%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU586^1 : 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 : n026.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 08:30:11 AM UTC 2026
% Result : Theorem 0.69s 0.39s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 31 unt; 0 typ; 11 def)
% Number of atoms : 2564 ( 702 equ; 0 cnn)
% Maximal formula atoms : 105 ( 26 avg)
% Number of connectives : 1511 ( 131 ~; 129 |; 450 &; 350 @)
% ( 18 <=>; 433 =>; 0 <=; 0 <~>)
% Maximal formula depth : 111 ( 13 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 : 252 ( 249 usr; 133 con; 0-4 aty)
% Number of variables : 125 ( 0 sgn 100 !; 25 ?; 125 :)
% 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_121,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_122,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_124,type,
vNOT: $o > $o ).
thf(func_def_125,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_126,type,
vAND: $o > $o > $o ).
thf(func_def_127,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_128,type,
vIMP: $o > $o > $o ).
thf(func_def_129,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
sP0: $i > $i > $o ).
thf(func_def_132,type,
sP1: $i > $o ).
thf(func_def_133,type,
sP2: $o ).
thf(func_def_136,type,
sK5: $i > $o ).
thf(func_def_137,type,
sK6: $i > $o ).
thf(func_def_138,type,
sK7: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_139,type,
sK8: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_143,type,
sK12: $o ).
thf(func_def_145,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_147,type,
sK16: $i > $o ).
thf(func_def_151,type,
sK20: $i > $i ).
thf(func_def_152,type,
sK21: $i > $i ).
thf(func_def_153,type,
sK22: $i > $o ).
thf(func_def_155,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_156,type,
sK25: $o ).
thf(func_def_164,type,
sK33: $o ).
thf(func_def_165,type,
sK34: $i > $i ).
thf(func_def_174,type,
sK43: $i > $i > $i ).
thf(func_def_180,type,
sK49: $i > $o ).
thf(func_def_187,type,
sK56: $i > $i > $i ).
thf(func_def_191,type,
sK60: $i > $o ).
thf(func_def_192,type,
sK61: $i > $o ).
thf(func_def_193,type,
sK62: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_194,type,
sK63: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_195,type,
sK64: $o > $i > $i > $i ).
thf(func_def_198,type,
sK67: $o ).
thf(func_def_204,type,
sK73: $i > $o ).
thf(func_def_207,type,
sK76: $i > $o ).
thf(func_def_210,type,
sK79: $i > $i > $i ).
thf(func_def_211,type,
sK80: $i > $o ).
thf(func_def_222,type,
sK91: $i > $o ).
thf(func_def_224,type,
sK93: ( $i > $o ) > $i > $i ).
thf(func_def_225,type,
sK94: $i > $i > $i ).
thf(func_def_228,type,
sK97: $i > $o ).
thf(func_def_230,type,
sK99: $i > ( $i > $o ) > $i ).
thf(func_def_231,type,
sK100: $i > $o ).
thf(func_def_234,type,
sK103: $i > ( $i > $o ) > $i ).
thf(func_def_239,type,
sK108: $i > $o ).
thf(func_def_245,type,
sK114: $i > $o ).
thf(func_def_247,type,
sK116: ( $i > $o ) > $i ).
thf(func_def_248,type,
sK117: ( $i > $o ) > $i ).
thf(func_def_250,type,
sK119: $i > $i ).
thf(func_def_251,type,
sK120: ( $i > $o ) > $i ).
thf(func_def_252,type,
sK121: $i > $o ).
thf(func_def_253,type,
sK122: $i > $i ).
thf(func_def_259,type,
sK128: $o ).
thf(func_def_261,type,
sK130: $i > $o ).
thf(func_def_264,type,
sK133: $i > $o ).
thf(func_def_265,type,
sK134: ( $i > $o ) > $i ).
thf(func_def_269,type,
sK138: $i > $o ).
thf(func_def_283,type,
sK152: $i > $o ).
thf(func_def_289,type,
sK158: $o ).
thf(func_def_290,type,
sK159: $i > $o ).
thf(func_def_293,type,
sK162: $i > ( $i > $o ) > $i ).
thf(func_def_296,type,
sK165: $i > $i > $i ).
thf(func_def_299,type,
sK168: $i > $o ).
thf(func_def_308,type,
sK177: $o ).
thf(func_def_313,type,
sK182: $i > $i > $o ).
thf(func_def_314,type,
sK183: $i > $i ).
thf(func_def_315,type,
sK184: $i > $i ).
thf(func_def_316,type,
sK185: ( $i > $i > $o ) > $i > $i ).
thf(func_def_317,type,
sK186: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_318,type,
sK187: ( $i > $i > $o ) > $i > $i ).
thf(func_def_328,type,
sK197: $i > $i > $i ).
thf(func_def_338,type,
sK207: $i > $o ).
thf(func_def_339,type,
sK208: $i > $o ).
thf(func_def_340,type,
sK209: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_341,type,
sK210: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_342,type,
sK211: ( $i > $o ) > $i > $i ).
thf(func_def_344,type,
sK213: $i > $o ).
thf(func_def_349,type,
sK218: $i > $i > $i ).
thf(func_def_350,type,
sK219: $i > $i > $i ).
thf(func_def_351,type,
sK220: ( $i > $o ) > $i > $i ).
thf(func_def_353,type,
sK222: $i > $o ).
thf(func_def_358,type,
sK227: $i > $i ).
thf(func_def_359,type,
sK228: $i > $i ).
thf(func_def_360,type,
sK229: $i > $i ).
thf(func_def_361,type,
sK230: $i > $i ).
thf(func_def_362,type,
sK231: $i > $i ).
thf(func_def_363,type,
sK232: $i > $i > $i > $i ).
thf(func_def_364,type,
sK233: $i > $i ).
thf(func_def_365,type,
sK234: $i > $i ).
thf(func_def_366,type,
sK235: $i > $i ).
thf(func_def_367,type,
sK236: $i > $i ).
thf(func_def_368,type,
sK237: $i > $i > $i ).
thf(func_def_369,type,
sK238: $i > $i > $i ).
thf(func_def_370,type,
sK239: $i > $i > $i > $i ).
thf(func_def_371,type,
sK240: $i > $i > $i > $i ).
thf(func_def_372,type,
sK241: $i > $i > $i > $i ).
thf(func_def_373,type,
sK242: $i > $i > $i ).
thf(func_def_374,type,
sK243: $i > $i > $i ).
thf(func_def_375,type,
sK244: $i > $i > $i ).
thf(func_def_382,type,
sK251: $i > $i ).
thf(func_def_383,type,
sK252: $i > $o ).
thf(func_def_393,type,
sK262: $i > $o ).
thf(func_def_394,type,
sK263: $i > $i ).
thf(func_def_395,type,
sK264: ( $i > $o ) > $i ).
thf(func_def_397,type,
sK266: $i > $i ).
thf(func_def_401,type,
sK270: $i > $o ).
thf(func_def_407,type,
sK276: $i > $i ).
thf(func_def_412,type,
sK281: $i > $o ).
thf(f83,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(f97,axiom,
( inPowerset
= ( ! [X0: $i] : ( in @ X0 @ ( powerset @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(f104,axiom,
! [X1: $i,X2: $i,X3: $o,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= binunionEcases ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(f105,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
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f106,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
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f105]) ).
thf(f170,plain,
( inPowerset
= ( ! [X0: $i] : ( in @ X0 @ ( powerset @ X0 ) ) ) ),
inference(rectify,[],[f97]) ).
thf(f171,plain,
( ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true )
<=> ( inPowerset = $true ) ),
inference(fool_elimination,[],[f170]) ).
thf(f218,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
=> ( ( in @ X0 @ X1 )
| ( in @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f106]) ).
thf(f219,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 )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
=> ( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f218]) ).
thf(f240,plain,
! [X0: $i,X1: $i,X2: $o,X3: $i] :
( ( ( in @ X1 @ ( binunion @ X3 @ X0 ) )
=> ( ( ( in @ X1 @ X3 )
=> X2 )
=> ( ( ( in @ X1 @ X0 )
=> X2 )
=> X2 ) ) )
= binunionEcases ),
inference(rectify,[],[f104]) ).
thf(f241,plain,
( ! [X0: $i,X3: $i,X1: $i,X2: $o] :
( ( $true
= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) )
=> ( ( ( ( in @ X1 @ X3 )
= $true )
=> ( $true = X2 ) )
=> ( ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X2 ) )
=> ( $true = X2 ) ) ) )
<=> ( binunionEcases = $true ) ),
inference(fool_elimination,[],[f240]) ).
thf(f299,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ X1 ) ) )
= subsetE ),
inference(rectify,[],[f83]) ).
thf(f300,plain,
( ( subsetE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f299]) ).
thf(f379,plain,
( ! [X0: $i,X3: $i,X1: $i,X2: $o] :
( ( $true = X2 )
| ( ( ( in @ X1 @ X0 )
= $true )
& ( $true != X2 ) )
| ( ( ( in @ X1 @ X3 )
= $true )
& ( $true != X2 ) )
| ( $true
!= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) ) )
<=> ( binunionEcases = $true ) ),
inference(ennf_transformation,[],[f241]) ).
thf(f380,plain,
( ( binunionEcases = $true )
<=> ! [X1: $i,X0: $i,X3: $i,X2: $o] :
( ( $true
!= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) )
| ( ( ( in @ X1 @ X3 )
= $true )
& ( $true != X2 ) )
| ( ( ( in @ X1 @ X0 )
= $true )
& ( $true != X2 ) )
| ( $true = X2 ) ) ),
inference(flattening,[],[f379]) ).
thf(f397,plain,
( ( subsetE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f300]) ).
thf(f398,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
<=> ( subsetE = $true ) ),
inference(flattening,[],[f397]) ).
thf(f414,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) )
& ( 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,[],[f219]) ).
thf(f415,plain,
( ( setadjoinSub = $true )
& ( setadjoinSub2 = $true )
& ( omegaIndAx = $true )
& ( exuE1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( powersetE = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( subsetTrans = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( descrp = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( setoftrueEq = $true )
& ( binunionEcases = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
& ( $true
!= ( in @ X0 @ X2 ) ) )
& ( emptysetsubset = $true )
& ( uniqinunit = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( omega__Cong = $true )
& ( sepSubset = $true )
& ( quantDeMorgan1 = $true )
& ( notequalI2 = $true )
& ( descr__Cong = $true )
& ( dsetconstrER = $true )
& ( eqimpsubset1 = $true )
& ( subsetE = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( notsubsetI = $true )
& ( upairsetIR = $true )
& ( foundationAx = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( emptyE1 = $true )
& ( setadjoinIL = $true )
& ( exuEu = $true )
& ( inPowerset = $true )
& ( setadjoinAx = $true )
& ( sepInPowerset = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( setunion__Cong = $true )
& ( subsetE2 = $true )
& ( powersetAx = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( setadjoinOr = $true )
& ( powersetsubset = $true )
& ( setext = $true )
& ( exuI2 = $true )
& ( nonemptyI1 = $true )
& ( prop2setI = $true )
& ( dsetconstrI = $true )
& ( powerset__Cong = $true )
& ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( upairset2IR = $true )
& ( upairsetE = $true )
& ( exuE3u = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyinPowerset = $true )
& ( exuE2 = $true )
& ( in__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( notdallE = $true )
& ( powersetI = $true )
& ( setadjoin__Cong = $true )
& ( setextsub = $true )
& ( binunionIL = $true )
& ( notequalI1 = $true )
& ( nonemptyI = $true )
& ( prop2set2propI = $true )
& ( setunionAx = $true )
& ( emptysetE = $true )
& ( eqinunit = $true )
& ( binunionIR = $true )
& ( setbeta = $true )
& ( emptyI = $true )
& ( subsetI1 = $true )
& ( emptyInPowerset = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE1 = $true )
& ( subsetI2 = $true )
& ( nonemptyE1 = $true )
& ( emptysetimpfalse = $true )
& ( exuI1 = $true )
& ( subset2powerset = $true )
& ( omega0Ax = $true )
& ( vacuousDall = $true )
& ( notdexE = $true )
& ( powersetI1 = $true )
& ( eqimpsubset2 = $true )
& ( notinemptyset = $true )
& ( subsetRefl = $true )
& ( singletonsswitch = $true )
& ( dsetconstrEL = $true )
& ( emptyset__Cong = $true ) ),
inference(flattening,[],[f414]) ).
thf(f472,plain,
( ( ( binunionEcases = $true )
| ? [X1: $i,X0: $i,X3: $i,X2: $o] :
( ( $true
= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) )
& ( ( ( in @ X1 @ X3 )
!= $true )
| ( $true = X2 ) )
& ( ( ( in @ X1 @ X0 )
!= $true )
| ( $true = X2 ) )
& ( $true != X2 ) ) )
& ( ! [X1: $i,X0: $i,X3: $i,X2: $o] :
( ( $true
!= ( in @ X1 @ ( binunion @ X3 @ X0 ) ) )
| ( ( ( in @ X1 @ X3 )
= $true )
& ( $true != X2 ) )
| ( ( ( in @ X1 @ X0 )
= $true )
& ( $true != X2 ) )
| ( $true = X2 ) )
| ( binunionEcases != $true ) ) ),
inference(nnf_transformation,[],[f380]) ).
thf(f473,plain,
( ( ( binunionEcases = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
& ( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true = X3 ) )
& ( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true = X3 ) )
& ( $true != X3 ) ) )
& ( ! [X4: $i,X5: $i,X6: $i,X7: $o] :
( ( $true
!= ( in @ X4 @ ( binunion @ X6 @ X5 ) ) )
| ( ( ( in @ X4 @ X6 )
= $true )
& ( $true != X7 ) )
| ( ( ( in @ X4 @ X5 )
= $true )
& ( $true != X7 ) )
| ( $true = X7 ) )
| ( binunionEcases != $true ) ) ),
inference(rectify,[],[f472]) ).
thf(f474,plain,
( ( ( binunionEcases = $true )
| ( ( $true
= ( in @ sK30 @ ( binunion @ sK32 @ sK31 ) ) )
& ( ( $true
!= ( in @ sK30 @ sK32 ) )
| ( sK33 = $true ) )
& ( ( $true
!= ( in @ sK30 @ sK31 ) )
| ( sK33 = $true ) )
& ( sK33 != $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i,X7: $o] :
( ( $true
!= ( in @ X4 @ ( binunion @ X6 @ X5 ) ) )
| ( ( ( in @ X4 @ X6 )
= $true )
& ( $true != X7 ) )
| ( ( ( in @ X4 @ X5 )
= $true )
& ( $true != X7 ) )
| ( $true = X7 ) )
| ( binunionEcases != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33]),skolemize(X0,sK30),skolemize(X1,sK31),skolemize(X2,sK32),skolemize(X3,sK33)],[f473]) ).
thf(f566,plain,
( ( setadjoinSub = $true )
& ( setadjoinSub2 = $true )
& ( omegaIndAx = $true )
& ( exuE1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( powersetE = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( subsetTrans = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( descrp = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( setoftrueEq = $true )
& ( binunionEcases = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X2 )
!= $true ) )
& ( emptysetsubset = $true )
& ( uniqinunit = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( omega__Cong = $true )
& ( sepSubset = $true )
& ( quantDeMorgan1 = $true )
& ( notequalI2 = $true )
& ( descr__Cong = $true )
& ( dsetconstrER = $true )
& ( eqimpsubset1 = $true )
& ( subsetE = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( notsubsetI = $true )
& ( upairsetIR = $true )
& ( foundationAx = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( emptyE1 = $true )
& ( setadjoinIL = $true )
& ( exuEu = $true )
& ( inPowerset = $true )
& ( setadjoinAx = $true )
& ( sepInPowerset = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( setunion__Cong = $true )
& ( subsetE2 = $true )
& ( powersetAx = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( setadjoinOr = $true )
& ( powersetsubset = $true )
& ( setext = $true )
& ( exuI2 = $true )
& ( nonemptyI1 = $true )
& ( prop2setI = $true )
& ( dsetconstrI = $true )
& ( powerset__Cong = $true )
& ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( upairset2IR = $true )
& ( upairsetE = $true )
& ( exuE3u = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyinPowerset = $true )
& ( exuE2 = $true )
& ( in__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( notdallE = $true )
& ( powersetI = $true )
& ( setadjoin__Cong = $true )
& ( setextsub = $true )
& ( binunionIL = $true )
& ( notequalI1 = $true )
& ( nonemptyI = $true )
& ( prop2set2propI = $true )
& ( setunionAx = $true )
& ( emptysetE = $true )
& ( eqinunit = $true )
& ( binunionIR = $true )
& ( setbeta = $true )
& ( emptyI = $true )
& ( subsetI1 = $true )
& ( emptyInPowerset = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE1 = $true )
& ( subsetI2 = $true )
& ( nonemptyE1 = $true )
& ( emptysetimpfalse = $true )
& ( exuI1 = $true )
& ( subset2powerset = $true )
& ( omega0Ax = $true )
& ( vacuousDall = $true )
& ( notdexE = $true )
& ( powersetI1 = $true )
& ( eqimpsubset2 = $true )
& ( notinemptyset = $true )
& ( subsetRefl = $true )
& ( singletonsswitch = $true )
& ( dsetconstrEL = $true )
& ( emptyset__Cong = $true ) ),
inference(rectify,[],[f415]) ).
thf(f567,plain,
( ( setadjoinSub = $true )
& ( setadjoinSub2 = $true )
& ( omegaIndAx = $true )
& ( exuE1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( powersetE = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( subsetTrans = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( descrp = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( setoftrueEq = $true )
& ( binunionEcases = $true )
& ( $true
!= ( in @ sK112 @ sK111 ) )
& ( $true
= ( in @ sK112 @ ( binunion @ sK113 @ sK111 ) ) )
& ( $true
!= ( in @ sK112 @ sK113 ) )
& ( emptysetsubset = $true )
& ( uniqinunit = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( omega__Cong = $true )
& ( sepSubset = $true )
& ( quantDeMorgan1 = $true )
& ( notequalI2 = $true )
& ( descr__Cong = $true )
& ( dsetconstrER = $true )
& ( eqimpsubset1 = $true )
& ( subsetE = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( notsubsetI = $true )
& ( upairsetIR = $true )
& ( foundationAx = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( emptyE1 = $true )
& ( setadjoinIL = $true )
& ( exuEu = $true )
& ( inPowerset = $true )
& ( setadjoinAx = $true )
& ( sepInPowerset = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( setunion__Cong = $true )
& ( subsetE2 = $true )
& ( powersetAx = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( setadjoinOr = $true )
& ( powersetsubset = $true )
& ( setext = $true )
& ( exuI2 = $true )
& ( nonemptyI1 = $true )
& ( prop2setI = $true )
& ( dsetconstrI = $true )
& ( powerset__Cong = $true )
& ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( upairset2IR = $true )
& ( upairsetE = $true )
& ( exuE3u = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyinPowerset = $true )
& ( exuE2 = $true )
& ( in__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( notdallE = $true )
& ( powersetI = $true )
& ( setadjoin__Cong = $true )
& ( setextsub = $true )
& ( binunionIL = $true )
& ( notequalI1 = $true )
& ( nonemptyI = $true )
& ( prop2set2propI = $true )
& ( setunionAx = $true )
& ( emptysetE = $true )
& ( eqinunit = $true )
& ( binunionIR = $true )
& ( setbeta = $true )
& ( emptyI = $true )
& ( subsetI1 = $true )
& ( emptyInPowerset = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE1 = $true )
& ( subsetI2 = $true )
& ( nonemptyE1 = $true )
& ( emptysetimpfalse = $true )
& ( exuI1 = $true )
& ( subset2powerset = $true )
& ( omega0Ax = $true )
& ( vacuousDall = $true )
& ( notdexE = $true )
& ( powersetI1 = $true )
& ( eqimpsubset2 = $true )
& ( notinemptyset = $true )
& ( subsetRefl = $true )
& ( singletonsswitch = $true )
& ( dsetconstrEL = $true )
& ( emptyset__Cong = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111,sK112,sK113]),skolemize(X0,sK111),skolemize(X1,sK112),skolemize(X2,sK113)],[f566]) ).
thf(f601,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
= ( subset @ X2 @ X1 ) )
& ( $true
= ( in @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[],[f398]) ).
thf(f602,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
& ( $true
= ( subset @ X3 @ X4 ) )
& ( $true
= ( in @ X5 @ X3 ) ) ) ) ),
inference(rectify,[],[f601]) ).
thf(f603,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( $true
!= ( in @ sK142 @ sK141 ) )
& ( $true
= ( subset @ sK140 @ sK141 ) )
& ( $true
= ( in @ sK142 @ sK140 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140,sK141,sK142]),skolemize(X3,sK140),skolemize(X4,sK141),skolemize(X5,sK142)],[f602]) ).
thf(f660,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true )
| ( inPowerset != $true ) )
& ( ( inPowerset = $true )
| ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f171]) ).
thf(f661,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true )
| ( inPowerset != $true ) )
& ( ( inPowerset = $true )
| ? [X1: $i] :
( $true
!= ( in @ X1 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[],[f660]) ).
thf(f662,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true )
| ( inPowerset != $true ) )
& ( ( inPowerset = $true )
| ( $true
!= ( in @ sK200 @ ( powerset @ sK200 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(X1,sK200)],[f661]) ).
thf(f792,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( binunionEcases != $true )
| ( $true = X7 )
| ( $true
!= ( in @ X4 @ ( binunion @ X6 @ X5 ) ) )
| ( ( in @ X4 @ X6 )
= $true ) ),
inference(cnf_transformation,[],[f474]) ).
thf(f971,plain,
inPowerset = $true,
inference(cnf_transformation,[],[f567]) ).
thf(f982,plain,
subsetE = $true,
inference(cnf_transformation,[],[f567]) ).
thf(f994,plain,
( $true
!= ( in @ sK112 @ sK113 ) ),
inference(cnf_transformation,[],[f567]) ).
thf(f995,plain,
( $true
= ( in @ sK112 @ ( binunion @ sK113 @ sK111 ) ) ),
inference(cnf_transformation,[],[f567]) ).
thf(f996,plain,
( $true
!= ( in @ sK112 @ sK111 ) ),
inference(cnf_transformation,[],[f567]) ).
thf(f997,plain,
binunionEcases = $true,
inference(cnf_transformation,[],[f567]) ).
thf(f1054,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[],[f603]) ).
thf(f1141,plain,
! [X0: $i] :
( ( inPowerset != $true )
| ( ( in @ X0 @ ( powerset @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f662]) ).
thf(f1516,definition,
( spl283_22
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ X4 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl283_22])],[avatar_definition]) ).
thf(f1517,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ X4 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true ) )
| ~ spl283_22 ),
inference(avatar_component_clause,[],[f1516]) ).
thf(f1642,definition,
( spl283_50
<=> ( binunionEcases = $true ) ),
introduced(definition,[new_symbols(definition,[spl283_50])],[avatar_definition]) ).
thf(f1646,definition,
( spl283_51
<=> ! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ X6 )
= $true )
| ( $true
!= ( in @ X4 @ ( binunion @ X6 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl283_51])],[avatar_definition]) ).
thf(f1647,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( binunion @ X6 @ X5 ) ) )
| ( ( in @ X4 @ X6 )
= $true )
| ( ( in @ X4 @ X5 )
= $true ) )
| ~ spl283_51 ),
inference(avatar_component_clause,[],[f1646]) ).
thf(f1649,definition,
( spl283_52
<=> ! [X7: $o] : ( $true = X7 ) ),
introduced(definition,[new_symbols(definition,[spl283_52])],[avatar_definition]) ).
thf(f1650,plain,
( ! [X7: $o] : ( $true = X7 )
| ~ spl283_52 ),
inference(avatar_component_clause,[],[f1649]) ).
thf(f1651,plain,
( ~ spl283_50
| spl283_51
| spl283_52 ),
inference(avatar_split_clause,[],[f792,f1649,f1646,f1642]) ).
thf(f2033,definition,
( spl283_140
<=> ( $true
= ( in @ sK112 @ sK111 ) ) ),
introduced(definition,[new_symbols(definition,[spl283_140])],[avatar_definition]) ).
thf(f2035,plain,
( ( $true
!= ( in @ sK112 @ sK111 ) )
| spl283_140 ),
inference(avatar_component_clause,[],[f2033]) ).
thf(f2036,plain,
~ spl283_140,
inference(avatar_split_clause,[],[f996,f2033]) ).
thf(f2272,definition,
( spl283_191
<=> ( subsetE = $true ) ),
introduced(definition,[new_symbols(definition,[spl283_191])],[avatar_definition]) ).
thf(f2275,plain,
( ~ spl283_191
| spl283_22 ),
inference(avatar_split_clause,[],[f1054,f1516,f2272]) ).
thf(f2788,definition,
( spl283_303
<=> ( $true
= ( in @ sK112 @ ( binunion @ sK113 @ sK111 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl283_303])],[avatar_definition]) ).
thf(f2790,plain,
( ( $true
= ( in @ sK112 @ ( binunion @ sK113 @ sK111 ) ) )
| ~ spl283_303 ),
inference(avatar_component_clause,[],[f2788]) ).
thf(f2791,plain,
spl283_303,
inference(avatar_split_clause,[],[f995,f2788]) ).
thf(f2880,plain,
spl283_50,
inference(avatar_split_clause,[],[f997,f1642]) ).
thf(f3208,definition,
( spl283_392
<=> ( inPowerset = $true ) ),
introduced(definition,[new_symbols(definition,[spl283_392])],[avatar_definition]) ).
thf(f3304,plain,
spl283_191,
inference(avatar_split_clause,[],[f982,f2272]) ).
thf(f3430,definition,
( spl283_437
<=> ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl283_437])],[avatar_definition]) ).
thf(f3431,plain,
( ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true )
| ~ spl283_437 ),
inference(avatar_component_clause,[],[f3430]) ).
thf(f3432,plain,
( spl283_437
| ~ spl283_392 ),
inference(avatar_split_clause,[],[f1141,f3208,f3430]) ).
thf(f3490,plain,
spl283_392,
inference(avatar_split_clause,[],[f971,f3208]) ).
thf(f3729,definition,
( spl283_496
<=> ( $true
= ( in @ sK112 @ sK113 ) ) ),
introduced(definition,[new_symbols(definition,[spl283_496])],[avatar_definition]) ).
thf(f3731,plain,
( ( $true
!= ( in @ sK112 @ sK113 ) )
| spl283_496 ),
inference(avatar_component_clause,[],[f3729]) ).
thf(f3732,plain,
~ spl283_496,
inference(avatar_split_clause,[],[f994,f3729]) ).
thf(f4063,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK112 @ X0 ) )
| ( ( subset @ X0 @ sK113 )
!= $true )
| ( $true != $true ) )
| ~ spl283_22
| spl283_496 ),
inference(superposition,[],[f3731,f1517]) ).
thf(f4065,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK112 @ X0 ) )
| ( ( subset @ X0 @ sK113 )
!= $true ) )
| ~ spl283_22
| spl283_496 ),
inference(trivial_inequality_removal,[],[f4063]) ).
thf(f4103,plain,
( ( $true != $true )
| ( $true
!= ( subset @ ( powerset @ sK112 ) @ sK113 ) )
| ~ spl283_22
| ~ spl283_437
| spl283_496 ),
inference(superposition,[],[f4065,f3431]) ).
thf(f4107,plain,
( ( $true
!= ( subset @ ( powerset @ sK112 ) @ sK113 ) )
| ~ spl283_22
| ~ spl283_437
| spl283_496 ),
inference(trivial_inequality_removal,[],[f4103]) ).
thf(f4117,definition,
( spl283_500
<=> ( $true
= ( subset @ ( powerset @ sK112 ) @ sK113 ) ) ),
introduced(definition,[new_symbols(definition,[spl283_500])],[avatar_definition]) ).
thf(f4119,plain,
( ( $true
!= ( subset @ ( powerset @ sK112 ) @ sK113 ) )
| spl283_500 ),
inference(avatar_component_clause,[],[f4117]) ).
thf(f4120,plain,
( ~ spl283_500
| ~ spl283_22
| ~ spl283_437
| spl283_496 ),
inference(avatar_split_clause,[],[f4107,f3729,f3430,f1516,f4117]) ).
thf(f4464,plain,
( ( $true != $true )
| ( $true
= ( in @ sK112 @ sK111 ) )
| ( $true
= ( in @ sK112 @ sK113 ) )
| ~ spl283_51
| ~ spl283_303 ),
inference(superposition,[],[f1647,f2790]) ).
thf(f4482,plain,
( ( $true
= ( in @ sK112 @ sK111 ) )
| ( $true
= ( in @ sK112 @ sK113 ) )
| ~ spl283_51
| ~ spl283_303 ),
inference(trivial_inequality_removal,[],[f4464]) ).
thf(f4488,plain,
( ( $true
= ( in @ sK112 @ sK113 ) )
| ~ spl283_51
| spl283_140
| ~ spl283_303 ),
inference(forward_subsumption_resolution,[],[f4482,f2035]) ).
thf(f4489,plain,
( $false
| ~ spl283_51
| spl283_140
| ~ spl283_303
| spl283_496 ),
inference(forward_subsumption_resolution,[],[f4488,f3731]) ).
thf(f4490,plain,
( ~ spl283_51
| spl283_140
| ~ spl283_303
| spl283_496 ),
inference(avatar_contradiction_clause,[],[f4489]) ).
thf(f4505,plain,
( $false
| ~ spl283_52
| spl283_500 ),
inference(forward_subsumption_resolution,[],[f4119,f1650]) ).
thf(f4506,plain,
( ~ spl283_52
| spl283_500 ),
inference(avatar_contradiction_clause,[],[f4505]) ).
cnf(s35,plain,
( ~ spl283_50
| spl283_51
| spl283_52 ),
inference(sat_conversion,[],[f1651]) ).
cnf(s98,plain,
~ spl283_140,
inference(sat_conversion,[],[f2036]) ).
cnf(s143,plain,
( spl283_22
| ~ spl283_191 ),
inference(sat_conversion,[],[f2275]) ).
cnf(s256,plain,
spl283_303,
inference(sat_conversion,[],[f2791]) ).
cnf(s278,plain,
spl283_50,
inference(sat_conversion,[],[f2880]) ).
cnf(s388,plain,
spl283_191,
inference(sat_conversion,[],[f3304]) ).
cnf(s420,plain,
( ~ spl283_392
| spl283_437 ),
inference(sat_conversion,[],[f3432]) ).
cnf(s437,plain,
spl283_392,
inference(sat_conversion,[],[f3490]) ).
cnf(s507,plain,
~ spl283_496,
inference(sat_conversion,[],[f3732]) ).
cnf(s514,plain,
( ~ spl283_22
| ~ spl283_437
| spl283_496
| ~ spl283_500 ),
inference(sat_conversion,[],[f4120]) ).
cnf(s524,plain,
( ~ spl283_51
| spl283_140
| ~ spl283_303
| spl283_496 ),
inference(sat_conversion,[],[f4490]) ).
cnf(s525,plain,
( ~ spl283_52
| spl283_500 ),
inference(sat_conversion,[],[f4506]) ).
cnf(s531,plain,
spl283_437,
inference(rat,[],[s420,s437]) ).
cnf(s597,plain,
spl283_22,
inference(rat,[],[s143,s388]) ).
cnf(s599,plain,
~ spl283_500,
inference(rat,[],[s514,s531,s507,s597]) ).
cnf(s600,plain,
~ spl283_52,
inference(rat,[],[s525,s599]) ).
cnf(s615,plain,
~ spl283_51,
inference(rat,[],[s524,s507,s256,s98]) ).
cnf(s649,plain,
$false,
inference(rat,[],[s35,s600,s615,s278]) ).
thf(f4507,plain,
$false,
inference(avatar_sat_refutation,[],[s649]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU586^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:55:28 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.25 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
% 0.69/0.38 % (634176)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.69/0.38 % (634186)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3948863972:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.69/0.38 % (634187)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.69/0.38 % (634187)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
% 0.69/0.38 % (634181)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=531698626:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.69/0.38 % (634182)lrs+10_16_si=on:nwc=1.5:random_seed=2006175087:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.69/0.38 % (634183)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=48049510:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.69/0.38 % (634185)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=512131908:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.69/0.38 % (634184)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=2260957040: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)
% 0.69/0.38 % (634187)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=902133925:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.69/0.38 % (634183)Instruction limit reached!
% 0.69/0.38 % (634183)------------------------------
% 0.69/0.38 % (634183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (634183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (634183)CaDiCaL version: 2.1.3
% 0.69/0.38 % (634183)Termination reason: Instruction limit
% 0.69/0.38 % (634183)Termination phase: shuffling
% 0.69/0.38 % (634183)Time elapsed: 0.002 s
% 0.69/0.38 % (634183)Peak memory usage: 10 MB
% 0.69/0.38 % (634183)Instructions burned: 4 (million)
% 0.69/0.38 % (634182)Instruction limit reached!
% 0.69/0.38 % (634182)------------------------------
% 0.69/0.38 % (634182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (634182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (634182)CaDiCaL version: 2.1.3
% 0.69/0.38 % (634182)Termination reason: Instruction limit
% 0.69/0.38 % (634182)Termination phase: Property scanning
% 0.69/0.38 % (634182)Time elapsed: 0.008 s
% 0.69/0.38 % (634182)Peak memory usage: 10 MB
% 0.69/0.38 % (634182)Instructions burned: 19 (million)
% 0.69/0.38 % (634185)Instruction limit reached!
% 0.69/0.38 % (634185)------------------------------
% 0.69/0.38 % (634185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (634185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (634185)CaDiCaL version: 2.1.3
% 0.69/0.38 % (634185)Termination reason: Instruction limit
% 0.69/0.38 % (634185)Termination phase: Preprocessing 3
% 0.69/0.38 % (634185)Time elapsed: 0.012 s
% 0.69/0.38 % (634185)Peak memory usage: 11 MB
% 0.69/0.38 % (634185)Instructions burned: 24 (million)
% 0.69/0.38 % (634186)Instruction limit reached!
% 0.69/0.38 % (634186)------------------------------
% 0.69/0.38 % (634186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (634186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (634186)CaDiCaL version: 2.1.3
% 0.69/0.38 % (634186)Termination reason: Instruction limit
% 0.69/0.38 % (634186)Termination phase: Saturation
% 0.69/0.38 % (634186)Time elapsed: 0.019 s
% 0.69/0.38 % (634186)Peak memory usage: 13 MB
% 0.69/0.38 % (634186)Instructions burned: 78 (million)
% 0.69/0.38 % (634195)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3827011591:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.69/0.38 % (634195)Instruction limit reached!
% 0.69/0.38 % (634195)------------------------------
% 0.69/0.38 % (634195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (634195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634195)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634195)Termination reason: Instruction limit
% 0.69/0.39 % (634195)Termination phase: shuffling
% 0.69/0.39 % (634195)Time elapsed: 0.002 s
% 0.69/0.39 % (634195)Peak memory usage: 10 MB
% 0.69/0.39 % (634195)Instructions burned: 4 (million)
% 0.69/0.39 % (634196)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3803581843:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.69/0.39 % (634197)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.69/0.39 % (634196)Instruction limit reached!
% 0.69/0.39 % (634196)------------------------------
% 0.69/0.39 % (634196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634196)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634196)Termination reason: Instruction limit
% 0.69/0.39 % (634196)Termination phase: shuffling
% 0.69/0.39 % (634196)Time elapsed: 0.003 s
% 0.69/0.39 % (634196)Peak memory usage: 10 MB
% 0.69/0.39 % (634196)Instructions burned: 7 (million)
% 0.69/0.39 % (634197)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3189027269:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.69/0.39 % (634198)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2815474484:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.69/0.39 % (634197)Instruction limit reached!
% 0.69/0.39 % (634197)------------------------------
% 0.69/0.39 % (634197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634197)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634197)Termination reason: Instruction limit
% 0.69/0.39 % (634197)Termination phase: shuffling
% 0.69/0.39 % (634197)Time elapsed: 0.004 s
% 0.69/0.39 % (634197)Peak memory usage: 10 MB
% 0.69/0.39 % (634197)Instructions burned: 9 (million)
% 0.69/0.39 % (634198)Instruction limit reached!
% 0.69/0.39 % (634198)------------------------------
% 0.69/0.39 % (634198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634198)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634198)Termination reason: Instruction limit
% 0.69/0.39 % (634198)Termination phase: Property scanning
% 0.69/0.39 % (634198)Time elapsed: 0.006 s
% 0.69/0.39 % (634198)Peak memory usage: 10 MB
% 0.69/0.39 % (634198)Instructions burned: 13 (million)
% 0.69/0.39 % (634200)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
% 0.69/0.39 % (634200)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.69/0.39 % (634181)Instruction limit reached!
% 0.69/0.39 % (634181)------------------------------
% 0.69/0.39 % (634181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634181)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634181)Termination reason: Instruction limit
% 0.69/0.39 % (634181)Termination phase: Saturation
% 0.69/0.39 % (634181)Time elapsed: 0.040 s
% 0.69/0.39 % (634181)Peak memory usage: 13 MB
% 0.69/0.39 % (634181)Instructions burned: 87 (million)
% 0.69/0.39 % (634203)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=1822308181:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.69/0.39 % (634200)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=955224325:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.69/0.39 % (634206)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.69/0.39 % (634200)Instruction limit reached!
% 0.69/0.39 % (634200)------------------------------
% 0.69/0.39 % (634200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634200)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634200)Termination reason: Instruction limit
% 0.69/0.39 % (634200)Termination phase: Property scanning
% 0.69/0.39 % (634200)Time elapsed: 0.012 s
% 0.69/0.39 % (634200)Peak memory usage: 10 MB
% 0.69/0.39 % (634200)Instructions burned: 29 (million)
% 0.69/0.39 % (634205)lrs+10_1_si=on:cs=on:random_seed=1633446281:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.69/0.39 % (634206)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=28925285:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.69/0.39 % (634207)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3015839837:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.69/0.39 % (634206)Instruction limit reached!
% 0.69/0.39 % (634206)------------------------------
% 0.69/0.39 % (634206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634206)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634206)Termination reason: Instruction limit
% 0.69/0.39 % (634206)Termination phase: shuffling
% 0.69/0.39 % (634206)Time elapsed: 0.001 s
% 0.69/0.39 % (634206)Peak memory usage: 10 MB
% 0.69/0.39 % (634206)Instructions burned: 2 (million)
% 0.69/0.39 % (634205)Instruction limit reached!
% 0.69/0.39 % (634205)------------------------------
% 0.69/0.39 % (634205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634205)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634205)Termination reason: Instruction limit
% 0.69/0.39 % (634205)Termination phase: shuffling
% 0.69/0.39 % (634205)Time elapsed: 0.004 s
% 0.69/0.39 % (634205)Peak memory usage: 10 MB
% 0.69/0.39 % (634205)Instructions burned: 9 (million)
% 0.69/0.39 % (634187)Instruction limit reached!
% 0.69/0.39 % (634187)------------------------------
% 0.69/0.39 % (634187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634187)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634187)Termination reason: Instruction limit
% 0.69/0.39 % (634187)Termination phase: Saturation
% 0.69/0.39 % (634187)Time elapsed: 0.066 s
% 0.69/0.39 % (634187)Peak memory usage: 13 MB
% 0.69/0.39 % (634187)Instructions burned: 158 (million)
% 0.69/0.39 % (634211)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=449076717:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.69/0.39 % (634203)Instruction limit reached!
% 0.69/0.39 % (634203)------------------------------
% 0.69/0.39 % (634203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634203)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634203)Termination reason: Instruction limit
% 0.69/0.39 % (634203)Termination phase: Saturation
% 0.69/0.39 % (634203)Time elapsed: 0.027 s
% 0.69/0.39 % (634203)Peak memory usage: 13 MB
% 0.69/0.39 % (634203)Instructions burned: 88 (million)
% 0.69/0.39 % (634214)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3616122991:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.69/0.39 % (634207)Instruction limit reached!
% 0.69/0.39 % (634207)------------------------------
% 0.69/0.39 % (634207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634207)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634207)Termination reason: Instruction limit
% 0.69/0.39 % (634207)Termination phase: Property scanning
% 0.69/0.39 % (634207)Time elapsed: 0.019 s
% 0.69/0.39 % (634207)Peak memory usage: 11 MB
% 0.69/0.39 % (634207)Instructions burned: 40 (million)
% 0.69/0.39 % (634215)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3093441308:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.69/0.39 % (634217)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3407068820:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.69/0.39 % (634215)Instruction limit reached!
% 0.69/0.39 % (634215)------------------------------
% 0.69/0.39 % (634215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634215)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634215)Termination reason: Instruction limit
% 0.69/0.39 % (634215)Termination phase: Property scanning
% 0.69/0.39 % (634215)Time elapsed: 0.006 s
% 0.69/0.39 % (634215)Peak memory usage: 10 MB
% 0.69/0.39 % (634184) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-634176-634184"...
% 0.69/0.39 % (634215)Instructions burned: 14 (million)
% 0.69/0.39 % (634218)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3365111321:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.69/0.39 % (634214)Instruction limit reached!
% 0.69/0.39 % (634214)------------------------------
% 0.69/0.39 % (634214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634214)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634214)Termination reason: Instruction limit
% 0.69/0.39 % (634214)Termination phase: Preprocessing 3
% 0.69/0.39 % (634214)Time elapsed: 0.013 s
% 0.69/0.39 % (634214)Peak memory usage: 11 MB
% 0.69/0.39 % (634214)Instructions burned: 26 (million)
% 0.69/0.39 % (634184)...printing done.
% 0.69/0.39 % (634184)Refutation found. Thanks to Tanya!
% 0.69/0.39 % SZS status Theorem for theBenchmark
% 0.69/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.69/0.39 % (634184)------------------------------
% 0.69/0.39 % (634184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.39 % (634184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.39 % (634184)CaDiCaL version: 2.1.3
% 0.69/0.39 % (634184)Termination reason: Refutation
% 0.69/0.39 % (634184)Time elapsed: 0.092 s
% 0.69/0.39 % (634184)Peak memory usage: 16 MB
% 0.69/0.39 % (634184)Instructions burned: 171 (million)
% 0.69/0.39 % (634176)Success in time 0.136 s
% 0.69/0.39 % Vampire exiting
%------------------------------------------------------------------------------