%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU536^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:29:58 AM UTC 2026
% Result : Theorem 0.23s 0.33s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 1026 ( 287 equ; 0 cnn)
% Maximal formula atoms : 56 ( 73 avg)
% Number of connectives : 521 ( 23 ~; 5 |; 167 &; 56 @)
% ( 0 <=>; 270 =>; 0 <=; 0 <~>)
% Maximal formula depth : 62 ( 35 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 151 ( 148 usr; 61 con; 0-4 aty)
% Number of variables : 30 ( 0 ^; 19 !; 11 ?; 30 :)
% 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_66,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_67,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_68,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_69,type,
vAND: $o > $o > $o ).
thf(func_def_70,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_71,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_72,type,
vIMP: $o > $o > $o ).
thf(func_def_73,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_74,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_75,type,
vNOT: $o > $o ).
thf(func_def_76,type,
sP0: $o ).
thf(func_def_77,type,
sP1: $i > $i > $o ).
thf(func_def_78,type,
sP2: $i > $o ).
thf(func_def_79,type,
sP3: $i > $i > $o ).
thf(func_def_80,type,
sP4: $i > $i > $o ).
thf(func_def_82,type,
sK6: $i > $o ).
thf(func_def_88,type,
sK12: $i > $i > $o ).
thf(func_def_90,type,
sK14: $i > $i ).
thf(func_def_91,type,
sK15: $i > $i ).
thf(func_def_92,type,
sK16: $i > ( $i > $i > $o ) > $i ).
thf(func_def_93,type,
sK17: $i > ( $i > $i > $o ) > $i ).
thf(func_def_94,type,
sK18: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_99,type,
sK23: $o ).
thf(func_def_103,type,
sK27: $i > $o ).
thf(func_def_104,type,
sK28: $i > $o ).
thf(func_def_109,type,
sK33: $i > $i > $i ).
thf(func_def_112,type,
sK36: $i > $i ).
thf(func_def_115,type,
sK39: $i > $i > $i ).
thf(func_def_116,type,
sK40: $i > $i > $i ).
thf(func_def_121,type,
sK45: $i > $o ).
thf(func_def_126,type,
sK50: $i > $i ).
thf(func_def_130,type,
sK54: $o ).
thf(func_def_132,type,
sK56: $i > $o ).
thf(func_def_140,type,
sK64: ( $i > $o ) > $i ).
thf(func_def_141,type,
sK65: $i > $o ).
thf(func_def_142,type,
sK66: $i > $i ).
thf(func_def_143,type,
sK67: $i > $i ).
thf(func_def_146,type,
sK70: $i > $i ).
thf(func_def_148,type,
sK72: $i > $i ).
thf(func_def_149,type,
sK73: $i > $i > $i ).
thf(func_def_150,type,
sK74: $i > $i > $i ).
thf(func_def_151,type,
sK75: $i > $i > $i ).
thf(func_def_152,type,
sK76: $i > $i > $i ).
thf(func_def_153,type,
sK77: $i > $i > $i > $i ).
thf(func_def_154,type,
sK78: $i > $i ).
thf(func_def_155,type,
sK79: $i > $i ).
thf(func_def_156,type,
sK80: $i > $i ).
thf(func_def_157,type,
sK81: $i > $i ).
thf(func_def_158,type,
sK82: $i > $i > $i > $i ).
thf(func_def_159,type,
sK83: $i > $i > $i > $i ).
thf(func_def_160,type,
sK84: $i > $i > $i ).
thf(func_def_161,type,
sK85: $i > $i > $i ).
thf(func_def_162,type,
sK86: $i > $i > $i ).
thf(func_def_163,type,
sK87: $i > $i ).
thf(func_def_164,type,
sK88: $i > $i > $i ).
thf(func_def_166,type,
sK90: $i > $i ).
thf(func_def_167,type,
sK91: $i > $i ).
thf(func_def_168,type,
sK92: ( $i > $o ) > $i ).
thf(func_def_169,type,
sK93: $i > $o ).
thf(func_def_171,type,
sK95: $i > $o ).
thf(func_def_172,type,
sK96: $i > $i ).
thf(func_def_173,type,
sK97: ( $i > $o ) > $i ).
thf(func_def_176,type,
sK100: $i > $o ).
thf(func_def_178,type,
sK102: $i > $i ).
thf(func_def_181,type,
sK105: $o ).
thf(func_def_184,type,
sK108: $i > $o ).
thf(func_def_193,type,
sK117: $i > $o ).
thf(func_def_196,type,
sK120: $i > $i ).
thf(func_def_198,type,
sK122: $i > $o ).
thf(func_def_200,type,
sK124: $o > $i > $i > $i ).
thf(func_def_203,type,
sK127: $o ).
thf(func_def_210,type,
sK134: $i > $i > $i ).
thf(func_def_217,type,
sK141: $i > $i > $i ).
thf(func_def_220,type,
sK144: $i > $i > $i ).
thf(func_def_227,type,
sK151: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_228,type,
sK152: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_229,type,
sK153: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_230,type,
sK154: ( $i > $o ) > $i > $i ).
thf(func_def_231,type,
sK155: $i > $i ).
thf(func_def_232,type,
sK156: $i > ( $i > $o ) > $i ).
thf(func_def_233,type,
sK157: $i > ( $i > $o ) > $i ).
thf(func_def_234,type,
sK158: ( $i > $o ) > $i > $i ).
thf(func_def_235,type,
sK159: ( $i > $o ) > $i > $i ).
thf(func_def_236,type,
sK160: $i > ( $i > $o ) > $i ).
thf(f56,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
=> ! [X0: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ~ ( X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(f57,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
=> ! [X0: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ~ ( X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
thf(f145,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
=> ! [X0: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) )
=> ? [X3: $i] :
( ~ ( X1 @ X3 )
& ( in @ X3 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f57]) ).
thf(f146,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 )
=> ! [X0: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( X1 @ X2 )
= $true ) )
=> ? [X3: $i] :
( ( ( X1 @ X3 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f145]) ).
thf(f177,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 )
=> ! [X1: $i > $o,X0: $i] :
( ~ ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( X1 @ X2 )
= $true ) )
=> ? [X3: $i] :
( ( ( X1 @ X3 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f146]) ).
thf(f221,plain,
( ? [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X3 )
= $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,[],[f177]) ).
thf(f222,plain,
( ( omega0Ax = $true )
& ( replAx = $true )
& ( emptyinPowerset = $true )
& ( eqinunit = $true )
& ( setadjoinE = $true )
& ( exuE1 = $true )
& ( singletonsswitch = $true )
& ( setadjoinAx = $true )
& ( upairsetE = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ? [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X3 )
= $true ) ) )
& ( subPowSU = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( exuE3e = $true )
& ( notinsingleton = $true )
& ( dsetconstrER = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIL = $true )
& ( powersetE = $true )
& ( nonemptyI1 = $true )
& ( emptysetE = $true )
& ( dsetconstrEL = $true )
& ( upairsetIL = $true )
& ( upairsetIR = $true )
& ( setoftrueEq = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIR = $true )
& ( setbeta = $true )
& ( omegaSAx = $true )
& ( notinemptyset = $true )
& ( setadjoinOr = $true )
& ( prop2setE = $true )
& ( emptyE1 = $true )
& ( nonemptyE1 = $true )
& ( emptysetAx = $true )
& ( setunionE = $true )
& ( noeltsimpempty = $true )
& ( nonemptyImpWitness = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrI = $true )
& ( vacuousDall = $true )
& ( omegaIndAx = $true )
& ( setunionI = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( powersetI = $true )
& ( wellorderingAx = $true )
& ( uniqinunit = $true )
& ( setunionAx = $true )
& ( descrp = $true )
& ( setextAx = $true ) ),
inference(flattening,[],[f221]) ).
thf(f363,plain,
( ( omega0Ax = $true )
& ( replAx = $true )
& ( emptyinPowerset = $true )
& ( eqinunit = $true )
& ( setadjoinE = $true )
& ( exuE1 = $true )
& ( singletonsswitch = $true )
& ( setadjoinAx = $true )
& ( upairsetE = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( ( in @ sK118 @ sK116 )
= $true )
& ( $true
!= ( sK117 @ sK118 ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK116 )
!= $true )
| ( ( sK117 @ X3 )
= $true ) )
& ( subPowSU = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( exuE3e = $true )
& ( notinsingleton = $true )
& ( dsetconstrER = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIL = $true )
& ( powersetE = $true )
& ( nonemptyI1 = $true )
& ( emptysetE = $true )
& ( dsetconstrEL = $true )
& ( upairsetIL = $true )
& ( upairsetIR = $true )
& ( setoftrueEq = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIR = $true )
& ( setbeta = $true )
& ( omegaSAx = $true )
& ( notinemptyset = $true )
& ( setadjoinOr = $true )
& ( prop2setE = $true )
& ( emptyE1 = $true )
& ( nonemptyE1 = $true )
& ( emptysetAx = $true )
& ( setunionE = $true )
& ( noeltsimpempty = $true )
& ( nonemptyImpWitness = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrI = $true )
& ( vacuousDall = $true )
& ( omegaIndAx = $true )
& ( setunionI = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( powersetI = $true )
& ( wellorderingAx = $true )
& ( uniqinunit = $true )
& ( setunionAx = $true )
& ( descrp = $true )
& ( setextAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116,sK117,sK118]),skolemize(X0,sK116),skolemize(X1,sK117),skolemize(X2,sK118)],[f222]) ).
thf(f627,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK116 )
!= $true )
| ( ( sK117 @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f363]) ).
thf(f628,plain,
( $true
!= ( sK117 @ sK118 ) ),
inference(cnf_transformation,[],[f363]) ).
thf(f629,plain,
( ( in @ sK118 @ sK116 )
= $true ),
inference(cnf_transformation,[],[f363]) ).
thf(f1155,plain,
( ( $true
= ( sK117 @ sK118 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f627,f629]) ).
thf(f1156,plain,
( $true
= ( sK117 @ sK118 ) ),
inference(trivial_inequality_removal,[],[f1155]) ).
thf(f1157,plain,
$false,
inference(forward_subsumption_resolution,[],[f1156,f628]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU536^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:52:18 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.33 % (3555944)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.33 % (3555961)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.33 % (3555961)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
% 0.23/0.33 % (3555961)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=1315843754:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.33 % (3555955)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3518207912:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.33 % (3555956)lrs+10_16_si=on:nwc=1.5:random_seed=1853944407:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.33 % (3555959)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2623084202:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.33 % (3555958)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=690625366: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)
% 0.23/0.33 % (3555957)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1989204794:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.33 % (3555960)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=627424496:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.33 % (3555957)Instruction limit reached!
% 0.23/0.33 % (3555957)------------------------------
% 0.23/0.33 % (3555957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3555957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3555957)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3555957)Termination reason: Instruction limit
% 0.23/0.33 % (3555957)Termination phase: shuffling
% 0.23/0.33 % (3555957)Time elapsed: 0.002 s
% 0.23/0.33 % (3555957)Peak memory usage: 9 MB
% 0.23/0.33 % (3555957)Instructions burned: 4 (million)
% 0.23/0.33 % (3555956)Instruction limit reached!
% 0.23/0.33 % (3555956)------------------------------
% 0.23/0.33 % (3555956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3555956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3555956)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3555956)Termination reason: Instruction limit
% 0.23/0.33 % (3555956)Termination phase: Property scanning
% 0.23/0.33 % (3555956)Time elapsed: 0.008 s
% 0.23/0.33 % (3555956)Peak memory usage: 10 MB
% 0.23/0.33 % (3555956)Instructions burned: 19 (million)
% 0.23/0.33 % (3555959)Instruction limit reached!
% 0.23/0.33 % (3555959)------------------------------
% 0.23/0.33 % (3555959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3555959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3555959)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3555959)Termination reason: Instruction limit
% 0.23/0.33 % (3555959)Termination phase: Property scanning
% 0.23/0.33 % (3555959)Time elapsed: 0.012 s
% 0.23/0.33 % (3555959)Peak memory usage: 11 MB
% 0.23/0.33 % (3555959)Instructions burned: 25 (million)
% 0.23/0.33 % (3555976)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2244280346:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.33 % (3555976)Instruction limit reached!
% 0.23/0.33 % (3555976)------------------------------
% 0.23/0.33 % (3555976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3555976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3555976)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3555976)Termination reason: Instruction limit
% 0.23/0.33 % (3555976)Termination phase: shuffling
% 0.23/0.33 % (3555976)Time elapsed: 0.002 s
% 0.23/0.33 % (3555976)Peak memory usage: 9 MB
% 0.23/0.33 % (3555976)Instructions burned: 4 (million)
% 0.23/0.33 % (3555955) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3555944-3555955"...
% 0.23/0.33 % (3555981)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.33 % (3555979)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1787142029:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.33 % (3555955)...printing done.
% 0.23/0.33 % (3555960) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3555944-3555960"...
% 0.23/0.33 % (3555958) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3555944-3555958"...
% 0.23/0.33 % (3555961)Instruction limit reached!
% 0.23/0.33 % (3555961)------------------------------
% 0.23/0.33 % (3555961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3555961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3555961)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3555961)Termination reason: Instruction limit
% 0.23/0.33 % (3555961)Termination phase: Saturation
% 0.23/0.33 % (3555961)Time elapsed: 0.037 s
% 0.23/0.33 % (3555961)Peak memory usage: 13 MB
% 0.23/0.33 % (3555961)Instructions burned: 158 (million)
% 0.23/0.33 % (3555955)Refutation found. Thanks to Tanya!
% 0.23/0.33 % SZS status Theorem for theBenchmark
% 0.23/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.33 % (3555955)------------------------------
% 0.23/0.33 % (3555955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3555955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3555955)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3555955)Termination reason: Refutation
% 0.23/0.33 % (3555955)Time elapsed: 0.028 s
% 0.23/0.33 % (3555955)Peak memory usage: 13 MB
% 0.23/0.33 % (3555955)Instructions burned: 57 (million)
% 0.23/0.33 % (3555944)Success in time 0.067 s
% 0.23/0.33 % Vampire exiting
%------------------------------------------------------------------------------