%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU783^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:31:21 AM UTC 2026
% Result : Theorem 1.77s 0.61s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 5705 (1569 equ; 0 cnn)
% Maximal formula atoms : 305 ( 135 avg)
% Number of connectives : 2779 ( 41 ~; 31 |;1222 &; 260 @)
% ( 6 <=>;1219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 315 ( 62 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 : 558 ( 555 usr; 335 con; 0-6 aty)
% Number of variables : 71 ( 0 sgn 50 !; 21 ?; 71 :)
% 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_297,type,
inIntersectImpInIntersectUnions: $o ).
thf(func_def_298,type,
intersectInPowersetIntersectUnions: $o ).
thf(func_def_299,type,
inComplementUnionImpNotIn1: $o ).
thf(func_def_300,type,
inComplementUnionImpInComplement1: $o ).
thf(func_def_301,type,
binunionTE: $o ).
thf(func_def_302,type,
binunionTEcontra: $o ).
thf(func_def_303,type,
demorgan2a1: $o ).
thf(func_def_304,type,
complementUnionInPowersetComplement: $o ).
thf(func_def_305,type,
demorgan2a2: $o ).
thf(func_def_306,type,
demorgan1a: $o ).
thf(func_def_307,type,
demorgan1b: $o ).
thf(func_def_308,type,
demorgan1: $o ).
thf(func_def_309,type,
demorgan2a: $o ).
thf(func_def_310,type,
demorgan2b2: $o ).
thf(func_def_311,type,
demorgan2b: $o ).
thf(func_def_312,type,
demorgan2: $o ).
thf(func_def_313,type,
woz13rule0: $o ).
thf(func_def_314,type,
woz13rule1: $o ).
thf(func_def_315,type,
woz13rule2: $o ).
thf(func_def_316,type,
woz13rule3: $o ).
thf(func_def_317,type,
woz13rule4: $o ).
thf(func_def_318,type,
woz1_1: $o ).
thf(func_def_319,type,
woz1_2: $o ).
thf(func_def_320,type,
woz1_3: $o ).
thf(func_def_321,type,
woz1_4: $o ).
thf(func_def_322,type,
woz1_5: $o ).
thf(func_def_323,type,
breln1: $i > $i > $o ).
thf(func_def_324,type,
breln1all2: $o ).
thf(func_def_325,type,
breln1Set: $i > $i ).
thf(func_def_326,type,
breln1SetBreln1: $o ).
thf(func_def_327,type,
transitive: $i > $i > $o ).
thf(func_def_328,type,
antisymmetric: $i > $i > $o ).
thf(func_def_329,type,
reflexive: $i > $i > $o ).
thf(func_def_330,type,
refltransitive: $i > $i > $o ).
thf(func_def_331,type,
refllinearorder: $i > $i > $o ).
thf(func_def_332,type,
reflwellordering: $i > $i > $o ).
thf(func_def_333,type,
choice2fnsingleton: $o ).
thf(func_def_334,type,
setOfPairsIsBReln1: $o ).
thf(func_def_335,type,
breln1all1: $o ).
thf(func_def_336,type,
subbreln1: $o ).
thf(func_def_337,type,
eqbreln1: $o ).
thf(func_def_338,type,
breln1invset: $i > $i > $i ).
thf(func_def_339,type,
breln1invprop: $o ).
thf(func_def_340,type,
breln1invI: $o ).
thf(func_def_341,type,
breln1invE: $o ).
thf(func_def_342,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_343,type,
breln1compprop: $o ).
thf(func_def_344,type,
breln1compI: $o ).
thf(func_def_345,type,
breln1compE: $o ).
thf(func_def_346,type,
breln1compEex: $o ).
thf(func_def_347,type,
breln1unionprop: $o ).
thf(func_def_350,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_351,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_352,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_353,type,
vNOT: $o > $o ).
thf(func_def_354,type,
vOR: $o > $o > $o ).
thf(func_def_355,type,
vAND: $o > $o > $o ).
thf(func_def_356,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_357,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_358,type,
vIMP: $o > $o > $o ).
thf(func_def_359,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_360,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_361,type,
sP0: $i > $i > $o ).
thf(func_def_362,type,
sP1: $i > $o ).
thf(func_def_363,type,
sP2: $o ).
thf(func_def_364,type,
sP3: $o ).
thf(func_def_365,type,
sP4: $o ).
thf(func_def_392,type,
sK31: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_393,type,
sK32: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_394,type,
sK33: $i > $o ).
thf(func_def_395,type,
sK34: $i > $o ).
thf(func_def_400,type,
sK39: $i > $o ).
thf(func_def_411,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_412,type,
sK51: $i > $o ).
thf(func_def_413,type,
sK52: $i > $i ).
thf(func_def_431,type,
sK70: $i > $i > $i > $i > $i ).
thf(func_def_432,type,
sK71: $i > $i > $i > $i > $i ).
thf(func_def_436,type,
sK75: $i > $i > $i ).
thf(func_def_445,type,
sK84: $i > $i > $i ).
thf(func_def_450,type,
sK89: $i > $i > $i > $i ).
thf(func_def_461,type,
sK100: $i > $o ).
thf(func_def_462,type,
sK101: ( $i > $o ) > $i > $i ).
thf(func_def_474,type,
sK113: $i > $i > $i ).
thf(func_def_475,type,
sK114: $i > $i > $i ).
thf(func_def_488,type,
sK127: ( $i > $i ) > $i > $i > $i ).
thf(func_def_491,type,
sK130: $i > $i ).
thf(func_def_495,type,
sK134: $i > $i > $o ).
thf(func_def_502,type,
sK141: $o ).
thf(func_def_509,type,
sK148: $o ).
thf(func_def_518,type,
sK157: ( $i > $o ) > $i > $i > $i ).
thf(func_def_519,type,
sK158: ( $i > $o ) > $i > $i > $i ).
thf(func_def_522,type,
sK161: $i > $o ).
thf(func_def_533,type,
sK172: $i > $i > $o ).
thf(func_def_550,type,
sK189: $o ).
thf(func_def_554,type,
sK193: $i > $i > $o ).
thf(func_def_566,type,
sK205: $i > $i > $o ).
thf(func_def_587,type,
sK226: $i > $i > $i ).
thf(func_def_588,type,
sK227: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_589,type,
sK228: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_592,type,
sK231: $i > $o ).
thf(func_def_593,type,
sK232: $i > $o ).
thf(func_def_601,type,
sK240: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_602,type,
sK241: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_603,type,
sK242: $i > $o ).
thf(func_def_604,type,
sK243: $i > $o ).
thf(func_def_613,type,
sK252: $i > $o ).
thf(func_def_616,type,
sK255: $i > $i > $o ).
thf(func_def_623,type,
sK262: $i > $o ).
thf(func_def_624,type,
sK263: $i > $i ).
thf(func_def_625,type,
sK264: ( $i > $o ) > $i ).
thf(func_def_631,type,
sK270: $i > $i ).
thf(func_def_632,type,
sK271: $i > $i ).
thf(func_def_633,type,
sK272: $i > $i ).
thf(func_def_634,type,
sK273: $i > $i ).
thf(func_def_635,type,
sK274: $i > $i ).
thf(func_def_636,type,
sK275: $i > $i > $i > $i ).
thf(func_def_637,type,
sK276: $i > $i ).
thf(func_def_638,type,
sK277: $i > $i ).
thf(func_def_639,type,
sK278: $i > $i ).
thf(func_def_640,type,
sK279: $i > $i ).
thf(func_def_641,type,
sK280: $i > $i > $i ).
thf(func_def_642,type,
sK281: $i > $i > $i > $i ).
thf(func_def_643,type,
sK282: $i > $i > $i > $i ).
thf(func_def_644,type,
sK283: $i > $i > $i > $i ).
thf(func_def_645,type,
sK284: $i > $i > $i ).
thf(func_def_646,type,
sK285: $i > $i > $i ).
thf(func_def_647,type,
sK286: $i > $i > $i ).
thf(func_def_648,type,
sK287: $i > $i > $i ).
thf(func_def_654,type,
sK293: $i > $i > $i ).
thf(func_def_664,type,
sK303: $i > $o ).
thf(func_def_670,type,
sK309: $i > ( $i > $i ) > $i > $i ).
thf(func_def_672,type,
sK311: $i > $i ).
thf(func_def_685,type,
sK324: $i > $o ).
thf(func_def_686,type,
sK325: $o > $i > $i > $i > $i > $i > $i ).
thf(func_def_692,type,
sK331: $o ).
thf(func_def_718,type,
sK357: $i > $o ).
thf(func_def_727,type,
sK366: $i > $i > $o ).
thf(func_def_728,type,
sK367: $i > $i ).
thf(func_def_729,type,
sK368: $i > $i ).
thf(func_def_730,type,
sK369: ( $i > $i > $o ) > $i > $i ).
thf(func_def_731,type,
sK370: ( $i > $i > $o ) > $i > $i ).
thf(func_def_732,type,
sK371: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_733,type,
sK372: $i > $o ).
thf(func_def_739,type,
sK378: $o ).
thf(func_def_745,type,
sK384: $i > $o ).
thf(func_def_748,type,
sK387: $i > ( $i > $o ) > $i ).
thf(func_def_752,type,
sK391: $i > $i > $i > $i ).
thf(func_def_753,type,
sK392: $i > $i > $i > $i ).
thf(func_def_754,type,
sK393: $i > $i > $i > $i ).
thf(func_def_755,type,
sK394: $i > $i > $i > $i ).
thf(func_def_761,type,
sK400: $o ).
thf(func_def_776,type,
sK415: ( $i > $o ) > $i > $i ).
thf(func_def_777,type,
sK416: ( $i > $o ) > $i > $i ).
thf(func_def_779,type,
sK418: $i > $o ).
thf(func_def_781,type,
sK420: $i > $i > $i ).
thf(func_def_797,type,
sK436: $i > $o ).
thf(func_def_799,type,
sK438: $i > $i > $i > $i ).
thf(func_def_800,type,
sK439: $i > $i > $i > $i ).
thf(func_def_811,type,
sK450: $i > $i ).
thf(func_def_815,type,
sK454: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_816,type,
sK455: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_820,type,
sK459: $i > $o ).
thf(func_def_826,type,
sK465: $o > $i > $i > $i ).
thf(func_def_829,type,
sK468: $o ).
thf(func_def_831,type,
sK470: $o ).
thf(func_def_834,type,
sK473: $i > $o ).
thf(func_def_852,type,
sK491: $i > $i ).
thf(func_def_858,type,
sK497: $i > $i ).
thf(func_def_860,type,
sK499: $i > $i ).
thf(func_def_870,type,
sK509: $i > $i > $i > $i > $i ).
thf(func_def_879,type,
sK518: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_881,type,
sK520: $i > $i > $o ).
thf(func_def_885,type,
sK524: $i > $i ).
thf(func_def_891,type,
sK530: $o ).
thf(func_def_895,type,
sK534: $i > $i > $i > $i ).
thf(func_def_896,type,
sK535: $i > $i > $i > $i ).
thf(func_def_900,type,
sK539: $o ).
thf(func_def_905,type,
sK544: $i > $i > ( $i > $i ) > $i ).
thf(func_def_906,type,
sK545: $i > $i ).
thf(func_def_927,type,
sK566: $i > $i > $i ).
thf(func_def_931,type,
sK570: $o ).
thf(func_def_937,type,
sK576: $i > $i > $o ).
thf(func_def_958,type,
sK597: $i > $i ).
thf(func_def_959,type,
sK598: ( $i > $i ) > $i > $i > $i ).
thf(func_def_960,type,
sK599: $i > $i > $o ).
thf(func_def_967,type,
sK606: $i > $i > $i > $i ).
thf(func_def_968,type,
sK607: $i > $i > $i > $i ).
thf(func_def_977,type,
sK616: $o ).
thf(func_def_979,type,
sK618: $o ).
thf(func_def_991,type,
sK630: $i > $o ).
thf(func_def_996,type,
sK635: $i > $i ).
thf(func_def_998,type,
sK637: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1000,type,
sK639: $o ).
thf(func_def_1013,type,
sK652: $i > $o ).
thf(func_def_1015,type,
sK654: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1016,type,
sK655: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1021,type,
sK660: $o ).
thf(func_def_1031,type,
sK670: $i > $i > $i > $i > $i > $i ).
thf(func_def_1056,type,
sK695: $i > ( $i > $o ) > $i ).
thf(func_def_1057,type,
sK696: $i > $o ).
thf(func_def_1068,type,
sK707: $i > $i > $o ).
thf(func_def_1070,type,
sK709: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1073,type,
sK712: $i > $o ).
thf(func_def_1081,type,
sK720: $i > $o ).
thf(func_def_1089,type,
sK728: $i > $i > $i > $i > $i ).
thf(func_def_1093,type,
sK732: $i > $i ).
thf(func_def_1106,type,
sK745: $i > $o ).
thf(func_def_1108,type,
sK747: ( $i > $o ) > $i > $i ).
thf(func_def_1110,type,
sK749: $i > $o ).
thf(func_def_1117,type,
sK756: ( $i > $o ) > $i ).
thf(func_def_1118,type,
sK757: ( $i > $o ) > $i ).
thf(func_def_1119,type,
sK758: $i > $o ).
thf(func_def_1140,type,
sK779: $i > $i > $i > $i > $i ).
thf(func_def_1147,type,
sK786: $i > $i > $i ).
thf(func_def_1155,type,
sK794: $o ).
thf(func_def_1159,type,
sK798: $i > $i > $i ).
thf(func_def_1166,type,
sK805: $o ).
thf(func_def_1192,type,
sK831: $o ).
thf(func_def_1198,type,
sK837: $i > $o ).
thf(func_def_1202,type,
sK841: ( $i > $o ) > $i > $i ).
thf(func_def_1204,type,
sK843: $i > $o ).
thf(func_def_1209,type,
sK848: $i > $o ).
thf(func_def_1212,type,
sK851: $i > ( $i > $o ) > $i ).
thf(func_def_1238,type,
sK877: $i > ( $i > $o ) > $i ).
thf(func_def_1239,type,
sK878: $i > ( $i > $o ) > $i ).
thf(func_def_1240,type,
sK879: $i > $o ).
thf(func_def_1248,type,
sK887: $i > $i ).
thf(func_def_1256,type,
sK895: $o ).
thf(func_def_1263,type,
sK902: $i > $i ).
thf(func_def_1265,type,
sK904: $i > $o ).
thf(func_def_1267,type,
sK906: $i > ( $i > $o ) > $i ).
thf(func_def_1285,type,
sK924: $i > $i > $i > $i > $i ).
thf(func_def_1286,type,
sK925: $i > $i > $i > $i > $i ).
thf(func_def_1287,type,
sK926: $i > $i > $i > $i > $i ).
thf(func_def_1288,type,
sK927: $i > $i > $i > $i > $i ).
thf(func_def_1289,type,
sK928: $i > ( $i > $o ) > $i ).
thf(func_def_1290,type,
sK929: $i > $o ).
thf(func_def_1292,type,
sK931: $i > $o ).
thf(func_def_1307,type,
sK946: $i > ( $i > $o ) > $i ).
thf(func_def_1308,type,
sK947: $i > $o ).
thf(func_def_1311,type,
sK950: $i > $i > $i > $i ).
thf(func_def_1322,type,
sK961: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1323,type,
sK962: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1327,type,
sK966: $i > $o ).
thf(func_def_1331,type,
sK970: $i > $i ).
thf(func_def_1334,type,
sK973: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1349,type,
sK988: ( $i > $o ) > $i ).
thf(func_def_1350,type,
sK989: $i > $o ).
thf(f101,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(f302,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
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionIL) ).
thf(f303,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
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f302]) ).
thf(f668,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
inference(rectify,[],[f101]) ).
thf(f669,plain,
( ( binunionIL = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f668]) ).
thf(f682,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
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f303]) ).
thf(f683,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 )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f682]) ).
thf(f1021,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( breln1unionprop = $true )
& ( breln1compEex = $true )
& ( breln1compE = $true )
& ( breln1compI = $true )
& ( breln1compprop = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $true )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $true )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $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,[],[f683]) ).
thf(f1022,plain,
( ( notinsingleton = $true )
& ( funcImageSingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( emptyE1 = $true )
& ( woz13rule4 = $true )
& ( ubforcartprodlem2 = $true )
& ( setext = $true )
& ( cartprodsndpairEq = $true )
& ( subsetRefl = $true )
& ( setukpairinjL2 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR = $true )
& ( complementTcontraSubset = $true )
& ( app = $true )
& ( contrasubsetT3 = $true )
& ( singletoninpowerset = $true )
& ( setadjoinOr = $true )
& ( replAx = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyI1 = $true )
& ( symdiffIneg2 = $true )
& ( doubleComplementSub1 = $true )
& ( binintersectTELcontra = $true )
& ( contrasubsetT1 = $true )
& ( setunionAx = $true )
& ( omega__Cong = $true )
& ( kfstsingleton = $true )
& ( contrasubsetT2 = $true )
& ( singletonsuniq = $true )
& ( inIntersectImpInUnion2 = $true )
& ( subsetTI = $true )
& ( setextsub = $true )
& ( binintersectER = $true )
& ( breln1all2 = $true )
& ( upairsetIR = $true )
& ( dpsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( emptysetE = $true )
& ( breln1SetBreln1 = $true )
& ( quantDeMorgan1 = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrEL2 = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( binunionTE = $true )
& ( setunion__Cong = $true )
& ( theeq = $true )
& ( emptysetimpfalse = $true )
& ( subbreln1 = $true )
& ( iffalseProp2 = $true )
& ( setOfPairsIsBReln = $true )
& ( eta2 = $true )
& ( setminusELneg = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjR1 = $true )
& ( binunionT_lem = $true )
& ( subset2powerset = $true )
& ( choice2fnsingleton = $true )
& ( upairsubunion = $true )
& ( cartprodpairsurjEq = $true )
& ( breln1compEex = $true )
& ( cartprodpairin = $true )
& ? [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true ) ) ) ) )
& ( symdiffE = $true )
& ( singletonsswitch = $true )
& ( subbreln = $true )
& ( ex1I = $true )
& ( demorgan2 = $true )
& ( binintersectSubset4 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( cartprodfstpairEq = $true )
& ( powersetI1 = $true )
& ( breln1all1 = $true )
& ( setunionsingleton = $true )
& ( descrp = $true )
& ( iffalse = $true )
& ( subPowSU = $true )
& ( funcext2 = $true )
& ( binintersectSubset1 = $true )
& ( setadjoinAx = $true )
& ( ksndsingleton = $true )
& ( doubleComplementI1 = $true )
& ( setunionE2 = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( ap2apEq1 = $true )
& ( iffalseProp1 = $true )
& ( funcinfuncset = $true )
& ( eqimpsubset2 = $true )
& ( omega0Ax = $true )
& ( funcGraphProp3 = $true )
& ( singletonsubset = $true )
& ( lam2p = $true )
& ( complementTE1 = $true )
& ( upairset2IR = $true )
& ( cartprodpairmemER = $true )
& ( cartprodsndin = $true )
& ( cartprodpairmemEL = $true )
& ( inCongP = $true )
& ( upairinpowunion = $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( setminusSubset2 = $true )
& ( iftrueProp1 = $true )
& ( setunionE = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinIL = $true )
& ( doubleComplementE1 = $true )
& ( demorgan2a1 = $true )
& ( sepSubset = $true )
& ( binunionTILcontra = $true )
& ( funcGraphProp2 = $true )
& ( binunionRsub = $true )
& ( notinemptyset = $true )
& ( binintersectSubset3 = $true )
& ( notdallE = $true )
& ( dpsetconstrERa = $true )
& ( eqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( emptyI = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem1 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodfstin = $true )
& ( woz1_4 = $true )
& ( emptyinPowerset = $true )
& ( setadjoinIR = $true )
& ( woz13rule3 = $true )
& ( emptysetAx = $true )
& ( subsetTrans = $true )
& ( bs114d = $true )
& ( binunionLsub = $true )
& ( complementImpComplementIntersect = $true )
& ( cartprodmempair1 = $true )
& ( exuI3 = $true )
& ( iftrueProp2 = $true )
& ( subsetemptysetimpeq = $true )
& ( in__Cong = $true )
& ( complementTnotintersectT = $true )
& ( prop2set2propI = $true )
& ( ap2p = $true )
& ( symdiffI1 = $true )
& ( exuI2 = $true )
& ( complementT_lem = $true )
& ( powerset__Cong = $true )
& ( powersetT_lem = $true )
& ( notdexE = $true )
& ( setadjoinSub2 = $true )
& ( beta2 = $true )
& ( upairset2E = $true )
& ( kfstpairEq = $true )
& ( quantDeMorgan4 = $true )
& ( cartprodmempair = $true )
& ( setoftrueEq = $true )
& ( demorgan2b = $true )
& ( woz1_3 = $true )
& ( beta1 = $true )
& ( singletoninpowunion = $true )
& ( doubleComplementEq = $true )
& ( contraSubsetComplement = $true )
& ( dsetconstrEL = $true )
& ( binunionIL = $true )
& ( upairequniteq = $true )
& ( singletonprop = $true )
& ( kpairsurjEq = $true )
& ( setukpairinjR11 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInUnion = $true )
& ( ifp = $true )
& ( ap2apEq2 = $true )
& ( setminusERneg = $true )
& ( breln1unionprop = $true )
& ( lam2lamEq = $true )
& ( prop2setI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( woz1_1 = $true )
& ( exuE1 = $true )
& ( breln1invprop = $true )
& ( binintersectTERcontra = $true )
& ( demorgan1 = $true )
& ( prop2setE = $true )
& ( binintersectSubset2 = $true )
& ( setunionI = $true )
& ( demorgan2b2 = $true )
& ( wellorderingAx = $true )
& ( eta1 = $true )
& ( demorgan2a2 = $true )
& ( setextT = $true )
& ( setOfPairsIsBReln1 = $true )
& ( notequalI1 = $true )
& ( ex1E1 = $true )
& ( subsetI1 = $true )
& ( funcextLem = $true )
& ( eqbreln1 = $true )
& ( sepInPowerset = $true )
& ( exuEu = $true )
& ( binintersectLsub = $true )
& ( contrasubsetT = $true )
& ( cartprodmempaircEq = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( binintersectRsub = $true )
& ( demorgan2a = $true )
& ( lamProp = $true )
& ( lamp = $true )
& ( emptyinunitempty = $true )
& ( omegaSAx = $true )
& ( breln1compprop = $true )
& ( binunionE = $true )
& ( setukpairIR = $true )
& ( exuE2 = $true )
& ( setminusT_lem = $true )
& ( foundationAx = $true )
& ( secondinupair = $true )
& ( dsetconstrI = $true )
& ( dpsetconstrI = $true )
& ( nonemptyE1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( binunionTIRcontra = $true )
& ( woz13rule2 = $true )
& ( upairsetIL = $true )
& ( setminusIRneg = $true )
& ( funcGraphProp1 = $true )
& ( setminusI = $true )
& ( setadjoinE = $true )
& ( brelnall2 = $true )
& ( setminusER = $true )
& ( subsetI2 = $true )
& ( demorgan1a = $true )
& ( doubleComplementSub2 = $true )
& ( setukpairinjR12 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan3 = $true )
& ( woz13rule1 = $true )
& ( setminusEL = $true )
& ( dpsetconstrEL1 = $true )
& ( vacuousDall = $true )
& ( infuncsetfunc = $true )
& ( dsetconstrER = $true )
& ( notequalI2 = $true )
& ( exu__Cong = $true )
& ( nonemptyI = $true )
& ( powersetsubset = $true )
& ( exuE3u = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffI2 = $true )
& ( binunionIR = $true )
& ( ex1E2 = $true )
& ( binintersectI = $true )
& ( omegaIndAx = $true )
& ( powersetTI1 = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyInPowerset = $true )
& ( breln1compI = $true )
& ( symdiffIneg1 = $true )
& ( powersetTE1 = $true )
& ( eqimpsubset1 = $true )
& ( setadjoin__Cong = $true )
& ( exuI1 = $true )
& ( ifSingleton = $true )
& ( uniqinunit = $true )
& ( setextAx = $true )
& ( woz1_2 = $true )
& ( iftrue = $true )
& ( setukpairinjL1 = $true )
& ( setminusSubset1 = $true )
& ( woz13rule0 = $true )
& ( eqbreln = $true )
& ( iftrueorfalse = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( demorgan1b = $true )
& ( setukpairinjR2 = $true )
& ( descr__Cong = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( powersetI = $true )
& ( brelnall1 = $true )
& ( setminusILneg = $true )
& ( woz1_5 = $true )
& ( noeltsimpempty = $true )
& ( funcext = $true )
& ( upairsetE = $true )
& ( complementTI1 = $true )
& ( binunionTEcontra = $true )
& ( subsetE2 = $true )
& ( theprop = $true )
& ( breln1invI = $true )
& ( setminusLsub = $true )
& ( subsetE = $true )
& ( setunionsingleton1 = $true )
& ( breln1invE = $true )
& ( kpairp = $true )
& ( binintersectT_lem = $true )
& ( setukpairinjL = $true )
& ( binintersectEL = $true )
& ( ksndpairEq = $true )
& ( exuE3e = $true )
& ( setukpairIL = $true )
& ( ex1I2 = $true )
& ( breln1compE = $true ) ),
inference(flattening,[],[f1021]) ).
thf(f1271,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
<=> ( binunionIL = $true ) ),
inference(ennf_transformation,[],[f669]) ).
thf(f1622,plain,
( ( notinsingleton = $true )
& ( funcImageSingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( emptyE1 = $true )
& ( woz13rule4 = $true )
& ( ubforcartprodlem2 = $true )
& ( setext = $true )
& ( cartprodsndpairEq = $true )
& ( subsetRefl = $true )
& ( setukpairinjL2 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR = $true )
& ( complementTcontraSubset = $true )
& ( app = $true )
& ( contrasubsetT3 = $true )
& ( singletoninpowerset = $true )
& ( setadjoinOr = $true )
& ( replAx = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyI1 = $true )
& ( symdiffIneg2 = $true )
& ( doubleComplementSub1 = $true )
& ( binintersectTELcontra = $true )
& ( contrasubsetT1 = $true )
& ( setunionAx = $true )
& ( omega__Cong = $true )
& ( kfstsingleton = $true )
& ( contrasubsetT2 = $true )
& ( singletonsuniq = $true )
& ( inIntersectImpInUnion2 = $true )
& ( subsetTI = $true )
& ( setextsub = $true )
& ( binintersectER = $true )
& ( breln1all2 = $true )
& ( upairsetIR = $true )
& ( dpsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( emptysetE = $true )
& ( breln1SetBreln1 = $true )
& ( quantDeMorgan1 = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrEL2 = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( binunionTE = $true )
& ( setunion__Cong = $true )
& ( theeq = $true )
& ( emptysetimpfalse = $true )
& ( subbreln1 = $true )
& ( iffalseProp2 = $true )
& ( setOfPairsIsBReln = $true )
& ( eta2 = $true )
& ( setminusELneg = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjR1 = $true )
& ( binunionT_lem = $true )
& ( subset2powerset = $true )
& ( choice2fnsingleton = $true )
& ( upairsubunion = $true )
& ( cartprodpairsurjEq = $true )
& ( breln1compEex = $true )
& ( cartprodpairin = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) ) ) ) ) )
& ( symdiffE = $true )
& ( singletonsswitch = $true )
& ( subbreln = $true )
& ( ex1I = $true )
& ( demorgan2 = $true )
& ( binintersectSubset4 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( cartprodfstpairEq = $true )
& ( powersetI1 = $true )
& ( breln1all1 = $true )
& ( setunionsingleton = $true )
& ( descrp = $true )
& ( iffalse = $true )
& ( subPowSU = $true )
& ( funcext2 = $true )
& ( binintersectSubset1 = $true )
& ( setadjoinAx = $true )
& ( ksndsingleton = $true )
& ( doubleComplementI1 = $true )
& ( setunionE2 = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( ap2apEq1 = $true )
& ( iffalseProp1 = $true )
& ( funcinfuncset = $true )
& ( eqimpsubset2 = $true )
& ( omega0Ax = $true )
& ( funcGraphProp3 = $true )
& ( singletonsubset = $true )
& ( lam2p = $true )
& ( complementTE1 = $true )
& ( upairset2IR = $true )
& ( cartprodpairmemER = $true )
& ( cartprodsndin = $true )
& ( cartprodpairmemEL = $true )
& ( inCongP = $true )
& ( upairinpowunion = $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( setminusSubset2 = $true )
& ( iftrueProp1 = $true )
& ( setunionE = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinIL = $true )
& ( doubleComplementE1 = $true )
& ( demorgan2a1 = $true )
& ( sepSubset = $true )
& ( binunionTILcontra = $true )
& ( funcGraphProp2 = $true )
& ( binunionRsub = $true )
& ( notinemptyset = $true )
& ( binintersectSubset3 = $true )
& ( notdallE = $true )
& ( dpsetconstrERa = $true )
& ( eqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( emptyI = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem1 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodfstin = $true )
& ( woz1_4 = $true )
& ( emptyinPowerset = $true )
& ( setadjoinIR = $true )
& ( woz13rule3 = $true )
& ( emptysetAx = $true )
& ( subsetTrans = $true )
& ( bs114d = $true )
& ( binunionLsub = $true )
& ( complementImpComplementIntersect = $true )
& ( cartprodmempair1 = $true )
& ( exuI3 = $true )
& ( iftrueProp2 = $true )
& ( subsetemptysetimpeq = $true )
& ( in__Cong = $true )
& ( complementTnotintersectT = $true )
& ( prop2set2propI = $true )
& ( ap2p = $true )
& ( symdiffI1 = $true )
& ( exuI2 = $true )
& ( complementT_lem = $true )
& ( powerset__Cong = $true )
& ( powersetT_lem = $true )
& ( notdexE = $true )
& ( setadjoinSub2 = $true )
& ( beta2 = $true )
& ( upairset2E = $true )
& ( kfstpairEq = $true )
& ( quantDeMorgan4 = $true )
& ( cartprodmempair = $true )
& ( setoftrueEq = $true )
& ( demorgan2b = $true )
& ( woz1_3 = $true )
& ( beta1 = $true )
& ( singletoninpowunion = $true )
& ( doubleComplementEq = $true )
& ( contraSubsetComplement = $true )
& ( dsetconstrEL = $true )
& ( binunionIL = $true )
& ( upairequniteq = $true )
& ( singletonprop = $true )
& ( kpairsurjEq = $true )
& ( setukpairinjR11 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInUnion = $true )
& ( ifp = $true )
& ( ap2apEq2 = $true )
& ( setminusERneg = $true )
& ( breln1unionprop = $true )
& ( lam2lamEq = $true )
& ( prop2setI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( woz1_1 = $true )
& ( exuE1 = $true )
& ( breln1invprop = $true )
& ( binintersectTERcontra = $true )
& ( demorgan1 = $true )
& ( prop2setE = $true )
& ( binintersectSubset2 = $true )
& ( setunionI = $true )
& ( demorgan2b2 = $true )
& ( wellorderingAx = $true )
& ( eta1 = $true )
& ( demorgan2a2 = $true )
& ( setextT = $true )
& ( setOfPairsIsBReln1 = $true )
& ( notequalI1 = $true )
& ( ex1E1 = $true )
& ( subsetI1 = $true )
& ( funcextLem = $true )
& ( eqbreln1 = $true )
& ( sepInPowerset = $true )
& ( exuEu = $true )
& ( binintersectLsub = $true )
& ( contrasubsetT = $true )
& ( cartprodmempaircEq = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( binintersectRsub = $true )
& ( demorgan2a = $true )
& ( lamProp = $true )
& ( lamp = $true )
& ( emptyinunitempty = $true )
& ( omegaSAx = $true )
& ( breln1compprop = $true )
& ( binunionE = $true )
& ( setukpairIR = $true )
& ( exuE2 = $true )
& ( setminusT_lem = $true )
& ( foundationAx = $true )
& ( secondinupair = $true )
& ( dsetconstrI = $true )
& ( dpsetconstrI = $true )
& ( nonemptyE1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( binunionTIRcontra = $true )
& ( woz13rule2 = $true )
& ( upairsetIL = $true )
& ( setminusIRneg = $true )
& ( funcGraphProp1 = $true )
& ( setminusI = $true )
& ( setadjoinE = $true )
& ( brelnall2 = $true )
& ( setminusER = $true )
& ( subsetI2 = $true )
& ( demorgan1a = $true )
& ( doubleComplementSub2 = $true )
& ( setukpairinjR12 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan3 = $true )
& ( woz13rule1 = $true )
& ( setminusEL = $true )
& ( dpsetconstrEL1 = $true )
& ( vacuousDall = $true )
& ( infuncsetfunc = $true )
& ( dsetconstrER = $true )
& ( notequalI2 = $true )
& ( exu__Cong = $true )
& ( nonemptyI = $true )
& ( powersetsubset = $true )
& ( exuE3u = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffI2 = $true )
& ( binunionIR = $true )
& ( ex1E2 = $true )
& ( binintersectI = $true )
& ( omegaIndAx = $true )
& ( powersetTI1 = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyInPowerset = $true )
& ( breln1compI = $true )
& ( symdiffIneg1 = $true )
& ( powersetTE1 = $true )
& ( eqimpsubset1 = $true )
& ( setadjoin__Cong = $true )
& ( exuI1 = $true )
& ( ifSingleton = $true )
& ( uniqinunit = $true )
& ( setextAx = $true )
& ( woz1_2 = $true )
& ( iftrue = $true )
& ( setukpairinjL1 = $true )
& ( setminusSubset1 = $true )
& ( woz13rule0 = $true )
& ( eqbreln = $true )
& ( iftrueorfalse = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( demorgan1b = $true )
& ( setukpairinjR2 = $true )
& ( descr__Cong = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( powersetI = $true )
& ( brelnall1 = $true )
& ( setminusILneg = $true )
& ( woz1_5 = $true )
& ( noeltsimpempty = $true )
& ( funcext = $true )
& ( upairsetE = $true )
& ( complementTI1 = $true )
& ( binunionTEcontra = $true )
& ( subsetE2 = $true )
& ( theprop = $true )
& ( breln1invI = $true )
& ( setminusLsub = $true )
& ( subsetE = $true )
& ( setunionsingleton1 = $true )
& ( breln1invE = $true )
& ( kpairp = $true )
& ( binintersectT_lem = $true )
& ( setukpairinjL = $true )
& ( binintersectEL = $true )
& ( ksndpairEq = $true )
& ( exuE3e = $true )
& ( setukpairIL = $true )
& ( ex1I2 = $true )
& ( breln1compE = $true ) ),
inference(rectify,[],[f1022]) ).
thf(f1623,plain,
( ( notinsingleton = $true )
& ( funcImageSingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( emptyE1 = $true )
& ( woz13rule4 = $true )
& ( ubforcartprodlem2 = $true )
& ( setext = $true )
& ( cartprodsndpairEq = $true )
& ( subsetRefl = $true )
& ( setukpairinjL2 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR = $true )
& ( complementTcontraSubset = $true )
& ( app = $true )
& ( contrasubsetT3 = $true )
& ( singletoninpowerset = $true )
& ( setadjoinOr = $true )
& ( replAx = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyI1 = $true )
& ( symdiffIneg2 = $true )
& ( doubleComplementSub1 = $true )
& ( binintersectTELcontra = $true )
& ( contrasubsetT1 = $true )
& ( setunionAx = $true )
& ( omega__Cong = $true )
& ( kfstsingleton = $true )
& ( contrasubsetT2 = $true )
& ( singletonsuniq = $true )
& ( inIntersectImpInUnion2 = $true )
& ( subsetTI = $true )
& ( setextsub = $true )
& ( binintersectER = $true )
& ( breln1all2 = $true )
& ( upairsetIR = $true )
& ( dpsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( emptysetE = $true )
& ( breln1SetBreln1 = $true )
& ( quantDeMorgan1 = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrEL2 = $true )
& ( apProp = $true )
& ( kpairiskpair = $true )
& ( binunionTE = $true )
& ( setunion__Cong = $true )
& ( theeq = $true )
& ( emptysetimpfalse = $true )
& ( subbreln1 = $true )
& ( iffalseProp2 = $true )
& ( setOfPairsIsBReln = $true )
& ( eta2 = $true )
& ( setminusELneg = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjR1 = $true )
& ( binunionT_lem = $true )
& ( subset2powerset = $true )
& ( choice2fnsingleton = $true )
& ( upairsubunion = $true )
& ( cartprodpairsurjEq = $true )
& ( breln1compEex = $true )
& ( cartprodpairin = $true )
& ( $true
= ( breln1 @ sK336 @ sK335 ) )
& ( $true
= ( breln1 @ sK336 @ sK337 ) )
& ( $true
= ( in @ sK338 @ sK336 ) )
& ( $true
= ( in @ sK339 @ sK336 ) )
& ( $true
= ( in @ ( kpair @ sK338 @ sK339 ) @ sK335 ) )
& ( ( in @ ( kpair @ sK338 @ sK339 ) @ ( binunion @ sK335 @ sK337 ) )
!= $true )
& ( symdiffE = $true )
& ( singletonsswitch = $true )
& ( subbreln = $true )
& ( ex1I = $true )
& ( demorgan2 = $true )
& ( binintersectSubset4 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( cartprodfstpairEq = $true )
& ( powersetI1 = $true )
& ( breln1all1 = $true )
& ( setunionsingleton = $true )
& ( descrp = $true )
& ( iffalse = $true )
& ( subPowSU = $true )
& ( funcext2 = $true )
& ( binintersectSubset1 = $true )
& ( setadjoinAx = $true )
& ( ksndsingleton = $true )
& ( doubleComplementI1 = $true )
& ( setunionE2 = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( ap2apEq1 = $true )
& ( iffalseProp1 = $true )
& ( funcinfuncset = $true )
& ( eqimpsubset2 = $true )
& ( omega0Ax = $true )
& ( funcGraphProp3 = $true )
& ( singletonsubset = $true )
& ( lam2p = $true )
& ( complementTE1 = $true )
& ( upairset2IR = $true )
& ( cartprodpairmemER = $true )
& ( cartprodsndin = $true )
& ( cartprodpairmemEL = $true )
& ( inCongP = $true )
& ( upairinpowunion = $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( setminusSubset2 = $true )
& ( iftrueProp1 = $true )
& ( setunionE = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinIL = $true )
& ( doubleComplementE1 = $true )
& ( demorgan2a1 = $true )
& ( sepSubset = $true )
& ( binunionTILcontra = $true )
& ( funcGraphProp2 = $true )
& ( binunionRsub = $true )
& ( notinemptyset = $true )
& ( binintersectSubset3 = $true )
& ( notdallE = $true )
& ( dpsetconstrERa = $true )
& ( eqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( emptyI = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem1 = $true )
& ( funcGraphProp4 = $true )
& ( cartprodfstin = $true )
& ( woz1_4 = $true )
& ( emptyinPowerset = $true )
& ( setadjoinIR = $true )
& ( woz13rule3 = $true )
& ( emptysetAx = $true )
& ( subsetTrans = $true )
& ( bs114d = $true )
& ( binunionLsub = $true )
& ( complementImpComplementIntersect = $true )
& ( cartprodmempair1 = $true )
& ( exuI3 = $true )
& ( iftrueProp2 = $true )
& ( subsetemptysetimpeq = $true )
& ( in__Cong = $true )
& ( complementTnotintersectT = $true )
& ( prop2set2propI = $true )
& ( ap2p = $true )
& ( symdiffI1 = $true )
& ( exuI2 = $true )
& ( complementT_lem = $true )
& ( powerset__Cong = $true )
& ( powersetT_lem = $true )
& ( notdexE = $true )
& ( setadjoinSub2 = $true )
& ( beta2 = $true )
& ( upairset2E = $true )
& ( kfstpairEq = $true )
& ( quantDeMorgan4 = $true )
& ( cartprodmempair = $true )
& ( setoftrueEq = $true )
& ( demorgan2b = $true )
& ( woz1_3 = $true )
& ( beta1 = $true )
& ( singletoninpowunion = $true )
& ( doubleComplementEq = $true )
& ( contraSubsetComplement = $true )
& ( dsetconstrEL = $true )
& ( binunionIL = $true )
& ( upairequniteq = $true )
& ( singletonprop = $true )
& ( kpairsurjEq = $true )
& ( setukpairinjR11 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInUnion = $true )
& ( ifp = $true )
& ( ap2apEq2 = $true )
& ( setminusERneg = $true )
& ( breln1unionprop = $true )
& ( lam2lamEq = $true )
& ( prop2setI = $true )
& ( complementSubsetComplementIntersect = $true )
& ( woz1_1 = $true )
& ( exuE1 = $true )
& ( breln1invprop = $true )
& ( binintersectTERcontra = $true )
& ( demorgan1 = $true )
& ( prop2setE = $true )
& ( binintersectSubset2 = $true )
& ( setunionI = $true )
& ( demorgan2b2 = $true )
& ( wellorderingAx = $true )
& ( eta1 = $true )
& ( demorgan2a2 = $true )
& ( setextT = $true )
& ( setOfPairsIsBReln1 = $true )
& ( notequalI1 = $true )
& ( ex1E1 = $true )
& ( subsetI1 = $true )
& ( funcextLem = $true )
& ( eqbreln1 = $true )
& ( sepInPowerset = $true )
& ( exuEu = $true )
& ( binintersectLsub = $true )
& ( contrasubsetT = $true )
& ( cartprodmempaircEq = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( binintersectRsub = $true )
& ( demorgan2a = $true )
& ( lamProp = $true )
& ( lamp = $true )
& ( emptyinunitempty = $true )
& ( omegaSAx = $true )
& ( breln1compprop = $true )
& ( binunionE = $true )
& ( setukpairIR = $true )
& ( exuE2 = $true )
& ( setminusT_lem = $true )
& ( foundationAx = $true )
& ( secondinupair = $true )
& ( dsetconstrI = $true )
& ( dpsetconstrI = $true )
& ( nonemptyE1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( binunionTIRcontra = $true )
& ( woz13rule2 = $true )
& ( upairsetIL = $true )
& ( setminusIRneg = $true )
& ( funcGraphProp1 = $true )
& ( setminusI = $true )
& ( setadjoinE = $true )
& ( brelnall2 = $true )
& ( setminusER = $true )
& ( subsetI2 = $true )
& ( demorgan1a = $true )
& ( doubleComplementSub2 = $true )
& ( setukpairinjR12 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan3 = $true )
& ( woz13rule1 = $true )
& ( setminusEL = $true )
& ( dpsetconstrEL1 = $true )
& ( vacuousDall = $true )
& ( infuncsetfunc = $true )
& ( dsetconstrER = $true )
& ( notequalI2 = $true )
& ( exu__Cong = $true )
& ( nonemptyI = $true )
& ( powersetsubset = $true )
& ( exuE3u = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffI2 = $true )
& ( binunionIR = $true )
& ( ex1E2 = $true )
& ( binintersectI = $true )
& ( omegaIndAx = $true )
& ( powersetTI1 = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyInPowerset = $true )
& ( breln1compI = $true )
& ( symdiffIneg1 = $true )
& ( powersetTE1 = $true )
& ( eqimpsubset1 = $true )
& ( setadjoin__Cong = $true )
& ( exuI1 = $true )
& ( ifSingleton = $true )
& ( uniqinunit = $true )
& ( setextAx = $true )
& ( woz1_2 = $true )
& ( iftrue = $true )
& ( setukpairinjL1 = $true )
& ( setminusSubset1 = $true )
& ( woz13rule0 = $true )
& ( eqbreln = $true )
& ( iftrueorfalse = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( demorgan1b = $true )
& ( setukpairinjR2 = $true )
& ( descr__Cong = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( powersetI = $true )
& ( brelnall1 = $true )
& ( setminusILneg = $true )
& ( woz1_5 = $true )
& ( noeltsimpempty = $true )
& ( funcext = $true )
& ( upairsetE = $true )
& ( complementTI1 = $true )
& ( binunionTEcontra = $true )
& ( subsetE2 = $true )
& ( theprop = $true )
& ( breln1invI = $true )
& ( setminusLsub = $true )
& ( subsetE = $true )
& ( setunionsingleton1 = $true )
& ( breln1invE = $true )
& ( kpairp = $true )
& ( binintersectT_lem = $true )
& ( setukpairinjL = $true )
& ( binintersectEL = $true )
& ( ksndpairEq = $true )
& ( exuE3e = $true )
& ( setukpairIL = $true )
& ( ex1I2 = $true )
& ( breln1compE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK335,sK336,sK337,sK338,sK339]),skolemize(X0,sK335),skolemize(X1,sK336),skolemize(X2,sK337),skolemize(X3,sK338),skolemize(X4,sK339)],[f1622]) ).
thf(f2067,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f1271]) ).
thf(f2068,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
& ( $true
!= ( in @ X4 @ ( binunion @ X5 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f2067]) ).
thf(f2069,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ( ( ( in @ sK827 @ sK828 )
= $true )
& ( $true
!= ( in @ sK827 @ ( binunion @ sK828 @ sK826 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK826,sK827,sK828]),skolemize(X3,sK826),skolemize(X4,sK827),skolemize(X5,sK828)],[f2068]) ).
thf(f2827,plain,
binunionIL = $true,
inference(cnf_transformation,[],[f1623]) ).
thf(f2926,plain,
( ( in @ ( kpair @ sK338 @ sK339 ) @ ( binunion @ sK335 @ sK337 ) )
!= $true ),
inference(cnf_transformation,[],[f1623]) ).
thf(f2927,plain,
( $true
= ( in @ ( kpair @ sK338 @ sK339 ) @ sK335 ) ),
inference(cnf_transformation,[],[f1623]) ).
thf(f3647,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[],[f2069]) ).
thf(f6723,definition,
( spl990_578
<=> ( binunionIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl990_578])],[avatar_definition]) ).
thf(f6727,definition,
( spl990_579
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl990_579])],[avatar_definition]) ).
thf(f6728,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ~ spl990_579 ),
inference(avatar_component_clause,[],[f6727]) ).
thf(f6729,plain,
( ~ spl990_578
| spl990_579 ),
inference(avatar_split_clause,[],[f3647,f6727,f6723]) ).
thf(f8297,definition,
( spl990_912
<=> ( $true
= ( in @ ( kpair @ sK338 @ sK339 ) @ sK335 ) ) ),
introduced(definition,[new_symbols(definition,[spl990_912])],[avatar_definition]) ).
thf(f8299,plain,
( ( $true
= ( in @ ( kpair @ sK338 @ sK339 ) @ sK335 ) )
| ~ spl990_912 ),
inference(avatar_component_clause,[],[f8297]) ).
thf(f8300,plain,
spl990_912,
inference(avatar_split_clause,[],[f2927,f8297]) ).
thf(f8499,definition,
( spl990_953
<=> ( ( in @ ( kpair @ sK338 @ sK339 ) @ ( binunion @ sK335 @ sK337 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl990_953])],[avatar_definition]) ).
thf(f8501,plain,
( ( ( in @ ( kpair @ sK338 @ sK339 ) @ ( binunion @ sK335 @ sK337 ) )
!= $true )
| spl990_953 ),
inference(avatar_component_clause,[],[f8499]) ).
thf(f8502,plain,
~ spl990_953,
inference(avatar_split_clause,[],[f2926,f8499]) ).
thf(f9868,plain,
spl990_578,
inference(avatar_split_clause,[],[f2827,f6723]) ).
thf(f12600,plain,
( ( $true != $true )
| ( $true
!= ( in @ ( kpair @ sK338 @ sK339 ) @ sK335 ) )
| ~ spl990_579
| spl990_953 ),
inference(superposition,[],[f8501,f6728]) ).
thf(f12613,plain,
( ( $true
!= ( in @ ( kpair @ sK338 @ sK339 ) @ sK335 ) )
| ~ spl990_579
| spl990_953 ),
inference(trivial_inequality_removal,[],[f12600]) ).
thf(f12629,plain,
( $false
| ~ spl990_579
| ~ spl990_912
| spl990_953 ),
inference(forward_subsumption_resolution,[],[f12613,f8299]) ).
thf(f12630,plain,
( ~ spl990_579
| ~ spl990_912
| spl990_953 ),
inference(avatar_contradiction_clause,[],[f12629]) ).
cnf(s430,plain,
( ~ spl990_578
| spl990_579 ),
inference(sat_conversion,[],[f6729]) ).
cnf(s781,plain,
spl990_912,
inference(sat_conversion,[],[f8300]) ).
cnf(s826,plain,
~ spl990_953,
inference(sat_conversion,[],[f8502]) ).
cnf(s1177,plain,
spl990_578,
inference(sat_conversion,[],[f9868]) ).
cnf(s1654,plain,
( ~ spl990_579
| ~ spl990_912
| spl990_953 ),
inference(sat_conversion,[],[f12630]) ).
cnf(s1762,plain,
~ spl990_579,
inference(rat,[],[s1654,s826,s781]) ).
cnf(s1873,plain,
$false,
inference(rat,[],[s430,s1762,s1177]) ).
thf(f12631,plain,
$false,
inference(avatar_sat_refutation,[],[s1873]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU783^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:26:11 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.23/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/0.45 % (3440122)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.32/0.45 % (3440128)lrs+10_16_si=on:nwc=1.5:random_seed=1593747584:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.32/0.45 % (3440133)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.32/0.45 % (3440133)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
% 0.32/0.45 % (3440128)Instruction limit reached!
% 0.32/0.45 % (3440128)------------------------------
% 0.32/0.45 % (3440128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3440128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3440128)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3440128)Termination reason: Instruction limit
% 0.32/0.45 % (3440128)Termination phase: shuffling
% 0.32/0.45 % (3440128)Time elapsed: 0.005 s
% 0.32/0.45 % (3440128)Peak memory usage: 10 MB
% 0.32/0.45 % (3440128)Instructions burned: 19 (million)
% 0.32/0.45 % (3440129)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3057704174:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.32/0.45 % (3440130)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=1502282142: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)
% 0.32/0.45 % (3440131)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2509842168:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.32/0.45 % (3440127)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3575549670:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.32/0.45 % (3440133)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=333770160:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.32/0.45 % (3440132)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2661650133:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.32/0.45 % (3440129)Instruction limit reached!
% 0.32/0.45 % (3440129)------------------------------
% 0.32/0.45 % (3440129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3440129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3440129)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3440129)Termination reason: Instruction limit
% 0.32/0.45 % (3440129)Termination phase: shuffling
% 0.32/0.45 % (3440129)Time elapsed: 0.002 s
% 0.32/0.45 % (3440129)Peak memory usage: 10 MB
% 0.32/0.45 % (3440129)Instructions burned: 4 (million)
% 0.32/0.45 % (3440136)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3599539019:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.32/0.45 % (3440136)Instruction limit reached!
% 0.32/0.45 % (3440136)------------------------------
% 0.32/0.45 % (3440136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3440136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3440136)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3440136)Termination reason: Instruction limit
% 0.32/0.45 % (3440136)Termination phase: shuffling
% 0.32/0.45 % (3440136)Time elapsed: 0.002 s
% 0.32/0.45 % (3440136)Peak memory usage: 10 MB
% 0.32/0.45 % (3440136)Instructions burned: 7 (million)
% 0.32/0.45 % (3440131)Instruction limit reached!
% 0.32/0.45 % (3440131)------------------------------
% 0.32/0.45 % (3440131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (3440131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (3440131)CaDiCaL version: 2.1.3
% 0.32/0.45 % (3440131)Termination reason: Instruction limit
% 0.32/0.45 % (3440131)Termination phase: shuffling
% 0.32/0.45 % (3440131)Time elapsed: 0.012 s
% 0.32/0.45 % (3440131)Peak memory usage: 10 MB
% 0.32/0.45 % (3440131)Instructions burned: 26 (million)
% 0.32/0.45 % (3440150)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.03/0.48 % (3440150)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=970757169:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.03/0.48 % (3440145)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2267723383:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.03/0.48 % (3440150)Instruction limit reached!
% 1.03/0.48 % (3440150)------------------------------
% 1.03/0.48 % (3440150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.48 % (3440150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.48 % (3440150)CaDiCaL version: 2.1.3
% 1.03/0.48 % (3440150)Termination reason: Instruction limit
% 1.03/0.48 % (3440150)Termination phase: shuffling
% 1.03/0.48 % (3440150)Time elapsed: 0.002 s
% 1.03/0.48 % (3440150)Peak memory usage: 10 MB
% 1.03/0.48 % (3440150)Instructions burned: 7 (million)
% 1.03/0.48 % (3440145)Instruction limit reached!
% 1.03/0.48 % (3440145)------------------------------
% 1.03/0.48 % (3440145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.48 % (3440145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.48 % (3440145)CaDiCaL version: 2.1.3
% 1.03/0.48 % (3440145)Termination reason: Instruction limit
% 1.03/0.48 % (3440145)Termination phase: shuffling
% 1.03/0.48 % (3440145)Time elapsed: 0.003 s
% 1.03/0.48 % (3440145)Peak memory usage: 10 MB
% 1.03/0.48 % (3440145)Instructions burned: 5 (million)
% 1.03/0.48 % (3440152)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4096222355:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.03/0.48 % (3440159)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
% 1.03/0.48 % (3440159)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.03/0.48 % (3440159)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2477032243:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.03/0.48 % (3440132)Instruction limit reached!
% 1.03/0.48 % (3440132)------------------------------
% 1.03/0.48 % (3440132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.48 % (3440132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.48 % (3440132)CaDiCaL version: 2.1.3
% 1.03/0.48 % (3440132)Termination reason: Instruction limit
% 1.03/0.48 % (3440132)Termination phase: Preprocessing 3
% 1.03/0.48 % (3440132)Time elapsed: 0.034 s
% 1.03/0.48 % (3440132)Peak memory usage: 12 MB
% 1.03/0.48 % (3440132)Instructions burned: 76 (million)
% 1.03/0.48 % (3440152)Instruction limit reached!
% 1.03/0.48 % (3440152)------------------------------
% 1.03/0.48 % (3440152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.48 % (3440152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.48 % (3440152)CaDiCaL version: 2.1.3
% 1.03/0.48 % (3440152)Termination reason: Instruction limit
% 1.03/0.48 % (3440152)Termination phase: shuffling
% 1.03/0.48 % (3440152)Time elapsed: 0.006 s
% 1.03/0.48 % (3440152)Peak memory usage: 10 MB
% 1.03/0.48 % (3440152)Instructions burned: 13 (million)
% 1.03/0.48 % (3440127)Instruction limit reached!
% 1.03/0.48 % (3440127)------------------------------
% 1.03/0.48 % (3440127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.48 % (3440127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.48 % (3440127)CaDiCaL version: 2.1.3
% 1.03/0.48 % (3440127)Termination reason: Instruction limit
% 1.03/0.48 % (3440127)Termination phase: Preprocessing 3
% 1.03/0.48 % (3440127)Time elapsed: 0.040 s
% 1.03/0.48 % (3440127)Peak memory usage: 12 MB
% 1.03/0.48 % (3440127)Instructions burned: 88 (million)
% 1.03/0.48 % (3440159)Instruction limit reached!
% 1.03/0.48 % (3440159)------------------------------
% 1.03/0.48 % (3440159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.48 % (3440159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.48 % (3440159)CaDiCaL version: 2.1.3
% 1.03/0.48 % (3440159)Termination reason: Instruction limit
% 1.03/0.51 % (3440159)Termination phase: shuffling
% 1.03/0.51 % (3440159)Time elapsed: 0.007 s
% 1.03/0.51 % (3440159)Peak memory usage: 11 MB
% 1.03/0.51 % (3440159)Instructions burned: 32 (million)
% 1.03/0.51 % (3440162)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=1757637455:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.03/0.51 % (3440175)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=659694240:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.03/0.51 % (3440171)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.03/0.51 % (3440169)lrs+10_1_si=on:cs=on:random_seed=4249984468:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.03/0.51 % (3440171)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=1385089711:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.03/0.51 % (3440169)Instruction limit reached!
% 1.03/0.51 % (3440169)------------------------------
% 1.03/0.51 % (3440169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.51 % (3440169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.51 % (3440169)CaDiCaL version: 2.1.3
% 1.03/0.51 % (3440169)Termination reason: Instruction limit
% 1.03/0.51 % (3440169)Termination phase: shuffling
% 1.03/0.51 % (3440169)Time elapsed: 0.004 s
% 1.03/0.51 % (3440169)Peak memory usage: 10 MB
% 1.03/0.51 % (3440169)Instructions burned: 8 (million)
% 1.03/0.51 % (3440171)Instruction limit reached!
% 1.03/0.51 % (3440171)------------------------------
% 1.03/0.51 % (3440171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.51 % (3440171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.51 % (3440171)CaDiCaL version: 2.1.3
% 1.03/0.51 % (3440171)Termination reason: Instruction limit
% 1.03/0.51 % (3440171)Termination phase: shuffling
% 1.03/0.51 % (3440171)Time elapsed: 0.002 s
% 1.03/0.51 % (3440171)Peak memory usage: 10 MB
% 1.03/0.51 % (3440171)Instructions burned: 3 (million)
% 1.03/0.51 % (3440174)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2381140966:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.03/0.51 % (3440133)Instruction limit reached!
% 1.03/0.51 % (3440133)------------------------------
% 1.03/0.51 % (3440133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.51 % (3440133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.51 % (3440133)CaDiCaL version: 2.1.3
% 1.03/0.51 % (3440133)Termination reason: Instruction limit
% 1.03/0.51 % (3440133)Termination phase: Property scanning
% 1.03/0.51 % (3440133)Time elapsed: 0.067 s
% 1.03/0.51 % (3440133)Peak memory usage: 13 MB
% 1.03/0.51 % (3440133)Instructions burned: 157 (million)
% 1.03/0.51 % (3440188)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1133923334:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.03/0.51 % (3440189)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2621483295:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.03/0.51 % (3440174)Instruction limit reached!
% 1.03/0.51 % (3440174)------------------------------
% 1.03/0.51 % (3440174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.51 % (3440174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.51 % (3440174)CaDiCaL version: 2.1.3
% 1.03/0.51 % (3440174)Termination reason: Instruction limit
% 1.03/0.51 % (3440174)Termination phase: Property scanning
% 1.03/0.51 % (3440174)Time elapsed: 0.019 s
% 1.03/0.51 % (3440174)Peak memory usage: 11 MB
% 1.03/0.51 % (3440174)Instructions burned: 44 (million)
% 1.03/0.51 % (3440162)Instruction limit reached!
% 1.03/0.51 % (3440162)------------------------------
% 1.03/0.51 % (3440162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.51 % (3440162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.51 % (3440162)CaDiCaL version: 2.1.3
% 1.03/0.51 % (3440162)Termination reason: Instruction limit
% 1.03/0.51 % (3440162)Termination phase: Property scanning
% 1.77/0.57 % (3440162)Time elapsed: 0.037 s
% 1.77/0.57 % (3440162)Peak memory usage: 12 MB
% 1.77/0.57 % (3440162)Instructions burned: 88 (million)
% 1.77/0.57 % (3440194)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1936182977:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.77/0.57 % (3440189)Instruction limit reached!
% 1.77/0.57 % (3440189)------------------------------
% 1.77/0.57 % (3440189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.57 % (3440189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.57 % (3440189)CaDiCaL version: 2.1.3
% 1.77/0.57 % (3440189)Termination reason: Instruction limit
% 1.77/0.57 % (3440189)Termination phase: shuffling
% 1.77/0.57 % (3440189)Time elapsed: 0.010 s
% 1.77/0.57 % (3440189)Peak memory usage: 10 MB
% 1.77/0.57 % (3440189)Instructions burned: 22 (million)
% 1.77/0.57 % (3440188)Instruction limit reached!
% 1.77/0.57 % (3440188)------------------------------
% 1.77/0.57 % (3440188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.57 % (3440188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.57 % (3440188)CaDiCaL version: 2.1.3
% 1.77/0.57 % (3440188)Termination reason: Instruction limit
% 1.77/0.57 % (3440188)Termination phase: shuffling
% 1.77/0.57 % (3440188)Time elapsed: 0.012 s
% 1.77/0.57 % (3440188)Peak memory usage: 11 MB
% 1.77/0.57 % (3440188)Instructions burned: 27 (million)
% 1.77/0.57 % (3440205)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=629871856:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.77/0.57 % (3440206)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1769658002: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)
% 1.77/0.57 % (3440206)Instruction limit reached!
% 1.77/0.57 % (3440206)------------------------------
% 1.77/0.57 % (3440206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.57 % (3440206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.57 % (3440206)CaDiCaL version: 2.1.3
% 1.77/0.57 % (3440206)Termination reason: Instruction limit
% 1.77/0.57 % (3440206)Termination phase: shuffling
% 1.77/0.57 % (3440206)Time elapsed: 0.002 s
% 1.77/0.57 % (3440206)Peak memory usage: 10 MB
% 1.77/0.57 % (3440206)Instructions burned: 4 (million)
% 1.77/0.57 % (3440175)Instruction limit reached!
% 1.77/0.57 % (3440175)------------------------------
% 1.77/0.57 % (3440175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.57 % (3440175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.57 % (3440175)CaDiCaL version: 2.1.3
% 1.77/0.57 % (3440175)Termination reason: Instruction limit
% 1.77/0.57 % (3440175)Termination phase: Saturation
% 1.77/0.57 % (3440175)Time elapsed: 0.055 s
% 1.77/0.57 % (3440175)Peak memory usage: 15 MB
% 1.77/0.57 % (3440175)Instructions burned: 250 (million)
% 1.77/0.57 % (3440208)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3237480907:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.77/0.57 % (3440205)Instruction limit reached!
% 1.77/0.57 % (3440205)------------------------------
% 1.77/0.57 % (3440205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.57 % (3440205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.57 % (3440205)CaDiCaL version: 2.1.3
% 1.77/0.57 % (3440205)Termination reason: Instruction limit
% 1.77/0.57 % (3440205)Termination phase: shuffling
% 1.77/0.57 % (3440205)Time elapsed: 0.007 s
% 1.77/0.57 % (3440205)Peak memory usage: 10 MB
% 1.77/0.57 % (3440205)Instructions burned: 14 (million)
% 1.77/0.57 % (3440209)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2636676358:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.77/0.57 % (3440219)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
% 1.77/0.57 % (3440219)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.77/0.57 % (3440219)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=4279917256:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.77/0.61 % (3440208)Instruction limit reached!
% 1.77/0.61 % (3440208)------------------------------
% 1.77/0.61 % (3440208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440208)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440208)Termination reason: Instruction limit
% 1.77/0.61 % (3440208)Termination phase: shuffling
% 1.77/0.61 % (3440208)Time elapsed: 0.012 s
% 1.77/0.61 % (3440208)Peak memory usage: 11 MB
% 1.77/0.61 % (3440208)Instructions burned: 27 (million)
% 1.77/0.61 % (3440209)Instruction limit reached!
% 1.77/0.61 % (3440209)------------------------------
% 1.77/0.61 % (3440209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440209)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440209)Termination reason: Instruction limit
% 1.77/0.61 % (3440209)Termination phase: shuffling
% 1.77/0.61 % (3440209)Time elapsed: 0.011 s
% 1.77/0.61 % (3440209)Peak memory usage: 11 MB
% 1.77/0.61 % (3440209)Instructions burned: 24 (million)
% 1.77/0.61 % (3440219)Instruction limit reached!
% 1.77/0.61 % (3440219)------------------------------
% 1.77/0.61 % (3440219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440219)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440219)Termination reason: Instruction limit
% 1.77/0.61 % (3440219)Termination phase: shuffling
% 1.77/0.61 % (3440219)Time elapsed: 0.004 s
% 1.77/0.61 % (3440219)Peak memory usage: 10 MB
% 1.77/0.61 % (3440219)Instructions burned: 16 (million)
% 1.77/0.61 % (3440222)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.77/0.61 % (3440218)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1815385539:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.77/0.61 % (3440222)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=2389686841:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.77/0.61 % (3440222)Instruction limit reached!
% 1.77/0.61 % (3440222)------------------------------
% 1.77/0.61 % (3440222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440222)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440222)Termination reason: Instruction limit
% 1.77/0.61 % (3440222)Termination phase: shuffling
% 1.77/0.61 % (3440222)Time elapsed: 0.004 s
% 1.77/0.61 % (3440222)Peak memory usage: 10 MB
% 1.77/0.61 % (3440222)Instructions burned: 8 (million)
% 1.77/0.61 % (3440233)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2435173756:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.77/0.61 % (3440233)Instruction limit reached!
% 1.77/0.61 % (3440233)------------------------------
% 1.77/0.61 % (3440233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440233)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440233)Termination reason: Instruction limit
% 1.77/0.61 % (3440233)Termination phase: shuffling
% 1.77/0.61 % (3440233)Time elapsed: 0.006 s
% 1.77/0.61 % (3440233)Peak memory usage: 11 MB
% 1.77/0.61 % (3440233)Instructions burned: 27 (million)
% 1.77/0.61 % (3440230)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=3782810430:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.77/0.61 % (3440231)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1716316803:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.77/0.61 % (3440231)Instruction limit reached!
% 1.77/0.61 % (3440231)------------------------------
% 1.77/0.61 % (3440231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440231)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440231)Termination reason: Instruction limit
% 1.77/0.61 % (3440231)Termination phase: shuffling
% 1.77/0.61 % (3440231)Time elapsed: 0.004 s
% 1.77/0.61 % (3440231)Peak memory usage: 10 MB
% 1.77/0.61 % (3440231)Instructions burned: 8 (million)
% 1.77/0.61 % (3440246)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=599409058:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.77/0.61 % (3440241)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3311807094:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.77/0.61 % (3440218)Instruction limit reached!
% 1.77/0.61 % (3440218)------------------------------
% 1.77/0.61 % (3440218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440218)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440218)Termination reason: Instruction limit
% 1.77/0.61 % (3440218)Termination phase: Preprocessing 3
% 1.77/0.61 % (3440218)Time elapsed: 0.027 s
% 1.77/0.61 % (3440218)Peak memory usage: 12 MB
% 1.77/0.61 % (3440218)Instructions burned: 60 (million)
% 1.77/0.61 % (3440230)Instruction limit reached!
% 1.77/0.61 % (3440230)------------------------------
% 1.77/0.61 % (3440230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440230)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440230)Termination reason: Instruction limit
% 1.77/0.61 % (3440230)Termination phase: shuffling
% 1.77/0.61 % (3440230)Time elapsed: 0.014 s
% 1.77/0.61 % (3440230)Peak memory usage: 11 MB
% 1.77/0.61 % (3440230)Instructions burned: 31 (million)
% 1.77/0.61 % (3440241)Instruction limit reached!
% 1.77/0.61 % (3440241)------------------------------
% 1.77/0.61 % (3440241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440241)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440241)Termination reason: Instruction limit
% 1.77/0.61 % (3440241)Termination phase: shuffling
% 1.77/0.61 % (3440241)Time elapsed: 0.009 s
% 1.77/0.61 % (3440241)Peak memory usage: 10 MB
% 1.77/0.61 % (3440241)Instructions burned: 21 (million)
% 1.77/0.61 % (3440253)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=795476597:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.77/0.61 % (3440259)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2673623922:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.77/0.61 % (3440260)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3968849584:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.77/0.61 % (3440261)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.77/0.61 % (3440261)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3204192992:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.77/0.61 % (3440261)Instruction limit reached!
% 1.77/0.61 % (3440261)------------------------------
% 1.77/0.61 % (3440261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440261)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440261)Termination reason: Instruction limit
% 1.77/0.61 % (3440261)Termination phase: shuffling
% 1.77/0.61 % (3440261)Time elapsed: 0.004 s
% 1.77/0.61 % (3440261)Peak memory usage: 10 MB
% 1.77/0.61 % (3440261)Instructions burned: 8 (million)
% 1.77/0.61 % (3440260)Instruction limit reached!
% 1.77/0.61 % (3440260)------------------------------
% 1.77/0.61 % (3440260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440260)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440260)Termination reason: Instruction limit
% 1.77/0.61 % (3440260)Termination phase: shuffling
% 1.77/0.61 % (3440260)Time elapsed: 0.020 s
% 1.77/0.61 % (3440260)Peak memory usage: 11 MB
% 1.77/0.61 % (3440260)Instructions burned: 44 (million)
% 1.77/0.61 % (3440273)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1465580905:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.77/0.61 % (3440276)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=2270339409: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)
% 1.77/0.61 % (3440253)Instruction limit reached!
% 1.77/0.61 % (3440253)------------------------------
% 1.77/0.61 % (3440253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440253)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440253)Termination reason: Instruction limit
% 1.77/0.61 % (3440253)Termination phase: Twee Goal Transformation
% 1.77/0.61 % (3440253)Time elapsed: 0.061 s
% 1.77/0.61 % (3440253)Peak memory usage: 12 MB
% 1.77/0.61 % (3440253)Instructions burned: 145 (million)
% 1.77/0.61 % (3440194)Instruction limit reached!
% 1.77/0.61 % (3440194)------------------------------
% 1.77/0.61 % (3440194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.61 % (3440194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.61 % (3440194)CaDiCaL version: 2.1.3
% 1.77/0.61 % (3440194)Termination reason: Instruction limit
% 1.77/0.61 % (3440194)Termination phase: Saturation
% 1.77/0.61 % (3440194)Time elapsed: 0.140 s
% 1.77/0.61 % (3440194)Peak memory usage: 15 MB
% 1.77/0.61 % (3440194)Instructions burned: 328 (million)
% 1.77/0.61 % (3440130) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3440122-3440130"...
% 1.77/0.61 % (3440293)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.77/0.61 % (3440293)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2327376634:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.77/0.61 % (3440130)...printing done.
% 1.77/0.61 % (3440295)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2367190331:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.77/0.61 % (3440130)Refutation found. Thanks to Tanya!
% 1.77/0.61 % SZS status Theorem for theBenchmark
% 1.77/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.77/0.62 % (3440130)------------------------------
% 1.77/0.62 % (3440130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.62 % (3440130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.62 % (3440130)CaDiCaL version: 2.1.3
% 1.77/0.62 % (3440130)Termination reason: Refutation
% 1.77/0.62 % (3440130)Time elapsed: 0.245 s
% 1.77/0.62 % (3440130)Peak memory usage: 22 MB
% 1.77/0.62 % (3440130)Instructions burned: 498 (million)
% 1.77/0.62 % (3440122)Success in time 0.312 s
% 1.77/0.62 % Vampire exiting
%------------------------------------------------------------------------------