%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU615^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:30:20 AM UTC 2026
% Result : Theorem 0.58s 0.45s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 93 ( 30 unt; 0 typ; 10 def)
% Number of atoms : 3495 ( 989 equ; 0 cnn)
% Maximal formula atoms : 134 ( 37 avg)
% Number of connectives : 1877 ( 153 ~; 109 |; 573 &; 328 @)
% ( 18 <=>; 696 =>; 0 <=; 0 <~>)
% Maximal formula depth : 142 ( 17 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 285 ( 282 usr; 161 con; 0-4 aty)
% Number of variables : 107 ( 0 sgn 86 !; 21 ?; 107 :)
% 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_154,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_155,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_156,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_157,type,
vAND: $o > $o > $o ).
thf(func_def_158,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_159,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_160,type,
vIMP: $o > $o > $o ).
thf(func_def_161,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_162,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_163,type,
vNOT: $o > $o ).
thf(func_def_164,type,
sP0: $i > $i > $o ).
thf(func_def_165,type,
sP1: $i > $o ).
thf(func_def_166,type,
sP2: $o ).
thf(func_def_168,type,
sK4: $i > $o ).
thf(func_def_170,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_175,type,
sK11: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_176,type,
sK12: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_177,type,
sK13: $i > $o ).
thf(func_def_178,type,
sK14: $i > $o ).
thf(func_def_186,type,
sK22: $i > $i ).
thf(func_def_187,type,
sK23: $i > $i ).
thf(func_def_188,type,
sK24: $i > $i ).
thf(func_def_189,type,
sK25: $i > $i ).
thf(func_def_190,type,
sK26: $i > $i ).
thf(func_def_191,type,
sK27: $i > $i > $i > $i ).
thf(func_def_192,type,
sK28: $i > $i ).
thf(func_def_193,type,
sK29: $i > $i ).
thf(func_def_194,type,
sK30: $i > $i ).
thf(func_def_195,type,
sK31: $i > $i ).
thf(func_def_196,type,
sK32: $i > $i > $i ).
thf(func_def_197,type,
sK33: $i > $i > $i > $i ).
thf(func_def_198,type,
sK34: $i > $i > $i > $i ).
thf(func_def_199,type,
sK35: $i > $i > $i > $i ).
thf(func_def_200,type,
sK36: $i > $i > $i ).
thf(func_def_201,type,
sK37: $i > $i > $i ).
thf(func_def_202,type,
sK38: $i > $i > $i ).
thf(func_def_203,type,
sK39: $i > $i > $i ).
thf(func_def_204,type,
sK40: $i > $o ).
thf(func_def_210,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_212,type,
sK48: $i > $o ).
thf(func_def_214,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_215,type,
sK51: $i > $o ).
thf(func_def_216,type,
sK52: $i > $i ).
thf(func_def_217,type,
sK53: $i > $o ).
thf(func_def_228,type,
sK64: $i > $o ).
thf(func_def_229,type,
sK65: $i > $o ).
thf(func_def_230,type,
sK66: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_231,type,
sK67: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_238,type,
sK74: $i > $i > $i ).
thf(func_def_239,type,
sK75: $i > $i > $i ).
thf(func_def_244,type,
sK80: $i > $i > $i ).
thf(func_def_247,type,
sK83: $i > $i > $i ).
thf(func_def_255,type,
sK91: $i > $i > $i ).
thf(func_def_263,type,
sK99: $i > $i ).
thf(func_def_271,type,
sK107: $i > $i ).
thf(func_def_273,type,
sK109: $i > $o ).
thf(func_def_275,type,
sK111: ( $i > $o ) > $i ).
thf(func_def_276,type,
sK112: $i > $o ).
thf(func_def_280,type,
sK116: $i > $o ).
thf(func_def_282,type,
sK118: ( $i > $o ) > $i ).
thf(func_def_283,type,
sK119: $i > $o ).
thf(func_def_284,type,
sK120: $i > $i ).
thf(func_def_285,type,
sK121: $i > ( $i > $o ) > $i ).
thf(func_def_286,type,
sK122: $i > $o ).
thf(func_def_298,type,
sK134: $o ).
thf(func_def_307,type,
sK143: ( $i > $o ) > $i > $i ).
thf(func_def_309,type,
sK145: $i > $o ).
thf(func_def_318,type,
sK154: $o ).
thf(func_def_320,type,
sK156: $i > $o ).
thf(func_def_323,type,
sK159: $i > ( $i > $o ) > $i ).
thf(func_def_327,type,
sK163: $o ).
thf(func_def_330,type,
sK166: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_331,type,
sK167: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_332,type,
sK168: $i > $o ).
thf(func_def_333,type,
sK169: $i > $o ).
thf(func_def_334,type,
sK170: $o ).
thf(func_def_337,type,
sK173: $i > $o ).
thf(func_def_340,type,
sK176: $i > ( $i > $o ) > $i ).
thf(func_def_341,type,
sK177: $i > $o ).
thf(func_def_343,type,
sK179: $i > $o ).
thf(func_def_349,type,
sK185: $o ).
thf(func_def_350,type,
sK186: $i > $i ).
thf(func_def_352,type,
sK188: $i > $o ).
thf(func_def_362,type,
sK198: $i > $i ).
thf(func_def_363,type,
sK199: $i > $i ).
thf(func_def_382,type,
sK218: $i > $o ).
thf(func_def_383,type,
sK219: $i > $o ).
thf(func_def_394,type,
sK230: $i > $i > $i ).
thf(func_def_399,type,
sK235: $i > $o ).
thf(func_def_401,type,
sK237: ( $i > $o ) > $i ).
thf(func_def_402,type,
sK238: ( $i > $o ) > $i ).
thf(func_def_404,type,
sK240: $i > $o ).
thf(func_def_435,type,
sK271: $o ).
thf(func_def_442,type,
sK278: $o > $i > $i > $i ).
thf(func_def_445,type,
sK281: $o ).
thf(func_def_447,type,
sK283: $i > ( $i > $i > $o ) > $i ).
thf(func_def_448,type,
sK284: $i > ( $i > $i > $o ) > $i ).
thf(func_def_449,type,
sK285: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_450,type,
sK286: $i > $i > $o ).
thf(func_def_452,type,
sK288: $i > $i ).
thf(func_def_453,type,
sK289: $i > $i ).
thf(func_def_463,type,
sK299: $i > $i ).
thf(func_def_466,type,
sK302: $i > $i > $i ).
thf(func_def_471,type,
sK307: $i > $o ).
thf(func_def_473,type,
sK309: ( $i > $o ) > $i > $i ).
thf(func_def_475,type,
sK311: $i > $i ).
thf(func_def_481,type,
sK317: $i > $i > $i ).
thf(func_def_482,type,
sK318: $o ).
thf(func_def_502,type,
sK338: $i > $i > $i ).
thf(func_def_511,type,
sK347: $i > $o ).
thf(func_def_517,type,
sK353: ( $i > $o ) > $i > $i ).
thf(func_def_519,type,
sK355: $i > $o ).
thf(func_def_523,type,
sK359: $i > $o ).
thf(f3,axiom,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(f94,axiom,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) )
= subsetemptysetimpeq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(f130,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) )
= symdiffE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(f134,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
=> ! [X2: $i,X0: $i,X1: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(f135,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
=> ! [X2: $i,X0: $i,X1: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f134]) ).
thf(f142,plain,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[],[f3]) ).
thf(f143,plain,
( ( emptysetAx = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(fool_elimination,[],[f142]) ).
thf(f174,plain,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) )
= subsetemptysetimpeq ),
inference(rectify,[],[f94]) ).
thf(f175,plain,
( ( subsetemptysetimpeq = $true )
<=> ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
=> ( emptyset = X0 ) ) ),
inference(fool_elimination,[],[f174]) ).
thf(f204,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
=> ! [X3: $o] :
( ( ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> X3 ) )
=> ( ( ~ ( in @ X1 @ X2 )
=> ( ( in @ X1 @ X0 )
=> X3 ) )
=> X3 ) ) )
= symdiffE ),
inference(rectify,[],[f130]) ).
thf(f205,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
=> ! [X3: $o] :
( ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) )
<=> ( symdiffE = $true ) ),
inference(fool_elimination,[],[f204]) ).
thf(f366,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ~ ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f135]) ).
thf(f367,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f366]) ).
thf(f396,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( emptysetAx = $true ) ),
inference(flattening,[],[f143]) ).
thf(f405,plain,
( ( symdiffE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
=> ! [X3: $o] :
( ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ),
inference(flattening,[],[f205]) ).
thf(f430,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 )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f367]) ).
thf(f433,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
!= $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,[],[f430]) ).
thf(f434,plain,
( ( setoftrueEq = $true )
& ( subsetE2 = $true )
& ( binunionIL = $true )
& ( binintersectEL = $true )
& ( nonemptyI = $true )
& ( setadjoinOr = $true )
& ( binintersectLsub = $true )
& ( subset2powerset = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset4 = $true )
& ( emptysetimpfalse = $true )
& ( setunion__Cong = $true )
& ( powersetI = $true )
& ( notinemptyset = $true )
& ( setadjoinSub = $true )
& ( setminusSubset1 = $true )
& ( powersetE1 = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( inCongP = $true )
& ( exuEu = $true )
& ( setminusILneg = $true )
& ( subsetTrans = $true )
& ( inPowerset = $true )
& ( foundationAx = $true )
& ( upairsetIL = $true )
& ( symdiffI2 = $true )
& ( binunionLsub = $true )
& ( eqinunit = $true )
& ( binintersectSubset3 = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) )
& ( exuE2 = $true )
& ( subsetRefl = $true )
& ( nonemptyE1 = $true )
& ( setminusIRneg = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetE = $true )
& ( nonemptyImpWitness = $true )
& ( exu__Cong = $true )
& ( descrp = $true )
& ( powerset__Cong = $true )
& ( descr__Cong = $true )
& ( setext = $true )
& ( notinsingleton = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( emptyinunitempty = $true )
& ( upairsetE = $true )
& ( binunionRsub = $true )
& ( setminusELneg = $true )
& ( binintersectER = $true )
& ( disjointsetsI1 = $true )
& ( emptyE1 = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinIL = $true )
& ( setadjoinIR = $true )
& ( setbeta = $true )
& ( symdiffE = $true )
& ( replAx = $true )
& ( setunionI = $true )
& ( setunionE = $true )
& ( emptyset__Cong = $true )
& ( setadjoinAx = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset1 = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true )
& ( quantDeMorgan4 = $true )
& ( notdexE = $true )
& ( eqimpsubset2 = $true )
& ( setextAx = $true )
& ( omegaIndAx = $true )
& ( uniqinunit = $true )
& ( powersetE = $true )
& ( notequalI1 = $true )
& ( omegaSAx = $true )
& ( symdiffI1 = $true )
& ( exuE3e = $true )
& ( binunionEcases = $true )
& ( binintersectSubset2 = $true )
& ( exuI1 = $true )
& ( upairset2IR = $true )
& ( subsetI2 = $true )
& ( setminusEL = $true )
& ( subPowSU = $true )
& ( setextsub = $true )
& ( setminusLsub = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( prop2set2propI = $true )
& ( emptyInPowerset = $true )
& ( notequalI2 = $true )
& ( omega0Ax = $true )
& ( prop2setI = $true )
& ( subsetE = $true )
& ( notdallE = $true )
& ( binunionIR = $true )
& ( in__Cong = $true )
& ( notsubsetI = $true )
& ( subsetI1 = $true )
& ( emptyinPowerset = $true )
& ( setminusER = $true )
& ( singletonsswitch = $true )
& ( setminusERneg = $true )
& ( emptysetsubset = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( binintersectI = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinSub2 = $true )
& ( exuI3 = $true )
& ( sepSubset = $true )
& ( dsetconstrER = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( setminusI = $true )
& ( vacuousDall = $true )
& ( binunionE = $true )
& ( wellorderingAx = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( exuI2 = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset5 = $true )
& ( bs114d = $true )
& ( symdiffIneg1 = $true )
& ( noeltsimpempty = $true )
& ( exuE3u = $true )
& ( setadjoinE = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true ) ),
inference(flattening,[],[f433]) ).
thf(f523,plain,
( ! [X0: $i] :
( ( emptyset = X0 )
| ( ( subset @ X0 @ emptyset )
!= $true ) )
<=> ( subsetemptysetimpeq = $true ) ),
inference(ennf_transformation,[],[f175]) ).
thf(f547,plain,
( ( symdiffE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
!= $true ) )
| ( ( $true != X3 )
& ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X2 )
= $true ) ) )
| ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f405]) ).
thf(f548,plain,
( ( symdiffE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true )
| ! [X3: $o] :
( ( $true = X3 )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( $true != X3 )
& ( ( in @ X1 @ X2 )
= $true ) )
| ( ( ( in @ X1 @ X2 )
!= $true )
& ( $true != X3 )
& ( ( in @ X1 @ X0 )
= $true ) ) ) ) ),
inference(flattening,[],[f547]) ).
thf(f667,plain,
( ( ! [X0: $i] :
( ( emptyset = X0 )
| ( ( subset @ X0 @ emptyset )
!= $true ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ? [X0: $i] :
( ( emptyset != X0 )
& ( ( subset @ X0 @ emptyset )
= $true ) ) ) ),
inference(nnf_transformation,[],[f523]) ).
thf(f668,plain,
( ( ! [X0: $i] :
( ( emptyset = X0 )
| ( ( subset @ X0 @ emptyset )
!= $true ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ? [X1: $i] :
( ( emptyset != X1 )
& ( ( subset @ X1 @ emptyset )
= $true ) ) ) ),
inference(rectify,[],[f667]) ).
thf(f669,plain,
( ( ! [X0: $i] :
( ( emptyset = X0 )
| ( ( subset @ X0 @ emptyset )
!= $true ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ( ( emptyset != sK101 )
& ( ( subset @ sK101 @ emptyset )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(X1,sK101)],[f668]) ).
thf(f760,plain,
( ( ( symdiffE = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( ( in @ X1 @ X0 )
= $true )
| ( $true = X3 )
| ( ( in @ X1 @ X2 )
!= $true ) )
& ( ( ( in @ X1 @ X2 )
= $true )
| ( $true = X3 )
| ( ( in @ X1 @ X0 )
!= $true ) ) ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true )
| ! [X3: $o] :
( ( $true = X3 )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( $true != X3 )
& ( ( in @ X1 @ X2 )
= $true ) )
| ( ( ( in @ X1 @ X2 )
!= $true )
& ( $true != X3 )
& ( ( in @ X1 @ X0 )
= $true ) ) ) )
| ( symdiffE != $true ) ) ),
inference(nnf_transformation,[],[f548]) ).
thf(f761,plain,
( ( ( symdiffE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( symdiff @ X2 @ X1 ) )
= $true )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( ( in @ X0 @ X1 )
= $true )
| ( $true = X3 )
| ( ( in @ X0 @ X2 )
!= $true ) )
& ( ( ( in @ X0 @ X2 )
= $true )
| ( $true = X3 )
| ( ( in @ X0 @ X1 )
!= $true ) ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X4 @ ( symdiff @ X6 @ X5 ) )
!= $true )
| ! [X7: $o] :
( ( $true = X7 )
| ( ( ( in @ X4 @ X5 )
!= $true )
& ( $true != X7 )
& ( ( in @ X4 @ X6 )
= $true ) )
| ( ( ( in @ X4 @ X6 )
!= $true )
& ( $true != X7 )
& ( ( in @ X4 @ X5 )
= $true ) ) ) )
| ( symdiffE != $true ) ) ),
inference(rectify,[],[f760]) ).
thf(f762,plain,
( ( ( symdiffE = $true )
| ( ( ( in @ sK182 @ ( symdiff @ sK184 @ sK183 ) )
= $true )
& ( sK185 != $true )
& ( ( ( in @ sK182 @ sK183 )
= $true )
| ( sK185 = $true )
| ( ( in @ sK182 @ sK184 )
!= $true ) )
& ( ( ( in @ sK182 @ sK184 )
= $true )
| ( sK185 = $true )
| ( ( in @ sK182 @ sK183 )
!= $true ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X4 @ ( symdiff @ X6 @ X5 ) )
!= $true )
| ! [X7: $o] :
( ( $true = X7 )
| ( ( ( in @ X4 @ X5 )
!= $true )
& ( $true != X7 )
& ( ( in @ X4 @ X6 )
= $true ) )
| ( ( ( in @ X4 @ X6 )
!= $true )
& ( $true != X7 )
& ( ( in @ X4 @ X5 )
= $true ) ) ) )
| ( symdiffE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182,sK183,sK184,sK185]),skolemize(X0,sK182),skolemize(X1,sK183),skolemize(X2,sK184),skolemize(X3,sK185)],[f761]) ).
thf(f847,plain,
( ( setoftrueEq = $true )
& ( subsetE2 = $true )
& ( binunionIL = $true )
& ( binintersectEL = $true )
& ( nonemptyI = $true )
& ( setadjoinOr = $true )
& ( binintersectLsub = $true )
& ( subset2powerset = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset4 = $true )
& ( emptysetimpfalse = $true )
& ( setunion__Cong = $true )
& ( powersetI = $true )
& ( notinemptyset = $true )
& ( setadjoinSub = $true )
& ( setminusSubset1 = $true )
& ( powersetE1 = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( inCongP = $true )
& ( exuEu = $true )
& ( setminusILneg = $true )
& ( subsetTrans = $true )
& ( inPowerset = $true )
& ( foundationAx = $true )
& ( upairsetIL = $true )
& ( symdiffI2 = $true )
& ( binunionLsub = $true )
& ( eqinunit = $true )
& ( binintersectSubset3 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( symdiff @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
& ( exuE2 = $true )
& ( subsetRefl = $true )
& ( nonemptyE1 = $true )
& ( setminusIRneg = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetE = $true )
& ( nonemptyImpWitness = $true )
& ( exu__Cong = $true )
& ( descrp = $true )
& ( powerset__Cong = $true )
& ( descr__Cong = $true )
& ( setext = $true )
& ( notinsingleton = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( emptyinunitempty = $true )
& ( upairsetE = $true )
& ( binunionRsub = $true )
& ( setminusELneg = $true )
& ( binintersectER = $true )
& ( disjointsetsI1 = $true )
& ( emptyE1 = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinIL = $true )
& ( setadjoinIR = $true )
& ( setbeta = $true )
& ( symdiffE = $true )
& ( replAx = $true )
& ( setunionI = $true )
& ( setunionE = $true )
& ( emptyset__Cong = $true )
& ( setadjoinAx = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset1 = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true )
& ( quantDeMorgan4 = $true )
& ( notdexE = $true )
& ( eqimpsubset2 = $true )
& ( setextAx = $true )
& ( omegaIndAx = $true )
& ( uniqinunit = $true )
& ( powersetE = $true )
& ( notequalI1 = $true )
& ( omegaSAx = $true )
& ( symdiffI1 = $true )
& ( exuE3e = $true )
& ( binunionEcases = $true )
& ( binintersectSubset2 = $true )
& ( exuI1 = $true )
& ( upairset2IR = $true )
& ( subsetI2 = $true )
& ( setminusEL = $true )
& ( subPowSU = $true )
& ( setextsub = $true )
& ( setminusLsub = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( prop2set2propI = $true )
& ( emptyInPowerset = $true )
& ( notequalI2 = $true )
& ( omega0Ax = $true )
& ( prop2setI = $true )
& ( subsetE = $true )
& ( notdallE = $true )
& ( binunionIR = $true )
& ( in__Cong = $true )
& ( notsubsetI = $true )
& ( subsetI1 = $true )
& ( emptyinPowerset = $true )
& ( setminusER = $true )
& ( singletonsswitch = $true )
& ( setminusERneg = $true )
& ( emptysetsubset = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( binintersectI = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinSub2 = $true )
& ( exuI3 = $true )
& ( sepSubset = $true )
& ( dsetconstrER = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( setminusI = $true )
& ( vacuousDall = $true )
& ( binunionE = $true )
& ( wellorderingAx = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( exuI2 = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset5 = $true )
& ( bs114d = $true )
& ( symdiffIneg1 = $true )
& ( noeltsimpempty = $true )
& ( exuE3u = $true )
& ( setadjoinE = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true ) ),
inference(rectify,[],[f434]) ).
thf(f848,plain,
( ( setoftrueEq = $true )
& ( subsetE2 = $true )
& ( binunionIL = $true )
& ( binintersectEL = $true )
& ( nonemptyI = $true )
& ( setadjoinOr = $true )
& ( binintersectLsub = $true )
& ( subset2powerset = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset4 = $true )
& ( emptysetimpfalse = $true )
& ( setunion__Cong = $true )
& ( powersetI = $true )
& ( notinemptyset = $true )
& ( setadjoinSub = $true )
& ( setminusSubset1 = $true )
& ( powersetE1 = $true )
& ( powersetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( inCongP = $true )
& ( exuEu = $true )
& ( setminusILneg = $true )
& ( subsetTrans = $true )
& ( inPowerset = $true )
& ( foundationAx = $true )
& ( upairsetIL = $true )
& ( symdiffI2 = $true )
& ( binunionLsub = $true )
& ( eqinunit = $true )
& ( binintersectSubset3 = $true )
& ( ( in @ sK260 @ sK258 )
!= $true )
& ( ( in @ sK260 @ ( symdiff @ sK259 @ sK258 ) )
= $true )
& ( ( in @ sK260 @ sK259 )
!= $true )
& ( exuE2 = $true )
& ( subsetRefl = $true )
& ( nonemptyE1 = $true )
& ( setminusIRneg = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetE = $true )
& ( nonemptyImpWitness = $true )
& ( exu__Cong = $true )
& ( descrp = $true )
& ( powerset__Cong = $true )
& ( descr__Cong = $true )
& ( setext = $true )
& ( notinsingleton = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( emptyinunitempty = $true )
& ( upairsetE = $true )
& ( binunionRsub = $true )
& ( setminusELneg = $true )
& ( binintersectER = $true )
& ( disjointsetsI1 = $true )
& ( emptyE1 = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinIL = $true )
& ( setadjoinIR = $true )
& ( setbeta = $true )
& ( symdiffE = $true )
& ( replAx = $true )
& ( setunionI = $true )
& ( setunionE = $true )
& ( emptyset__Cong = $true )
& ( setadjoinAx = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset1 = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true )
& ( quantDeMorgan4 = $true )
& ( notdexE = $true )
& ( eqimpsubset2 = $true )
& ( setextAx = $true )
& ( omegaIndAx = $true )
& ( uniqinunit = $true )
& ( powersetE = $true )
& ( notequalI1 = $true )
& ( omegaSAx = $true )
& ( symdiffI1 = $true )
& ( exuE3e = $true )
& ( binunionEcases = $true )
& ( binintersectSubset2 = $true )
& ( exuI1 = $true )
& ( upairset2IR = $true )
& ( subsetI2 = $true )
& ( setminusEL = $true )
& ( subPowSU = $true )
& ( setextsub = $true )
& ( setminusLsub = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( prop2set2propI = $true )
& ( emptyInPowerset = $true )
& ( notequalI2 = $true )
& ( omega0Ax = $true )
& ( prop2setI = $true )
& ( subsetE = $true )
& ( notdallE = $true )
& ( binunionIR = $true )
& ( in__Cong = $true )
& ( notsubsetI = $true )
& ( subsetI1 = $true )
& ( emptyinPowerset = $true )
& ( setminusER = $true )
& ( singletonsswitch = $true )
& ( setminusERneg = $true )
& ( emptysetsubset = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( binintersectI = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinSub2 = $true )
& ( exuI3 = $true )
& ( sepSubset = $true )
& ( dsetconstrER = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( setminusI = $true )
& ( vacuousDall = $true )
& ( binunionE = $true )
& ( wellorderingAx = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( exuI2 = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset5 = $true )
& ( bs114d = $true )
& ( symdiffIneg1 = $true )
& ( noeltsimpempty = $true )
& ( exuE3u = $true )
& ( setadjoinE = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258,sK259,sK260]),skolemize(X0,sK258),skolemize(X1,sK259),skolemize(X2,sK260)],[f847]) ).
thf(f873,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) ) ),
inference(nnf_transformation,[],[f396]) ).
thf(f874,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ? [X1: $i] :
( ( in @ X1 @ emptyset )
= $true ) ) ),
inference(rectify,[],[f873]) ).
thf(f875,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ( ( in @ sK282 @ emptyset )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(X1,sK282)],[f874]) ).
thf(f1121,plain,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( subsetemptysetimpeq != $true )
| ( emptyset = X0 ) ),
inference(cnf_transformation,[],[f669]) ).
thf(f1237,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true = X7 )
| ( symdiffE != $true )
| ( ( in @ X4 @ X6 )
= $true )
| ( ( in @ X4 @ ( symdiff @ X6 @ X5 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f762]) ).
thf(f1371,plain,
emptysetAx = $true,
inference(cnf_transformation,[],[f848]) ).
thf(f1411,plain,
subsetemptysetimpeq = $true,
inference(cnf_transformation,[],[f848]) ).
thf(f1420,plain,
symdiffE = $true,
inference(cnf_transformation,[],[f848]) ).
thf(f1448,plain,
( ( in @ sK260 @ sK259 )
!= $true ),
inference(cnf_transformation,[],[f848]) ).
thf(f1449,plain,
( ( in @ sK260 @ ( symdiff @ sK259 @ sK258 ) )
= $true ),
inference(cnf_transformation,[],[f848]) ).
thf(f1450,plain,
( ( in @ sK260 @ sK258 )
!= $true ),
inference(cnf_transformation,[],[f848]) ).
thf(f1511,plain,
! [X0: $i] :
( ( emptysetAx != $true )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(cnf_transformation,[],[f875]) ).
thf(f1781,definition,
( spl360_2
<=> ( subsetemptysetimpeq = $true ) ),
introduced(definition,[new_symbols(definition,[spl360_2])],[avatar_definition]) ).
thf(f1926,definition,
( spl360_35
<=> ! [X7: $o] : ( $true = X7 ) ),
introduced(definition,[new_symbols(definition,[spl360_35])],[avatar_definition]) ).
thf(f1927,plain,
( ! [X7: $o] : ( $true = X7 )
| ~ spl360_35 ),
inference(avatar_component_clause,[],[f1926]) ).
thf(f1929,definition,
( spl360_36
<=> ( symdiffE = $true ) ),
introduced(definition,[new_symbols(definition,[spl360_36])],[avatar_definition]) ).
thf(f1933,definition,
( spl360_37
<=> ! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X6 )
= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ ( symdiff @ X6 @ X5 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl360_37])],[avatar_definition]) ).
thf(f1934,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( symdiff @ X6 @ X5 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ X6 )
= $true ) )
| ~ spl360_37 ),
inference(avatar_component_clause,[],[f1933]) ).
thf(f1935,plain,
( spl360_35
| ~ spl360_36
| spl360_37 ),
inference(avatar_split_clause,[],[f1237,f1933,f1929,f1926]) ).
thf(f2148,definition,
( spl360_86
<=> ( ( in @ sK260 @ sK258 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl360_86])],[avatar_definition]) ).
thf(f2150,plain,
( ( ( in @ sK260 @ sK258 )
!= $true )
| spl360_86 ),
inference(avatar_component_clause,[],[f2148]) ).
thf(f2151,plain,
~ spl360_86,
inference(avatar_split_clause,[],[f1450,f2148]) ).
thf(f2333,definition,
( spl360_127
<=> ( ( in @ sK260 @ ( symdiff @ sK259 @ sK258 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl360_127])],[avatar_definition]) ).
thf(f2335,plain,
( ( ( in @ sK260 @ ( symdiff @ sK259 @ sK258 ) )
= $true )
| ~ spl360_127 ),
inference(avatar_component_clause,[],[f2333]) ).
thf(f2336,plain,
spl360_127,
inference(avatar_split_clause,[],[f1449,f2333]) ).
thf(f2592,definition,
( spl360_185
<=> ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl360_185])],[avatar_definition]) ).
thf(f2593,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
| ~ spl360_185 ),
inference(avatar_component_clause,[],[f2592]) ).
thf(f2594,plain,
( ~ spl360_2
| spl360_185 ),
inference(avatar_split_clause,[],[f1121,f2592,f1781]) ).
thf(f2600,definition,
( spl360_187
<=> ( emptysetAx = $true ) ),
introduced(definition,[new_symbols(definition,[spl360_187])],[avatar_definition]) ).
thf(f2870,definition,
( spl360_246
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl360_246])],[avatar_definition]) ).
thf(f2871,plain,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ~ spl360_246 ),
inference(avatar_component_clause,[],[f2870]) ).
thf(f3055,plain,
spl360_2,
inference(avatar_split_clause,[],[f1411,f1781]) ).
thf(f3879,plain,
spl360_187,
inference(avatar_split_clause,[],[f1371,f2600]) ).
thf(f4065,plain,
spl360_36,
inference(avatar_split_clause,[],[f1420,f1929]) ).
thf(f4418,plain,
( spl360_246
| ~ spl360_187 ),
inference(avatar_split_clause,[],[f1511,f2600,f2870]) ).
thf(f4551,definition,
( spl360_594
<=> ( ( in @ sK260 @ sK259 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl360_594])],[avatar_definition]) ).
thf(f4553,plain,
( ( ( in @ sK260 @ sK259 )
!= $true )
| spl360_594 ),
inference(avatar_component_clause,[],[f4551]) ).
thf(f4554,plain,
~ spl360_594,
inference(avatar_split_clause,[],[f1448,f4551]) ).
thf(f4692,plain,
( ! [X0: $i] : ( emptyset = X0 )
| ~ spl360_35
| ~ spl360_185 ),
inference(forward_subsumption_resolution,[],[f2593,f1927]) ).
thf(f4694,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
| ~ spl360_35
| ~ spl360_185
| ~ spl360_246 ),
inference(superposition,[],[f2871,f4692]) ).
thf(f4695,plain,
( $false
| ~ spl360_35
| ~ spl360_185
| ~ spl360_246 ),
inference(forward_subsumption_resolution,[],[f4694,f1927]) ).
thf(f4696,plain,
( ~ spl360_35
| ~ spl360_185
| ~ spl360_246 ),
inference(avatar_contradiction_clause,[],[f4695]) ).
thf(f5833,plain,
( ( ( in @ sK260 @ sK258 )
= $true )
| ( $true != $true )
| ( ( in @ sK260 @ sK259 )
= $true )
| ~ spl360_37
| ~ spl360_127 ),
inference(superposition,[],[f1934,f2335]) ).
thf(f5851,plain,
( ( ( in @ sK260 @ sK258 )
= $true )
| ( ( in @ sK260 @ sK259 )
= $true )
| ~ spl360_37
| ~ spl360_127 ),
inference(trivial_inequality_removal,[],[f5833]) ).
thf(f5861,plain,
( ( ( in @ sK260 @ sK259 )
= $true )
| ~ spl360_37
| spl360_86
| ~ spl360_127 ),
inference(forward_subsumption_resolution,[],[f5851,f2150]) ).
thf(f5862,plain,
( $false
| ~ spl360_37
| spl360_86
| ~ spl360_127
| spl360_594 ),
inference(forward_subsumption_resolution,[],[f5861,f4553]) ).
thf(f5863,plain,
( ~ spl360_37
| spl360_86
| ~ spl360_127
| spl360_594 ),
inference(avatar_contradiction_clause,[],[f5862]) ).
cnf(s20,plain,
( spl360_35
| ~ spl360_36
| spl360_37 ),
inference(sat_conversion,[],[f1935]) ).
cnf(s48,plain,
~ spl360_86,
inference(sat_conversion,[],[f2151]) ).
cnf(s78,plain,
spl360_127,
inference(sat_conversion,[],[f2336]) ).
cnf(s127,plain,
( ~ spl360_2
| spl360_185 ),
inference(sat_conversion,[],[f2594]) ).
cnf(s220,plain,
spl360_2,
inference(sat_conversion,[],[f3055]) ).
cnf(s417,plain,
spl360_187,
inference(sat_conversion,[],[f3879]) ).
cnf(s464,plain,
spl360_36,
inference(sat_conversion,[],[f4065]) ).
cnf(s559,plain,
( ~ spl360_187
| spl360_246 ),
inference(sat_conversion,[],[f4418]) ).
cnf(s603,plain,
~ spl360_594,
inference(sat_conversion,[],[f4554]) ).
cnf(s631,plain,
( ~ spl360_35
| ~ spl360_185
| ~ spl360_246 ),
inference(sat_conversion,[],[f4696]) ).
cnf(s648,plain,
( ~ spl360_37
| spl360_86
| ~ spl360_127
| spl360_594 ),
inference(sat_conversion,[],[f5863]) ).
cnf(s668,plain,
spl360_246,
inference(rat,[],[s559,s417]) ).
cnf(s749,plain,
spl360_185,
inference(rat,[],[s127,s220]) ).
cnf(s750,plain,
~ spl360_35,
inference(rat,[],[s631,s668,s749]) ).
cnf(s795,plain,
~ spl360_37,
inference(rat,[],[s648,s603,s78,s48]) ).
cnf(s803,plain,
$false,
inference(rat,[],[s20,s795,s464,s750]) ).
thf(f5864,plain,
$false,
inference(avatar_sat_refutation,[],[s803]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU615^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n018.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:00:26 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.22/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.41 % (119563)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.58/0.41 % (119572)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2663999210:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.58/0.41 % (119574)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.58/0.41 % (119574)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
% 0.58/0.41 % (119572)Instruction limit reached!
% 0.58/0.41 % (119572)------------------------------
% 0.58/0.41 % (119572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (119572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (119572)CaDiCaL version: 2.1.3
% 0.58/0.41 % (119569)lrs+10_16_si=on:nwc=1.5:random_seed=2622210136:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.58/0.41 % (119572)Termination reason: Instruction limit
% 0.58/0.41 % (119572)Termination phase: Preprocessing 3
% 0.58/0.41 % (119572)Time elapsed: 0.007 s
% 0.58/0.41 % (119572)Peak memory usage: 11 MB
% 0.58/0.41 % (119572)Instructions burned: 25 (million)
% 0.58/0.41 % (119570)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=457082980:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.58/0.41 % (119568)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=543355937:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.58/0.41 % (119571)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=1969618030: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)
% 0.58/0.41 % (119573)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=575737307:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.58/0.41 % (119574)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=3680813061:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.58/0.41 % (119570)Instruction limit reached!
% 0.58/0.41 % (119570)------------------------------
% 0.58/0.41 % (119570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (119570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (119570)CaDiCaL version: 2.1.3
% 0.58/0.41 % (119570)Termination reason: Instruction limit
% 0.58/0.41 % (119570)Termination phase: shuffling
% 0.58/0.41 % (119570)Time elapsed: 0.002 s
% 0.58/0.41 % (119570)Peak memory usage: 10 MB
% 0.58/0.41 % (119570)Instructions burned: 5 (million)
% 0.58/0.41 % (119569)Instruction limit reached!
% 0.58/0.41 % (119569)------------------------------
% 0.58/0.41 % (119569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (119569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (119569)CaDiCaL version: 2.1.3
% 0.58/0.41 % (119569)Termination reason: Instruction limit
% 0.58/0.41 % (119569)Termination phase: Property scanning
% 0.58/0.41 % (119569)Time elapsed: 0.009 s
% 0.58/0.41 % (119569)Peak memory usage: 10 MB
% 0.58/0.41 % (119569)Instructions burned: 20 (million)
% 0.58/0.41 % (119581)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3064438130:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.58/0.41 % (119581)Instruction limit reached!
% 0.58/0.41 % (119581)------------------------------
% 0.58/0.41 % (119581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.41 % (119581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.41 % (119581)CaDiCaL version: 2.1.3
% 0.58/0.41 % (119581)Termination reason: Instruction limit
% 0.58/0.41 % (119581)Termination phase: shuffling
% 0.58/0.41 % (119581)Time elapsed: 0.001 s
% 0.58/0.41 % (119581)Peak memory usage: 10 MB
% 0.58/0.41 % (119581)Instructions burned: 6 (million)
% 0.58/0.41 % (119583)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3184827257:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.58/0.41 % (119584)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.58/0.45 % (119583)Instruction limit reached!
% 0.58/0.45 % (119583)------------------------------
% 0.58/0.45 % (119583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119583)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119583)Termination reason: Instruction limit
% 0.58/0.45 % (119583)Termination phase: shuffling
% 0.58/0.45 % (119583)Time elapsed: 0.003 s
% 0.58/0.45 % (119583)Peak memory usage: 10 MB
% 0.58/0.45 % (119583)Instructions burned: 5 (million)
% 0.58/0.45 % (119584)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=552933679:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.58/0.45 % (119568)Instruction limit reached!
% 0.58/0.45 % (119568)------------------------------
% 0.58/0.45 % (119568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119568)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119568)Termination reason: Instruction limit
% 0.58/0.45 % (119568)Termination phase: Saturation
% 0.58/0.45 % (119568)Time elapsed: 0.030 s
% 0.58/0.45 % (119568)Peak memory usage: 13 MB
% 0.58/0.45 % (119568)Instructions burned: 90 (million)
% 0.58/0.45 % (119584)Instruction limit reached!
% 0.58/0.45 % (119584)------------------------------
% 0.58/0.45 % (119584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119584)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119584)Termination reason: Instruction limit
% 0.58/0.45 % (119584)Termination phase: shuffling
% 0.58/0.45 % (119584)Time elapsed: 0.004 s
% 0.58/0.45 % (119584)Peak memory usage: 10 MB
% 0.58/0.45 % (119584)Instructions burned: 8 (million)
% 0.58/0.45 % (119573)Instruction limit reached!
% 0.58/0.45 % (119573)------------------------------
% 0.58/0.45 % (119573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119573)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119573)Termination reason: Instruction limit
% 0.58/0.45 % (119573)Termination phase: Saturation
% 0.58/0.45 % (119573)Time elapsed: 0.035 s
% 0.58/0.45 % (119573)Peak memory usage: 13 MB
% 0.58/0.45 % (119573)Instructions burned: 76 (million)
% 0.58/0.45 % (119588)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
% 0.58/0.45 % (119588)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.58/0.45 % (119590)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=1319189425:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.58/0.45 % (119586)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2181097031:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.58/0.45 % (119588)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2761176360:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.58/0.45 % (119592)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.58/0.45 % (119591)lrs+10_1_si=on:cs=on:random_seed=2177712181:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.58/0.45 % (119592)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=3796259344:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.58/0.45 % (119591)Instruction limit reached!
% 0.58/0.45 % (119591)------------------------------
% 0.58/0.45 % (119591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119591)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119591)Termination reason: Instruction limit
% 0.58/0.45 % (119591)Termination phase: shuffling
% 0.58/0.45 % (119591)Time elapsed: 0.004 s
% 0.58/0.45 % (119591)Peak memory usage: 10 MB
% 0.58/0.45 % (119591)Instructions burned: 9 (million)
% 0.58/0.45 % (119592)Instruction limit reached!
% 0.58/0.45 % (119592)------------------------------
% 0.58/0.45 % (119592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119592)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119592)Termination reason: Instruction limit
% 0.58/0.45 % (119592)Termination phase: shuffling
% 0.58/0.45 % (119592)Time elapsed: 0.002 s
% 0.58/0.45 % (119592)Peak memory usage: 10 MB
% 0.58/0.45 % (119592)Instructions burned: 4 (million)
% 0.58/0.45 % (119586)Instruction limit reached!
% 0.58/0.45 % (119586)------------------------------
% 0.58/0.45 % (119586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119586)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119586)Termination reason: Instruction limit
% 0.58/0.45 % (119586)Termination phase: shuffling
% 0.58/0.45 % (119586)Time elapsed: 0.011 s
% 0.58/0.45 % (119586)Peak memory usage: 10 MB
% 0.58/0.45 % (119586)Instructions burned: 12 (million)
% 0.58/0.45 % (119588)Instruction limit reached!
% 0.58/0.45 % (119588)------------------------------
% 0.58/0.45 % (119588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119588)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119588)Termination reason: Instruction limit
% 0.58/0.45 % (119588)Termination phase: Property scanning
% 0.58/0.45 % (119588)Time elapsed: 0.014 s
% 0.58/0.45 % (119588)Peak memory usage: 11 MB
% 0.58/0.45 % (119588)Instructions burned: 33 (million)
% 0.58/0.45 % (119574)Instruction limit reached!
% 0.58/0.45 % (119574)------------------------------
% 0.58/0.45 % (119574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119574)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119574)Termination reason: Instruction limit
% 0.58/0.45 % (119574)Termination phase: Saturation
% 0.58/0.45 % (119574)Time elapsed: 0.069 s
% 0.58/0.45 % (119574)Peak memory usage: 14 MB
% 0.58/0.45 % (119574)Instructions burned: 159 (million)
% 0.58/0.45 % (119590)Instruction limit reached!
% 0.58/0.45 % (119590)------------------------------
% 0.58/0.45 % (119590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119590)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119590)Termination reason: Instruction limit
% 0.58/0.45 % (119590)Termination phase: Saturation
% 0.58/0.45 % (119590)Time elapsed: 0.024 s
% 0.58/0.45 % (119590)Peak memory usage: 13 MB
% 0.58/0.45 % (119590)Instructions burned: 89 (million)
% 0.58/0.45 % (119598)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1541595036:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.58/0.45 % (119599)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=223344731:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.58/0.45 % (119600)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=375953723:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.58/0.45 % (119601)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3513302918:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.58/0.45 % (119601)Instruction limit reached!
% 0.58/0.45 % (119601)------------------------------
% 0.58/0.45 % (119601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119601)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119601)Termination reason: Instruction limit
% 0.58/0.45 % (119601)Termination phase: Property scanning
% 0.58/0.45 % (119601)Time elapsed: 0.004 s
% 0.58/0.45 % (119601)Peak memory usage: 10 MB
% 0.58/0.45 % (119601)Instructions burned: 17 (million)
% 0.58/0.45 % (119602)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4197341188:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.58/0.45 % (119600)Instruction limit reached!
% 0.58/0.45 % (119600)------------------------------
% 0.58/0.45 % (119600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119600)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119600)Termination reason: Instruction limit
% 0.58/0.45 % (119600)Termination phase: Preprocessing 3
% 0.58/0.45 % (119600)Time elapsed: 0.012 s
% 0.58/0.45 % (119600)Peak memory usage: 11 MB
% 0.58/0.45 % (119600)Instructions burned: 25 (million)
% 0.58/0.45 % (119608)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2088719091: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)
% 0.58/0.45 % (119608)Instruction limit reached!
% 0.58/0.45 % (119608)------------------------------
% 0.58/0.45 % (119608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119608)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119608)Termination reason: Instruction limit
% 0.58/0.45 % (119608)Termination phase: shuffling
% 0.58/0.45 % (119608)Time elapsed: 0.003 s
% 0.58/0.45 % (119608)Peak memory usage: 10 MB
% 0.58/0.45 % (119608)Instructions burned: 11 (million)
% 0.58/0.45 % (119603)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3137577641:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.58/0.45 % (119598)Instruction limit reached!
% 0.58/0.45 % (119598)------------------------------
% 0.58/0.45 % (119598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119598)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119598)Termination reason: Instruction limit
% 0.58/0.45 % (119598)Termination phase: Clausification
% 0.58/0.45 % (119598)Time elapsed: 0.033 s
% 0.58/0.45 % (119598)Peak memory usage: 12 MB
% 0.58/0.45 % (119598)Instructions burned: 39 (million)
% 0.58/0.45 % (119610)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2972492245:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.58/0.45 % (119612)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1850626514:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.58/0.45 % (119603)Instruction limit reached!
% 0.58/0.45 % (119603)------------------------------
% 0.58/0.45 % (119603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119603)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119603)Termination reason: Instruction limit
% 0.58/0.45 % (119603)Termination phase: shuffling
% 0.58/0.45 % (119603)Time elapsed: 0.012 s
% 0.58/0.45 % (119603)Peak memory usage: 9 MB
% 0.58/0.45 % (119603)Instructions burned: 14 (million)
% 0.58/0.45 % (119614)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4057234506:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.58/0.45 % (119571) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-119563-119571"...
% 0.58/0.45 % (119612)Instruction limit reached!
% 0.58/0.45 % (119612)------------------------------
% 0.58/0.45 % (119612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.45 % (119612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.45 % (119612)CaDiCaL version: 2.1.3
% 0.58/0.45 % (119612)Termination reason: Instruction limit
% 0.58/0.45 % (119612)Termination phase: Property scanning
% 0.58/0.45 % (119612)Time elapsed: 0.010 s
% 0.58/0.45 % (119612)Peak memory usage: 10 MB
% 0.58/0.45 % (119612)Instructions burned: 24 (million)
% 0.58/0.45 % (119571)...printing done.
% 0.58/0.45 % (119571)Refutation found. Thanks to Tanya!
% 0.58/0.45 % SZS status Theorem for theBenchmark
% 0.58/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.58/0.46 % (119571)------------------------------
% 0.58/0.46 % (119571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.46 % (119571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.46 % (119571)CaDiCaL version: 2.1.3
% 0.58/0.46 % (119571)Termination reason: Refutation
% 0.58/0.46 % (119571)Time elapsed: 0.128 s
% 0.58/0.46 % (119571)Peak memory usage: 17 MB
% 0.58/0.46 % (119571)Instructions burned: 241 (million)
% 0.58/0.46 % (119563)Success in time 0.181 s
% 0.58/0.46 % Vampire exiting
%------------------------------------------------------------------------------