
% 6.53/1.28 % (788944)Instructions burned: 1473 (million)
% 6.53/1.28 % (789047)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.53/1.28 % (789063)dis+21_1_sil=32000:sas=cadical:random_seed=3137186730:i=3773:amm=off_2991 on theBenchmark for (2991ds/3773Mi)
% 6.53/1.28 % (788964)Instruction limit reached!
% 6.53/1.28 % (788964)------------------------------
% 6.53/1.28 % (788964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.28 % (788964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.28 % (788964)CaDiCaL version: 2.1.3
% 6.53/1.28 % (788964)Termination reason: Instruction limit
% 6.53/1.28 % (788964)Termination phase: Saturation
% 6.53/1.28 % (788964)Time elapsed: 0.332 s
% 6.53/1.28 % (788964)Peak memory usage: 16 MB
% 6.53/1.28 % (788964)Instructions burned: 872 (million)
% 6.53/1.28 % (789065)ott+11_1_sil=16000:gs=on:random_seed=1500924130:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2990 on theBenchmark for (2990ds/2251Mi)
% 6.53/1.28 % (789065)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.53/1.28 % (788980) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-788813-788980"...
% 6.53/1.28 % (788980)...printing done.
% 6.53/1.28 % (788980)Refutation found. Thanks to Tanya!
% 6.53/1.28 % SZS status Theorem for theBenchmark
% 6.53/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 6.53/1.29 % (788980)------------------------------
% 6.53/1.29 % (788980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.53/1.29 % (788980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.29 % (788980)CaDiCaL version: 2.1.3
% 6.53/1.29 % (788980)Termination reason: Refutation
% 6.53/1.29 % (788980)Time elapsed: 0.399 s
% 6.53/1.29 % (788980)Peak memory usage: 18 MB
% 6.53/1.29 % (788980)Instructions burned: 888 (million)
% 6.53/1.29 % (788813)Success in time 1.049 s
% 6.53/1.29 % Vampire exiting
%------------------------------------------------------------------------------