%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU754^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:33:16 AM UTC 2026
% Result : Theorem 7.14s 1.69s
% Output : Refutation 8.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 132 ( 74 unt; 0 typ; 4 def)
% Number of atoms : 5003 (1264 equ; 0 cnn)
% Maximal formula atoms : 275 ( 37 avg)
% Number of connectives : 3484 ( 89 ~; 79 |; 822 &;1186 @)
% ( 4 <=>;1217 =>; 0 <=; 0 <~>)
% Maximal formula depth : 285 ( 17 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 : 439 ( 435 usr; 281 con; 0-4 aty)
% ( 87 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 270 ( 0 sgn 159 !; 8 ?; 270 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_310,type,
vAND: $o > $o > $o ).
thf(func_def_311,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_312,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_313,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_314,type,
vIMP: $o > $o > $o ).
thf(func_def_315,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_316,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_317,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_318,type,
vIFF: $o > $o > $o ).
thf(func_def_319,type,
vNOT: $o > $o ).
thf(func_def_320,type,
vOR: $o > $o > $o ).
thf(func_def_321,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_322,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_325,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_330,type,
sK4: $i > $i > $i > $i ).
thf(func_def_331,type,
sK5: $i > $i > $i > $i ).
thf(func_def_332,type,
sK6: $i > $i > $i > $i ).
thf(func_def_333,type,
sK7: $i > $i > $i > $i ).
thf(func_def_334,type,
sK8: $i > ( $i > $i ) > $i > $i ).
thf(func_def_335,type,
sK9: $i > ( $i > $i ) > $i > $i ).
thf(func_def_336,type,
sK10: $i > ( $i > $i ) > $i > $i ).
thf(func_def_337,type,
sK11: $i > $i > $i > $i > $i ).
thf(func_def_338,type,
sK12: $i > $i > $i > $i > $i ).
thf(func_def_339,type,
sK13: $i > $i > $i > $i > $i ).
thf(func_def_340,type,
sK14: $i > $i > $i > $i > $i ).
thf(func_def_341,type,
sK15: $i > $i > $i > $i > $i ).
thf(func_def_342,type,
sK16: $i > $i > $i > $i > $i ).
thf(func_def_343,type,
sK17: $i > $i > $i > $i > $i ).
thf(func_def_344,type,
sK18: $i > $i > $i > $i > $i ).
thf(func_def_345,type,
sK19: $i > $i > $i > $i > $i ).
thf(func_def_346,type,
sK20: $i > $i > $i > $i > $i ).
thf(func_def_347,type,
sK21: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_348,type,
sK22: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_349,type,
sK23: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_350,type,
sK24: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_351,type,
sK25: ( $i > $i ) > $i > $i > $i ).
thf(func_def_352,type,
sK26: ( $i > $i ) > $i > $i > $i ).
thf(func_def_353,type,
sK27: ( $i > $i ) > $i > $i > $i ).
thf(func_def_354,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_355,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_356,type,
sK30: $i > ( $i > $o ) > $i > $i ).
thf(func_def_357,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_358,type,
sK32: ( $i > $o ) > $i > $i ).
thf(func_def_359,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_360,type,
sK34: $i > $i > $i ).
thf(func_def_361,type,
sK35: $i > $i > $i > $i ).
thf(func_def_362,type,
sK36: $i > $i > $i > $i ).
thf(func_def_363,type,
sK37: $i > $i > $i ).
thf(func_def_364,type,
sK38: $i > $i > $i ).
thf(func_def_365,type,
sK39: $i > $i > $i ).
thf(func_def_366,type,
sK40: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_367,type,
sK41: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_368,type,
sK42: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_369,type,
sK43: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_370,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_371,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_372,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_373,type,
sK47: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_374,type,
sK48: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_375,type,
sK49: ( $i > $o ) > $i ).
thf(func_def_376,type,
sK50: ( $i > $o ) > $i > $i ).
thf(func_def_377,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_378,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_379,type,
sK53: ( $i > $o ) > $i > $i ).
thf(func_def_380,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_381,type,
sK55: ( $i > $o ) > $i > $i ).
thf(func_def_382,type,
sK56: ( $i > $o ) > $i ).
thf(func_def_383,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_384,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_385,type,
sK59: ( $i > $o ) > $i ).
thf(func_def_386,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_387,type,
sK61: ( $i > $o ) > $i ).
thf(func_def_388,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_389,type,
sK63: ( $i > $o ) > $i > $i ).
thf(func_def_390,type,
sK64: ( $i > $o ) > $i > $i ).
thf(func_def_391,type,
sK65: ( $i > $o ) > $i ).
thf(func_def_392,type,
sK66: ( $i > $o ) > $i > $i ).
thf(func_def_393,type,
sK67: ( $i > $o ) > $i ).
thf(func_def_394,type,
sK68: ( $i > $o ) > $i ).
thf(func_def_395,type,
sK69: ( $i > $o ) > $i ).
thf(func_def_396,type,
sK70: ( $i > $o ) > $i ).
thf(func_def_397,type,
sK71: ( $i > $o ) > $i > $i ).
thf(func_def_398,type,
sK72: ( $i > $o ) > $i > $i ).
thf(func_def_399,type,
sK73: ( $i > $o ) > $i > $i ).
thf(func_def_400,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_401,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_402,type,
sK76: ( $i > $o ) > $i > $i ).
thf(func_def_403,type,
sK77: ( $i > $o ) > $i > $i ).
thf(func_def_404,type,
sK78: $i > $i ).
thf(func_def_405,type,
sK79: ( $i > $o ) > $i ).
thf(func_def_406,type,
sK80: ( $i > $o ) > $i > $i ).
thf(func_def_407,type,
sK81: $i > $o > $i > $i ).
thf(func_def_408,type,
sK82: $i > $i > $i ).
thf(func_def_409,type,
sK83: $i > $i ).
thf(func_def_410,type,
sK84: $i > $i ).
thf(func_def_411,type,
sK85: $i > $i ).
thf(func_def_412,type,
sK86: $i > $i > $i ).
thf(func_def_413,type,
sK87: $i > $i > $i ).
thf(func_def_414,type,
sK88: ( $i > $o ) > $i ).
thf(func_def_415,type,
sK89: ( $i > $o ) > $i > $i ).
thf(func_def_416,type,
sK90: ( $i > $o ) > $i ).
thf(func_def_417,type,
sK91: ( $i > $o ) > $i > $i ).
thf(func_def_418,type,
sK92: ( $i > $o ) > $i > $i ).
thf(func_def_419,type,
sK93: $i > $i ).
thf(func_def_420,type,
sK94: $i > $i > $i > $i ).
thf(func_def_421,type,
sK95: $i > $i > $i ).
thf(func_def_422,type,
sK96: $i > $i > $i ).
thf(func_def_423,type,
sK97: $i > $i > $i ).
thf(func_def_424,type,
sK98: $i > $i ).
thf(func_def_425,type,
sK99: $i > ( $i > $i > $o ) > $i ).
thf(func_def_426,type,
sK100: $i > ( $i > $i > $o ) > $i ).
thf(func_def_427,type,
sK101: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_428,type,
sK102: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_429,type,
sK103: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_430,type,
sK104: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_431,type,
sK105: $i > $i ).
thf(func_def_432,type,
sK106: $i > $i > $i ).
thf(func_def_433,type,
sK107: $i > $i > $i ).
thf(func_def_434,type,
sK108: $i > $i > $i ).
thf(f101,axiom,
( binunionIL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(f108,axiom,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(f125,axiom,
( setminusELneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(f127,axiom,
( setminusIRneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(f271,axiom,
( demorgan2a2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a2) ).
thf(f275,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a) ).
thf(f276,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f275]) ).
thf(f467,plain,
( binunionIL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f101]) ).
thf(f468,plain,
( binunionIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f467]) ).
thf(f481,plain,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f108]) ).
thf(f482,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f481]) ).
thf(f514,plain,
( setminusELneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f125]) ).
thf(f515,plain,
( setminusELneg
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ( ~ ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f514]) ).
thf(f518,plain,
( setminusIRneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f127]) ).
thf(f519,plain,
( setminusIRneg
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f518]) ).
thf(f793,plain,
( demorgan2a2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f271]) ).
thf(f794,plain,
( demorgan2a2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f793]) ).
thf(f801,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f276]) ).
thf(f802,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f801]) ).
thf(f803,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $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,[],[f802]) ).
thf(f804,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $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(flattening,[],[f803]) ).
thf(f805,plain,
( ( $true
!= ( in @ sK3 @ ( binintersect @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f804]) ).
thf(f906,plain,
( binunionIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f468]) ).
thf(f913,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f482]) ).
thf(f930,plain,
( setminusELneg
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ( ~ ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f515]) ).
thf(f932,plain,
( setminusIRneg
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f519]) ).
thf(f1076,plain,
( demorgan2a2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f794]) ).
thf(f1178,plain,
binunionIL = $true,
inference(cnf_transformation,[],[f805]) ).
thf(f1185,plain,
binintersectI = $true,
inference(cnf_transformation,[],[f805]) ).
thf(f1202,plain,
setminusELneg = $true,
inference(cnf_transformation,[],[f805]) ).
thf(f1204,plain,
setminusIRneg = $true,
inference(cnf_transformation,[],[f805]) ).
thf(f1346,plain,
demorgan2a2 = $true,
inference(cnf_transformation,[],[f805]) ).
thf(f1350,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f805]) ).
thf(f1351,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f805]) ).
thf(f1352,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f805]) ).
thf(f1353,plain,
( $true
= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(cnf_transformation,[],[f805]) ).
thf(f1354,plain,
( $true
!= ( in @ sK3 @ ( binintersect @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(cnf_transformation,[],[f805]) ).
thf(f1455,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f906,f1178]) ).
thf(f1462,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f913,f1185]) ).
thf(f1479,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ( ~ ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f930,f1202]) ).
thf(f1481,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f932,f1204]) ).
thf(f1623,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f1076,f1346]) ).
thf(f1660,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1623]) ).
thf(f1661,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( binunion @ X1 @ Y1 ) ) )
=> ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1660]) ).
thf(f1662,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( binunion @ X1 @ Y1 ) ) )
=> ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1661]) ).
thf(f1663,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1662]) ).
thf(f1664,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ ( setminus @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1663]) ).
thf(f1665,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ ( setminus @ X2 @ Y0 ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1664]) ).
thf(f1666,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ( in @ Y0 @ ( setminus @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1665]) ).
thf(f1667,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ( in @ Y0 @ ( setminus @ X2 @ X3 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1666]) ).
thf(f1668,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ( in @ Y0 @ ( setminus @ X2 @ X3 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1667]) ).
thf(f1669,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X2 @ X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1668]) ).
thf(f1670,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( $true
= ( ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X2 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1669]) ).
thf(f1671,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( in @ X4 @ ( setminus @ X2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f1670]) ).
thf(f3219,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1481]) ).
thf(f3220,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y0 )
=> ~ ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3219]) ).
thf(f3221,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y0 )
=> ~ ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f3220]) ).
thf(f3222,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3221]) ).
thf(f3223,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f3222]) ).
thf(f3224,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f3223]) ).
thf(f3225,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3224]) ).
thf(f3226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f3225]) ).
thf(f3236,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ( ~ ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1479]) ).
thf(f3237,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ( ~ ( in @ X1 @ Y0 )
=> ~ ( in @ X1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3236]) ).
thf(f3238,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ( ~ ( in @ X1 @ Y0 )
=> ~ ( in @ X1 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f3237]) ).
thf(f3239,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ( ~ ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3238]) ).
thf(f3240,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ( ~ ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ Y0 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f3239]) ).
thf(f3241,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ~ ( in @ X1 @ ( setminus @ X3 @ X2 ) )
=> ( ~ ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3240]) ).
thf(f3242,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) )
| ( $true
= ( ~ ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f3241]) ).
thf(f3243,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $true
= ( ~ ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f3242]) ).
thf(f3244,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $false
= ( ~ ( in @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( in @ X1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f3243]) ).
thf(f3245,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( $true
= ( ~ ( in @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f3244]) ).
thf(f3246,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f3245]) ).
thf(f3358,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1462]) ).
thf(f3359,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3358]) ).
thf(f3360,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f3359]) ).
thf(f3361,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3360]) ).
thf(f3362,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f3361]) ).
thf(f3363,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3362]) ).
thf(f3364,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
= $false )
| ( $true
= ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3363]) ).
thf(f3365,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $false )
| ( ( in @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3364]) ).
thf(f3412,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1455]) ).
thf(f3413,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( in @ X1 @ ( binunion @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3412]) ).
thf(f3414,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( in @ X1 @ ( binunion @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f3413]) ).
thf(f3415,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( binunion @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3414]) ).
thf(f3416,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( binunion @ Y0 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f3415]) ).
thf(f3417,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( in @ X1 @ ( binunion @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f3416]) ).
thf(f3418,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3417]) ).
thf(f5613,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(constrained_superposition,[],[f1353,f3226]) ).
thf(f5614,plain,
( $false
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f5613]) ).
thf(f13968,plain,
( ( $false = $true )
| ( $false
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(constrained_superposition,[],[f1353,f1671]) ).
thf(f13969,plain,
( ( $false
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[],[f13968]) ).
thf(f14006,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(forward_demodulation,[],[f13969,f1351]) ).
thf(f14007,plain,
( ( $false
= ( in @ sK3 @ sK0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[],[f14006]) ).
thf(f14010,plain,
( ( $false = $true )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(forward_demodulation,[],[f14007,f1352]) ).
thf(f14011,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[],[f14010]) ).
thf(f14014,plain,
( ( $false = $true )
| ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
inference(forward_demodulation,[],[f14011,f1350]) ).
thf(f14015,plain,
( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f14014]) ).
thf(f14141,definition,
( spl109_53
<=> ( $false
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl109_53])],[avatar_definition]) ).
thf(f14143,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl109_53 ),
inference(avatar_component_clause,[],[f14141]) ).
thf(f14175,definition,
( spl109_55
<=> ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl109_55])],[avatar_definition]) ).
thf(f14177,plain,
( ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) )
| ~ spl109_55 ),
inference(avatar_component_clause,[],[f14175]) ).
thf(f14179,definition,
( spl109_56
<=> ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl109_56])],[avatar_definition]) ).
thf(f14181,plain,
( ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ~ spl109_56 ),
inference(avatar_component_clause,[],[f14179]) ).
thf(f18371,plain,
( ( $true != $true )
| ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f1354,f3365]) ).
thf(f18383,plain,
( ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ( $false
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f18371]) ).
thf(f18406,definition,
( spl109_92
<=> ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl109_92])],[avatar_definition]) ).
thf(f18408,plain,
( ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
| ~ spl109_92 ),
inference(avatar_component_clause,[],[f18406]) ).
thf(f18415,plain,
( spl109_55
| spl109_56 ),
inference(avatar_split_clause,[],[f18383,f14179,f14175]) ).
thf(f22205,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f3418,f5614]) ).
thf(f22212,plain,
( $false
= ( in @ sK3 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f22205]) ).
thf(f22228,plain,
spl109_92,
inference(avatar_split_clause,[],[f14015,f18406]) ).
thf(f22237,plain,
( ( $false = $true )
| ( $true
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ~ spl109_55 ),
inference(constrained_superposition,[],[f3246,f14177]) ).
thf(f22242,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ~ spl109_55 ),
inference(trivial_inequality_removal,[],[f22237]) ).
thf(f22247,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ~ spl109_53
| ~ spl109_55 ),
inference(forward_demodulation,[],[f22242,f14143]) ).
thf(f22248,plain,
( ( $false
= ( in @ sK3 @ sK0 ) )
| ~ spl109_53
| ~ spl109_55 ),
inference(trivial_inequality_removal,[],[f22247]) ).
thf(f22309,plain,
( ( $false = $true )
| ~ spl109_53
| ~ spl109_55 ),
inference(constrained_superposition,[],[f22248,f1352]) ).
thf(f22317,plain,
( $false
| ~ spl109_53
| ~ spl109_55 ),
inference(trivial_inequality_removal,[],[f22309]) ).
thf(f22318,plain,
( ~ spl109_53
| ~ spl109_55 ),
inference(avatar_contradiction_clause,[],[f22317]) ).
thf(f22322,plain,
spl109_53,
inference(avatar_split_clause,[],[f22212,f14141]) ).
thf(f22444,plain,
( ( $false = $true )
| ~ spl109_56
| ~ spl109_92 ),
inference(constrained_superposition,[],[f14181,f18408]) ).
thf(f22454,plain,
( $false
| ~ spl109_56
| ~ spl109_92 ),
inference(trivial_inequality_removal,[],[f22444]) ).
thf(f22455,plain,
( ~ spl109_56
| ~ spl109_92 ),
inference(avatar_contradiction_clause,[],[f22454]) ).
cnf(s133,plain,
( spl109_55
| spl109_56 ),
inference(sat_conversion,[],[f18415]) ).
cnf(s213,plain,
spl109_92,
inference(sat_conversion,[],[f22228]) ).
cnf(s220,plain,
( ~ spl109_53
| ~ spl109_55 ),
inference(sat_conversion,[],[f22318]) ).
cnf(s221,plain,
spl109_53,
inference(sat_conversion,[],[f22322]) ).
cnf(s227,plain,
( ~ spl109_56
| ~ spl109_92 ),
inference(sat_conversion,[],[f22455]) ).
cnf(s228,plain,
~ spl109_55,
inference(rat,[],[s220,s221]) ).
cnf(s229,plain,
~ spl109_56,
inference(rat,[],[s227,s213]) ).
cnf(s231,plain,
$false,
inference(rat,[],[s133,s229,s228]) ).
thf(f22464,plain,
$false,
inference(avatar_sat_refutation,[],[s231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU754^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n014.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:21:30 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.14/1.69 % (2737144)Will run a generic schedule for satisfiability detection.
% 7.14/1.69 % (2737150)% WARNING: option uhcvi not known.
% 7.14/1.69 % (2737150)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=628725604:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.14/1.69 % (2737150)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.14/1.69 % (2737155)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1222309482:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.14/1.69 % (2737153)dis+10_1_sil=32000:sp=arity:random_seed=3899063842:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.14/1.69 % (2737149)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1854878795_2999 on theBenchmark for (2999ds/0Mi)
% 7.14/1.69 % (2737156)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=413226908:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.14/1.69 % (2737154)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=223947191:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.14/1.69 % (2737152)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1618223421:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.14/1.69 % (2737150)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.14/1.69 % (2737154)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.14/1.69 % (2737154)Instruction limit reached!
% 7.14/1.69 % (2737154)------------------------------
% 7.14/1.69 % (2737154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737154)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737154)Termination reason: Instruction limit
% 7.14/1.69 % (2737154)Termination phase: Property scanning
% 7.14/1.69 % (2737154)Time elapsed: 0.095 s
% 7.14/1.69 % (2737154)Peak memory usage: 11 MB
% 7.14/1.69 % (2737154)Instructions burned: 117 (million)
% 7.14/1.69 % (2737153)Instruction limit reached!
% 7.14/1.69 % (2737153)------------------------------
% 7.14/1.69 % (2737153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737153)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737153)Termination reason: Instruction limit
% 7.14/1.69 % (2737153)Termination phase: Function definition elimination
% 7.14/1.69 % (2737153)Time elapsed: 0.116 s
% 7.14/1.69 % (2737153)Peak memory usage: 11 MB
% 7.14/1.69 % (2737153)Instructions burned: 103 (million)
% 7.14/1.69 % (2737164)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2546271792:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 7.14/1.69 % (2737155)Instruction limit reached!
% 7.14/1.69 % (2737155)------------------------------
% 7.14/1.69 % (2737155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737155)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737155)Termination reason: Instruction limit
% 7.14/1.69 % (2737155)Termination phase: Property scanning
% 7.14/1.69 % (2737155)Time elapsed: 0.141 s
% 7.14/1.69 % (2737155)Peak memory usage: 12 MB
% 7.14/1.69 % (2737155)Instructions burned: 132 (million)
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % (2737156)Instruction limit reached!
% 7.14/1.69 % (2737156)------------------------------
% 7.14/1.69 % (2737156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737156)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737156)Termination reason: Instruction limit
% 7.14/1.69 % (2737156)Termination phase: Saturation
% 7.14/1.69 % (2737156)Time elapsed: 0.149 s
% 7.14/1.69 % (2737156)Peak memory usage: 13 MB
% 7.14/1.69 % (2737156)Instructions burned: 159 (million)
% 7.14/1.69 % (2737165)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=92775388:i=131:bd=preordered:fsd=on_2997 on theBenchmark for (2997ds/131Mi)
% 7.14/1.69 % (2737168)ott-21_1_sil=16000:fs=off:random_seed=1596973133:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 7.14/1.69 % (2737167)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3863899561:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2997 on theBenchmark for (2997ds/684Mi)
% 7.14/1.69 % (2737169)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=786614248:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 7.14/1.69 % (2737167)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.14/1.69 % (2737167)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % (2737165)Instruction limit reached!
% 7.14/1.69 % (2737165)------------------------------
% 7.14/1.69 % (2737165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737165)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737165)Termination reason: Instruction limit
% 7.14/1.69 % (2737165)Termination phase: Property scanning
% 7.14/1.69 % (2737165)Time elapsed: 0.125 s
% 7.14/1.69 % (2737165)Peak memory usage: 11 MB
% 7.14/1.69 % (2737165)Instructions burned: 131 (million)
% 7.14/1.69 % (2737168)Instruction limit reached!
% 7.14/1.69 % (2737168)------------------------------
% 7.14/1.69 % (2737168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737168)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737168)Termination reason: Instruction limit
% 7.14/1.69 % (2737168)Termination phase: Saturation
% 7.14/1.69 % (2737168)Time elapsed: 0.139 s
% 7.14/1.69 % (2737168)Peak memory usage: 13 MB
% 7.14/1.69 % (2737168)Instructions burned: 181 (million)
% 7.14/1.69 % (2737174)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2051318320:fmbsr=1.3:i=865:ins=25_2996 on theBenchmark for (2996ds/865Mi)
% 7.14/1.69 % (2737175)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=736424021:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 7.14/1.69 % (2737177)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1050826964:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % (2737181)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2687921007:i=879:kws=inv_precedence:fsr=off_2994 on theBenchmark for (2994ds/879Mi)
% 7.14/1.69 % (2737180)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1047493028:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 7.14/1.69 % (2737181)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.14/1.69 % (2737180)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.14/1.69 % (2737169)Instruction limit reached!
% 7.14/1.69 % (2737169)------------------------------
% 7.14/1.69 % (2737169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737169)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737169)Termination reason: Instruction limit
% 7.14/1.69 % (2737169)Termination phase: Saturation
% 7.14/1.69 % (2737169)Time elapsed: 0.410 s
% 7.14/1.69 % (2737169)Peak memory usage: 15 MB
% 7.14/1.69 % (2737169)Instructions burned: 477 (million)
% 7.14/1.69 % (2737167)Instruction limit reached!
% 7.14/1.69 % (2737167)------------------------------
% 7.14/1.69 % (2737167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737167)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737167)Termination reason: Instruction limit
% 7.14/1.69 % (2737167)Termination phase: Saturation
% 7.14/1.69 % (2737167)Time elapsed: 0.427 s
% 7.14/1.69 % (2737167)Peak memory usage: 16 MB
% 7.14/1.69 % (2737167)Instructions burned: 684 (million)
% 7.14/1.69 % (2737184)fmb+10_1_sil=64000:random_seed=457642272:i=22061:nm=2:gsp=on_2992 on theBenchmark for (2992ds/22061Mi)
% 7.14/1.69 % (2737185)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2829154153:i=9515:nm=5_2992 on theBenchmark for (2992ds/9515Mi)
% 7.14/1.69 % (2737184)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % (2737189)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=40095141:i=5131_2991 on theBenchmark for (2991ds/5131Mi)
% 7.14/1.69 % (2737188)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2385550827:fmbsr=1.7:i=920_2991 on theBenchmark for (2991ds/920Mi)
% 7.14/1.69 % (2737189)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % (2737192)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2599760394:i=1472:ins=7:fdi=8:gsp=on_2989 on theBenchmark for (2989ds/1472Mi)
% 7.14/1.69 % (2737192)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.14/1.69 % (2737192)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.14/1.69 % (2737180)Instruction limit reached!
% 7.14/1.69 % (2737180)------------------------------
% 7.14/1.69 % (2737180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737180)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737180)Termination reason: Instruction limit
% 7.14/1.69 % (2737180)Termination phase: Saturation
% 7.14/1.69 % (2737180)Time elapsed: 0.561 s
% 7.14/1.69 % (2737180)Peak memory usage: 17 MB
% 7.14/1.69 % (2737180)Instructions burned: 692 (million)
% 7.14/1.69 % (2737194)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2910314215:i=6324_2988 on theBenchmark for (2988ds/6324Mi)
% 7.14/1.69 % (2737181)Instruction limit reached!
% 7.14/1.69 % (2737181)------------------------------
% 7.14/1.69 % (2737181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737181)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737181)Termination reason: Instruction limit
% 7.14/1.69 % (2737181)Termination phase: Saturation
% 7.14/1.69 % (2737181)Time elapsed: 0.627 s
% 7.14/1.69 % (2737181)Peak memory usage: 18 MB
% 7.14/1.69 % (2737181)Instructions burned: 880 (million)
% 7.14/1.69 % (2737196)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=580014017:fmbsr=2.30978:i=2174_2988 on theBenchmark for (2988ds/2174Mi)
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % (2737198)ott-2_1_sil=16000:newcnf=on:random_seed=1318876039:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2986 on theBenchmark for (2986ds/869Mi)
% 7.14/1.69 % (2737198)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.14/1.69 % Exception at run slice level
% 7.14/1.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.14/1.69 % (2737175)Instruction limit reached!
% 7.14/1.69 % (2737175)------------------------------
% 7.14/1.69 % (2737175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.14/1.69 % (2737175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/1.69 % (2737175)CaDiCaL version: 2.1.3
% 7.14/1.69 % (2737175)Termination reason: Instruction limit
% 7.14/1.69 % (2737175)Termination phase: Saturation
% 7.14/1.69 % (2737175)Time elapsed: 0.951 s
% 7.14/1.69 % (2737175)Peak memory usage: 20 MB
% 7.14/1.69 % (2737175)Instructions burned: 1180 (million)
% 7.14/1.69 % (2737150) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2737144-2737150"...
% 7.14/1.69 % (2737150)...printing done.
% 7.14/1.69 % (2737150)Refutation found. Thanks to Tanya!
% 7.14/1.69 % SZS status Theorem for theBenchmark
% 7.14/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 8.61/1.70 % (2737150)------------------------------
% 8.61/1.70 % (2737150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.70 % (2737150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.70 % (2737150)CaDiCaL version: 2.1.3
% 8.61/1.70 % (2737150)Termination reason: Refutation
% 8.61/1.70 % (2737150)Time elapsed: 1.385 s
% 8.61/1.70 % (2737150)Peak memory usage: 22 MB
% 8.61/1.70 % (2737150)Instructions burned: 2992 (million)
% 8.61/1.70 % (2737144)Success in time 1.444 s
% 8.61/1.70 % Vampire exiting
%------------------------------------------------------------------------------