%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU591^1 : 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 : n009.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 08:30:13 AM UTC 2026
% Result : Theorem 0.70s 0.42s
% Output : Refutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 2082 ( 570 equ; 0 cnn)
% Maximal formula atoms : 109 ( 65 avg)
% Number of connectives : 1099 ( 8 ~; 2 |; 432 &; 199 @)
% ( 0 <=>; 443 =>; 0 <=; 0 <~>)
% Maximal formula depth : 116 ( 29 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 220 ( 216 usr; 113 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 82 ( 40 ^; 33 !; 9 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_126,type,
vIMP: $o > $o > $o ).
thf(func_def_127,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_130,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_131,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vOR: $o > $o > $o ).
thf(func_def_133,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_134,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
vNOT: $o > $o ).
thf(func_def_136,type,
vAND: $o > $o > $o ).
thf(func_def_137,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
vIFF: $o > $o > $o ).
thf(func_def_141,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_145,type,
sK3: $i > $i ).
thf(func_def_146,type,
sK4: $o > $i > $i > $i ).
thf(func_def_147,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_148,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_149,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_150,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_152,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_154,type,
sK12: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_155,type,
sK13: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_156,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_157,type,
sK15: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_158,type,
sK16: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_159,type,
sK17: ( $i > $o ) > $i ).
thf(func_def_160,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_161,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_162,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_163,type,
sK21: ( $i > $o ) > $i > $i ).
thf(func_def_164,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_165,type,
sK23: ( $i > $o ) > $i > $i ).
thf(func_def_166,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_167,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_168,type,
sK26: ( $i > $o ) > $i > $i ).
thf(func_def_169,type,
sK27: ( $i > $o ) > $i ).
thf(func_def_170,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_171,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_172,type,
sK30: ( $i > $o ) > $i ).
thf(func_def_173,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_174,type,
sK32: ( $i > $o ) > $i > $i ).
thf(func_def_175,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_176,type,
sK34: $i > $i ).
thf(func_def_177,type,
sK35: $i > $i ).
thf(func_def_178,type,
sK36: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_179,type,
sK37: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_180,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_181,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_182,type,
sK40: $i > $i > $i ).
thf(func_def_183,type,
sK41: $i > ( $i > $o ) > $i ).
thf(func_def_184,type,
sK42: $i > $i > $i ).
thf(func_def_185,type,
sK43: $i > $i > $i ).
thf(func_def_186,type,
sK44: ( $i > $i > $o ) > $i > $i ).
thf(func_def_187,type,
sK45: ( $i > $i > $o ) > $i > $i ).
thf(func_def_188,type,
sK46: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_189,type,
sK47: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_190,type,
sK48: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_191,type,
sK49: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_192,type,
sK50: $i > $i ).
thf(func_def_193,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_194,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_195,type,
sK53: $i > $i ).
thf(func_def_196,type,
sK54: $i > $i > $i ).
thf(func_def_197,type,
sK55: $i > $i > $i ).
thf(func_def_198,type,
sK56: $i > $i > $i ).
thf(func_def_199,type,
sK57: $i > $i > $i ).
thf(func_def_200,type,
sK58: $i > $i > $i > $i ).
thf(func_def_201,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_202,type,
sK60: ( $i > $o ) > $i ).
thf(func_def_203,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_204,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_205,type,
sK63: $i > $i ).
thf(func_def_206,type,
sK64: $i > $i > $i ).
thf(func_def_207,type,
sK65: ( $i > $o ) > $i ).
thf(func_def_208,type,
sK66: ( $i > $o ) > $i > $i ).
thf(func_def_209,type,
sK67: $i > $i > $i ).
thf(func_def_210,type,
sK68: ( $i > $o ) > $i > $i ).
thf(func_def_211,type,
sK69: $i > $i > $i ).
thf(func_def_212,type,
sK70: ( $i > $o ) > $i ).
thf(func_def_213,type,
sK71: ( $i > $o ) > $i > $i ).
thf(func_def_214,type,
sK72: $i > ( $i > $o ) > $i ).
thf(func_def_215,type,
sK73: ( $i > $o ) > $i > $i ).
thf(func_def_216,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_217,type,
sK75: $i > $i > $i ).
thf(func_def_218,type,
sK76: $i > $i ).
thf(func_def_219,type,
sK77: $i > $i > $i ).
thf(f15,axiom,
( dsetconstrEL
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f108,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) )
= binintersect ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersect) ).
thf(f111,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(f112,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f111]) ).
thf(f133,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f134,plain,
( dsetconstrEL
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f133]) ).
thf(f166,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
=> ( in @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f112]) ).
thf(f167,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
=> ( ( in @ X1 @ X2 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f166]) ).
thf(f178,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) )
= binintersect ),
inference(rectify,[],[f108]) ).
thf(f179,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f178]) ).
thf(f327,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X2 )
!= $true ) )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f167]) ).
thf(f328,plain,
( ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( sepInPowerset = $true )
& ( singletonsswitch = $true )
& ( omegaSAx = $true )
& ( subsetemptysetimpeq = $true )
& ( nonemptyImpWitness = $true )
& ( subsetE2 = $true )
& ( powersetAx = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( powersetI1 = $true )
& ( emptyE1 = $true )
& ( dsetconstrI = $true )
& ( setadjoin__Cong = $true )
& ( binunionIR = $true )
& ( exuE1 = $true )
& ( exuE3u = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinSub = $true )
& ( setadjoinE = $true )
& ( setadjoinSub2 = $true )
& ( setextAx = $true )
& ( powersetI = $true )
& ( binunionIL = $true )
& ( replAx = $true )
& ( binunionLsub = $true )
& ( prop2setE = $true )
& ( binunionEcases = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( sepSubset = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetsubset = $true )
& ( exuI1 = $true )
& ( emptyset__Cong = $true )
& ( inCongP = $true )
& ( nonemptyE1 = $true )
& ( omega__Cong = $true )
& ( subPowSU = $true )
& ( subsetI1 = $true )
& ( exuI2 = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( wellorderingAx = $true )
& ( powersetE1 = $true )
& ( quantDeMorgan3 = $true )
& ( setunionI = $true )
& ( exuI3 = $true )
& ( notequalI2 = $true )
& ( setadjoinOr = $true )
& ( setext = $true )
& ( emptyinunitempty = $true )
& ( upairset2IR = $true )
& ( notinsingleton = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( prop2set2propI = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetE = $true )
& ( subsetE = $true )
& ( notdexE = $true )
& ( setunion__Cong = $true )
& ( subsetTrans = $true )
& ( exuE3e = $true )
& ( binunionE = $true )
& ( emptyI = $true )
& ( subsetRefl = $true )
& ( setadjoinIL = $true )
& ( prop2setI = $true )
& ( powerset__Cong = $true )
& ( subsetI2 = $true )
& ( setadjoinAx = $true )
& ( powersetE = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X2 )
!= $true ) )
& ( upairsetIL = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( emptyinPowerset = $true )
& ( omega0Ax = $true )
& ( emptysetAx = $true )
& ( exuE2 = $true )
& ( exu__Cong = $true )
& ( powersetsubset = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( descr__Cong = $true )
& ( binintersectI = $true )
& ( eqimpsubset2 = $true )
& ( setunionE = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( subset2powerset = $true )
& ( binintersectSubset5 = $true )
& ( setoftrueEq = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ( in__Cong = $true )
& ( setextsub = $true )
& ( uniqinunit = $true )
& ( exuEu = $true )
& ( quantDeMorgan1 = $true )
& ( inPowerset = $true ) ),
inference(flattening,[],[f327]) ).
thf(f329,plain,
( ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( sepInPowerset = $true )
& ( singletonsswitch = $true )
& ( omegaSAx = $true )
& ( subsetemptysetimpeq = $true )
& ( nonemptyImpWitness = $true )
& ( subsetE2 = $true )
& ( powersetAx = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( powersetI1 = $true )
& ( emptyE1 = $true )
& ( dsetconstrI = $true )
& ( setadjoin__Cong = $true )
& ( binunionIR = $true )
& ( exuE1 = $true )
& ( exuE3u = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinSub = $true )
& ( setadjoinE = $true )
& ( setadjoinSub2 = $true )
& ( setextAx = $true )
& ( powersetI = $true )
& ( binunionIL = $true )
& ( replAx = $true )
& ( binunionLsub = $true )
& ( prop2setE = $true )
& ( binunionEcases = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( sepSubset = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetsubset = $true )
& ( exuI1 = $true )
& ( emptyset__Cong = $true )
& ( inCongP = $true )
& ( nonemptyE1 = $true )
& ( omega__Cong = $true )
& ( subPowSU = $true )
& ( subsetI1 = $true )
& ( exuI2 = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( wellorderingAx = $true )
& ( powersetE1 = $true )
& ( quantDeMorgan3 = $true )
& ( setunionI = $true )
& ( exuI3 = $true )
& ( notequalI2 = $true )
& ( setadjoinOr = $true )
& ( setext = $true )
& ( emptyinunitempty = $true )
& ( upairset2IR = $true )
& ( notinsingleton = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( prop2set2propI = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetE = $true )
& ( subsetE = $true )
& ( notdexE = $true )
& ( setunion__Cong = $true )
& ( subsetTrans = $true )
& ( exuE3e = $true )
& ( binunionE = $true )
& ( emptyI = $true )
& ( subsetRefl = $true )
& ( setadjoinIL = $true )
& ( prop2setI = $true )
& ( powerset__Cong = $true )
& ( subsetI2 = $true )
& ( setadjoinAx = $true )
& ( powersetE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
& ( ( in @ X1 @ X0 )
!= $true ) )
& ( upairsetIL = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( emptyinPowerset = $true )
& ( omega0Ax = $true )
& ( emptysetAx = $true )
& ( exuE2 = $true )
& ( exu__Cong = $true )
& ( powersetsubset = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( descr__Cong = $true )
& ( binintersectI = $true )
& ( eqimpsubset2 = $true )
& ( setunionE = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( subset2powerset = $true )
& ( binintersectSubset5 = $true )
& ( setoftrueEq = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ( in__Cong = $true )
& ( setextsub = $true )
& ( uniqinunit = $true )
& ( exuEu = $true )
& ( quantDeMorgan1 = $true )
& ( inPowerset = $true ) ),
inference(rectify,[],[f328]) ).
thf(f330,plain,
( ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( sepInPowerset = $true )
& ( singletonsswitch = $true )
& ( omegaSAx = $true )
& ( subsetemptysetimpeq = $true )
& ( nonemptyImpWitness = $true )
& ( subsetE2 = $true )
& ( powersetAx = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( powersetI1 = $true )
& ( emptyE1 = $true )
& ( dsetconstrI = $true )
& ( setadjoin__Cong = $true )
& ( binunionIR = $true )
& ( exuE1 = $true )
& ( exuE3u = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinSub = $true )
& ( setadjoinE = $true )
& ( setadjoinSub2 = $true )
& ( setextAx = $true )
& ( powersetI = $true )
& ( binunionIL = $true )
& ( replAx = $true )
& ( binunionLsub = $true )
& ( prop2setE = $true )
& ( binunionEcases = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( sepSubset = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetsubset = $true )
& ( exuI1 = $true )
& ( emptyset__Cong = $true )
& ( inCongP = $true )
& ( nonemptyE1 = $true )
& ( omega__Cong = $true )
& ( subPowSU = $true )
& ( subsetI1 = $true )
& ( exuI2 = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( wellorderingAx = $true )
& ( powersetE1 = $true )
& ( quantDeMorgan3 = $true )
& ( setunionI = $true )
& ( exuI3 = $true )
& ( notequalI2 = $true )
& ( setadjoinOr = $true )
& ( setext = $true )
& ( emptyinunitempty = $true )
& ( upairset2IR = $true )
& ( notinsingleton = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( prop2set2propI = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetE = $true )
& ( subsetE = $true )
& ( notdexE = $true )
& ( setunion__Cong = $true )
& ( subsetTrans = $true )
& ( exuE3e = $true )
& ( binunionE = $true )
& ( emptyI = $true )
& ( subsetRefl = $true )
& ( setadjoinIL = $true )
& ( prop2setI = $true )
& ( powerset__Cong = $true )
& ( subsetI2 = $true )
& ( setadjoinAx = $true )
& ( powersetE = $true )
& ( ( in @ sK1 @ ( binintersect @ sK0 @ sK2 ) )
= $true )
& ( ( in @ sK1 @ sK0 )
!= $true )
& ( upairsetIL = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( emptyinPowerset = $true )
& ( omega0Ax = $true )
& ( emptysetAx = $true )
& ( exuE2 = $true )
& ( exu__Cong = $true )
& ( powersetsubset = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( descr__Cong = $true )
& ( binintersectI = $true )
& ( eqimpsubset2 = $true )
& ( setunionE = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( subset2powerset = $true )
& ( binintersectSubset5 = $true )
& ( setoftrueEq = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ( in__Cong = $true )
& ( setextsub = $true )
& ( uniqinunit = $true )
& ( exuEu = $true )
& ( quantDeMorgan1 = $true )
& ( inPowerset = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f329]) ).
thf(f344,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f179]) ).
thf(f373,plain,
( ( in @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f330]) ).
thf(f374,plain,
( ( in @ sK1 @ ( binintersect @ sK0 @ sK2 ) )
= $true ),
inference(cnf_transformation,[],[f330]) ).
thf(f408,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f330]) ).
thf(f503,plain,
( dsetconstrEL
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f134]) ).
thf(f565,plain,
( $true
= ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK2 ) ) ),
inference(definition_unfolding,[],[f374,f344]) ).
thf(f614,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f503,f408]) ).
thf(f1695,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f614]) ).
thf(f1696,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( in @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1695]) ).
thf(f1697,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( in @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1696]) ).
thf(f1698,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( in @ X2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f1697]) ).
thf(f1699,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( in @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f1698]) ).
thf(f1700,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
=> ( in @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1699]) ).
thf(f1701,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) )
| ( $true
= ( in @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1700]) ).
thf(f1892,plain,
( $true
= ( in @ sK1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f565]) ).
thf(f2666,plain,
( ( ( in @ sK1 @ sK0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[],[f1892,f1701]) ).
thf(f2680,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(trivial_inequality_removal,[],[f2666]) ).
thf(f2684,plain,
$false,
inference(forward_subsumption_resolution,[],[f2680,f373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU591^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:54:00 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.25 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
% 0.70/0.37 % (4037165)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.70/0.37 % (4037184)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2124776126:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.70/0.37 % (4037184)Instruction limit reached!
% 0.70/0.37 % (4037184)------------------------------
% 0.70/0.37 % (4037184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.37 % (4037184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.37 % (4037184)CaDiCaL version: 2.1.3
% 0.70/0.37 % (4037184)Termination reason: Instruction limit
% 0.70/0.37 % (4037184)Termination phase: shuffling
% 0.70/0.37 % (4037184)Time elapsed: 0.001 s
% 0.70/0.37 % (4037184)Peak memory usage: 10 MB
% 0.70/0.37 % (4037184)Instructions burned: 4 (million)
% 0.70/0.37 % (4037189)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.70/0.37 % (4037189)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
% 0.70/0.37 % (4037182)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2940379943:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.70/0.37 % (4037183)lrs+10_16_si=on:nwc=1.5:random_seed=419042551:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.70/0.37 % (4037185)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=1103673262: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)
% 0.70/0.37 % (4037186)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2465594584:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.70/0.37 % (4037189)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=1849772109:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.70/0.37 % (4037187)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=842245161:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.70/0.37 % (4037195)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3465014458:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.70/0.37 % (4037195)Instruction limit reached!
% 0.70/0.37 % (4037195)------------------------------
% 0.70/0.37 % (4037195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.37 % (4037195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.37 % (4037195)CaDiCaL version: 2.1.3
% 0.70/0.37 % (4037195)Termination reason: Instruction limit
% 0.70/0.37 % (4037195)Termination phase: shuffling
% 0.70/0.37 % (4037195)Time elapsed: 0.001 s
% 0.70/0.37 % (4037195)Peak memory usage: 10 MB
% 0.70/0.37 % (4037195)Instructions burned: 4 (million)
% 0.70/0.37 % (4037183)Instruction limit reached!
% 0.70/0.37 % (4037183)------------------------------
% 0.70/0.37 % (4037183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.37 % (4037183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.37 % (4037183)CaDiCaL version: 2.1.3
% 0.70/0.37 % (4037183)Termination reason: Instruction limit
% 0.70/0.37 % (4037183)Termination phase: Property scanning
% 0.70/0.37 % (4037183)Time elapsed: 0.008 s
% 0.70/0.37 % (4037183)Peak memory usage: 10 MB
% 0.70/0.37 % (4037183)Instructions burned: 19 (million)
% 0.70/0.37 % (4037186)Instruction limit reached!
% 0.70/0.37 % (4037186)------------------------------
% 0.70/0.37 % (4037186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.37 % (4037186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.37 % (4037186)CaDiCaL version: 2.1.3
% 0.70/0.37 % (4037186)Termination reason: Instruction limit
% 0.70/0.37 % (4037186)Termination phase: Preprocessing 3
% 0.70/0.37 % (4037186)Time elapsed: 0.012 s
% 0.70/0.37 % (4037186)Peak memory usage: 11 MB
% 0.70/0.37 % (4037186)Instructions burned: 25 (million)
% 0.70/0.37 % (4037211)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3479072186:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.70/0.41 % (4037211)Instruction limit reached!
% 0.70/0.41 % (4037211)------------------------------
% 0.70/0.41 % (4037211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.41 % (4037211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.41 % (4037211)CaDiCaL version: 2.1.3
% 0.70/0.41 % (4037211)Termination reason: Instruction limit
% 0.70/0.41 % (4037211)Termination phase: shuffling
% 0.70/0.41 % (4037211)Time elapsed: 0.002 s
% 0.70/0.41 % (4037211)Peak memory usage: 10 MB
% 0.70/0.41 % (4037211)Instructions burned: 8 (million)
% 0.70/0.41 % (4037214)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.70/0.41 % (4037219)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
% 0.70/0.41 % (4037219)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.70/0.41 % (4037214)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1562691889:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.70/0.41 % (4037219)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1174691865:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.70/0.41 % (4037217)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3248926209:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.70/0.41 % (4037214)Instruction limit reached!
% 0.70/0.41 % (4037214)------------------------------
% 0.70/0.41 % (4037214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.41 % (4037214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.41 % (4037214)CaDiCaL version: 2.1.3
% 0.70/0.41 % (4037214)Termination reason: Instruction limit
% 0.70/0.41 % (4037214)Termination phase: shuffling
% 0.70/0.41 % (4037214)Time elapsed: 0.004 s
% 0.70/0.41 % (4037214)Peak memory usage: 10 MB
% 0.70/0.41 % (4037214)Instructions burned: 9 (million)
% 0.70/0.41 % (4037219)Instruction limit reached!
% 0.70/0.41 % (4037219)------------------------------
% 0.70/0.41 % (4037219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.41 % (4037219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.41 % (4037219)CaDiCaL version: 2.1.3
% 0.70/0.41 % (4037219)Termination reason: Instruction limit
% 0.70/0.41 % (4037219)Termination phase: Property scanning
% 0.70/0.41 % (4037219)Time elapsed: 0.006 s
% 0.70/0.41 % (4037219)Peak memory usage: 10 MB
% 0.70/0.41 % (4037219)Instructions burned: 30 (million)
% 0.70/0.41 % (4037187)Instruction limit reached!
% 0.70/0.41 % (4037187)------------------------------
% 0.70/0.41 % (4037187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.41 % (4037187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.41 % (4037187)CaDiCaL version: 2.1.3
% 0.70/0.41 % (4037187)Termination reason: Instruction limit
% 0.70/0.41 % (4037187)Termination phase: Saturation
% 0.70/0.41 % (4037187)Time elapsed: 0.036 s
% 0.70/0.41 % (4037187)Peak memory usage: 13 MB
% 0.70/0.41 % (4037187)Instructions burned: 78 (million)
% 0.70/0.41 % (4037217)Instruction limit reached!
% 0.70/0.41 % (4037217)------------------------------
% 0.70/0.41 % (4037217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.41 % (4037217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.41 % (4037217)CaDiCaL version: 2.1.3
% 0.70/0.41 % (4037217)Termination reason: Instruction limit
% 0.70/0.41 % (4037217)Termination phase: Property scanning
% 0.70/0.41 % (4037217)Time elapsed: 0.006 s
% 0.70/0.41 % (4037217)Peak memory usage: 10 MB
% 0.70/0.41 % (4037217)Instructions burned: 14 (million)
% 0.70/0.41 % (4037182)Instruction limit reached!
% 0.70/0.41 % (4037182)------------------------------
% 0.70/0.41 % (4037182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.41 % (4037182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.41 % (4037182)CaDiCaL version: 2.1.3
% 0.70/0.41 % (4037182)Termination reason: Instruction limit
% 0.70/0.42 % (4037182)Termination phase: Saturation
% 0.70/0.42 % (4037182)Time elapsed: 0.041 s
% 0.70/0.42 % (4037182)Peak memory usage: 13 MB
% 0.70/0.42 % (4037182)Instructions burned: 88 (million)
% 0.70/0.42 % (4037230)lrs+10_1_si=on:cs=on:random_seed=2294622363:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.70/0.42 % (4037230)Instruction limit reached!
% 0.70/0.42 % (4037230)------------------------------
% 0.70/0.42 % (4037230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037230)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037230)Termination reason: Instruction limit
% 0.70/0.42 % (4037230)Termination phase: shuffling
% 0.70/0.42 % (4037230)Time elapsed: 0.002 s
% 0.70/0.42 % (4037230)Peak memory usage: 10 MB
% 0.70/0.42 % (4037230)Instructions burned: 8 (million)
% 0.70/0.42 % (4037231)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.70/0.42 % (4037227)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=2859735853:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.70/0.42 % (4037231)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=2829813592:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.70/0.42 % (4037232)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1799550588:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.70/0.42 % (4037231)Instruction limit reached!
% 0.70/0.42 % (4037231)------------------------------
% 0.70/0.42 % (4037231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037231)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037231)Termination reason: Instruction limit
% 0.70/0.42 % (4037231)Termination phase: shuffling
% 0.70/0.42 % (4037231)Time elapsed: 0.002 s
% 0.70/0.42 % (4037231)Peak memory usage: 10 MB
% 0.70/0.42 % (4037231)Instructions burned: 4 (million)
% 0.70/0.42 % (4037234)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=866499078:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.70/0.42 % (4037241)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4159432017:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.70/0.42 % (4037241)Instruction limit reached!
% 0.70/0.42 % (4037241)------------------------------
% 0.70/0.42 % (4037241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037241)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037241)Termination reason: Instruction limit
% 0.70/0.42 % (4037241)Termination phase: Preprocessing 3
% 0.70/0.42 % (4037241)Time elapsed: 0.006 s
% 0.70/0.42 % (4037241)Peak memory usage: 11 MB
% 0.70/0.42 % (4037241)Instructions burned: 27 (million)
% 0.70/0.42 % (4037189)Instruction limit reached!
% 0.70/0.42 % (4037189)------------------------------
% 0.70/0.42 % (4037189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037189)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037189)Termination reason: Instruction limit
% 0.70/0.42 % (4037189)Termination phase: Saturation
% 0.70/0.42 % (4037189)Time elapsed: 0.067 s
% 0.70/0.42 % (4037189)Peak memory usage: 13 MB
% 0.70/0.42 % (4037189)Instructions burned: 159 (million)
% 0.70/0.42 % (4037232)Instruction limit reached!
% 0.70/0.42 % (4037232)------------------------------
% 0.70/0.42 % (4037232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037232)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037232)Termination reason: Instruction limit
% 0.70/0.42 % (4037232)Termination phase: Property scanning
% 0.70/0.42 % (4037232)Time elapsed: 0.018 s
% 0.70/0.42 % (4037232)Peak memory usage: 11 MB
% 0.70/0.42 % (4037232)Instructions burned: 38 (million)
% 0.70/0.42 % (4037256)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4010874246:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.70/0.42 % (4037251)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3496123541:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.70/0.42 % (4037251)Instruction limit reached!
% 0.70/0.42 % (4037251)------------------------------
% 0.70/0.42 % (4037251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037251)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037251)Termination reason: Instruction limit
% 0.70/0.42 % (4037251)Termination phase: Property scanning
% 0.70/0.42 % (4037251)Time elapsed: 0.006 s
% 0.70/0.42 % (4037251)Peak memory usage: 10 MB
% 0.70/0.42 % (4037251)Instructions burned: 14 (million)
% 0.70/0.42 % (4037258)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2599032840:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.70/0.42 % (4037227)Instruction limit reached!
% 0.70/0.42 % (4037227)------------------------------
% 0.70/0.42 % (4037227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037227)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037227)Termination reason: Instruction limit
% 0.70/0.42 % (4037227)Termination phase: Saturation
% 0.70/0.42 % (4037227)Time elapsed: 0.039 s
% 0.70/0.42 % (4037227)Peak memory usage: 13 MB
% 0.70/0.42 % (4037227)Instructions burned: 86 (million)
% 0.70/0.42 % (4037258)Instruction limit reached!
% 0.70/0.42 % (4037258)------------------------------
% 0.70/0.42 % (4037258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037258)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037258)Termination reason: Instruction limit
% 0.70/0.42 % (4037258)Termination phase: Property scanning
% 0.70/0.42 % (4037258)Time elapsed: 0.006 s
% 0.70/0.42 % (4037258)Peak memory usage: 10 MB
% 0.70/0.42 % (4037258)Instructions burned: 14 (million)
% 0.70/0.42 % (4037264)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=624359712:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.70/0.42 % (4037264)Instruction limit reached!
% 0.70/0.42 % (4037264)------------------------------
% 0.70/0.42 % (4037264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037264)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037264)Termination reason: Instruction limit
% 0.70/0.42 % (4037264)Termination phase: shuffling
% 0.70/0.42 % (4037264)Time elapsed: 0.002 s
% 0.70/0.42 % (4037264)Peak memory usage: 10 MB
% 0.70/0.42 % (4037264)Instructions burned: 4 (million)
% 0.70/0.42 % (4037269)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1920975548:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.70/0.42 % (4037271)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1495744232:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.70/0.42 % (4037274)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3093355113:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.70/0.42 % (4037278)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.70/0.42 % (4037278)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.70/0.42 % (4037269)Instruction limit reached!
% 0.70/0.42 % (4037269)------------------------------
% 0.70/0.42 % (4037269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037269)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037269)Termination reason: Instruction limit
% 0.70/0.42 % (4037269)Termination phase: Property scanning
% 0.70/0.42 % (4037269)Time elapsed: 0.011 s
% 0.70/0.42 % (4037269)Peak memory usage: 10 MB
% 0.70/0.42 % (4037269)Instructions burned: 28 (million)
% 0.70/0.42 % (4037256) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4037165-4037256"...
% 0.70/0.42 % (4037278)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1818344929:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.70/0.42 % (4037256)...printing done.
% 0.70/0.42 % (4037256)Refutation found. Thanks to Tanya!
% 0.70/0.42 % SZS status Theorem for theBenchmark
% 0.70/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.70/0.42 % (4037256)------------------------------
% 0.70/0.42 % (4037256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (4037256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (4037256)CaDiCaL version: 2.1.3
% 0.70/0.42 % (4037256)Termination reason: Refutation
% 0.70/0.42 % (4037256)Time elapsed: 0.040 s
% 0.70/0.42 % (4037256)Peak memory usage: 14 MB
% 0.70/0.42 % (4037256)Instructions burned: 155 (million)
% 0.70/0.42 % (4037165)Success in time 0.163 s
% 0.70/0.42 % Vampire exiting
%------------------------------------------------------------------------------