%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU583^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:30:10 AM UTC 2026
% Result : Theorem 0.52s 0.51s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 1942 ( 526 equ; 0 cnn)
% Maximal formula atoms : 101 ( 53 avg)
% Number of connectives : 980 ( 26 ~; 17 |; 399 &; 138 @)
% ( 4 <=>; 396 =>; 0 <=; 0 <~>)
% Maximal formula depth : 107 ( 25 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 : 235 ( 232 usr; 116 con; 0-4 aty)
% Number of variables : 36 ( 0 sgn 26 !; 10 ?; 36 :)
% 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_118,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_119,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_120,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_121,type,
vAND: $o > $o > $o ).
thf(func_def_122,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_124,type,
vIMP: $o > $o > $o ).
thf(func_def_125,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_127,type,
vNOT: $o > $o ).
thf(func_def_128,type,
sP0: $i > $i > $o ).
thf(func_def_129,type,
sP1: $i > $o ).
thf(func_def_130,type,
sP2: $o ).
thf(func_def_135,type,
sK7: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_136,type,
sK8: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_137,type,
sK9: $i > $o ).
thf(func_def_138,type,
sK10: $i > $o ).
thf(func_def_145,type,
sK17: $i > $i ).
thf(func_def_148,type,
sK20: $i > $i ).
thf(func_def_151,type,
sK23: $i > $i ).
thf(func_def_152,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_154,type,
sK26: $i > $o ).
thf(func_def_159,type,
sK31: $o ).
thf(func_def_161,type,
sK33: $i > $o ).
thf(func_def_164,type,
sK36: $i > $o ).
thf(func_def_166,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_168,type,
sK40: $i > $o ).
thf(func_def_170,type,
sK42: $o ).
thf(func_def_177,type,
sK49: $i > $o ).
thf(func_def_181,type,
sK53: $i > $o ).
thf(func_def_188,type,
sK60: $i > $i > $i ).
thf(func_def_191,type,
sK63: $i > $i > $i ).
thf(func_def_192,type,
sK64: $i > $i > $i ).
thf(func_def_195,type,
sK67: $i > $o ).
thf(func_def_200,type,
sK72: $i > $o ).
thf(func_def_203,type,
sK75: $i > $o ).
thf(func_def_205,type,
sK77: ( $i > $o ) > $i > $i ).
thf(func_def_206,type,
sK78: $o > $i > $i > $i ).
thf(func_def_209,type,
sK81: $o ).
thf(func_def_215,type,
sK87: ( $i > $o ) > $i > $i ).
thf(func_def_217,type,
sK89: $i > $o ).
thf(func_def_219,type,
sK91: $i > $o ).
thf(func_def_225,type,
sK97: $i > $o ).
thf(func_def_230,type,
sK102: $i > $i ).
thf(func_def_238,type,
sK110: $i > $i ).
thf(func_def_239,type,
sK111: $o ).
thf(func_def_240,type,
sK112: $i > $o ).
thf(func_def_242,type,
sK114: $i > ( $i > $o ) > $i ).
thf(func_def_243,type,
sK115: $i > $o ).
thf(func_def_244,type,
sK116: $i > $i ).
thf(func_def_245,type,
sK117: ( $i > $o ) > $i ).
thf(func_def_256,type,
sK128: $o ).
thf(func_def_264,type,
sK136: $i > $o ).
thf(func_def_265,type,
sK137: $i > $o ).
thf(func_def_266,type,
sK138: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_267,type,
sK139: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_268,type,
sK140: $i > $o ).
thf(func_def_269,type,
sK141: ( $i > $o ) > $i ).
thf(func_def_279,type,
sK151: $i > $o ).
thf(func_def_282,type,
sK154: $i > ( $i > $o ) > $i ).
thf(func_def_284,type,
sK156: $i > $i ).
thf(func_def_285,type,
sK157: $i > $i ).
thf(func_def_287,type,
sK159: $i > $o ).
thf(func_def_291,type,
sK163: $i > $o ).
thf(func_def_300,type,
sK172: $i > $i > $i ).
thf(func_def_307,type,
sK179: $i > $o ).
thf(func_def_308,type,
sK180: $i > $o ).
thf(func_def_309,type,
sK181: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_310,type,
sK182: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_313,type,
sK185: $i > $o ).
thf(func_def_318,type,
sK190: $i > $o ).
thf(func_def_319,type,
sK191: $i > $i ).
thf(func_def_320,type,
sK192: ( $i > $o ) > $i ).
thf(func_def_322,type,
sK194: $i > $i ).
thf(func_def_323,type,
sK195: $i > $i ).
thf(func_def_324,type,
sK196: $i > $i ).
thf(func_def_325,type,
sK197: $i > $i ).
thf(func_def_326,type,
sK198: $i > $i ).
thf(func_def_327,type,
sK199: $i > $i > $i > $i ).
thf(func_def_328,type,
sK200: $i > $i ).
thf(func_def_329,type,
sK201: $i > $i ).
thf(func_def_330,type,
sK202: $i > $i ).
thf(func_def_331,type,
sK203: $i > $i ).
thf(func_def_332,type,
sK204: $i > $i > $i ).
thf(func_def_333,type,
sK205: $i > $i > $i ).
thf(func_def_334,type,
sK206: $i > $i > $i > $i ).
thf(func_def_335,type,
sK207: $i > $i > $i > $i ).
thf(func_def_336,type,
sK208: $i > $i > $i > $i ).
thf(func_def_337,type,
sK209: $i > $i > $i ).
thf(func_def_338,type,
sK210: $i > $i > $i ).
thf(func_def_339,type,
sK211: $i > $i > $i ).
thf(func_def_345,type,
sK217: $i > $i > $i ).
thf(func_def_346,type,
sK218: $i > $i > $i ).
thf(func_def_353,type,
sK225: $i > $i > $i ).
thf(func_def_354,type,
sK226: $i > $i > $o ).
thf(func_def_356,type,
sK228: $i > $i ).
thf(func_def_357,type,
sK229: $i > $i ).
thf(func_def_358,type,
sK230: $i > ( $i > $i > $o ) > $i ).
thf(func_def_359,type,
sK231: $i > ( $i > $i > $o ) > $i ).
thf(func_def_360,type,
sK232: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_380,type,
sK252: $i > $o ).
thf(func_def_382,type,
sK254: ( $i > $o ) > $i ).
thf(func_def_383,type,
sK255: ( $i > $o ) > $i ).
thf(func_def_386,type,
sK258: $o ).
thf(func_def_387,type,
sK259: $i > $o ).
thf(func_def_389,type,
sK261: $i > ( $i > $o ) > $i ).
thf(func_def_391,type,
sK263: $i > $o ).
thf(func_def_393,type,
sK265: ( $i > $o ) > $i > $i ).
thf(func_def_396,type,
sK268: $i > $i > $i ).
thf(func_def_398,type,
sK270: $i > $o ).
thf(f52,axiom,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairsetIR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(f103,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
=> ! [X1: $i,X0: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(f104,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
=> ! [X1: $i,X0: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f103]) ).
thf(f118,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
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f104]) ).
thf(f119,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 )
=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f205,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairsetIR ),
inference(rectify,[],[f52]) ).
thf(f206,plain,
( ( upairsetIR = $true )
<=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ) ),
inference(fool_elimination,[],[f205]) ).
thf(f327,plain,
( ? [X1: $i,X0: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( 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,[],[f119]) ).
thf(f328,plain,
( ( omega0Ax = $true )
& ( exuI3 = $true )
& ( omegaSAx = $true )
& ( uniqinunit = $true )
& ( sepInPowerset = $true )
& ? [X1: $i,X0: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( setunionE = $true )
& ( notinsingleton = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( exuE3e = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( notsubsetI = $true )
& ( eqimpsubset2 = $true )
& ( exuE3u = $true )
& ( dsetconstr__Cong = $true )
& ( singletonsswitch = $true )
& ( setadjoinIR = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( subsetE2 = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( exuI2 = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinAx = $true )
& ( emptyI = $true )
& ( exuE1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIL = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notequalI2 = $true )
& ( emptyinPowerset = $true )
& ( setadjoin__Cong = $true )
& ( powerset__Cong = $true )
& ( exuEu = $true )
& ( nonemptyE1 = $true )
& ( notequalI1 = $true )
& ( dsetconstrEL = $true )
& ( setunionI = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( setadjoinOr = $true )
& ( emptyinunitempty = $true )
& ( subsetI2 = $true )
& ( subsetTrans = $true )
& ( subset2powerset = $true )
& ( prop2setE = $true )
& ( upairsetIL = $true )
& ( prop2set2propI = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( omega__Cong = $true )
& ( inCongP = $true )
& ( sepSubset = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( powersetI1 = $true )
& ( upairsetE = $true )
& ( setoftrueEq = $true )
& ( inPowerset = $true )
& ( powersetAx = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( in__Cong = $true )
& ( exuI1 = $true )
& ( eqimpsubset1 = $true )
& ( subsetE = $true )
& ( powersetE1 = $true )
& ( powersetI = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIR = $true )
& ( prop2setI = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( subsetI1 = $true )
& ( powersetE = $true )
& ( exu__Cong = $true )
& ( emptysetimpfalse = $true )
& ( notdexE = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( replAx = $true )
& ( emptysetE = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( descr__Cong = $true )
& ( exuE2 = $true )
& ( descrp = $true )
& ( setext = $true )
& ( binunionIL = $true ) ),
inference(flattening,[],[f327]) ).
thf(f649,plain,
( ( ( upairsetIR = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) )
& ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairsetIR != $true ) ) ),
inference(nnf_transformation,[],[f206]) ).
thf(f650,plain,
( ( ( upairsetIR = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( upairsetIR != $true ) ) ),
inference(rectify,[],[f649]) ).
thf(f651,plain,
( ( ( upairsetIR = $true )
| ( ( in @ sK184 @ ( setadjoin @ sK183 @ ( setadjoin @ sK184 @ emptyset ) ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( upairsetIR != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183,sK184]),skolemize(X0,sK183),skolemize(X1,sK184)],[f650]) ).
thf(f655,plain,
( ( omega0Ax = $true )
& ( exuI3 = $true )
& ( omegaSAx = $true )
& ( uniqinunit = $true )
& ( sepInPowerset = $true )
& ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true )
& ( setunionE = $true )
& ( notinsingleton = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( exuE3e = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( notsubsetI = $true )
& ( eqimpsubset2 = $true )
& ( exuE3u = $true )
& ( dsetconstr__Cong = $true )
& ( singletonsswitch = $true )
& ( setadjoinIR = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( subsetE2 = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( exuI2 = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinAx = $true )
& ( emptyI = $true )
& ( exuE1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIL = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notequalI2 = $true )
& ( emptyinPowerset = $true )
& ( setadjoin__Cong = $true )
& ( powerset__Cong = $true )
& ( exuEu = $true )
& ( nonemptyE1 = $true )
& ( notequalI1 = $true )
& ( dsetconstrEL = $true )
& ( setunionI = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( setadjoinOr = $true )
& ( emptyinunitempty = $true )
& ( subsetI2 = $true )
& ( subsetTrans = $true )
& ( subset2powerset = $true )
& ( prop2setE = $true )
& ( upairsetIL = $true )
& ( prop2set2propI = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( omega__Cong = $true )
& ( inCongP = $true )
& ( sepSubset = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( powersetI1 = $true )
& ( upairsetE = $true )
& ( setoftrueEq = $true )
& ( inPowerset = $true )
& ( powersetAx = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( in__Cong = $true )
& ( exuI1 = $true )
& ( eqimpsubset1 = $true )
& ( subsetE = $true )
& ( powersetE1 = $true )
& ( powersetI = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIR = $true )
& ( prop2setI = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( subsetI1 = $true )
& ( powersetE = $true )
& ( exu__Cong = $true )
& ( emptysetimpfalse = $true )
& ( notdexE = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( replAx = $true )
& ( emptysetE = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( descr__Cong = $true )
& ( exuE2 = $true )
& ( descrp = $true )
& ( setext = $true )
& ( binunionIL = $true ) ),
inference(rectify,[],[f328]) ).
thf(f656,plain,
( ( omega0Ax = $true )
& ( exuI3 = $true )
& ( omegaSAx = $true )
& ( uniqinunit = $true )
& ( sepInPowerset = $true )
& ( $true
!= ( in @ sK189 @ ( setadjoin @ sK188 @ ( setadjoin @ sK189 @ emptyset ) ) ) )
& ( setunionE = $true )
& ( notinsingleton = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( exuE3e = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( notsubsetI = $true )
& ( eqimpsubset2 = $true )
& ( exuE3u = $true )
& ( dsetconstr__Cong = $true )
& ( singletonsswitch = $true )
& ( setadjoinIR = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( subsetE2 = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( exuI2 = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinAx = $true )
& ( emptyI = $true )
& ( exuE1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIL = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notequalI2 = $true )
& ( emptyinPowerset = $true )
& ( setadjoin__Cong = $true )
& ( powerset__Cong = $true )
& ( exuEu = $true )
& ( nonemptyE1 = $true )
& ( notequalI1 = $true )
& ( dsetconstrEL = $true )
& ( setunionI = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( setadjoinOr = $true )
& ( emptyinunitempty = $true )
& ( subsetI2 = $true )
& ( subsetTrans = $true )
& ( subset2powerset = $true )
& ( prop2setE = $true )
& ( upairsetIL = $true )
& ( prop2set2propI = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( omega__Cong = $true )
& ( inCongP = $true )
& ( sepSubset = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( powersetI1 = $true )
& ( upairsetE = $true )
& ( setoftrueEq = $true )
& ( inPowerset = $true )
& ( powersetAx = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( in__Cong = $true )
& ( exuI1 = $true )
& ( eqimpsubset1 = $true )
& ( subsetE = $true )
& ( powersetE1 = $true )
& ( powersetI = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIR = $true )
& ( prop2setI = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( subsetI1 = $true )
& ( powersetE = $true )
& ( exu__Cong = $true )
& ( emptysetimpfalse = $true )
& ( notdexE = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( replAx = $true )
& ( emptysetE = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( descr__Cong = $true )
& ( exuE2 = $true )
& ( descrp = $true )
& ( setext = $true )
& ( binunionIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188,sK189]),skolemize(X0,sK188),skolemize(X1,sK189)],[f655]) ).
thf(f995,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( upairsetIR != $true ) ),
inference(cnf_transformation,[],[f651]) ).
thf(f1024,plain,
upairsetIR = $true,
inference(cnf_transformation,[],[f656]) ).
thf(f1096,plain,
( $true
!= ( in @ sK189 @ ( setadjoin @ sK188 @ ( setadjoin @ sK189 @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f656]) ).
thf(f1468,definition,
( spl273_20
<=> ( upairsetIR = $true ) ),
introduced(definition,[new_symbols(definition,[spl273_20])],[avatar_definition]) ).
thf(f3013,definition,
( spl273_358
<=> ( $true
= ( in @ sK189 @ ( setadjoin @ sK188 @ ( setadjoin @ sK189 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl273_358])],[avatar_definition]) ).
thf(f3015,plain,
( ( $true
!= ( in @ sK189 @ ( setadjoin @ sK188 @ ( setadjoin @ sK189 @ emptyset ) ) ) )
| spl273_358 ),
inference(avatar_component_clause,[],[f3013]) ).
thf(f3016,plain,
~ spl273_358,
inference(avatar_split_clause,[],[f1096,f3013]) ).
thf(f3225,definition,
( spl273_401
<=> ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl273_401])],[avatar_definition]) ).
thf(f3226,plain,
( ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ~ spl273_401 ),
inference(avatar_component_clause,[],[f3225]) ).
thf(f3227,plain,
( spl273_401
| ~ spl273_20 ),
inference(avatar_split_clause,[],[f995,f1468,f3225]) ).
thf(f3585,plain,
spl273_20,
inference(avatar_split_clause,[],[f1024,f1468]) ).
thf(f3878,plain,
( ( $true != $true )
| spl273_358
| ~ spl273_401 ),
inference(superposition,[],[f3015,f3226]) ).
thf(f3880,plain,
( $false
| spl273_358
| ~ spl273_401 ),
inference(trivial_inequality_removal,[],[f3878]) ).
thf(f3881,plain,
( spl273_358
| ~ spl273_401 ),
inference(avatar_contradiction_clause,[],[f3880]) ).
cnf(s327,plain,
~ spl273_358,
inference(sat_conversion,[],[f3016]) ).
cnf(s383,plain,
( ~ spl273_20
| spl273_401 ),
inference(sat_conversion,[],[f3227]) ).
cnf(s481,plain,
spl273_20,
inference(sat_conversion,[],[f3585]) ).
cnf(s503,plain,
( spl273_358
| ~ spl273_401 ),
inference(sat_conversion,[],[f3881]) ).
cnf(s510,plain,
spl273_401,
inference(rat,[],[s383,s481]) ).
cnf(s511,plain,
spl273_358,
inference(rat,[],[s503,s510]) ).
cnf(s519,plain,
$false,
inference(rat,[],[s327,s511]) ).
thf(f3883,plain,
$false,
inference(avatar_sat_refutation,[],[s519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU583^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n018.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 13:54:41 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.25/0.31 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.51 % (111829)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.52/0.51 % (111839)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1460631813:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.52/0.51 % (111840)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.52/0.51 % (111840)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.52/0.51 % (111834)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=161213495:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.52/0.51 % (111836)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3310985572:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.52/0.51 % (111835)lrs+10_16_si=on:nwc=1.5:random_seed=877812911:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.52/0.51 % (111837)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2289136814:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.52/0.51 % (111840)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3851899466:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.52/0.51 % (111838)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3385733029:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.52/0.51 % (111836)Instruction limit reached!
% 0.52/0.51 % (111836)------------------------------
% 0.52/0.51 % (111836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111836)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111836)Termination reason: Instruction limit
% 0.52/0.51 % (111836)Termination phase: shuffling
% 0.52/0.51 % (111836)Time elapsed: 0.003 s
% 0.52/0.51 % (111836)Peak memory usage: 10 MB
% 0.52/0.51 % (111836)Instructions burned: 3 (million)
% 0.52/0.51 % (111835)Instruction limit reached!
% 0.52/0.51 % (111835)------------------------------
% 0.52/0.51 % (111835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111835)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111835)Termination reason: Instruction limit
% 0.52/0.51 % (111835)Termination phase: Property scanning
% 0.52/0.51 % (111835)Time elapsed: 0.016 s
% 0.52/0.51 % (111835)Peak memory usage: 10 MB
% 0.52/0.51 % (111835)Instructions burned: 18 (million)
% 0.52/0.51 % (111839)Instruction limit reached!
% 0.52/0.51 % (111839)------------------------------
% 0.52/0.51 % (111839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111839)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111839)Termination reason: Instruction limit
% 0.52/0.51 % (111839)Termination phase: Saturation
% 0.52/0.51 % (111839)Time elapsed: 0.034 s
% 0.52/0.51 % (111839)Peak memory usage: 13 MB
% 0.52/0.51 % (111839)Instructions burned: 76 (million)
% 0.52/0.51 % (111838)Instruction limit reached!
% 0.52/0.51 % (111838)------------------------------
% 0.52/0.51 % (111838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111838)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111838)Termination reason: Instruction limit
% 0.52/0.51 % (111838)Termination phase: Preprocessing 3
% 0.52/0.51 % (111838)Time elapsed: 0.023 s
% 0.52/0.51 % (111838)Peak memory usage: 11 MB
% 0.52/0.51 % (111838)Instructions burned: 24 (million)
% 0.52/0.51 % (111848)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2767134568:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.52/0.51 % (111848)Instruction limit reached!
% 0.52/0.51 % (111848)------------------------------
% 0.52/0.51 % (111848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111848)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111848)Termination reason: Instruction limit
% 0.52/0.51 % (111848)Termination phase: shuffling
% 0.52/0.51 % (111848)Time elapsed: 0.002 s
% 0.52/0.51 % (111848)Peak memory usage: 10 MB
% 0.52/0.51 % (111848)Instructions burned: 3 (million)
% 0.52/0.51 % (111849)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=795010798:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.52/0.51 % (111853)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.52/0.51 % (111853)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.51 % (111853)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3538226028:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.52/0.51 % (111849)Instruction limit reached!
% 0.52/0.51 % (111849)------------------------------
% 0.52/0.51 % (111849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111849)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111849)Termination reason: Instruction limit
% 0.52/0.51 % (111849)Termination phase: shuffling
% 0.52/0.51 % (111849)Time elapsed: 0.005 s
% 0.52/0.51 % (111849)Peak memory usage: 10 MB
% 0.52/0.51 % (111849)Instructions burned: 5 (million)
% 0.52/0.51 % (111850)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.51 % (111851)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=198805582:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.52/0.51 % (111850)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2440728599:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.52/0.51 % (111853)Instruction limit reached!
% 0.52/0.51 % (111853)------------------------------
% 0.52/0.51 % (111853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111853)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111853)Termination reason: Instruction limit
% 0.52/0.51 % (111853)Termination phase: Property scanning
% 0.52/0.51 % (111853)Time elapsed: 0.012 s
% 0.52/0.51 % (111853)Peak memory usage: 10 MB
% 0.52/0.51 % (111853)Instructions burned: 28 (million)
% 0.52/0.51 % (111850)Instruction limit reached!
% 0.52/0.51 % (111850)------------------------------
% 0.52/0.51 % (111850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111850)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111850)Termination reason: Instruction limit
% 0.52/0.51 % (111850)Termination phase: shuffling
% 0.52/0.51 % (111850)Time elapsed: 0.006 s
% 0.52/0.51 % (111850)Peak memory usage: 10 MB
% 0.52/0.51 % (111850)Instructions burned: 7 (million)
% 0.52/0.51 % (111851)Instruction limit reached!
% 0.52/0.51 % (111851)------------------------------
% 0.52/0.51 % (111851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111851)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111851)Termination reason: Instruction limit
% 0.52/0.51 % (111851)Termination phase: Property scanning
% 0.52/0.51 % (111851)Time elapsed: 0.012 s
% 0.52/0.51 % (111851)Peak memory usage: 10 MB
% 0.52/0.51 % (111851)Instructions burned: 13 (million)
% 0.52/0.51 % (111834)Instruction limit reached!
% 0.52/0.51 % (111834)------------------------------
% 0.52/0.51 % (111834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111834)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111834)Termination reason: Instruction limit
% 0.52/0.51 % (111834)Termination phase: Saturation
% 0.52/0.51 % (111834)Time elapsed: 0.077 s
% 0.52/0.51 % (111834)Peak memory usage: 13 MB
% 0.52/0.51 % (111834)Instructions burned: 87 (million)
% 0.52/0.51 % (111859)lrs+10_1_si=on:cs=on:random_seed=441359677:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.52/0.51 % (111856)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=4035126254:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.52/0.51 % (111859)Instruction limit reached!
% 0.52/0.51 % (111859)------------------------------
% 0.52/0.51 % (111859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111859)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111859)Termination reason: Instruction limit
% 0.52/0.51 % (111859)Termination phase: shuffling
% 0.52/0.51 % (111859)Time elapsed: 0.004 s
% 0.52/0.51 % (111859)Peak memory usage: 10 MB
% 0.52/0.51 % (111859)Instructions burned: 8 (million)
% 0.52/0.51 % (111860)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.52/0.51 % (111861)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1397586309:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.52/0.51 % (111837) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-111829-111837"...
% 0.52/0.51 % (111860)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3065142:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.52/0.51 % (111865)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1482493069:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.52/0.51 % (111860)Instruction limit reached!
% 0.52/0.51 % (111860)------------------------------
% 0.52/0.51 % (111860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111860)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111860)Termination reason: Instruction limit
% 0.52/0.51 % (111860)Termination phase: shuffling
% 0.52/0.51 % (111860)Time elapsed: 0.002 s
% 0.52/0.51 % (111860)Peak memory usage: 9 MB
% 0.52/0.51 % (111860)Instructions burned: 2 (million)
% 0.52/0.51 % (111862)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=530826076:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.52/0.51 % (111837)...printing done.
% 0.52/0.51 % (111837)Refutation found. Thanks to Tanya!
% 0.52/0.51 % SZS status Theorem for theBenchmark
% 0.52/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.52/0.51 % (111837)------------------------------
% 0.52/0.51 % (111837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.51 % (111837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.51 % (111837)CaDiCaL version: 2.1.3
% 0.52/0.51 % (111837)Termination reason: Refutation
% 0.52/0.51 % (111837)Time elapsed: 0.110 s
% 0.52/0.51 % (111837)Peak memory usage: 15 MB
% 0.52/0.51 % (111837)Instructions burned: 117 (million)
% 0.52/0.51 % (111829)Success in time 0.178 s
% 0.52/0.51 % Vampire exiting
%------------------------------------------------------------------------------