%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU626^1 : 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 : n017.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 08:30:23 AM UTC 2026
% Result : Theorem 1.44s 0.49s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 25 unt; 0 typ; 8 def)
% Number of atoms : 3085 ( 826 equ; 0 cnn)
% Maximal formula atoms : 146 ( 42 avg)
% Number of connectives : 1753 ( 85 ~; 74 |; 591 &; 406 @)
% ( 12 <=>; 585 =>; 0 <=; 0 <~>)
% Maximal formula depth : 155 ( 20 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 : 300 ( 297 usr; 172 con; 0-4 aty)
% Number of variables : 100 ( 0 sgn 76 !; 24 ?; 100 :)
% 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_168,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_169,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_170,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_171,type,
vNOT: $o > $o ).
thf(func_def_172,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_173,type,
vAND: $o > $o > $o ).
thf(func_def_174,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_175,type,
vIMP: $o > $o > $o ).
thf(func_def_176,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_177,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_178,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_179,type,
sP0: $i > $i > $o ).
thf(func_def_180,type,
sP1: $i > $o ).
thf(func_def_181,type,
sP2: $o ).
thf(func_def_182,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_183,type,
sK4: $i > $o ).
thf(func_def_201,type,
sK22: $i > $i > $i ).
thf(func_def_233,type,
sK54: $o ).
thf(func_def_238,type,
sK59: $i > $o ).
thf(func_def_241,type,
sK62: $i > ( $i > $o ) > $i ).
thf(func_def_251,type,
sK72: $i > $i > $i ).
thf(func_def_255,type,
sK76: $i > $o ).
thf(func_def_269,type,
sK90: $i > $i ).
thf(func_def_273,type,
sK94: $o ).
thf(func_def_274,type,
sK95: $i > $o ).
thf(func_def_275,type,
sK96: $i > $i > $i ).
thf(func_def_291,type,
sK112: $o ).
thf(func_def_296,type,
sK117: $i > $i ).
thf(func_def_297,type,
sK118: $i > $i ).
thf(func_def_298,type,
sK119: $i > $i ).
thf(func_def_299,type,
sK120: $i > $i ).
thf(func_def_300,type,
sK121: $i > $i ).
thf(func_def_301,type,
sK122: $i > $i > $i > $i ).
thf(func_def_302,type,
sK123: $i > $i ).
thf(func_def_303,type,
sK124: $i > $i ).
thf(func_def_304,type,
sK125: $i > $i ).
thf(func_def_305,type,
sK126: $i > $i ).
thf(func_def_306,type,
sK127: $i > $i > $i ).
thf(func_def_307,type,
sK128: $i > $i > $i > $i ).
thf(func_def_308,type,
sK129: $i > $i > $i > $i ).
thf(func_def_309,type,
sK130: $i > $i > $i > $i ).
thf(func_def_310,type,
sK131: $i > $i > $i ).
thf(func_def_311,type,
sK132: $i > $i > $i ).
thf(func_def_312,type,
sK133: $i > $i > $i ).
thf(func_def_313,type,
sK134: $i > $i > $i ).
thf(func_def_314,type,
sK135: $i > ( $i > $o ) > $i ).
thf(func_def_315,type,
sK136: $i > $o ).
thf(func_def_320,type,
sK141: $o ).
thf(func_def_321,type,
sK142: $o > $i > $i > $i ).
thf(func_def_322,type,
sK143: $i > $o ).
thf(func_def_330,type,
sK151: $i > $o ).
thf(func_def_344,type,
sK165: $i > $o ).
thf(func_def_354,type,
sK175: $i > $o ).
thf(func_def_356,type,
sK177: ( $i > $o ) > $i ).
thf(func_def_357,type,
sK178: ( $i > $o ) > $i ).
thf(func_def_358,type,
sK179: $i > ( $i > $i > $o ) > $i ).
thf(func_def_359,type,
sK180: $i > ( $i > $i > $o ) > $i ).
thf(func_def_360,type,
sK181: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_361,type,
sK182: $i > $i > $o ).
thf(func_def_363,type,
sK184: $i > $i ).
thf(func_def_364,type,
sK185: $i > $i ).
thf(func_def_370,type,
sK191: $i > $i ).
thf(func_def_373,type,
sK194: $o ).
thf(func_def_374,type,
sK195: $i > $o ).
thf(func_def_377,type,
sK198: $i > $i ).
thf(func_def_381,type,
sK202: $i > ( $i > $o ) > $i ).
thf(func_def_382,type,
sK203: $i > $o ).
thf(func_def_391,type,
sK212: $o ).
thf(func_def_404,type,
sK225: $i > $i > $i ).
thf(func_def_407,type,
sK228: $i > $o ).
thf(func_def_408,type,
sK229: ( $i > $o ) > $i ).
thf(func_def_409,type,
sK230: $i > $o ).
thf(func_def_410,type,
sK231: $o ).
thf(func_def_429,type,
sK250: $i > $o ).
thf(func_def_433,type,
sK254: $i > $i ).
thf(func_def_435,type,
sK256: $i > $i ).
thf(func_def_450,type,
sK271: $i > $o ).
thf(func_def_453,type,
sK274: $i > $i ).
thf(func_def_456,type,
sK277: $i > $o ).
thf(func_def_458,type,
sK279: ( $i > $o ) > $i > $i ).
thf(func_def_461,type,
sK282: $o ).
thf(func_def_463,type,
sK284: ( $i > $o ) > $i ).
thf(func_def_464,type,
sK285: $i > $o ).
thf(func_def_465,type,
sK286: $i > $i ).
thf(func_def_471,type,
sK292: $i > $o ).
thf(func_def_473,type,
sK294: ( $i > $o ) > $i > $i ).
thf(func_def_477,type,
sK298: ( $i > $o ) > $i > $i ).
thf(func_def_479,type,
sK300: $i > $o ).
thf(func_def_488,type,
sK309: $i > $i ).
thf(func_def_495,type,
sK316: $i > $o ).
thf(func_def_505,type,
sK326: $i > $i > $i ).
thf(func_def_511,type,
sK332: $i > $i > $i ).
thf(func_def_521,type,
sK342: $i > $o ).
thf(func_def_524,type,
sK345: $i > $o ).
thf(func_def_525,type,
sK346: $i > $o ).
thf(func_def_526,type,
sK347: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_527,type,
sK348: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_528,type,
sK349: $i > $o ).
thf(func_def_529,type,
sK350: $i > $o ).
thf(func_def_530,type,
sK351: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_531,type,
sK352: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_532,type,
sK353: $i > $o ).
thf(func_def_533,type,
sK354: $i > $o ).
thf(func_def_534,type,
sK355: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_535,type,
sK356: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_538,type,
sK359: $i > $o ).
thf(func_def_548,type,
sK369: $i > $i > $i ).
thf(func_def_549,type,
sK370: $i > $i > $i ).
thf(func_def_554,type,
sK375: $i > $i > $i ).
thf(func_def_558,type,
sK379: $i > $o ).
thf(func_def_560,type,
sK381: $i > ( $i > $o ) > $i ).
thf(func_def_561,type,
sK382: $i > $o ).
thf(func_def_562,type,
sK383: $i > $i ).
thf(func_def_563,type,
sK384: ( $i > $o ) > $i ).
thf(f95,axiom,
! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(f147,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) ) ) )
= upairsubunion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(f148,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
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(f149,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
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f148]) ).
thf(f181,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f149]) ).
thf(f182,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 )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X0 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f181]) ).
thf(f242,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI1 ),
inference(rectify,[],[f95]) ).
thf(f243,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
<=> ( powersetI1 = $true ) ),
inference(fool_elimination,[],[f242]) ).
thf(f315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
= upairsubunion ),
inference(rectify,[],[f147]) ).
thf(f316,plain,
( ( upairsubunion = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( $true
= ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f315]) ).
thf(f497,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
<=> ( powersetI1 = $true ) ),
inference(ennf_transformation,[],[f243]) ).
thf(f539,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ! [X3: $i] :
( ( $true
= ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( upairsubunion = $true ) ),
inference(ennf_transformation,[],[f316]) ).
thf(f551,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X0 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $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,[],[f182]) ).
thf(f552,plain,
( ( quantDeMorgan1 = $true )
& ( notequalI1 = $true )
& ( vacuousDall = $true )
& ( emptyset__Cong = $true )
& ( upairsetIR = $true )
& ( singletoninpowerset = $true )
& ( powersetsubset = $true )
& ( emptysetE = $true )
& ( kpairiskpair = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( notequalI2 = $true )
& ( setextAx = $true )
& ( nonemptyI1 = $true )
& ( noeltsimpempty = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( eqinunit = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionEcases = $true )
& ( emptyE1 = $true )
& ( omega0Ax = $true )
& ( binunionIL = $true )
& ( setminusEL = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( powerset__Cong = $true )
& ( binunionRsub = $true )
& ( exuI2 = $true )
& ( setadjoinOr = $true )
& ( binintersectSubset5 = $true )
& ( sepInPowerset = $true )
& ( omega__Cong = $true )
& ( subsetI2 = $true )
& ( setminusSubset2 = $true )
& ( dsetconstr__Cong = $true )
& ( setminusILneg = $true )
& ( binunionIR = $true )
& ( powersetI = $true )
& ( singletonsubset = $true )
& ( upairset2E = $true )
& ( binintersectER = $true )
& ( symdiffI1 = $true )
& ( subPowSU = $true )
& ( setadjoin__Cong = $true )
& ( replAx = $true )
& ( subsetRefl = $true )
& ( uniqinunit = $true )
& ( exuI1 = $true )
& ( bs114d = $true )
& ( setadjoinIR = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( binintersectSubset3 = $true )
& ( emptyinunitempty = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( setadjoinAx = $true )
& ( exuI3 = $true )
& ( symdiffIneg1 = $true )
& ( upairsetIL = $true )
& ( prop2set2propI = $true )
& ( binintersectI = $true )
& ( subsetTrans = $true )
& ( setoftrueEq = $true )
& ( setminusERneg = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( binintersectLsub = $true )
& ( kpairp = $true )
& ( subsetE2 = $true )
& ( emptysetimpfalse = $true )
& ( symdiffIneg2 = $true )
& ( setadjoinIL = $true )
& ( exuE2 = $true )
& ( wellorderingAx = $true )
& ( powersetI1 = $true )
& ( nonemptyE1 = $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset4 = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X0 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( notsubsetI = $true )
& ( binintersectRsub = $true )
& ( upairset2IR = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrER = $true )
& ( subsetE = $true )
& ( quantDeMorgan4 = $true )
& ( setunionI = $true )
& ( setminusSubset1 = $true )
& ( setukpairIL = $true )
& ( binintersectSubset2 = $true )
& ( nonemptyI = $true )
& ( setukpairIR = $true )
& ( notinemptyset = $true )
& ( descr__Cong = $true )
& ( setunionE = $true )
& ( setadjoinE = $true )
& ( binintersectEL = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset1 = $true )
& ( exuE3u = $true )
& ( prop2setI = $true )
& ( binunionLsub = $true )
& ( upairsetE = $true )
& ( disjointsetsI1 = $true )
& ( symdiffE = $true )
& ( dsetconstrI = $true )
& ( setminusLsub = $true )
& ( setunion__Cong = $true )
& ( powersetE1 = $true )
& ( in__Cong = $true )
& ( sepSubset = $true )
& ( emptyInPowerset = $true )
& ( setminusELneg = $true )
& ( exuE3e = $true )
& ( subsetI1 = $true )
& ( binunionE = $true )
& ( exuE1 = $true )
& ( setadjoinSub2 = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset2 = $true )
& ( omegaSAx = $true )
& ( symdiffI2 = $true )
& ( secondinupair = $true )
& ( subset2powerset = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( exu__Cong = $true )
& ( setadjoinSub = $true )
& ( descrp = $true )
& ( upairsubunion = $true )
& ( notdallE = $true )
& ( setminusER = $true )
& ( setextsub = $true )
& ( exuEu = $true )
& ( setminusIRneg = $true )
& ( dsetconstrEL = $true )
& ( prop2setE = $true ) ),
inference(flattening,[],[f551]) ).
thf(f636,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ! [X3: $i] :
( ( $true
= ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ? [X3: $i] :
( ( $true
!= ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f539]) ).
thf(f637,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( ( subset @ ( setadjoin @ X6 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ X5 @ X4 ) )
!= $true )
& ( $true
= ( in @ X7 @ X4 ) ) )
& ( ( in @ X6 @ X5 )
= $true ) ) ) ),
inference(rectify,[],[f636]) ).
thf(f638,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ( ( $true
!= ( subset @ ( setadjoin @ sK18 @ ( setadjoin @ sK19 @ emptyset ) ) @ ( binunion @ sK17 @ sK16 ) ) )
& ( ( in @ sK19 @ sK16 )
= $true )
& ( $true
= ( in @ sK18 @ sK17 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19]),skolemize(X4,sK16),skolemize(X5,sK17),skolemize(X6,sK18),skolemize(X7,sK19)],[f637]) ).
thf(f675,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f497]) ).
thf(f676,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
& ( ( in @ X2 @ ( powerset @ X3 ) )
!= $true ) ) ) ),
inference(rectify,[],[f675]) ).
thf(f677,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ( ( ( subset @ sK49 @ sK50 )
= $true )
& ( ( in @ sK49 @ ( powerset @ sK50 ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50]),skolemize(X2,sK49),skolemize(X3,sK50)],[f676]) ).
thf(f714,plain,
( ( quantDeMorgan1 = $true )
& ( notequalI1 = $true )
& ( vacuousDall = $true )
& ( emptyset__Cong = $true )
& ( upairsetIR = $true )
& ( singletoninpowerset = $true )
& ( powersetsubset = $true )
& ( emptysetE = $true )
& ( kpairiskpair = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( notequalI2 = $true )
& ( setextAx = $true )
& ( nonemptyI1 = $true )
& ( noeltsimpempty = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( eqinunit = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionEcases = $true )
& ( emptyE1 = $true )
& ( omega0Ax = $true )
& ( binunionIL = $true )
& ( setminusEL = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( powerset__Cong = $true )
& ( binunionRsub = $true )
& ( exuI2 = $true )
& ( setadjoinOr = $true )
& ( binintersectSubset5 = $true )
& ( sepInPowerset = $true )
& ( omega__Cong = $true )
& ( subsetI2 = $true )
& ( setminusSubset2 = $true )
& ( dsetconstr__Cong = $true )
& ( setminusILneg = $true )
& ( binunionIR = $true )
& ( powersetI = $true )
& ( singletonsubset = $true )
& ( upairset2E = $true )
& ( binintersectER = $true )
& ( symdiffI1 = $true )
& ( subPowSU = $true )
& ( setadjoin__Cong = $true )
& ( replAx = $true )
& ( subsetRefl = $true )
& ( uniqinunit = $true )
& ( exuI1 = $true )
& ( bs114d = $true )
& ( setadjoinIR = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( binintersectSubset3 = $true )
& ( emptyinunitempty = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( setadjoinAx = $true )
& ( exuI3 = $true )
& ( symdiffIneg1 = $true )
& ( upairsetIL = $true )
& ( prop2set2propI = $true )
& ( binintersectI = $true )
& ( subsetTrans = $true )
& ( setoftrueEq = $true )
& ( setminusERneg = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( binintersectLsub = $true )
& ( kpairp = $true )
& ( subsetE2 = $true )
& ( emptysetimpfalse = $true )
& ( symdiffIneg2 = $true )
& ( setadjoinIL = $true )
& ( exuE2 = $true )
& ( wellorderingAx = $true )
& ( powersetI1 = $true )
& ( nonemptyE1 = $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset4 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( notsubsetI = $true )
& ( binintersectRsub = $true )
& ( upairset2IR = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrER = $true )
& ( subsetE = $true )
& ( quantDeMorgan4 = $true )
& ( setunionI = $true )
& ( setminusSubset1 = $true )
& ( setukpairIL = $true )
& ( binintersectSubset2 = $true )
& ( nonemptyI = $true )
& ( setukpairIR = $true )
& ( notinemptyset = $true )
& ( descr__Cong = $true )
& ( setunionE = $true )
& ( setadjoinE = $true )
& ( binintersectEL = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset1 = $true )
& ( exuE3u = $true )
& ( prop2setI = $true )
& ( binunionLsub = $true )
& ( upairsetE = $true )
& ( disjointsetsI1 = $true )
& ( symdiffE = $true )
& ( dsetconstrI = $true )
& ( setminusLsub = $true )
& ( setunion__Cong = $true )
& ( powersetE1 = $true )
& ( in__Cong = $true )
& ( sepSubset = $true )
& ( emptyInPowerset = $true )
& ( setminusELneg = $true )
& ( exuE3e = $true )
& ( subsetI1 = $true )
& ( binunionE = $true )
& ( exuE1 = $true )
& ( setadjoinSub2 = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset2 = $true )
& ( omegaSAx = $true )
& ( symdiffI2 = $true )
& ( secondinupair = $true )
& ( subset2powerset = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( exu__Cong = $true )
& ( setadjoinSub = $true )
& ( descrp = $true )
& ( upairsubunion = $true )
& ( notdallE = $true )
& ( setminusER = $true )
& ( setextsub = $true )
& ( exuEu = $true )
& ( setminusIRneg = $true )
& ( dsetconstrEL = $true )
& ( prop2setE = $true ) ),
inference(rectify,[],[f552]) ).
thf(f715,plain,
( ( quantDeMorgan1 = $true )
& ( notequalI1 = $true )
& ( vacuousDall = $true )
& ( emptyset__Cong = $true )
& ( upairsetIR = $true )
& ( singletoninpowerset = $true )
& ( powersetsubset = $true )
& ( emptysetE = $true )
& ( kpairiskpair = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( notequalI2 = $true )
& ( setextAx = $true )
& ( nonemptyI1 = $true )
& ( noeltsimpempty = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( eqinunit = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionEcases = $true )
& ( emptyE1 = $true )
& ( omega0Ax = $true )
& ( binunionIL = $true )
& ( setminusEL = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( powerset__Cong = $true )
& ( binunionRsub = $true )
& ( exuI2 = $true )
& ( setadjoinOr = $true )
& ( binintersectSubset5 = $true )
& ( sepInPowerset = $true )
& ( omega__Cong = $true )
& ( subsetI2 = $true )
& ( setminusSubset2 = $true )
& ( dsetconstr__Cong = $true )
& ( setminusILneg = $true )
& ( binunionIR = $true )
& ( powersetI = $true )
& ( singletonsubset = $true )
& ( upairset2E = $true )
& ( binintersectER = $true )
& ( symdiffI1 = $true )
& ( subPowSU = $true )
& ( setadjoin__Cong = $true )
& ( replAx = $true )
& ( subsetRefl = $true )
& ( uniqinunit = $true )
& ( exuI1 = $true )
& ( bs114d = $true )
& ( setadjoinIR = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( binintersectSubset3 = $true )
& ( emptyinunitempty = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( setadjoinAx = $true )
& ( exuI3 = $true )
& ( symdiffIneg1 = $true )
& ( upairsetIL = $true )
& ( prop2set2propI = $true )
& ( binintersectI = $true )
& ( subsetTrans = $true )
& ( setoftrueEq = $true )
& ( setminusERneg = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( binintersectLsub = $true )
& ( kpairp = $true )
& ( subsetE2 = $true )
& ( emptysetimpfalse = $true )
& ( symdiffIneg2 = $true )
& ( setadjoinIL = $true )
& ( exuE2 = $true )
& ( wellorderingAx = $true )
& ( powersetI1 = $true )
& ( nonemptyE1 = $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset4 = $true )
& ( $true
= ( in @ sK82 @ sK84 ) )
& ( ( in @ ( setadjoin @ sK82 @ ( setadjoin @ sK85 @ emptyset ) ) @ ( powerset @ ( binunion @ sK84 @ sK83 ) ) )
!= $true )
& ( $true
= ( in @ sK85 @ sK83 ) )
& ( notsubsetI = $true )
& ( binintersectRsub = $true )
& ( upairset2IR = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrER = $true )
& ( subsetE = $true )
& ( quantDeMorgan4 = $true )
& ( setunionI = $true )
& ( setminusSubset1 = $true )
& ( setukpairIL = $true )
& ( binintersectSubset2 = $true )
& ( nonemptyI = $true )
& ( setukpairIR = $true )
& ( notinemptyset = $true )
& ( descr__Cong = $true )
& ( setunionE = $true )
& ( setadjoinE = $true )
& ( binintersectEL = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset1 = $true )
& ( exuE3u = $true )
& ( prop2setI = $true )
& ( binunionLsub = $true )
& ( upairsetE = $true )
& ( disjointsetsI1 = $true )
& ( symdiffE = $true )
& ( dsetconstrI = $true )
& ( setminusLsub = $true )
& ( setunion__Cong = $true )
& ( powersetE1 = $true )
& ( in__Cong = $true )
& ( sepSubset = $true )
& ( emptyInPowerset = $true )
& ( setminusELneg = $true )
& ( exuE3e = $true )
& ( subsetI1 = $true )
& ( binunionE = $true )
& ( exuE1 = $true )
& ( setadjoinSub2 = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset2 = $true )
& ( omegaSAx = $true )
& ( symdiffI2 = $true )
& ( secondinupair = $true )
& ( subset2powerset = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( exu__Cong = $true )
& ( setadjoinSub = $true )
& ( descrp = $true )
& ( upairsubunion = $true )
& ( notdallE = $true )
& ( setminusER = $true )
& ( setextsub = $true )
& ( exuEu = $true )
& ( setminusIRneg = $true )
& ( dsetconstrEL = $true )
& ( prop2setE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82,sK83,sK84,sK85]),skolemize(X0,sK82),skolemize(X1,sK83),skolemize(X2,sK84),skolemize(X3,sK85)],[f714]) ).
thf(f1069,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( upairsubunion != $true )
| ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f638]) ).
thf(f1113,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( powersetI1 != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f677]) ).
thf(f1174,plain,
upairsubunion = $true,
inference(cnf_transformation,[],[f715]) ).
thf(f1227,plain,
( $true
= ( in @ sK85 @ sK83 ) ),
inference(cnf_transformation,[],[f715]) ).
thf(f1228,plain,
( ( in @ ( setadjoin @ sK82 @ ( setadjoin @ sK85 @ emptyset ) ) @ ( powerset @ ( binunion @ sK84 @ sK83 ) ) )
!= $true ),
inference(cnf_transformation,[],[f715]) ).
thf(f1229,plain,
( $true
= ( in @ sK82 @ sK84 ) ),
inference(cnf_transformation,[],[f715]) ).
thf(f1233,plain,
powersetI1 = $true,
inference(cnf_transformation,[],[f715]) ).
thf(f2645,definition,
( spl388_168
<=> ( $true
= ( in @ sK82 @ sK84 ) ) ),
introduced(definition,[new_symbols(definition,[spl388_168])],[avatar_definition]) ).
thf(f2647,plain,
( ( $true
= ( in @ sK82 @ sK84 ) )
| ~ spl388_168 ),
inference(avatar_component_clause,[],[f2645]) ).
thf(f2648,plain,
spl388_168,
inference(avatar_split_clause,[],[f1229,f2645]) ).
thf(f3272,definition,
( spl388_304
<=> ( upairsubunion = $true ) ),
introduced(definition,[new_symbols(definition,[spl388_304])],[avatar_definition]) ).
thf(f3275,plain,
spl388_304,
inference(avatar_split_clause,[],[f1174,f3272]) ).
thf(f3483,definition,
( spl388_348
<=> ( powersetI1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl388_348])],[avatar_definition]) ).
thf(f3557,definition,
( spl388_364
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl388_364])],[avatar_definition]) ).
thf(f3558,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ~ spl388_364 ),
inference(avatar_component_clause,[],[f3557]) ).
thf(f4041,definition,
( spl388_464
<=> ( ( in @ ( setadjoin @ sK82 @ ( setadjoin @ sK85 @ emptyset ) ) @ ( powerset @ ( binunion @ sK84 @ sK83 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl388_464])],[avatar_definition]) ).
thf(f4043,plain,
( ( ( in @ ( setadjoin @ sK82 @ ( setadjoin @ sK85 @ emptyset ) ) @ ( powerset @ ( binunion @ sK84 @ sK83 ) ) )
!= $true )
| spl388_464 ),
inference(avatar_component_clause,[],[f4041]) ).
thf(f4044,plain,
~ spl388_464,
inference(avatar_split_clause,[],[f1228,f4041]) ).
thf(f4082,definition,
( spl388_472
<=> ( $true
= ( in @ sK85 @ sK83 ) ) ),
introduced(definition,[new_symbols(definition,[spl388_472])],[avatar_definition]) ).
thf(f4084,plain,
( ( $true
= ( in @ sK85 @ sK83 ) )
| ~ spl388_472 ),
inference(avatar_component_clause,[],[f4082]) ).
thf(f4085,plain,
spl388_472,
inference(avatar_split_clause,[],[f1227,f4082]) ).
thf(f4220,plain,
spl388_348,
inference(avatar_split_clause,[],[f1233,f3483]) ).
thf(f4249,plain,
( ~ spl388_348
| spl388_364 ),
inference(avatar_split_clause,[],[f1113,f3557,f3483]) ).
thf(f4510,definition,
( spl388_560
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl388_560])],[avatar_definition]) ).
thf(f4511,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ~ spl388_560 ),
inference(avatar_component_clause,[],[f4510]) ).
thf(f4512,plain,
( spl388_560
| ~ spl388_304 ),
inference(avatar_split_clause,[],[f1069,f3272,f4510]) ).
thf(f5341,plain,
( ( ( subset @ ( setadjoin @ sK82 @ ( setadjoin @ sK85 @ emptyset ) ) @ ( binunion @ sK84 @ sK83 ) )
!= $true )
| ( $true != $true )
| ~ spl388_364
| spl388_464 ),
inference(superposition,[],[f4043,f3558]) ).
thf(f5358,plain,
( ( ( subset @ ( setadjoin @ sK82 @ ( setadjoin @ sK85 @ emptyset ) ) @ ( binunion @ sK84 @ sK83 ) )
!= $true )
| ~ spl388_364
| spl388_464 ),
inference(trivial_inequality_removal,[],[f5341]) ).
thf(f5360,definition,
( spl388_664
<=> ( ( subset @ ( setadjoin @ sK82 @ ( setadjoin @ sK85 @ emptyset ) ) @ ( binunion @ sK84 @ sK83 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl388_664])],[avatar_definition]) ).
thf(f5362,plain,
( ( ( subset @ ( setadjoin @ sK82 @ ( setadjoin @ sK85 @ emptyset ) ) @ ( binunion @ sK84 @ sK83 ) )
!= $true )
| spl388_664 ),
inference(avatar_component_clause,[],[f5360]) ).
thf(f5363,plain,
( ~ spl388_664
| ~ spl388_364
| spl388_464 ),
inference(avatar_split_clause,[],[f5358,f4041,f3557,f5360]) ).
thf(f6828,plain,
( ( $true
!= ( in @ sK85 @ sK83 ) )
| ( $true != $true )
| ( $true
!= ( in @ sK82 @ sK84 ) )
| ~ spl388_560
| spl388_664 ),
inference(superposition,[],[f5362,f4511]) ).
thf(f6831,plain,
( ( $true
!= ( in @ sK85 @ sK83 ) )
| ( $true
!= ( in @ sK82 @ sK84 ) )
| ~ spl388_560
| spl388_664 ),
inference(trivial_inequality_removal,[],[f6828]) ).
thf(f6832,plain,
( ( $true
!= ( in @ sK82 @ sK84 ) )
| ~ spl388_472
| ~ spl388_560
| spl388_664 ),
inference(forward_subsumption_resolution,[],[f6831,f4084]) ).
thf(f6833,plain,
( $false
| ~ spl388_168
| ~ spl388_472
| ~ spl388_560
| spl388_664 ),
inference(forward_subsumption_resolution,[],[f6832,f2647]) ).
thf(f6834,plain,
( ~ spl388_168
| ~ spl388_472
| ~ spl388_560
| spl388_664 ),
inference(avatar_contradiction_clause,[],[f6833]) ).
cnf(s116,plain,
spl388_168,
inference(sat_conversion,[],[f2648]) ).
cnf(s236,plain,
spl388_304,
inference(sat_conversion,[],[f3275]) ).
cnf(s420,plain,
~ spl388_464,
inference(sat_conversion,[],[f4044]) ).
cnf(s431,plain,
spl388_472,
inference(sat_conversion,[],[f4085]) ).
cnf(s470,plain,
spl388_348,
inference(sat_conversion,[],[f4220]) ).
cnf(s480,plain,
( ~ spl388_348
| spl388_364 ),
inference(sat_conversion,[],[f4249]) ).
cnf(s542,plain,
( ~ spl388_304
| spl388_560 ),
inference(sat_conversion,[],[f4512]) ).
cnf(s691,plain,
( ~ spl388_364
| spl388_464
| ~ spl388_664 ),
inference(sat_conversion,[],[f5363]) ).
cnf(s716,plain,
( ~ spl388_168
| ~ spl388_472
| ~ spl388_560
| spl388_664 ),
inference(sat_conversion,[],[f6834]) ).
cnf(s737,plain,
spl388_364,
inference(rat,[],[s480,s470]) ).
cnf(s747,plain,
~ spl388_664,
inference(rat,[],[s691,s737,s420]) ).
cnf(s804,plain,
spl388_560,
inference(rat,[],[s542,s236]) ).
cnf(s805,plain,
~ spl388_168,
inference(rat,[],[s716,s747,s431,s804]) ).
cnf(s850,plain,
$false,
inference(rat,[],[s116,s805]) ).
thf(f6835,plain,
$false,
inference(avatar_sat_refutation,[],[s850]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU626^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n017.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 13:54:22 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.25 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
% 0.63/0.38 % (377799)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.63/0.38 % (377804)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1963147066:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.63/0.38 % (377810)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.63/0.38 % (377810)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
% 0.63/0.38 % (377805)lrs+10_16_si=on:nwc=1.5:random_seed=3713544690:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.63/0.38 % (377806)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3371952755:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.63/0.38 % (377808)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2042016842:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.63/0.38 % (377810)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=2475072598:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.63/0.38 % (377807)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=1157531866: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)
% 0.63/0.38 % (377809)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=201985418:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.63/0.38 % (377806)Instruction limit reached!
% 0.63/0.38 % (377806)------------------------------
% 0.63/0.38 % (377806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (377806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (377806)CaDiCaL version: 2.1.3
% 0.63/0.38 % (377806)Termination reason: Instruction limit
% 0.63/0.38 % (377806)Termination phase: shuffling
% 0.63/0.38 % (377806)Time elapsed: 0.002 s
% 0.63/0.38 % (377806)Peak memory usage: 10 MB
% 0.63/0.38 % (377806)Instructions burned: 4 (million)
% 0.63/0.38 % (377805)Instruction limit reached!
% 0.63/0.38 % (377805)------------------------------
% 0.63/0.38 % (377805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (377805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (377805)CaDiCaL version: 2.1.3
% 0.63/0.38 % (377805)Termination reason: Instruction limit
% 0.63/0.38 % (377805)Termination phase: Property scanning
% 0.63/0.38 % (377805)Time elapsed: 0.009 s
% 0.63/0.38 % (377805)Peak memory usage: 10 MB
% 0.63/0.38 % (377805)Instructions burned: 19 (million)
% 0.63/0.38 % (377808)Instruction limit reached!
% 0.63/0.38 % (377808)------------------------------
% 0.63/0.38 % (377808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (377808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (377808)CaDiCaL version: 2.1.3
% 0.63/0.38 % (377808)Termination reason: Instruction limit
% 0.63/0.38 % (377808)Termination phase: Preprocessing 3
% 0.63/0.38 % (377808)Time elapsed: 0.012 s
% 0.63/0.38 % (377808)Peak memory usage: 11 MB
% 0.63/0.38 % (377808)Instructions burned: 24 (million)
% 0.63/0.38 % (377804)Instruction limit reached!
% 0.63/0.38 % (377804)------------------------------
% 0.63/0.38 % (377804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (377804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (377804)CaDiCaL version: 2.1.3
% 0.63/0.38 % (377804)Termination reason: Instruction limit
% 0.63/0.38 % (377804)Termination phase: Saturation
% 0.63/0.38 % (377804)Time elapsed: 0.023 s
% 0.63/0.38 % (377804)Peak memory usage: 13 MB
% 0.63/0.38 % (377804)Instructions burned: 91 (million)
% 0.63/0.38 % (377818)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4085882612:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.38 % (377818)Instruction limit reached!
% 0.63/0.38 % (377818)------------------------------
% 0.63/0.38 % (377818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (377818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (377818)CaDiCaL version: 2.1.3
% 0.63/0.42 % (377818)Termination reason: Instruction limit
% 0.63/0.42 % (377818)Termination phase: shuffling
% 0.63/0.42 % (377818)Time elapsed: 0.002 s
% 0.63/0.42 % (377818)Peak memory usage: 10 MB
% 0.63/0.42 % (377818)Instructions burned: 3 (million)
% 0.63/0.42 % (377821)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2792075229:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.63/0.42 % (377820)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.42 % (377819)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1909007460:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.63/0.42 % (377821)Instruction limit reached!
% 0.63/0.42 % (377821)------------------------------
% 0.63/0.42 % (377821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (377821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (377821)CaDiCaL version: 2.1.3
% 0.63/0.42 % (377821)Termination reason: Instruction limit
% 0.63/0.42 % (377821)Termination phase: shuffling
% 0.63/0.42 % (377821)Time elapsed: 0.003 s
% 0.63/0.42 % (377821)Peak memory usage: 10 MB
% 0.63/0.42 % (377821)Instructions burned: 15 (million)
% 0.63/0.42 % (377820)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3528835227:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.63/0.42 % (377819)Instruction limit reached!
% 0.63/0.42 % (377819)------------------------------
% 0.63/0.42 % (377819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (377819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (377819)CaDiCaL version: 2.1.3
% 0.63/0.42 % (377819)Termination reason: Instruction limit
% 0.63/0.42 % (377819)Termination phase: shuffling
% 0.63/0.42 % (377819)Time elapsed: 0.003 s
% 0.63/0.42 % (377819)Peak memory usage: 10 MB
% 0.63/0.42 % (377819)Instructions burned: 6 (million)
% 0.63/0.42 % (377809)Instruction limit reached!
% 0.63/0.42 % (377809)------------------------------
% 0.63/0.42 % (377809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (377809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (377809)CaDiCaL version: 2.1.3
% 0.63/0.42 % (377809)Termination reason: Instruction limit
% 0.63/0.42 % (377809)Termination phase: Property scanning
% 0.63/0.42 % (377809)Time elapsed: 0.035 s
% 0.63/0.42 % (377809)Peak memory usage: 12 MB
% 0.63/0.42 % (377809)Instructions burned: 75 (million)
% 0.63/0.42 % (377820)Instruction limit reached!
% 0.63/0.42 % (377820)------------------------------
% 0.63/0.42 % (377820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (377820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (377820)CaDiCaL version: 2.1.3
% 0.63/0.42 % (377820)Termination reason: Instruction limit
% 0.63/0.42 % (377820)Termination phase: shuffling
% 0.63/0.42 % (377820)Time elapsed: 0.004 s
% 0.63/0.42 % (377820)Peak memory usage: 10 MB
% 0.63/0.42 % (377820)Instructions burned: 8 (million)
% 0.63/0.42 % (377823)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
% 0.63/0.42 % (377823)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.42 % (377826)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=340679176:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.63/0.42 % (377823)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3024345763:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.63/0.42 % (377829)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.63/0.42 % (377828)lrs+10_1_si=on:cs=on:random_seed=1750328001:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.44/0.46 % (377829)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=3553756918:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.44/0.46 % (377830)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1344154905:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.44/0.46 % (377823)Instruction limit reached!
% 1.44/0.46 % (377823)------------------------------
% 1.44/0.46 % (377823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.46 % (377823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.46 % (377823)CaDiCaL version: 2.1.3
% 1.44/0.46 % (377823)Termination reason: Instruction limit
% 1.44/0.46 % (377823)Termination phase: Property scanning
% 1.44/0.46 % (377823)Time elapsed: 0.012 s
% 1.44/0.46 % (377823)Peak memory usage: 10 MB
% 1.44/0.46 % (377823)Instructions burned: 29 (million)
% 1.44/0.46 % (377829)Instruction limit reached!
% 1.44/0.46 % (377829)------------------------------
% 1.44/0.46 % (377829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.46 % (377829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.46 % (377829)CaDiCaL version: 2.1.3
% 1.44/0.46 % (377829)Termination reason: Instruction limit
% 1.44/0.46 % (377829)Termination phase: shuffling
% 1.44/0.46 % (377829)Time elapsed: 0.002 s
% 1.44/0.46 % (377829)Peak memory usage: 10 MB
% 1.44/0.46 % (377829)Instructions burned: 4 (million)
% 1.44/0.46 % (377828)Instruction limit reached!
% 1.44/0.46 % (377828)------------------------------
% 1.44/0.46 % (377828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.46 % (377828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.46 % (377828)CaDiCaL version: 2.1.3
% 1.44/0.46 % (377828)Termination reason: Instruction limit
% 1.44/0.46 % (377828)Termination phase: shuffling
% 1.44/0.46 % (377828)Time elapsed: 0.005 s
% 1.44/0.46 % (377828)Peak memory usage: 10 MB
% 1.44/0.46 % (377828)Instructions burned: 10 (million)
% 1.44/0.46 % (377826)Instruction limit reached!
% 1.44/0.46 % (377826)------------------------------
% 1.44/0.46 % (377826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.46 % (377826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.46 % (377826)CaDiCaL version: 2.1.3
% 1.44/0.46 % (377826)Termination reason: Instruction limit
% 1.44/0.46 % (377826)Termination phase: Saturation
% 1.44/0.46 % (377826)Time elapsed: 0.020 s
% 1.44/0.46 % (377826)Peak memory usage: 13 MB
% 1.44/0.46 % (377826)Instructions burned: 91 (million)
% 1.44/0.46 % (377810)Instruction limit reached!
% 1.44/0.46 % (377810)------------------------------
% 1.44/0.46 % (377810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.46 % (377810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.46 % (377810)CaDiCaL version: 2.1.3
% 1.44/0.46 % (377810)Termination reason: Instruction limit
% 1.44/0.46 % (377810)Termination phase: Saturation
% 1.44/0.46 % (377810)Time elapsed: 0.070 s
% 1.44/0.46 % (377810)Peak memory usage: 14 MB
% 1.44/0.46 % (377810)Instructions burned: 159 (million)
% 1.44/0.46 % (377839)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=107735304:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.44/0.46 % (377830)Instruction limit reached!
% 1.44/0.46 % (377830)------------------------------
% 1.44/0.46 % (377830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.46 % (377830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.46 % (377830)CaDiCaL version: 2.1.3
% 1.44/0.46 % (377830)Termination reason: Instruction limit
% 1.44/0.46 % (377830)Termination phase: Preprocessing 3
% 1.44/0.46 % (377830)Time elapsed: 0.019 s
% 1.44/0.46 % (377830)Peak memory usage: 11 MB
% 1.44/0.46 % (377830)Instructions burned: 39 (million)
% 1.44/0.46 % (377836)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3816554868:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.44/0.46 % (377837)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=619508427:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.44/0.46 % (377838)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=97972891:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.49 % (377838)Instruction limit reached!
% 1.44/0.49 % (377838)------------------------------
% 1.44/0.49 % (377838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377838)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377838)Termination reason: Instruction limit
% 1.44/0.49 % (377838)Termination phase: Property scanning
% 1.44/0.49 % (377838)Time elapsed: 0.007 s
% 1.44/0.49 % (377838)Peak memory usage: 10 MB
% 1.44/0.49 % (377838)Instructions burned: 16 (million)
% 1.44/0.49 % (377840)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2907857960:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.49 % (377837)Instruction limit reached!
% 1.44/0.49 % (377837)------------------------------
% 1.44/0.49 % (377837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377837)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377837)Termination reason: Instruction limit
% 1.44/0.49 % (377837)Termination phase: Preprocessing 3
% 1.44/0.49 % (377837)Time elapsed: 0.012 s
% 1.44/0.49 % (377837)Peak memory usage: 11 MB
% 1.44/0.49 % (377837)Instructions burned: 25 (million)
% 1.44/0.49 % (377842)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=419688625:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.44/0.49 % (377842)Instruction limit reached!
% 1.44/0.49 % (377842)------------------------------
% 1.44/0.49 % (377842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377842)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377842)Termination reason: Instruction limit
% 1.44/0.49 % (377842)Termination phase: shuffling
% 1.44/0.49 % (377842)Time elapsed: 0.002 s
% 1.44/0.49 % (377842)Peak memory usage: 10 MB
% 1.44/0.49 % (377842)Instructions burned: 4 (million)
% 1.44/0.49 % (377840)Instruction limit reached!
% 1.44/0.49 % (377840)------------------------------
% 1.44/0.49 % (377840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377840)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377840)Termination reason: Instruction limit
% 1.44/0.49 % (377840)Termination phase: Property scanning
% 1.44/0.49 % (377840)Time elapsed: 0.007 s
% 1.44/0.49 % (377840)Peak memory usage: 10 MB
% 1.44/0.49 % (377840)Instructions burned: 16 (million)
% 1.44/0.49 % (377846)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=521802685:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.44/0.49 % (377848)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2407654273:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.44/0.49 % (377851)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.44/0.49 % (377851)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.44/0.49 % (377850)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2706867835:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.44/0.49 % (377851)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3868798691:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.49 % (377846)Instruction limit reached!
% 1.44/0.49 % (377846)------------------------------
% 1.44/0.49 % (377846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377846)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377846)Termination reason: Instruction limit
% 1.44/0.49 % (377846)Termination phase: Property scanning
% 1.44/0.49 % (377846)Time elapsed: 0.012 s
% 1.44/0.49 % (377846)Peak memory usage: 10 MB
% 1.44/0.49 % (377846)Instructions burned: 28 (million)
% 1.44/0.49 % (377848)Instruction limit reached!
% 1.44/0.49 % (377848)------------------------------
% 1.44/0.49 % (377848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377848)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377848)Termination reason: Instruction limit
% 1.44/0.49 % (377848)Termination phase: Property scanning
% 1.44/0.49 % (377848)Time elapsed: 0.011 s
% 1.44/0.49 % (377848)Peak memory usage: 10 MB
% 1.44/0.49 % (377848)Instructions burned: 25 (million)
% 1.44/0.49 % (377851)Instruction limit reached!
% 1.44/0.49 % (377851)------------------------------
% 1.44/0.49 % (377851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377851)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377851)Termination reason: Instruction limit
% 1.44/0.49 % (377851)Termination phase: shuffling
% 1.44/0.49 % (377851)Time elapsed: 0.006 s
% 1.44/0.49 % (377851)Peak memory usage: 10 MB
% 1.44/0.49 % (377851)Instructions burned: 14 (million)
% 1.44/0.49 % (377856)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.44/0.49 % (377857)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1672396468:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.44/0.49 % (377856)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1746774310:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.44/0.49 % (377858)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=157420260:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.44/0.49 % (377850)Instruction limit reached!
% 1.44/0.49 % (377850)------------------------------
% 1.44/0.49 % (377850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377850)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377850)Termination reason: Instruction limit
% 1.44/0.49 % (377850)Termination phase: Property scanning
% 1.44/0.49 % (377850)Time elapsed: 0.027 s
% 1.44/0.49 % (377850)Peak memory usage: 12 MB
% 1.44/0.49 % (377850)Instructions burned: 60 (million)
% 1.44/0.49 % (377858)Instruction limit reached!
% 1.44/0.49 % (377858)------------------------------
% 1.44/0.49 % (377858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377858)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377858)Termination reason: Instruction limit
% 1.44/0.49 % (377858)Termination phase: shuffling
% 1.44/0.49 % (377858)Time elapsed: 0.003 s
% 1.44/0.49 % (377856)Instruction limit reached!
% 1.44/0.49 % (377856)------------------------------
% 1.44/0.49 % (377856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377858)Peak memory usage: 10 MB
% 1.44/0.49 % (377858)Instructions burned: 7 (million)
% 1.44/0.49 % (377856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377856)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377856)Termination reason: Instruction limit
% 1.44/0.49 % (377856)Termination phase: shuffling
% 1.44/0.49 % (377856)Time elapsed: 0.005 s
% 1.44/0.49 % (377856)Peak memory usage: 10 MB
% 1.44/0.49 % (377856)Instructions burned: 10 (million)
% 1.44/0.49 % (377857)Instruction limit reached!
% 1.44/0.49 % (377857)------------------------------
% 1.44/0.49 % (377857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377857)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377857)Termination reason: Instruction limit
% 1.44/0.49 % (377857)Termination phase: Property scanning
% 1.44/0.49 % (377857)Time elapsed: 0.013 s
% 1.44/0.49 % (377857)Peak memory usage: 10 MB
% 1.44/0.49 % (377857)Instructions burned: 31 (million)
% 1.44/0.49 % (377839)Instruction limit reached!
% 1.44/0.49 % (377839)------------------------------
% 1.44/0.49 % (377839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377839)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377839)Termination reason: Instruction limit
% 1.44/0.49 % (377839)Termination phase: Saturation
% 1.44/0.49 % (377839)Time elapsed: 0.085 s
% 1.44/0.49 % (377839)Peak memory usage: 14 MB
% 1.44/0.49 % (377839)Instructions burned: 331 (million)
% 1.44/0.49 % (377862)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2831529322:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.44/0.49 % (377864)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2079324547:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.44/0.49 % (377863)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2942859721:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.44/0.49 % (377866)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1581064290:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.44/0.49 % (377865)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3853396318:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.44/0.49 % (377862)Instruction limit reached!
% 1.44/0.49 % (377862)------------------------------
% 1.44/0.49 % (377862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377862)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377862)Termination reason: Instruction limit
% 1.44/0.49 % (377862)Termination phase: Property scanning
% 1.44/0.49 % (377862)Time elapsed: 0.011 s
% 1.44/0.49 % (377862)Peak memory usage: 10 MB
% 1.44/0.49 % (377862)Instructions burned: 24 (million)
% 1.44/0.49 % (377807) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-377799-377807"...
% 1.44/0.49 % (377863)Instruction limit reached!
% 1.44/0.49 % (377863)------------------------------
% 1.44/0.49 % (377863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377863)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377863)Termination reason: Instruction limit
% 1.44/0.49 % (377863)Termination phase: Property scanning
% 1.44/0.49 % (377863)Time elapsed: 0.009 s
% 1.44/0.49 % (377863)Peak memory usage: 10 MB
% 1.44/0.49 % (377863)Instructions burned: 21 (million)
% 1.44/0.49 % (377807)...printing done.
% 1.44/0.49 % (377807)Refutation found. Thanks to Tanya!
% 1.44/0.49 % SZS status Theorem for theBenchmark
% 1.44/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 1.44/0.49 % (377807)------------------------------
% 1.44/0.49 % (377807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (377807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (377807)CaDiCaL version: 2.1.3
% 1.44/0.49 % (377807)Termination reason: Refutation
% 1.44/0.49 % (377807)Time elapsed: 0.179 s
% 1.44/0.49 % (377807)Peak memory usage: 17 MB
% 1.44/0.49 % (377807)Instructions burned: 334 (million)
% 1.44/0.49 % (377799)Success in time 0.23 s
% 1.44/0.49 % Vampire exiting
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