%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU539^1 : 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 : n005.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 08:29:59 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 1255 ( 361 equ; 0 cnn)
% Maximal formula atoms : 59 ( 83 avg)
% Number of connectives : 611 ( 25 ~; 6 |; 233 &; 62 @)
% ( 0 <=>; 285 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 38 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 160 ( 157 usr; 64 con; 0-4 aty)
% Number of variables : 34 ( 0 ^; 20 !; 14 ?; 34 :)
% 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_69,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_70,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_71,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_72,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_73,type,
vAND: $o > $o > $o ).
thf(func_def_74,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_75,type,
vIMP: $o > $o > $o ).
thf(func_def_76,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_77,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_78,type,
vNOT: $o > $o ).
thf(func_def_79,type,
sP0: $i > $i > $o ).
thf(func_def_80,type,
sP1: $i > $o ).
thf(func_def_81,type,
sP2: $i > $i > $o ).
thf(func_def_82,type,
sP3: $i > $i > $o ).
thf(func_def_83,type,
sP4: $o ).
thf(func_def_88,type,
sK9: $i > $i ).
thf(func_def_89,type,
sK10: $i > $i ).
thf(func_def_92,type,
sK13: $i > $o ).
thf(func_def_97,type,
sK18: $o ).
thf(func_def_104,type,
sK25: $i > $o ).
thf(func_def_109,type,
sK30: ( $i > $o ) > $i ).
thf(func_def_110,type,
sK31: $i > $o ).
thf(func_def_111,type,
sK32: $i > $o ).
thf(func_def_114,type,
sK35: $i > $i ).
thf(func_def_116,type,
sK37: $i > $i > $i ).
thf(func_def_117,type,
sK38: $i > $i > $i ).
thf(func_def_118,type,
sK39: $i > $i > $i ).
thf(func_def_119,type,
sK40: $i > $i > $i ).
thf(func_def_120,type,
sK41: $i > $i > $i ).
thf(func_def_121,type,
sK42: $i > $i > $i > $i ).
thf(func_def_122,type,
sK43: $i > $i ).
thf(func_def_123,type,
sK44: $i > $i ).
thf(func_def_124,type,
sK45: $i > $i ).
thf(func_def_125,type,
sK46: $i > $i ).
thf(func_def_126,type,
sK47: $i > $i > $i ).
thf(func_def_127,type,
sK48: $i > $i > $i > $i ).
thf(func_def_128,type,
sK49: $i > $i > $i > $i ).
thf(func_def_129,type,
sK50: $i > $i > $i ).
thf(func_def_130,type,
sK51: $i > $i > $i ).
thf(func_def_132,type,
sK53: $i > $i ).
thf(func_def_133,type,
sK54: $i > $i ).
thf(func_def_134,type,
sK55: $i > $i ).
thf(func_def_135,type,
sK56: $i > $o ).
thf(func_def_140,type,
sK61: $i > $i > $i ).
thf(func_def_142,type,
sK63: $i > $i > $o ).
thf(func_def_143,type,
sK64: $i > $i ).
thf(func_def_144,type,
sK65: $i > $i ).
thf(func_def_145,type,
sK66: ( $i > $i > $o ) > $i > $i ).
thf(func_def_146,type,
sK67: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_147,type,
sK68: ( $i > $i > $o ) > $i > $i ).
thf(func_def_149,type,
sK70: $i > $o ).
thf(func_def_152,type,
sK73: $o ).
thf(func_def_154,type,
sK75: $i > $o ).
thf(func_def_158,type,
sK79: $i > $i > $i ).
thf(func_def_159,type,
sK80: $i > $i > $i ).
thf(func_def_164,type,
sK85: $i > $o ).
thf(func_def_167,type,
sK88: $i > $i > $i ).
thf(func_def_173,type,
sK94: $i > $o ).
thf(func_def_176,type,
sK97: $i > ( $i > $o ) > $i ).
thf(func_def_189,type,
sK110: $i > $i ).
thf(func_def_190,type,
sK111: ( $i > $o ) > $i ).
thf(func_def_191,type,
sK112: $i > $o ).
thf(func_def_192,type,
sK113: $i > $i ).
thf(func_def_198,type,
sK119: $o ).
thf(func_def_199,type,
sK120: $o > $i > $i > $i ).
thf(func_def_200,type,
sK121: $i > $i ).
thf(func_def_204,type,
sK125: ( $i > $o ) > $i ).
thf(func_def_205,type,
sK126: $i > $o ).
thf(func_def_206,type,
sK127: $i > $i ).
thf(func_def_210,type,
sK131: $i > $i > $i ).
thf(func_def_212,type,
sK133: $i > $o ).
thf(func_def_215,type,
sK136: $i > ( $i > $o ) > $i ).
thf(func_def_218,type,
sK139: $i > $o ).
thf(func_def_221,type,
sK142: $i > $i > $i ).
thf(func_def_225,type,
sK146: $i > $o ).
thf(func_def_230,type,
sK151: $o ).
thf(func_def_233,type,
sK154: $i > $i ).
thf(func_def_234,type,
sK155: $i > ( $i > $o ) > $i ).
thf(func_def_235,type,
sK156: $i > $o ).
thf(func_def_238,type,
sK159: $i > $i ).
thf(func_def_242,type,
sK163: ( $i > $o ) > $i > $i ).
thf(func_def_243,type,
sK164: $i > ( $i > $o ) > $i ).
thf(func_def_244,type,
sK165: $i > ( $i > $o ) > $i ).
thf(func_def_245,type,
sK166: $i > $i ).
thf(func_def_246,type,
sK167: $i > ( $i > $o ) > $i ).
thf(func_def_247,type,
sK168: $i > ( $i > $o ) > $i ).
thf(func_def_248,type,
sK169: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_249,type,
sK170: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_250,type,
sK171: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_251,type,
sK172: $i > ( $i > $o ) > $i ).
thf(f59,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
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(f60,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
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f59]) ).
thf(f164,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
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f60]) ).
thf(f165,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 )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
=> ~ ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f164]) ).
thf(f187,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 )
=> ! [X1: $i > $o,X0: $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ~ ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f165]) ).
thf(f226,plain,
( ? [X0: $i,X1: $i > $o] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ? [X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2 @ X0 )
= $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,[],[f187]) ).
thf(f227,plain,
( ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( setunionE = $true )
& ( setadjoinOr = $true )
& ( nonemptyE1 = $true )
& ( setadjoinE = $true )
& ( dsetconstrEL = $true )
& ( singletonsswitch = $true )
& ( exuE3e = $true )
& ( wellorderingAx = $true )
& ( subPowSU = $true )
& ( nonemptyI = $true )
& ( vacuousDall = $true )
& ( notinemptyset = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI1 = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( quantDeMorgan2 = $true )
& ( emptyInPowerset = $true )
& ( powersetI = $true )
& ( uniqinunit = $true )
& ? [X0: $i,X1: $i > $o] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ? [X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( quantDeMorgan3 = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( setoftrueEq = $true )
& ( setadjoinIL = $true )
& ( upairsetE = $true )
& ( setunionI = $true )
& ( eqinunit = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ( emptyI = $true )
& ( noeltsimpempty = $true )
& ( setext = $true )
& ( emptysetimpfalse = $true )
& ( upairsetIL = $true )
& ( omega0Ax = $true )
& ( powersetE = $true )
& ( setadjoinIR = $true )
& ( exuE1 = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( upairsetIR = $true )
& ( notinsingleton = $true )
& ( emptyE1 = $true )
& ( emptysetAx = $true )
& ( emptyinPowerset = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan1 = $true ) ),
inference(flattening,[],[f226]) ).
thf(f325,plain,
( ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( setunionE = $true )
& ( setadjoinOr = $true )
& ( nonemptyE1 = $true )
& ( setadjoinE = $true )
& ( dsetconstrEL = $true )
& ( singletonsswitch = $true )
& ( exuE3e = $true )
& ( wellorderingAx = $true )
& ( subPowSU = $true )
& ( nonemptyI = $true )
& ( vacuousDall = $true )
& ( notinemptyset = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI1 = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( quantDeMorgan2 = $true )
& ( emptyInPowerset = $true )
& ( powersetI = $true )
& ( uniqinunit = $true )
& ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ? [X3: $i] :
( ( ( X1 @ X3 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( quantDeMorgan3 = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( setoftrueEq = $true )
& ( setadjoinIL = $true )
& ( upairsetE = $true )
& ( setunionI = $true )
& ( eqinunit = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ( emptyI = $true )
& ( noeltsimpempty = $true )
& ( setext = $true )
& ( emptysetimpfalse = $true )
& ( upairsetIL = $true )
& ( omega0Ax = $true )
& ( powersetE = $true )
& ( setadjoinIR = $true )
& ( exuE1 = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( upairsetIR = $true )
& ( notinsingleton = $true )
& ( emptyE1 = $true )
& ( emptysetAx = $true )
& ( emptyinPowerset = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan1 = $true ) ),
inference(rectify,[],[f227]) ).
thf(f326,plain,
( ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( setunionE = $true )
& ( setadjoinOr = $true )
& ( nonemptyE1 = $true )
& ( setadjoinE = $true )
& ( dsetconstrEL = $true )
& ( singletonsswitch = $true )
& ( exuE3e = $true )
& ( wellorderingAx = $true )
& ( subPowSU = $true )
& ( nonemptyI = $true )
& ( vacuousDall = $true )
& ( notinemptyset = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI1 = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( quantDeMorgan2 = $true )
& ( emptyInPowerset = $true )
& ( powersetI = $true )
& ( uniqinunit = $true )
& ! [X2: $i] :
( ( ( sK75 @ X2 )
= $true )
| ( ( in @ X2 @ sK74 )
!= $true ) )
& ( ( sK75 @ sK76 )
!= $true )
& ( ( in @ sK76 @ sK74 )
= $true )
& ( quantDeMorgan3 = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( setoftrueEq = $true )
& ( setadjoinIL = $true )
& ( upairsetE = $true )
& ( setunionI = $true )
& ( eqinunit = $true )
& ( setbeta = $true )
& ( foundationAx = $true )
& ( emptyI = $true )
& ( noeltsimpempty = $true )
& ( setext = $true )
& ( emptysetimpfalse = $true )
& ( upairsetIL = $true )
& ( omega0Ax = $true )
& ( powersetE = $true )
& ( setadjoinIR = $true )
& ( exuE1 = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( upairsetIR = $true )
& ( notinsingleton = $true )
& ( emptyE1 = $true )
& ( emptysetAx = $true )
& ( emptyinPowerset = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74,sK75,sK76]),skolemize(X0,sK74),skolemize(X1,sK75),skolemize(X3,sK76)],[f325]) ).
thf(f577,plain,
( ( in @ sK76 @ sK74 )
= $true ),
inference(cnf_transformation,[],[f326]) ).
thf(f578,plain,
( ( sK75 @ sK76 )
!= $true ),
inference(cnf_transformation,[],[f326]) ).
thf(f579,plain,
! [X2: $i] :
( ( ( in @ X2 @ sK74 )
!= $true )
| ( ( sK75 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f326]) ).
thf(f1217,plain,
( ( $true != $true )
| ( ( sK75 @ sK76 )
= $true ) ),
inference(constrained_superposition,[],[f579,f577]) ).
thf(f1218,plain,
( ( sK75 @ sK76 )
= $true ),
inference(trivial_inequality_removal,[],[f1217]) ).
thf(f1219,plain,
$false,
inference(forward_subsumption_resolution,[],[f1218,f578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU539^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n005.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:48:46 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.29 % (1695563)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1695584)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3880651126:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (1695585)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (1695585)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
% 0.21/0.29 % (1695578)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3480595643:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (1695580)lrs+10_16_si=on:nwc=1.5:random_seed=2003165317:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (1695581)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=121092148:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (1695582)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=4137753564: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)
% 0.21/0.29 % (1695583)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1945878560:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (1695585)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=128752316:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (1695581)Instruction limit reached!
% 0.21/0.29 % (1695581)------------------------------
% 0.21/0.29 % (1695581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1695581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1695581)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1695581)Termination reason: Instruction limit
% 0.21/0.29 % (1695581)Termination phase: shuffling
% 0.21/0.29 % (1695581)Time elapsed: 0.002 s
% 0.21/0.29 % (1695581)Peak memory usage: 10 MB
% 0.21/0.29 % (1695581)Instructions burned: 4 (million)
% 0.21/0.29 % (1695580)Instruction limit reached!
% 0.21/0.29 % (1695580)------------------------------
% 0.21/0.29 % (1695580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1695580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1695580)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1695580)Termination reason: Instruction limit
% 0.21/0.29 % (1695580)Termination phase: Property scanning
% 0.21/0.29 % (1695580)Time elapsed: 0.008 s
% 0.21/0.29 % (1695580)Peak memory usage: 11 MB
% 0.21/0.29 % (1695580)Instructions burned: 19 (million)
% 0.21/0.29 % (1695584) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1695563-1695584"...
% 0.21/0.29 % (1695584)...printing done.
% 0.21/0.29 % (1695584)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (1695584)------------------------------
% 0.21/0.30 % (1695584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1695584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1695584)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1695584)Termination reason: Refutation
% 0.21/0.30 % (1695584)Time elapsed: 0.018 s
% 0.21/0.30 % (1695584)Peak memory usage: 13 MB
% 0.21/0.30 % (1695584)Instructions burned: 68 (million)
% 0.21/0.30 % (1695563)Success in time 0.055 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------