%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU742^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:04 AM UTC 2026
% Result : Theorem 2.20s 0.64s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 122 ( 36 unt; 0 typ; 14 def)
% Number of atoms : 4766 (1243 equ; 0 cnn)
% Maximal formula atoms : 264 ( 39 avg)
% Number of connectives : 2795 ( 146 ~; 138 |; 816 &; 605 @)
% ( 23 <=>;1067 =>; 0 <=; 0 <~>)
% Maximal formula depth : 275 ( 19 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 505 ( 502 usr; 310 con; 0-4 aty)
% Number of variables : 177 ( 0 sgn 143 !; 34 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_279,type,
contrasubsetT1: $o ).
thf(func_def_280,type,
contrasubsetT2: $o ).
thf(func_def_281,type,
contrasubsetT3: $o ).
thf(func_def_282,type,
doubleComplementI1: $o ).
thf(func_def_283,type,
doubleComplementE1: $o ).
thf(func_def_284,type,
doubleComplementSub1: $o ).
thf(func_def_285,type,
doubleComplementSub2: $o ).
thf(func_def_286,type,
doubleComplementEq: $o ).
thf(func_def_287,type,
complementTnotintersectT: $o ).
thf(func_def_288,type,
complementImpComplementIntersect: $o ).
thf(func_def_289,type,
complementSubsetComplementIntersect: $o ).
thf(func_def_290,type,
complementInPowersetComplementIntersect: $o ).
thf(func_def_291,type,
contraSubsetComplement: $o ).
thf(func_def_292,type,
complementTcontraSubset: $o ).
thf(func_def_293,type,
binunionTILcontra: $o ).
thf(func_def_294,type,
binunionTIRcontra: $o ).
thf(func_def_295,type,
inIntersectImpInUnion: $o ).
thf(func_def_296,type,
inIntersectImpInUnion2: $o ).
thf(func_def_299,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_300,type,
vOR: $o > $o > $o ).
thf(func_def_301,type,
vAND: $o > $o > $o ).
thf(func_def_302,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_303,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_304,type,
vNOT: $o > $o ).
thf(func_def_305,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_306,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_307,type,
vIMP: $o > $o > $o ).
thf(func_def_308,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_309,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_310,type,
sP0: $o ).
thf(func_def_311,type,
sP1: $i > $i > $o ).
thf(func_def_312,type,
sP2: $i > $o ).
thf(func_def_313,type,
sP3: $o ).
thf(func_def_320,type,
sK10: $o ).
thf(func_def_333,type,
sK23: $i > ( $i > $i > $o ) > $i ).
thf(func_def_334,type,
sK24: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_335,type,
sK25: $i > ( $i > $i > $o ) > $i ).
thf(func_def_336,type,
sK26: $i > $i > $o ).
thf(func_def_338,type,
sK28: $i > $i ).
thf(func_def_339,type,
sK29: $i > $i ).
thf(func_def_352,type,
sK42: $i > $i ).
thf(func_def_367,type,
sK57: $o ).
thf(func_def_372,type,
sK62: $i > $o ).
thf(func_def_374,type,
sK64: $i > ( $i > $o ) > $i ).
thf(func_def_377,type,
sK67: $i > $o ).
thf(func_def_385,type,
sK75: $i > $i > $i > $i > $i ).
thf(func_def_386,type,
sK76: $i > $i > $i > $i > $i ).
thf(func_def_387,type,
sK77: $i > $i > $i > $i > $i ).
thf(func_def_388,type,
sK78: $i > $i > $i > $i > $i ).
thf(func_def_398,type,
sK88: $i > $i ).
thf(func_def_400,type,
sK90: $i > $i ).
thf(func_def_401,type,
sK91: $i > $i > $i > $i ).
thf(func_def_402,type,
sK92: $i > $i > $i > $i ).
thf(func_def_414,type,
sK104: $i > $i > $i > $i ).
thf(func_def_416,type,
sK106: $o ).
thf(func_def_422,type,
sK112: $i > $i ).
thf(func_def_425,type,
sK115: $i > ( $i > $i ) > $i > $i ).
thf(func_def_426,type,
sK116: $i > $i > $i ).
thf(func_def_447,type,
sK137: $o ).
thf(func_def_453,type,
sK143: ( $i > $o ) > $i > $i ).
thf(func_def_455,type,
sK145: $i > $o ).
thf(func_def_463,type,
sK153: $i > $i ).
thf(func_def_477,type,
sK167: ( $i > $o ) > $i ).
thf(func_def_478,type,
sK168: $i > $o ).
thf(func_def_479,type,
sK169: $i > $i ).
thf(func_def_494,type,
sK184: ( $i > $o ) > $i ).
thf(func_def_495,type,
sK185: $i > $o ).
thf(func_def_496,type,
sK186: $i > $i ).
thf(func_def_515,type,
sK205: $o ).
thf(func_def_522,type,
sK212: $i > $o ).
thf(func_def_540,type,
sK230: $i > $i > $i ).
thf(func_def_565,type,
sK255: $i > $o ).
thf(func_def_566,type,
sK256: $i > $o ).
thf(func_def_567,type,
sK257: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_568,type,
sK258: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_572,type,
sK262: $i > $i ).
thf(func_def_573,type,
sK263: $i > $i ).
thf(func_def_574,type,
sK264: $i > $i ).
thf(func_def_575,type,
sK265: $i > $i ).
thf(func_def_576,type,
sK266: $i > $i ).
thf(func_def_577,type,
sK267: $i > $i > $i > $i ).
thf(func_def_578,type,
sK268: $i > $i ).
thf(func_def_579,type,
sK269: $i > $i ).
thf(func_def_580,type,
sK270: $i > $i ).
thf(func_def_581,type,
sK271: $i > $i ).
thf(func_def_582,type,
sK272: $i > $i > $i ).
thf(func_def_583,type,
sK273: $i > $i > $i ).
thf(func_def_584,type,
sK274: $i > $i > $i > $i ).
thf(func_def_585,type,
sK275: $i > $i > $i > $i ).
thf(func_def_586,type,
sK276: $i > $i > $i > $i ).
thf(func_def_587,type,
sK277: $i > $i > $i ).
thf(func_def_588,type,
sK278: $i > $i > $i ).
thf(func_def_589,type,
sK279: $i > $i > $i ).
thf(func_def_591,type,
sK281: $i > $i > $o ).
thf(func_def_599,type,
sK289: $i > $i > $i > $i ).
thf(func_def_600,type,
sK290: $i > $i > $i > $i ).
thf(func_def_605,type,
sK295: $i > $i > $o ).
thf(func_def_609,type,
sK299: $i > ( $i > $o ) > $i > $i ).
thf(func_def_611,type,
sK301: $i > $o ).
thf(func_def_634,type,
sK324: $i > $o ).
thf(func_def_636,type,
sK326: ( $i > $o ) > $i > $i ).
thf(func_def_639,type,
sK329: $i > $i > $i ).
thf(func_def_656,type,
sK346: $o ).
thf(func_def_660,type,
sK350: $i > $i > $i ).
thf(func_def_671,type,
sK361: $o ).
thf(func_def_675,type,
sK365: $o ).
thf(func_def_678,type,
sK368: $o > $i > $i > $i ).
thf(func_def_681,type,
sK371: $o ).
thf(func_def_685,type,
sK375: $o ).
thf(func_def_688,type,
sK378: $i > $i > $i ).
thf(func_def_691,type,
sK381: $o ).
thf(func_def_698,type,
sK388: $i > $o ).
thf(func_def_700,type,
sK390: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_701,type,
sK391: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_703,type,
sK393: $i > $i ).
thf(func_def_705,type,
sK395: $i > ( $i > $i ) > $i > $i ).
thf(func_def_718,type,
sK408: $o ).
thf(func_def_721,type,
sK411: $i > $o ).
thf(func_def_729,type,
sK419: $i > $i > $o ).
thf(func_def_734,type,
sK424: $i > $o ).
thf(func_def_752,type,
sK442: $i > $o ).
thf(func_def_753,type,
sK443: $i > $i > $i ).
thf(func_def_758,type,
sK448: $i > $i > $o ).
thf(func_def_772,type,
sK462: $i > $i ).
thf(func_def_774,type,
sK464: ( $i > $i ) > $i > $i > $i ).
thf(func_def_776,type,
sK466: $i > $o ).
thf(func_def_782,type,
sK472: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_783,type,
sK473: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_787,type,
sK477: $i > $o ).
thf(func_def_806,type,
sK496: $i > $i > $i > $i > $i ).
thf(func_def_807,type,
sK497: $i > $o ).
thf(func_def_809,type,
sK499: $i > ( $i > $o ) > $i ).
thf(func_def_827,type,
sK517: $i > $o ).
thf(func_def_830,type,
sK520: $i > $o ).
thf(func_def_831,type,
sK521: $i > $o ).
thf(func_def_832,type,
sK522: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_833,type,
sK523: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_834,type,
sK524: $i > $o ).
thf(func_def_837,type,
sK527: $i > ( $i > $o ) > $i ).
thf(func_def_838,type,
sK528: $i > ( $i > $o ) > $i ).
thf(func_def_844,type,
sK534: $i > $i > $i > $i > $i ).
thf(func_def_845,type,
sK535: $i > $i > $i > $i > $i ).
thf(func_def_850,type,
sK540: $i > $o ).
thf(func_def_852,type,
sK542: ( $i > $o ) > $i ).
thf(func_def_853,type,
sK543: ( $i > $o ) > $i ).
thf(func_def_859,type,
sK549: $i > ( $i > $i ) > $i > $i ).
thf(func_def_861,type,
sK551: $i > $i ).
thf(func_def_882,type,
sK572: $i > $o ).
thf(func_def_889,type,
sK579: $o ).
thf(func_def_893,type,
sK583: $i > $o ).
thf(func_def_903,type,
sK593: $i > $i > $i > $i > $i ).
thf(func_def_910,type,
sK600: $i > $o ).
thf(func_def_913,type,
sK603: $i > ( $i > $o ) > $i ).
thf(func_def_914,type,
sK604: $i > $i > $i ).
thf(func_def_921,type,
sK611: $i > $i > $o ).
thf(func_def_924,type,
sK614: $o ).
thf(func_def_934,type,
sK624: $i > $i ).
thf(func_def_937,type,
sK627: $i > $i > ( $i > $i ) > $i ).
thf(func_def_938,type,
sK628: $i > $i > ( $i > $i ) > $i ).
thf(func_def_939,type,
sK629: $i > $i ).
thf(func_def_949,type,
sK639: $i > $o ).
thf(func_def_952,type,
sK642: $o ).
thf(func_def_958,type,
sK648: ( $i > $o ) > $i > $i ).
thf(func_def_960,type,
sK650: $i > $o ).
thf(func_def_969,type,
sK659: $i > ( $i > $o ) > $i ).
thf(func_def_970,type,
sK660: $i > $o ).
thf(func_def_972,type,
sK662: $o ).
thf(func_def_982,type,
sK672: $i > ( $i > $o ) > $i ).
thf(func_def_983,type,
sK673: $i > $o ).
thf(func_def_998,type,
sK688: $i > $o ).
thf(func_def_1000,type,
sK690: ( $i > $o ) > $i > $i ).
thf(func_def_1001,type,
sK691: ( $i > $o ) > $i > $i ).
thf(func_def_1006,type,
sK696: $i > $i ).
thf(func_def_1009,type,
sK699: $i > $i > $i ).
thf(func_def_1038,type,
sK728: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1039,type,
sK729: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1040,type,
sK730: $i > $o ).
thf(func_def_1041,type,
sK731: $i > $o ).
thf(func_def_1043,type,
sK733: $i > $i > $o ).
thf(func_def_1061,type,
sK751: $i > $i > $i > $i ).
thf(func_def_1067,type,
sK757: $i > $i > $i > $i > $i ).
thf(func_def_1072,type,
sK762: $i > $i ).
thf(func_def_1082,type,
sK772: $i > $o ).
thf(func_def_1084,type,
sK774: $o ).
thf(func_def_1089,type,
sK779: $i > $o ).
thf(func_def_1100,type,
sK790: ( $i > $o ) > $i ).
thf(func_def_1101,type,
sK791: $i > $o ).
thf(func_def_1102,type,
sK792: $i > $i ).
thf(func_def_1103,type,
sK793: $i > $i > $i ).
thf(func_def_1104,type,
sK794: $i > $i > $i ).
thf(func_def_1107,type,
sK797: $i > $o ).
thf(func_def_1118,type,
sK808: ( $i > $o ) > $i > $i ).
thf(func_def_1120,type,
sK810: $i > $o ).
thf(func_def_1122,type,
sK812: $i > $i > $o ).
thf(f101,axiom,
( binunionIL
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(f108,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(f110,axiom,
( binintersectEL
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(f114,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) )
= binintersectER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(f263,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(f264,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f263]) ).
thf(f404,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) )
= binintersectER ),
inference(rectify,[],[f114]) ).
thf(f405,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
<=> ( binintersectER = $true ) ),
inference(fool_elimination,[],[f404]) ).
thf(f454,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) ) )
= binintersectI ),
inference(rectify,[],[f108]) ).
thf(f455,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true ) ) )
<=> ( binintersectI = $true ) ),
inference(fool_elimination,[],[f454]) ).
thf(f513,plain,
( binunionIL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f101]) ).
thf(f514,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) )
<=> ( binunionIL = $true ) ),
inference(fool_elimination,[],[f513]) ).
thf(f558,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
=> ( in @ X0 @ X2 ) ) ) ),
inference(rectify,[],[f110]) ).
thf(f559,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f558]) ).
thf(f631,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f264]) ).
thf(f632,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
=> ( ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f631]) ).
thf(f849,plain,
( ( binintersectER = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[],[f405]) ).
thf(f906,plain,
( ( binintersectEL = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f559]) ).
thf(f910,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( binunionIL = $true ) ),
inference(ennf_transformation,[],[f514]) ).
thf(f1009,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( binintersectI = $true ) ),
inference(ennf_transformation,[],[f455]) ).
thf(f1010,plain,
( ( binintersectI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f1009]) ).
thf(f1033,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) )
!= $true )
& ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f632]) ).
thf(f1034,plain,
( ( iffalseProp1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( doubleComplementSub1 = $true )
& ( funcGraphProp4 = $true )
& ( secondinupair = $true )
& ( ubforcartprodlem2 = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( cartprodpairin = $true )
& ( powersetT_lem = $true )
& ( setukpairinjR = $true )
& ( sepSubset = $true )
& ( complementTnotintersectT = $true )
& ( iftrueProp2 = $true )
& ( brelnall2 = $true )
& ( subsetemptysetimpeq = $true )
& ( ap2apEq1 = $true )
& ( dpsetconstrEL1 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( omega0Ax = $true )
& ( setadjoinSub = $true )
& ( setminusSubset2 = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( ubforcartprodlem1 = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) )
!= $true )
& ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( upairsubunion = $true )
& ( setextT = $true )
& ( subsetE2 = $true )
& ( setunionsingleton = $true )
& ( setbeta = $true )
& ( binintersectER = $true )
& ( subsetI1 = $true )
& ( setunionI = $true )
& ( ap2p = $true )
& ( singletoninpowunion = $true )
& ( noeltsimpempty = $true )
& ( inIntersectImpInUnion = $true )
& ( nonemptyI = $true )
& ( notsubsetI = $true )
& ( funcGraphProp3 = $true )
& ( subbreln = $true )
& ( iftrue = $true )
& ( setadjoinOr = $true )
& ( omega__Cong = $true )
& ( dsetconstrER = $true )
& ( uniqinunit = $true )
& ( brelnall1 = $true )
& ( powersetI = $true )
& ( contraSubsetComplement = $true )
& ( singletonsubset = $true )
& ( symdiffI2 = $true )
& ( lam2p = $true )
& ( cartprodpairmemEL = $true )
& ( lam2lamEq = $true )
& ( complementSubsetComplementIntersect = $true )
& ( infuncsetfunc = $true )
& ( exuE3u = $true )
& ( prop2setI = $true )
& ( doubleComplementSub2 = $true )
& ( setukpairinjL2 = $true )
& ( binintersectTERcontra = $true )
& ( iftrueorfalse = $true )
& ( complementTE1 = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( powersetTE1 = $true )
& ( binintersectSubset1 = $true )
& ( complementTI1 = $true )
& ( powersetAx = $true )
& ( singletoninpowerset = $true )
& ( setextAx = $true )
& ( complementT_lem = $true )
& ( setukpairIL = $true )
& ( setukpairinjR2 = $true )
& ( quantDeMorgan4 = $true )
& ( funcextLem = $true )
& ( setunion__Cong = $true )
& ( cartprodpairmemER = $true )
& ( iftrueProp1 = $true )
& ( setadjoinIL = $true )
& ( ubforcartprodlem3 = $true )
& ( prop2set2propI = $true )
& ( setminusERneg = $true )
& ( vacuousDall = $true )
& ( cartprodsndin = $true )
& ( eta2 = $true )
& ( funcext = $true )
& ( binunionLsub = $true )
& ( contrasubsetT3 = $true )
& ( descrp = $true )
& ( contrasubsetT1 = $true )
& ( powerset__Cong = $true )
& ( ex1E2 = $true )
& ( binunionRsub = $true )
& ( symdiffE = $true )
& ( setoftrueEq = $true )
& ( iffalseProp2 = $true )
& ( singletonsuniq = $true )
& ( symdiffIneg1 = $true )
& ( subsetTrans = $true )
& ( cartprodmempair = $true )
& ( dpsetconstrER = $true )
& ( notinemptyset = $true )
& ( setextsub = $true )
& ( omegaIndAx = $true )
& ( emptyinunitempty = $true )
& ( bs114d = $true )
& ( binunionEcases = $true )
& ( wellorderingAx = $true )
& ( kpairsurjEq = $true )
& ( ksndsingleton = $true )
& ( setadjoinSub2 = $true )
& ( setukpairIR = $true )
& ( quantDeMorgan2 = $true )
& ( ex1E1 = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinAx = $true )
& ( upairsetIR = $true )
& ( binunionTILcontra = $true )
& ( binunionT_lem = $true )
& ( quantDeMorgan1 = $true )
& ( ex1I = $true )
& ( binunionIR = $true )
& ( setOfPairsIsBReln = $true )
& ( complementImpComplementIntersect = $true )
& ( singletonprop = $true )
& ( exuI3 = $true )
& ( nonemptyImpWitness = $true )
& ( upairinpowunion = $true )
& ( emptysetsubset = $true )
& ( eqinunit = $true )
& ( eqbreln = $true )
& ( cartprodmempair1 = $true )
& ( subset2powerset = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( cartprodfstpairEq = $true )
& ( setext = $true )
& ( notdallE = $true )
& ( iffalse = $true )
& ( dpsetconstrI = $true )
& ( inIntersectImpInUnion2 = $true )
& ( emptyI = $true )
& ( theeq = $true )
& ( setminusLsub = $true )
& ( beta1 = $true )
& ( powersetTI1 = $true )
& ( powersetI1 = $true )
& ( notdexE = $true )
& ( exu__Cong = $true )
& ( doubleComplementI1 = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( setminusI = $true )
& ( descr__Cong = $true )
& ( binintersectSubset2 = $true )
& ( setminusT_lem = $true )
& ( dpsetconstrERa = $true )
& ( binintersectT_lem = $true )
& ( replAx = $true )
& ( ifSingleton = $true )
& ( exuI2 = $true )
& ( symdiffI1 = $true )
& ( setukpairinjL = $true )
& ( inPowerset = $true )
& ( upairset2IR = $true )
& ( subPowSU = $true )
& ( subsetI2 = $true )
& ( setunionE = $true )
& ( eqimpsubset2 = $true )
& ( setukpairinjR11 = $true )
& ( binintersectSubset5 = $true )
& ( kpairiskpair = $true )
& ( setminusEL = $true )
& ( powersetE1 = $true )
& ( setminusSubset1 = $true )
& ( setukpairinjL1 = $true )
& ( funcGraphProp2 = $true )
& ( theprop = $true )
& ( setunionsingleton1 = $true )
& ( upairset2E = $true )
& ( doubleComplementEq = $true )
& ( funcImageSingleton = $true )
& ( lamProp = $true )
& ( setadjoinIR = $true )
& ( binunionTIRcontra = $true )
& ( emptyInPowerset = $true )
& ( exuE3e = $true )
& ( exuEu = $true )
& ( nonemptyI1 = $true )
& ( funcinfuncset = $true )
& ( binunionIL = $true )
& ( subsetRefl = $true )
& ( setunionE2 = $true )
& ( setukpairinjR12 = $true )
& ( binintersectRsub = $true )
& ( emptysetAx = $true )
& ( doubleComplementE1 = $true )
& ( setminusER = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectLsub = $true )
& ( inCongP = $true )
& ( setadjoin__Cong = $true )
& ( binintersectEL = $true )
& ( singletonsswitch = $true )
& ( setunionsingleton2 = $true )
& ( dpsetconstrSub = $true )
& ( dsetconstrEL = $true )
& ( exuI1 = $true )
& ( setminusILneg = $true )
& ( kfstsingleton = $true )
& ( binunionE = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyE1 = $true )
& ( cartprodsndpairEq = $true )
& ( funcext2 = $true )
& ( ex1I2 = $true )
& ( contrasubsetT2 = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinE = $true )
& ( sepInPowerset = $true )
& ( binintersectTELcontra = $true )
& ( notequalI2 = $true )
& ( complementTcontraSubset = $true )
& ( eta1 = $true )
& ( dsetconstrI = $true )
& ( cartprodmempaircEq = $true )
& ( app = $true )
& ( disjointsetsI1 = $true )
& ( upairequniteq = $true )
& ( binintersectSubset3 = $true )
& ( beta2 = $true )
& ( upairsetIL = $true )
& ( notequalI1 = $true )
& ( nonemptyE1 = $true )
& ( ap2apEq2 = $true )
& ( setukpairinjR1 = $true )
& ( subsetTI = $true )
& ( exuE2 = $true )
& ( lamp = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset4 = $true )
& ( in__Cong = $true )
& ( kpairp = $true )
& ( emptyset__Cong = $true )
& ( ksndpairEq = $true )
& ( upairsetE = $true )
& ( emptyinPowerset = $true )
& ( apProp = $true )
& ( contrasubsetT = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( funcGraphProp1 = $true )
& ( setminusELneg = $true )
& ( exuE1 = $true )
& ( symdiffIneg2 = $true )
& ( ifp = $true ) ),
inference(flattening,[],[f1033]) ).
thf(f1177,plain,
( ( ( binintersectER = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectER != $true ) ) ),
inference(nnf_transformation,[],[f849]) ).
thf(f1178,plain,
( ( ( binintersectER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X4 )
= $true ) )
| ( binintersectER != $true ) ) ),
inference(rectify,[],[f1177]) ).
thf(f1179,plain,
( ( ( binintersectER = $true )
| ( ( ( in @ sK47 @ ( binintersect @ sK49 @ sK48 ) )
= $true )
& ( ( in @ sK47 @ sK48 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X4 )
= $true ) )
| ( binintersectER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47,sK48,sK49]),skolemize(X0,sK47),skolemize(X1,sK48),skolemize(X2,sK49)],[f1178]) ).
thf(f1180,plain,
( ( ( binintersectEL = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[],[f906]) ).
thf(f1181,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[],[f1180]) ).
thf(f1182,plain,
( ( ( binintersectEL = $true )
| ( ( ( in @ sK51 @ sK50 )
!= $true )
& ( $true
= ( in @ sK51 @ ( binintersect @ sK50 @ sK52 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50,sK51,sK52]),skolemize(X0,sK50),skolemize(X1,sK51),skolemize(X2,sK52)],[f1181]) ).
thf(f1575,plain,
( ( ( binintersectI = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( binintersectI != $true ) ) ),
inference(nnf_transformation,[],[f1010]) ).
thf(f1576,plain,
( ( ( binintersectI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( $true
= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( binintersectI != $true ) ) ),
inference(rectify,[],[f1575]) ).
thf(f1577,plain,
( ( ( binintersectI = $true )
| ( ( ( in @ sK457 @ sK458 )
= $true )
& ( $true
!= ( in @ sK457 @ ( binintersect @ sK459 @ sK458 ) ) )
& ( ( in @ sK457 @ sK459 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( $true
= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( binintersectI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK457,sK458,sK459]),skolemize(X0,sK457),skolemize(X1,sK458),skolemize(X2,sK459)],[f1576]) ).
thf(f1587,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f910]) ).
thf(f1588,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X3 @ X5 ) )
!= $true )
& ( ( in @ X4 @ X3 )
= $true ) ) ) ),
inference(rectify,[],[f1587]) ).
thf(f1589,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ( ( ( in @ sK470 @ ( binunion @ sK469 @ sK471 ) )
!= $true )
& ( ( in @ sK470 @ sK469 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK469,sK470,sK471]),skolemize(X3,sK469),skolemize(X4,sK470),skolemize(X5,sK471)],[f1588]) ).
thf(f1884,plain,
( ( iffalseProp1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( doubleComplementSub1 = $true )
& ( funcGraphProp4 = $true )
& ( secondinupair = $true )
& ( ubforcartprodlem2 = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( cartprodpairin = $true )
& ( powersetT_lem = $true )
& ( setukpairinjR = $true )
& ( sepSubset = $true )
& ( complementTnotintersectT = $true )
& ( iftrueProp2 = $true )
& ( brelnall2 = $true )
& ( subsetemptysetimpeq = $true )
& ( ap2apEq1 = $true )
& ( dpsetconstrEL1 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( omega0Ax = $true )
& ( setadjoinSub = $true )
& ( setminusSubset2 = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( ubforcartprodlem1 = $true )
& ( ( in @ sK784 @ ( powerset @ sK783 ) )
= $true )
& ( $true
= ( in @ sK785 @ ( powerset @ sK783 ) ) )
& ( ( in @ sK787 @ ( binintersect @ ( binunion @ sK784 @ sK786 ) @ ( binunion @ sK785 @ sK786 ) ) )
!= $true )
& ( ( in @ sK787 @ ( binintersect @ sK784 @ sK785 ) )
= $true )
& ( $true
= ( in @ sK787 @ sK783 ) )
& ( ( in @ sK786 @ ( powerset @ sK783 ) )
= $true )
& ( upairsubunion = $true )
& ( setextT = $true )
& ( subsetE2 = $true )
& ( setunionsingleton = $true )
& ( setbeta = $true )
& ( binintersectER = $true )
& ( subsetI1 = $true )
& ( setunionI = $true )
& ( ap2p = $true )
& ( singletoninpowunion = $true )
& ( noeltsimpempty = $true )
& ( inIntersectImpInUnion = $true )
& ( nonemptyI = $true )
& ( notsubsetI = $true )
& ( funcGraphProp3 = $true )
& ( subbreln = $true )
& ( iftrue = $true )
& ( setadjoinOr = $true )
& ( omega__Cong = $true )
& ( dsetconstrER = $true )
& ( uniqinunit = $true )
& ( brelnall1 = $true )
& ( powersetI = $true )
& ( contraSubsetComplement = $true )
& ( singletonsubset = $true )
& ( symdiffI2 = $true )
& ( lam2p = $true )
& ( cartprodpairmemEL = $true )
& ( lam2lamEq = $true )
& ( complementSubsetComplementIntersect = $true )
& ( infuncsetfunc = $true )
& ( exuE3u = $true )
& ( prop2setI = $true )
& ( doubleComplementSub2 = $true )
& ( setukpairinjL2 = $true )
& ( binintersectTERcontra = $true )
& ( iftrueorfalse = $true )
& ( complementTE1 = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( powersetTE1 = $true )
& ( binintersectSubset1 = $true )
& ( complementTI1 = $true )
& ( powersetAx = $true )
& ( singletoninpowerset = $true )
& ( setextAx = $true )
& ( complementT_lem = $true )
& ( setukpairIL = $true )
& ( setukpairinjR2 = $true )
& ( quantDeMorgan4 = $true )
& ( funcextLem = $true )
& ( setunion__Cong = $true )
& ( cartprodpairmemER = $true )
& ( iftrueProp1 = $true )
& ( setadjoinIL = $true )
& ( ubforcartprodlem3 = $true )
& ( prop2set2propI = $true )
& ( setminusERneg = $true )
& ( vacuousDall = $true )
& ( cartprodsndin = $true )
& ( eta2 = $true )
& ( funcext = $true )
& ( binunionLsub = $true )
& ( contrasubsetT3 = $true )
& ( descrp = $true )
& ( contrasubsetT1 = $true )
& ( powerset__Cong = $true )
& ( ex1E2 = $true )
& ( binunionRsub = $true )
& ( symdiffE = $true )
& ( setoftrueEq = $true )
& ( iffalseProp2 = $true )
& ( singletonsuniq = $true )
& ( symdiffIneg1 = $true )
& ( subsetTrans = $true )
& ( cartprodmempair = $true )
& ( dpsetconstrER = $true )
& ( notinemptyset = $true )
& ( setextsub = $true )
& ( omegaIndAx = $true )
& ( emptyinunitempty = $true )
& ( bs114d = $true )
& ( binunionEcases = $true )
& ( wellorderingAx = $true )
& ( kpairsurjEq = $true )
& ( ksndsingleton = $true )
& ( setadjoinSub2 = $true )
& ( setukpairIR = $true )
& ( quantDeMorgan2 = $true )
& ( ex1E1 = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinAx = $true )
& ( upairsetIR = $true )
& ( binunionTILcontra = $true )
& ( binunionT_lem = $true )
& ( quantDeMorgan1 = $true )
& ( ex1I = $true )
& ( binunionIR = $true )
& ( setOfPairsIsBReln = $true )
& ( complementImpComplementIntersect = $true )
& ( singletonprop = $true )
& ( exuI3 = $true )
& ( nonemptyImpWitness = $true )
& ( upairinpowunion = $true )
& ( emptysetsubset = $true )
& ( eqinunit = $true )
& ( eqbreln = $true )
& ( cartprodmempair1 = $true )
& ( subset2powerset = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( cartprodfstpairEq = $true )
& ( setext = $true )
& ( notdallE = $true )
& ( iffalse = $true )
& ( dpsetconstrI = $true )
& ( inIntersectImpInUnion2 = $true )
& ( emptyI = $true )
& ( theeq = $true )
& ( setminusLsub = $true )
& ( beta1 = $true )
& ( powersetTI1 = $true )
& ( powersetI1 = $true )
& ( notdexE = $true )
& ( exu__Cong = $true )
& ( doubleComplementI1 = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( setminusI = $true )
& ( descr__Cong = $true )
& ( binintersectSubset2 = $true )
& ( setminusT_lem = $true )
& ( dpsetconstrERa = $true )
& ( binintersectT_lem = $true )
& ( replAx = $true )
& ( ifSingleton = $true )
& ( exuI2 = $true )
& ( symdiffI1 = $true )
& ( setukpairinjL = $true )
& ( inPowerset = $true )
& ( upairset2IR = $true )
& ( subPowSU = $true )
& ( subsetI2 = $true )
& ( setunionE = $true )
& ( eqimpsubset2 = $true )
& ( setukpairinjR11 = $true )
& ( binintersectSubset5 = $true )
& ( kpairiskpair = $true )
& ( setminusEL = $true )
& ( powersetE1 = $true )
& ( setminusSubset1 = $true )
& ( setukpairinjL1 = $true )
& ( funcGraphProp2 = $true )
& ( theprop = $true )
& ( setunionsingleton1 = $true )
& ( upairset2E = $true )
& ( doubleComplementEq = $true )
& ( funcImageSingleton = $true )
& ( lamProp = $true )
& ( setadjoinIR = $true )
& ( binunionTIRcontra = $true )
& ( emptyInPowerset = $true )
& ( exuE3e = $true )
& ( exuEu = $true )
& ( nonemptyI1 = $true )
& ( funcinfuncset = $true )
& ( binunionIL = $true )
& ( subsetRefl = $true )
& ( setunionE2 = $true )
& ( setukpairinjR12 = $true )
& ( binintersectRsub = $true )
& ( emptysetAx = $true )
& ( doubleComplementE1 = $true )
& ( setminusER = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectLsub = $true )
& ( inCongP = $true )
& ( setadjoin__Cong = $true )
& ( binintersectEL = $true )
& ( singletonsswitch = $true )
& ( setunionsingleton2 = $true )
& ( dpsetconstrSub = $true )
& ( dsetconstrEL = $true )
& ( exuI1 = $true )
& ( setminusILneg = $true )
& ( kfstsingleton = $true )
& ( binunionE = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyE1 = $true )
& ( cartprodsndpairEq = $true )
& ( funcext2 = $true )
& ( ex1I2 = $true )
& ( contrasubsetT2 = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinE = $true )
& ( sepInPowerset = $true )
& ( binintersectTELcontra = $true )
& ( notequalI2 = $true )
& ( complementTcontraSubset = $true )
& ( eta1 = $true )
& ( dsetconstrI = $true )
& ( cartprodmempaircEq = $true )
& ( app = $true )
& ( disjointsetsI1 = $true )
& ( upairequniteq = $true )
& ( binintersectSubset3 = $true )
& ( beta2 = $true )
& ( upairsetIL = $true )
& ( notequalI1 = $true )
& ( nonemptyE1 = $true )
& ( ap2apEq2 = $true )
& ( setukpairinjR1 = $true )
& ( subsetTI = $true )
& ( exuE2 = $true )
& ( lamp = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset4 = $true )
& ( in__Cong = $true )
& ( kpairp = $true )
& ( emptyset__Cong = $true )
& ( ksndpairEq = $true )
& ( upairsetE = $true )
& ( emptyinPowerset = $true )
& ( apProp = $true )
& ( contrasubsetT = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( funcGraphProp1 = $true )
& ( setminusELneg = $true )
& ( exuE1 = $true )
& ( symdiffIneg2 = $true )
& ( ifp = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK783,sK784,sK785,sK786,sK787]),skolemize(X0,sK783),skolemize(X1,sK784),skolemize(X2,sK785),skolemize(X3,sK786),skolemize(X4,sK787)],[f1034]) ).
thf(f1965,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( binintersectER != $true )
| ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) ) ),
inference(cnf_transformation,[],[f1179]) ).
thf(f1968,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( binintersectEL != $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true ) ),
inference(cnf_transformation,[],[f1182]) ).
thf(f2545,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( binintersectI != $true )
| ( ( in @ X3 @ X4 )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true )
| ( $true
= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) ) ),
inference(cnf_transformation,[],[f1577]) ).
thf(f2563,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[],[f1589]) ).
thf(f3024,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f1884]) ).
thf(f3036,plain,
binunionIL = $true,
inference(cnf_transformation,[],[f1884]) ).
thf(f3075,plain,
binintersectI = $true,
inference(cnf_transformation,[],[f1884]) ).
thf(f3197,plain,
binintersectER = $true,
inference(cnf_transformation,[],[f1884]) ).
thf(f3205,plain,
( ( in @ sK787 @ ( binintersect @ sK784 @ sK785 ) )
= $true ),
inference(cnf_transformation,[],[f1884]) ).
thf(f3206,plain,
( ( in @ sK787 @ ( binintersect @ ( binunion @ sK784 @ sK786 ) @ ( binunion @ sK785 @ sK786 ) ) )
!= $true ),
inference(cnf_transformation,[],[f1884]) ).
thf(f3578,definition,
( spl817_20
<=> ( binunionIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl817_20])],[avatar_definition]) ).
thf(f3581,plain,
spl817_20,
inference(avatar_split_clause,[],[f3036,f3578]) ).
thf(f4061,definition,
( spl817_130
<=> ( binintersectEL = $true ) ),
introduced(definition,[new_symbols(definition,[spl817_130])],[avatar_definition]) ).
thf(f4744,definition,
( spl817_283
<=> ( binintersectI = $true ) ),
introduced(definition,[new_symbols(definition,[spl817_283])],[avatar_definition]) ).
thf(f4747,plain,
spl817_283,
inference(avatar_split_clause,[],[f3075,f4744]) ).
thf(f5025,definition,
( spl817_343
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl817_343])],[avatar_definition]) ).
thf(f5026,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ~ spl817_343 ),
inference(avatar_component_clause,[],[f5025]) ).
thf(f5027,plain,
( ~ spl817_20
| spl817_343 ),
inference(avatar_split_clause,[],[f2563,f5025,f3578]) ).
thf(f5719,definition,
( spl817_495
<=> ( ( in @ sK787 @ ( binintersect @ ( binunion @ sK784 @ sK786 ) @ ( binunion @ sK785 @ sK786 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl817_495])],[avatar_definition]) ).
thf(f5721,plain,
( ( ( in @ sK787 @ ( binintersect @ ( binunion @ sK784 @ sK786 ) @ ( binunion @ sK785 @ sK786 ) ) )
!= $true )
| spl817_495 ),
inference(avatar_component_clause,[],[f5719]) ).
thf(f5722,plain,
~ spl817_495,
inference(avatar_split_clause,[],[f3206,f5719]) ).
thf(f5841,definition,
( spl817_520
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl817_520])],[avatar_definition]) ).
thf(f5842,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X4 )
= $true ) )
| ~ spl817_520 ),
inference(avatar_component_clause,[],[f5841]) ).
thf(f5844,definition,
( spl817_521
<=> ( binintersectER = $true ) ),
introduced(definition,[new_symbols(definition,[spl817_521])],[avatar_definition]) ).
thf(f5847,plain,
( spl817_520
| ~ spl817_521 ),
inference(avatar_split_clause,[],[f1965,f5844,f5841]) ).
thf(f7042,definition,
( spl817_774
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl817_774])],[avatar_definition]) ).
thf(f7043,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true )
| ( ( in @ X4 @ X3 )
= $true ) )
| ~ spl817_774 ),
inference(avatar_component_clause,[],[f7042]) ).
thf(f7044,plain,
( spl817_774
| ~ spl817_130 ),
inference(avatar_split_clause,[],[f1968,f4061,f7042]) ).
thf(f7545,definition,
( spl817_879
<=> ( ( in @ sK787 @ ( binintersect @ sK784 @ sK785 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl817_879])],[avatar_definition]) ).
thf(f7547,plain,
( ( ( in @ sK787 @ ( binintersect @ sK784 @ sK785 ) )
= $true )
| ~ spl817_879 ),
inference(avatar_component_clause,[],[f7545]) ).
thf(f7548,plain,
spl817_879,
inference(avatar_split_clause,[],[f3205,f7545]) ).
thf(f8920,definition,
( spl817_1161
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( $true
= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl817_1161])],[avatar_definition]) ).
thf(f8921,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ~ spl817_1161 ),
inference(avatar_component_clause,[],[f8920]) ).
thf(f8922,plain,
( ~ spl817_283
| spl817_1161 ),
inference(avatar_split_clause,[],[f2545,f8920,f4744]) ).
thf(f9310,plain,
spl817_130,
inference(avatar_split_clause,[],[f3024,f4061]) ).
thf(f9401,plain,
spl817_521,
inference(avatar_split_clause,[],[f3197,f5844]) ).
thf(f10124,definition,
( spl817_1320
<=> ( $true
= ( in @ sK787 @ sK785 ) ) ),
introduced(definition,[new_symbols(definition,[spl817_1320])],[avatar_definition]) ).
thf(f10133,definition,
( spl817_1322
<=> ( ( in @ sK787 @ ( binunion @ sK785 @ sK786 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl817_1322])],[avatar_definition]) ).
thf(f10134,plain,
( ( ( in @ sK787 @ ( binunion @ sK785 @ sK786 ) )
= $true )
| ~ spl817_1322 ),
inference(avatar_component_clause,[],[f10133]) ).
thf(f10135,plain,
( ( ( in @ sK787 @ ( binunion @ sK785 @ sK786 ) )
!= $true )
| spl817_1322 ),
inference(avatar_component_clause,[],[f10133]) ).
thf(f10160,definition,
( spl817_1325
<=> ( $true
= ( in @ sK787 @ sK784 ) ) ),
introduced(definition,[new_symbols(definition,[spl817_1325])],[avatar_definition]) ).
thf(f10162,plain,
( ( $true
= ( in @ sK787 @ sK784 ) )
| ~ spl817_1325 ),
inference(avatar_component_clause,[],[f10160]) ).
thf(f10165,definition,
( spl817_1326
<=> ( ( in @ sK787 @ ( binunion @ sK784 @ sK786 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl817_1326])],[avatar_definition]) ).
thf(f10167,plain,
( ( ( in @ sK787 @ ( binunion @ sK784 @ sK786 ) )
!= $true )
| spl817_1326 ),
inference(avatar_component_clause,[],[f10165]) ).
thf(f10611,plain,
( ( $true
!= ( in @ sK787 @ sK785 ) )
| ( $true != $true )
| ~ spl817_343
| spl817_1322 ),
inference(superposition,[],[f10135,f5026]) ).
thf(f10617,plain,
( ( $true
!= ( in @ sK787 @ sK785 ) )
| ~ spl817_343
| spl817_1322 ),
inference(trivial_inequality_removal,[],[f10611]) ).
thf(f10619,plain,
( ~ spl817_1320
| ~ spl817_343
| spl817_1322 ),
inference(avatar_split_clause,[],[f10617,f10133,f5025,f10124]) ).
thf(f10656,plain,
( ( $true
= ( in @ sK787 @ sK785 ) )
| ( $true != $true )
| ~ spl817_520
| ~ spl817_879 ),
inference(superposition,[],[f5842,f7547]) ).
thf(f10666,plain,
( ( $true
= ( in @ sK787 @ sK785 ) )
| ~ spl817_520
| ~ spl817_879 ),
inference(trivial_inequality_removal,[],[f10656]) ).
thf(f10671,plain,
( spl817_1320
| ~ spl817_520
| ~ spl817_879 ),
inference(avatar_split_clause,[],[f10666,f7545,f5841,f10124]) ).
thf(f10712,plain,
( ( $true != $true )
| ( $true
= ( in @ sK787 @ sK784 ) )
| ~ spl817_774
| ~ spl817_879 ),
inference(superposition,[],[f7043,f7547]) ).
thf(f10713,plain,
( ( $true
= ( in @ sK787 @ sK784 ) )
| ~ spl817_774
| ~ spl817_879 ),
inference(trivial_inequality_removal,[],[f10712]) ).
thf(f10724,plain,
( spl817_1325
| ~ spl817_774
| ~ spl817_879 ),
inference(avatar_split_clause,[],[f10713,f7545,f7042,f10160]) ).
thf(f12005,plain,
( ( ( in @ sK787 @ ( binunion @ sK785 @ sK786 ) )
!= $true )
| ( ( in @ sK787 @ ( binunion @ sK784 @ sK786 ) )
!= $true )
| ( $true != $true )
| spl817_495
| ~ spl817_1161 ),
inference(superposition,[],[f5721,f8921]) ).
thf(f12017,plain,
( ( ( in @ sK787 @ ( binunion @ sK785 @ sK786 ) )
!= $true )
| ( ( in @ sK787 @ ( binunion @ sK784 @ sK786 ) )
!= $true )
| spl817_495
| ~ spl817_1161 ),
inference(trivial_inequality_removal,[],[f12005]) ).
thf(f12020,plain,
( ( ( in @ sK787 @ ( binunion @ sK784 @ sK786 ) )
!= $true )
| spl817_495
| ~ spl817_1161
| ~ spl817_1322 ),
inference(forward_subsumption_resolution,[],[f12017,f10134]) ).
thf(f12021,plain,
( ~ spl817_1326
| spl817_495
| ~ spl817_1161
| ~ spl817_1322 ),
inference(avatar_split_clause,[],[f12020,f10133,f8920,f5719,f10165]) ).
thf(f12144,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK787 @ sK784 ) )
| ~ spl817_343
| spl817_1326 ),
inference(superposition,[],[f10167,f5026]) ).
thf(f12148,plain,
( ( $true
!= ( in @ sK787 @ sK784 ) )
| ~ spl817_343
| spl817_1326 ),
inference(trivial_inequality_removal,[],[f12144]) ).
thf(f12150,plain,
( $false
| ~ spl817_343
| ~ spl817_1325
| spl817_1326 ),
inference(forward_subsumption_resolution,[],[f12148,f10162]) ).
thf(f12151,plain,
( ~ spl817_343
| ~ spl817_1325
| spl817_1326 ),
inference(avatar_contradiction_clause,[],[f12150]) ).
cnf(s12,plain,
spl817_20,
inference(sat_conversion,[],[f3581]) ).
cnf(s182,plain,
spl817_283,
inference(sat_conversion,[],[f4747]) ).
cnf(s237,plain,
( ~ spl817_20
| spl817_343 ),
inference(sat_conversion,[],[f5027]) ).
cnf(s375,plain,
~ spl817_495,
inference(sat_conversion,[],[f5722]) ).
cnf(s399,plain,
( spl817_520
| ~ spl817_521 ),
inference(sat_conversion,[],[f5847]) ).
cnf(s677,plain,
( ~ spl817_130
| spl817_774 ),
inference(sat_conversion,[],[f7044]) ).
cnf(s793,plain,
spl817_879,
inference(sat_conversion,[],[f7548]) ).
cnf(s1147,plain,
( ~ spl817_283
| spl817_1161 ),
inference(sat_conversion,[],[f8922]) ).
cnf(s1248,plain,
spl817_130,
inference(sat_conversion,[],[f9310]) ).
cnf(s1272,plain,
spl817_521,
inference(sat_conversion,[],[f9401]) ).
cnf(s1377,plain,
( ~ spl817_343
| ~ spl817_1320
| spl817_1322 ),
inference(sat_conversion,[],[f10619]) ).
cnf(s1380,plain,
( ~ spl817_520
| ~ spl817_879
| spl817_1320 ),
inference(sat_conversion,[],[f10671]) ).
cnf(s1384,plain,
( ~ spl817_774
| ~ spl817_879
| spl817_1325 ),
inference(sat_conversion,[],[f10724]) ).
cnf(s1403,plain,
( spl817_495
| ~ spl817_1161
| ~ spl817_1322
| ~ spl817_1326 ),
inference(sat_conversion,[],[f12021]) ).
cnf(s1409,plain,
( ~ spl817_343
| ~ spl817_1325
| spl817_1326 ),
inference(sat_conversion,[],[f12151]) ).
cnf(s1481,plain,
spl817_774,
inference(rat,[],[s677,s1248]) ).
cnf(s1482,plain,
spl817_1325,
inference(rat,[],[s1384,s793,s1481]) ).
cnf(s1569,plain,
spl817_520,
inference(rat,[],[s399,s1272]) ).
cnf(s1570,plain,
spl817_1320,
inference(rat,[],[s1380,s793,s1569]) ).
cnf(s1659,plain,
spl817_1161,
inference(rat,[],[s1147,s182]) ).
cnf(s1758,plain,
spl817_343,
inference(rat,[],[s237,s12]) ).
cnf(s1759,plain,
spl817_1326,
inference(rat,[],[s1409,s1482,s1758]) ).
cnf(s1760,plain,
spl817_1322,
inference(rat,[],[s1377,s1570,s1758]) ).
cnf(s1762,plain,
$false,
inference(rat,[],[s1403,s1659,s375,s1759,s1760]) ).
thf(f12153,plain,
$false,
inference(avatar_sat_refutation,[],[s1762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU742^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n002.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:22:08 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.20/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.43 % (1360908)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.45/0.43 % (1360926)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=424676164:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.45/0.43 % (1360928)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.45/0.43 % (1360928)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.45/0.43 % (1360926)Instruction limit reached!
% 0.45/0.43 % (1360926)------------------------------
% 0.45/0.43 % (1360926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.43 % (1360926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.43 % (1360926)CaDiCaL version: 2.1.3
% 0.45/0.43 % (1360926)Termination reason: Instruction limit
% 0.45/0.43 % (1360926)Termination phase: shuffling
% 0.45/0.43 % (1360926)Time elapsed: 0.006 s
% 0.45/0.43 % (1360926)Peak memory usage: 10 MB
% 0.45/0.43 % (1360926)Instructions burned: 25 (million)
% 0.45/0.43 % (1360922)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=148146509:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.45/0.43 % (1360924)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=646477266:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.45/0.43 % (1360925)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3414858190:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.45/0.43 % (1360928)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=179518505:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.45/0.43 % (1360924)Instruction limit reached!
% 0.45/0.43 % (1360924)------------------------------
% 0.45/0.43 % (1360924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.43 % (1360924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.43 % (1360924)CaDiCaL version: 2.1.3
% 0.45/0.43 % (1360924)Termination reason: Instruction limit
% 0.45/0.43 % (1360924)Termination phase: shuffling
% 0.45/0.43 % (1360924)Time elapsed: 0.002 s
% 0.45/0.43 % (1360924)Peak memory usage: 10 MB
% 0.45/0.43 % (1360924)Instructions burned: 3 (million)
% 0.45/0.43 % (1360942)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1689740064:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.45/0.43 % (1360942)Instruction limit reached!
% 0.45/0.43 % (1360942)------------------------------
% 0.45/0.43 % (1360942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.43 % (1360942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.43 % (1360942)CaDiCaL version: 2.1.3
% 0.45/0.43 % (1360942)Termination reason: Instruction limit
% 0.45/0.43 % (1360942)Termination phase: shuffling
% 0.45/0.43 % (1360942)Time elapsed: 0.001 s
% 0.45/0.43 % (1360942)Peak memory usage: 10 MB
% 0.45/0.43 % (1360942)Instructions burned: 3 (million)
% 0.45/0.43 % (1360927)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1753140889:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.45/0.43 % (1360923)lrs+10_16_si=on:nwc=1.5:random_seed=1935122820:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.45/0.43 % (1360955)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.45/0.43 % (1360947)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2743163035:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.45/0.43 % (1360955)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=523687315:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.45/0.43 % (1360947)Instruction limit reached!
% 0.45/0.43 % (1360947)------------------------------
% 0.45/0.43 % (1360947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.46 % (1360947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.46 % (1360947)CaDiCaL version: 2.1.3
% 0.45/0.46 % (1360947)Termination reason: Instruction limit
% 0.45/0.46 % (1360947)Termination phase: shuffling
% 0.45/0.46 % (1360947)Time elapsed: 0.003 s
% 0.45/0.46 % (1360947)Peak memory usage: 10 MB
% 0.45/0.46 % (1360947)Instructions burned: 6 (million)
% 0.45/0.46 % (1360955)Instruction limit reached!
% 0.45/0.46 % (1360955)------------------------------
% 0.45/0.46 % (1360955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.46 % (1360955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.46 % (1360955)CaDiCaL version: 2.1.3
% 0.45/0.46 % (1360955)Termination reason: Instruction limit
% 0.45/0.46 % (1360955)Termination phase: shuffling
% 0.45/0.46 % (1360955)Time elapsed: 0.002 s
% 0.45/0.46 % (1360955)Peak memory usage: 10 MB
% 0.45/0.46 % (1360955)Instructions burned: 8 (million)
% 0.45/0.46 % (1360923)Instruction limit reached!
% 0.45/0.46 % (1360923)------------------------------
% 0.45/0.46 % (1360923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.46 % (1360923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.46 % (1360923)CaDiCaL version: 2.1.3
% 1.16/0.46 % (1360923)Termination reason: Instruction limit
% 1.16/0.46 % (1360923)Termination phase: shuffling
% 1.16/0.46 % (1360923)Time elapsed: 0.011 s
% 1.16/0.46 % (1360923)Peak memory usage: 10 MB
% 1.16/0.46 % (1360923)Instructions burned: 18 (million)
% 1.16/0.46 % (1360968)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.16/0.46 % (1360968)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.16/0.46 % (1360968)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4084512035:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.16/0.46 % (1360922)Instruction limit reached!
% 1.16/0.46 % (1360922)------------------------------
% 1.16/0.46 % (1360922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.46 % (1360922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.46 % (1360922)CaDiCaL version: 2.1.3
% 1.16/0.46 % (1360922)Termination reason: Instruction limit
% 1.16/0.46 % (1360922)Termination phase: Preprocessing 3
% 1.16/0.46 % (1360922)Time elapsed: 0.041 s
% 1.16/0.46 % (1360922)Peak memory usage: 13 MB
% 1.16/0.46 % (1360922)Instructions burned: 88 (million)
% 1.16/0.46 % (1360967)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1676647296:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.16/0.46 % (1360968)Instruction limit reached!
% 1.16/0.46 % (1360968)------------------------------
% 1.16/0.46 % (1360968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.46 % (1360968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.46 % (1360968)CaDiCaL version: 2.1.3
% 1.16/0.46 % (1360968)Termination reason: Instruction limit
% 1.16/0.46 % (1360968)Termination phase: shuffling
% 1.16/0.46 % (1360968)Time elapsed: 0.007 s
% 1.16/0.46 % (1360968)Peak memory usage: 11 MB
% 1.16/0.46 % (1360968)Instructions burned: 31 (million)
% 1.16/0.46 % (1360970)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3783799439:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.16/0.46 % (1360967)Instruction limit reached!
% 1.16/0.46 % (1360967)------------------------------
% 1.16/0.46 % (1360967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.46 % (1360967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.46 % (1360967)CaDiCaL version: 2.1.3
% 1.16/0.46 % (1360967)Termination reason: Instruction limit
% 1.16/0.46 % (1360967)Termination phase: shuffling
% 1.16/0.46 % (1360967)Time elapsed: 0.006 s
% 1.16/0.46 % (1360967)Peak memory usage: 10 MB
% 1.16/0.46 % (1360967)Instructions burned: 13 (million)
% 1.16/0.46 % (1360927)Instruction limit reached!
% 1.16/0.46 % (1360927)------------------------------
% 1.16/0.46 % (1360927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.50 % (1360927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.50 % (1360927)CaDiCaL version: 2.1.3
% 1.16/0.50 % (1360927)Termination reason: Instruction limit
% 1.16/0.50 % (1360927)Termination phase: Preprocessing 3
% 1.16/0.50 % (1360927)Time elapsed: 0.038 s
% 1.16/0.50 % (1360927)Peak memory usage: 12 MB
% 1.16/0.50 % (1360927)Instructions burned: 76 (million)
% 1.16/0.50 % (1360977)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.16/0.50 % (1360977)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=584612659:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.16/0.50 % (1360977)Instruction limit reached!
% 1.16/0.50 % (1360977)------------------------------
% 1.16/0.50 % (1360977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.50 % (1360977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.50 % (1360977)CaDiCaL version: 2.1.3
% 1.16/0.50 % (1360977)Termination reason: Instruction limit
% 1.16/0.50 % (1360977)Termination phase: shuffling
% 1.16/0.50 % (1360977)Time elapsed: 0.001 s
% 1.16/0.50 % (1360977)Peak memory usage: 10 MB
% 1.16/0.50 % (1360977)Instructions burned: 3 (million)
% 1.16/0.50 % (1360974)lrs+10_1_si=on:cs=on:random_seed=4210445557:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.16/0.50 % (1360974)Instruction limit reached!
% 1.16/0.50 % (1360974)------------------------------
% 1.16/0.50 % (1360974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.50 % (1360974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.50 % (1360974)CaDiCaL version: 2.1.3
% 1.16/0.50 % (1360974)Termination reason: Instruction limit
% 1.16/0.50 % (1360974)Termination phase: shuffling
% 1.16/0.50 % (1360974)Time elapsed: 0.004 s
% 1.16/0.50 % (1360974)Peak memory usage: 10 MB
% 1.16/0.50 % (1360974)Instructions burned: 8 (million)
% 1.16/0.50 % (1360928)Instruction limit reached!
% 1.16/0.50 % (1360928)------------------------------
% 1.16/0.50 % (1360928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.50 % (1360928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.50 % (1360928)CaDiCaL version: 2.1.3
% 1.16/0.50 % (1360928)Termination reason: Instruction limit
% 1.16/0.50 % (1360928)Termination phase: Saturation
% 1.16/0.50 % (1360928)Time elapsed: 0.066 s
% 1.16/0.50 % (1360928)Peak memory usage: 12 MB
% 1.16/0.50 % (1360928)Instructions burned: 158 (million)
% 1.16/0.50 % (1360985)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1538893357:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 1.16/0.50 % (1360979)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=172946461:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.16/0.50 % (1360981)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3783886911:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.16/0.50 % (1360985)Instruction limit reached!
% 1.16/0.50 % (1360985)------------------------------
% 1.16/0.50 % (1360985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.50 % (1360985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.50 % (1360985)CaDiCaL version: 2.1.3
% 1.16/0.50 % (1360985)Termination reason: Instruction limit
% 1.16/0.50 % (1360985)Termination phase: Property scanning
% 1.16/0.50 % (1360985)Time elapsed: 0.006 s
% 1.16/0.50 % (1360985)Peak memory usage: 11 MB
% 1.16/0.50 % (1360985)Instructions burned: 26 (million)
% 1.16/0.50 % (1360988)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1308561314:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.16/0.50 % (1360970)Instruction limit reached!
% 1.16/0.50 % (1360970)------------------------------
% 1.16/0.50 % (1360970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.50 % (1360970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.50 % (1360970)CaDiCaL version: 2.1.3
% 1.16/0.50 % (1360970)Termination reason: Instruction limit
% 1.16/0.50 % (1360970)Termination phase: Property scanning
% 1.16/0.50 % (1360970)Time elapsed: 0.037 s
% 1.16/0.55 % (1360970)Peak memory usage: 11 MB
% 1.16/0.55 % (1360970)Instructions burned: 89 (million)
% 1.16/0.55 % (1360993)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3014496701:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.16/0.55 % (1360990)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3201992858:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.16/0.55 % (1360979)Instruction limit reached!
% 1.16/0.55 % (1360979)------------------------------
% 1.16/0.55 % (1360979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.55 % (1360979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.55 % (1360979)CaDiCaL version: 2.1.3
% 1.16/0.55 % (1360979)Termination reason: Instruction limit
% 1.16/0.55 % (1360979)Termination phase: Property scanning
% 1.16/0.55 % (1360979)Time elapsed: 0.017 s
% 1.16/0.55 % (1360979)Peak memory usage: 11 MB
% 1.16/0.55 % (1360979)Instructions burned: 39 (million)
% 1.16/0.55 % (1360993)Instruction limit reached!
% 1.16/0.55 % (1360993)------------------------------
% 1.16/0.55 % (1360993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.55 % (1360993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.55 % (1360993)CaDiCaL version: 2.1.3
% 1.16/0.55 % (1360993)Termination reason: Instruction limit
% 1.16/0.55 % (1360993)Termination phase: shuffling
% 1.16/0.55 % (1360993)Time elapsed: 0.004 s
% 1.16/0.55 % (1360993)Peak memory usage: 10 MB
% 1.16/0.55 % (1360993)Instructions burned: 19 (million)
% 1.16/0.55 % (1360988)Instruction limit reached!
% 1.16/0.55 % (1360988)------------------------------
% 1.16/0.55 % (1360988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.55 % (1360988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.55 % (1360988)CaDiCaL version: 2.1.3
% 1.16/0.55 % (1360988)Termination reason: Instruction limit
% 1.16/0.55 % (1360988)Termination phase: shuffling
% 1.16/0.55 % (1360988)Time elapsed: 0.007 s
% 1.16/0.55 % (1360988)Peak memory usage: 10 MB
% 1.16/0.55 % (1360988)Instructions burned: 16 (million)
% 1.16/0.55 % (1360999)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3288834553:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.16/0.55 % (1360995)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2160660083:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.16/0.55 % (1360998)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1836834385:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.16/0.55 % (1360995)Instruction limit reached!
% 1.16/0.55 % (1360995)------------------------------
% 1.16/0.55 % (1360995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.55 % (1360995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.55 % (1360995)CaDiCaL version: 2.1.3
% 1.16/0.55 % (1360995)Termination reason: Instruction limit
% 1.16/0.55 % (1360995)Termination phase: shuffling
% 1.16/0.55 % (1360995)Time elapsed: 0.003 s
% 1.16/0.55 % (1360995)Peak memory usage: 10 MB
% 1.16/0.55 % (1360995)Instructions burned: 6 (million)
% 1.16/0.55 % (1360999)Instruction limit reached!
% 1.16/0.55 % (1360999)------------------------------
% 1.16/0.55 % (1360999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.55 % (1360999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.55 % (1360999)CaDiCaL version: 2.1.3
% 1.16/0.55 % (1360999)Termination reason: Instruction limit
% 1.16/0.55 % (1360999)Termination phase: shuffling
% 1.16/0.55 % (1360999)Time elapsed: 0.006 s
% 1.16/0.55 % (1360999)Peak memory usage: 11 MB
% 1.16/0.55 % (1360999)Instructions burned: 26 (million)
% 1.16/0.55 % (1361000)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1467885774:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.16/0.55 % (1361005)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.16/0.55 % (1360998)Instruction limit reached!
% 1.16/0.55 % (1360998)------------------------------
% 1.16/0.55 % (1360998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.55 % (1360998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.60 % (1360998)CaDiCaL version: 2.1.3
% 1.85/0.60 % (1360998)Termination reason: Instruction limit
% 1.85/0.60 % (1360998)Termination phase: shuffling
% 1.85/0.60 % (1360998)Time elapsed: 0.012 s
% 1.85/0.60 % (1360998)Peak memory usage: 11 MB
% 1.85/0.60 % (1360998)Instructions burned: 28 (million)
% 1.85/0.60 % (1361005)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1771930303:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.85/0.60 % (1361004)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.85/0.60 % (1361004)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.85/0.60 % (1361005)Instruction limit reached!
% 1.85/0.60 % (1361005)------------------------------
% 1.85/0.60 % (1361005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.60 % (1361005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.60 % (1361005)CaDiCaL version: 2.1.3
% 1.85/0.60 % (1361005)Termination reason: Instruction limit
% 1.85/0.60 % (1361005)Termination phase: shuffling
% 1.85/0.60 % (1361005)Time elapsed: 0.003 s
% 1.85/0.60 % (1361005)Peak memory usage: 11 MB
% 1.85/0.60 % (1361005)Instructions burned: 12 (million)
% 1.85/0.60 % (1361004)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3540003600:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.85/0.60 % (1361004)Instruction limit reached!
% 1.85/0.60 % (1361004)------------------------------
% 1.85/0.60 % (1361004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.60 % (1361004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.60 % (1361004)CaDiCaL version: 2.1.3
% 1.85/0.60 % (1361004)Termination reason: Instruction limit
% 1.85/0.60 % (1361004)Termination phase: shuffling
% 1.85/0.60 % (1361004)Time elapsed: 0.007 s
% 1.85/0.60 % (1361004)Peak memory usage: 10 MB
% 1.85/0.60 % (1361004)Instructions burned: 15 (million)
% 1.85/0.60 % (1361009)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2311604575:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.85/0.60 % (1361009)Instruction limit reached!
% 1.85/0.60 % (1361009)------------------------------
% 1.85/0.60 % (1361009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.60 % (1361009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.60 % (1361009)CaDiCaL version: 2.1.3
% 1.85/0.60 % (1361009)Termination reason: Instruction limit
% 1.85/0.60 % (1361009)Termination phase: shuffling
% 1.85/0.60 % (1361009)Time elapsed: 0.002 s
% 1.85/0.60 % (1361009)Peak memory usage: 10 MB
% 1.85/0.60 % (1361009)Instructions burned: 8 (million)
% 1.85/0.60 % (1361008)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3931017117:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.85/0.60 % (1361000)Instruction limit reached!
% 1.85/0.60 % (1361000)------------------------------
% 1.85/0.60 % (1361000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.60 % (1361000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.60 % (1361000)CaDiCaL version: 2.1.3
% 1.85/0.60 % (1361000)Termination reason: Instruction limit
% 1.85/0.60 % (1361000)Termination phase: Preprocessing 3
% 1.85/0.60 % (1361000)Time elapsed: 0.029 s
% 1.85/0.60 % (1361000)Peak memory usage: 12 MB
% 1.85/0.60 % (1361000)Instructions burned: 62 (million)
% 1.85/0.60 % (1361013)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=41311462:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.85/0.60 % (1361013)Instruction limit reached!
% 1.85/0.60 % (1361013)------------------------------
% 1.85/0.60 % (1361013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.60 % (1361013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.60 % (1361013)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361013)Termination reason: Instruction limit
% 2.20/0.64 % (1361013)Termination phase: shuffling
% 2.20/0.64 % (1361013)Time elapsed: 0.005 s
% 2.20/0.64 % (1361013)Peak memory usage: 10 MB
% 2.20/0.64 % (1361013)Instructions burned: 22 (million)
% 2.20/0.64 % (1361012)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2200110916:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.20/0.64 % (1361008)Instruction limit reached!
% 2.20/0.64 % (1361008)------------------------------
% 2.20/0.64 % (1361008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361008)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361008)Termination reason: Instruction limit
% 2.20/0.64 % (1361008)Termination phase: shuffling
% 2.20/0.64 % (1361008)Time elapsed: 0.014 s
% 2.20/0.64 % (1361008)Peak memory usage: 11 MB
% 2.20/0.64 % (1361008)Instructions burned: 31 (million)
% 2.20/0.64 % (1361015)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=884617177:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.20/0.64 % (1361018)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3809905787:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.20/0.64 % (1361012)Instruction limit reached!
% 2.20/0.64 % (1361012)------------------------------
% 2.20/0.64 % (1361012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361012)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361012)Termination reason: Instruction limit
% 2.20/0.64 % (1361012)Termination phase: shuffling
% 2.20/0.64 % (1361012)Time elapsed: 0.010 s
% 2.20/0.64 % (1361012)Peak memory usage: 11 MB
% 2.20/0.64 % (1361012)Instructions burned: 24 (million)
% 2.20/0.64 % (1361019)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3869392393:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.20/0.64 % (1360981)Instruction limit reached!
% 2.20/0.64 % (1360981)------------------------------
% 2.20/0.64 % (1360981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1360981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1360981)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1360981)Termination reason: Instruction limit
% 2.20/0.64 % (1360981)Termination phase: Saturation
% 2.20/0.64 % (1360981)Time elapsed: 0.110 s
% 2.20/0.64 % (1360981)Peak memory usage: 15 MB
% 2.20/0.64 % (1360981)Instructions burned: 251 (million)
% 2.20/0.64 % (1361022)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=329373998:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.20/0.64 % (1361018)Instruction limit reached!
% 2.20/0.64 % (1361018)------------------------------
% 2.20/0.64 % (1361018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361018)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361018)Termination reason: Instruction limit
% 2.20/0.64 % (1361018)Termination phase: Property scanning
% 2.20/0.64 % (1361018)Time elapsed: 0.032 s
% 2.20/0.64 % (1361018)Peak memory usage: 13 MB
% 2.20/0.64 % (1361018)Instructions burned: 144 (million)
% 2.20/0.64 % (1361024)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.20/0.64 % (1361024)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1580362250:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.20/0.64 % (1361022)Instruction limit reached!
% 2.20/0.64 % (1361022)------------------------------
% 2.20/0.64 % (1361022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361022)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361022)Termination reason: Instruction limit
% 2.20/0.64 % (1361022)Termination phase: Property scanning
% 2.20/0.64 % (1361022)Time elapsed: 0.018 s
% 2.20/0.64 % (1361022)Peak memory usage: 11 MB
% 2.20/0.64 % (1361022)Instructions burned: 42 (million)
% 2.20/0.64 % (1361024)Instruction limit reached!
% 2.20/0.64 % (1361024)------------------------------
% 2.20/0.64 % (1361024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361024)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361024)Termination reason: Instruction limit
% 2.20/0.64 % (1361024)Termination phase: shuffling
% 2.20/0.64 % (1361024)Time elapsed: 0.003 s
% 2.20/0.64 % (1361024)Peak memory usage: 10 MB
% 2.20/0.64 % (1361024)Instructions burned: 7 (million)
% 2.20/0.64 % (1361026)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=336300081:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.20/0.64 % (1361030)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.20/0.64 % (1361029)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=600649355:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.20/0.64 % (1361030)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1832599483:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.20/0.64 % (1361030)Instruction limit reached!
% 2.20/0.64 % (1361030)------------------------------
% 2.20/0.64 % (1361030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361030)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361030)Termination reason: Instruction limit
% 2.20/0.64 % (1361030)Termination phase: shuffling
% 2.20/0.64 % (1361030)Time elapsed: 0.003 s
% 2.20/0.64 % (1361030)Peak memory usage: 10 MB
% 2.20/0.64 % (1361030)Instructions burned: 6 (million)
% 2.20/0.64 % (1360990)Instruction limit reached!
% 2.20/0.64 % (1360990)------------------------------
% 2.20/0.64 % (1360990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1360990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1360990)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1360990)Termination reason: Instruction limit
% 2.20/0.64 % (1360990)Termination phase: Saturation
% 2.20/0.64 % (1360990)Time elapsed: 0.149 s
% 2.20/0.64 % (1360990)Peak memory usage: 15 MB
% 2.20/0.64 % (1360990)Instructions burned: 328 (million)
% 2.20/0.64 % (1361026)Instruction limit reached!
% 2.20/0.64 % (1361026)------------------------------
% 2.20/0.64 % (1361026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361026)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361026)Termination reason: Instruction limit
% 2.20/0.64 % (1361026)Termination phase: Saturation
% 2.20/0.64 % (1361026)Time elapsed: 0.041 s
% 2.20/0.64 % (1361026)Peak memory usage: 14 MB
% 2.20/0.64 % (1361026)Instructions burned: 181 (million)
% 2.20/0.64 % (1361033)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1504913096:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.20/0.64 % (1361034)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=261198649:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.20/0.64 % (1361019)Instruction limit reached!
% 2.20/0.64 % (1361019)------------------------------
% 2.20/0.64 % (1361019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361019)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361019)Termination reason: Instruction limit
% 2.20/0.64 % (1361019)Termination phase: Saturation
% 2.20/0.64 % (1361019)Time elapsed: 0.085 s
% 2.20/0.64 % (1361019)Peak memory usage: 13 MB
% 2.20/0.64 % (1361019)Instructions burned: 195 (million)
% 2.20/0.64 % (1361036)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=120114107:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.20/0.64 % (1361033)Instruction limit reached!
% 2.20/0.64 % (1361033)------------------------------
% 2.20/0.64 % (1361033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361033)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361033)Termination reason: Instruction limit
% 2.20/0.64 % (1361033)Termination phase: shuffling
% 2.20/0.64 % (1361033)Time elapsed: 0.011 s
% 2.20/0.64 % (1361033)Peak memory usage: 10 MB
% 2.20/0.64 % (1361033)Instructions burned: 24 (million)
% 2.20/0.64 % (1361034)Instruction limit reached!
% 2.20/0.64 % (1361034)------------------------------
% 2.20/0.64 % (1361034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361034)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361034)Termination reason: Instruction limit
% 2.20/0.64 % (1361034)Termination phase: shuffling
% 2.20/0.64 % (1361034)Time elapsed: 0.009 s
% 2.20/0.64 % (1361034)Peak memory usage: 10 MB
% 2.20/0.64 % (1361034)Instructions burned: 19 (million)
% 2.20/0.64 % (1361040)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2920334572:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 2.20/0.64 % (1361039)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3443585857:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.20/0.64 % (1361041)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1980414620:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.20/0.64 % (1360925) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1360908-1360925"...
% 2.20/0.64 % (1361029)Instruction limit reached!
% 2.20/0.64 % (1361029)------------------------------
% 2.20/0.64 % (1361029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361029)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361029)Termination reason: Instruction limit
% 2.20/0.64 % (1361029)Termination phase: Saturation
% 2.20/0.64 % (1361029)Time elapsed: 0.071 s
% 2.20/0.64 % (1361029)Peak memory usage: 13 MB
% 2.20/0.64 % (1361029)Instructions burned: 171 (million)
% 2.20/0.64 % (1360925)...printing done.
% 2.20/0.64 % (1361040)Instruction limit reached!
% 2.20/0.64 % (1361040)------------------------------
% 2.20/0.64 % (1361040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.64 % (1361040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.64 % (1361040)CaDiCaL version: 2.1.3
% 2.20/0.64 % (1361040)Termination reason: Instruction limit
% 2.20/0.64 % (1361040)Termination phase: Property scanning
% 2.20/0.64 % (1361040)Time elapsed: 0.020 s
% 2.20/0.64 % (1361040)Peak memory usage: 11 MB
% 2.20/0.64 % (1361040)Instructions burned: 47 (million)
% 2.20/0.64 % (1360925)Refutation found. Thanks to Tanya!
% 2.20/0.64 % SZS status Theorem for theBenchmark
% 2.20/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.20/0.65 % (1360925)------------------------------
% 2.20/0.65 % (1360925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.65 % (1360925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.65 % (1360925)CaDiCaL version: 2.1.3
% 2.20/0.65 % (1360925)Termination reason: Refutation
% 2.20/0.65 % (1360925)Time elapsed: 0.295 s
% 2.20/0.65 % (1360925)Peak memory usage: 21 MB
% 2.20/0.65 % (1360925)Instructions burned: 567 (million)
% 2.20/0.65 % (1360908)Success in time 0.341 s
% 2.20/0.65 % Vampire exiting
%------------------------------------------------------------------------------