%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU595^1 : 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 : n013.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 08:30:14 AM UTC 2026
% Result : Theorem 0.77s 0.44s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 2147 ( 591 equ; 0 cnn)
% Maximal formula atoms : 113 ( 65 avg)
% Number of connectives : 1123 ( 8 ~; 2 |; 448 &; 191 @)
% ( 0 <=>; 459 =>; 0 <=; 0 <~>)
% Maximal formula depth : 120 ( 29 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 219 ( 215 usr; 117 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 84 ( 42 ^; 33 !; 9 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_130,type,
vIMP: $o > $o > $o ).
thf(func_def_131,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
vNOT: $o > $o ).
thf(func_def_134,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_136,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_137,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_138,type,
vIFF: $o > $o > $o ).
thf(func_def_139,type,
vAND: $o > $o > $o ).
thf(func_def_140,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_141,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_142,type,
vOR: $o > $o > $o ).
thf(func_def_148,type,
sK3: $i > $i > $i ).
thf(func_def_149,type,
sK4: $i > $i > $i ).
thf(func_def_150,type,
sK5: $i > $i > $i ).
thf(func_def_151,type,
sK6: $i > $i ).
thf(func_def_152,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_154,type,
sK9: $o > $i > $i > $i ).
thf(func_def_155,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_156,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_157,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_158,type,
sK13: $i > $i > $i ).
thf(func_def_159,type,
sK14: $i > $i ).
thf(func_def_160,type,
sK15: ( $i > $o ) > $i > $i ).
thf(func_def_161,type,
sK16: $i > $i > $i ).
thf(func_def_162,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_163,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_164,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_165,type,
sK20: $i > $i ).
thf(func_def_166,type,
sK21: $i > ( $i > $o ) > $i ).
thf(func_def_167,type,
sK22: $i > $i > $i ).
thf(func_def_168,type,
sK23: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_169,type,
sK24: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_170,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_171,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_172,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_173,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_174,type,
sK29: $i > ( $i > $o ) > $i ).
thf(func_def_175,type,
sK30: $i > ( $i > $o ) > $i ).
thf(func_def_176,type,
sK31: ( $i > $o ) > $i ).
thf(func_def_177,type,
sK32: $i > ( $i > $o ) > $i ).
thf(func_def_178,type,
sK33: $i > ( $i > $o ) > $i ).
thf(func_def_179,type,
sK34: ( $i > $o ) > $i ).
thf(func_def_180,type,
sK35: $i > ( $i > $o ) > $i ).
thf(func_def_181,type,
sK36: $i > ( $i > $o ) > $i ).
thf(func_def_182,type,
sK37: $i > ( $i > $o ) > $i ).
thf(func_def_183,type,
sK38: ( $i > $o ) > $i ).
thf(func_def_184,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_185,type,
sK40: $i > $i ).
thf(func_def_186,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_187,type,
sK42: ( $i > $o ) > $i ).
thf(func_def_188,type,
sK43: ( $i > $o ) > $i ).
thf(func_def_189,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_190,type,
sK45: ( $i > $o ) > $i ).
thf(func_def_191,type,
sK46: $i > $i ).
thf(func_def_192,type,
sK47: ( $i > $i > $o ) > $i > $i ).
thf(func_def_193,type,
sK48: ( $i > $i > $o ) > $i > $i ).
thf(func_def_194,type,
sK49: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_195,type,
sK50: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_196,type,
sK51: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_197,type,
sK52: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_198,type,
sK53: $i > $i > $i ).
thf(func_def_199,type,
sK54: $i > $i > $i ).
thf(func_def_200,type,
sK55: $i > ( $i > $o ) > $i ).
thf(func_def_201,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_202,type,
sK57: ( $i > $o ) > $i ).
thf(func_def_203,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_204,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_205,type,
sK60: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_206,type,
sK61: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_207,type,
sK62: $i > ( $i > $o ) > $i ).
thf(func_def_208,type,
sK63: $i > ( $i > $o ) > $i ).
thf(func_def_209,type,
sK64: $i > ( $i > $o ) > $i ).
thf(func_def_210,type,
sK65: $i > $i ).
thf(func_def_211,type,
sK66: $i > $i > $i > $i ).
thf(func_def_212,type,
sK67: $i > $i > $i ).
thf(func_def_213,type,
sK68: $i > $i > $i ).
thf(func_def_214,type,
sK69: $i > $i > $i ).
thf(func_def_215,type,
sK70: $i > ( $i > $o ) > $i ).
thf(func_def_216,type,
sK71: $i > $i ).
thf(func_def_217,type,
sK72: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_218,type,
sK73: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(f16,axiom,
( dsetconstrER
= ( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f108,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) )
= binintersect ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersect) ).
thf(f115,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(f116,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
thf(f196,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) )
= binintersect ),
inference(rectify,[],[f108]) ).
thf(f197,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f196]) ).
thf(f274,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X0 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f275,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f274]) ).
thf(f312,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
=> ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f116]) ).
thf(f313,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f312]) ).
thf(f340,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true ) )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f313]) ).
thf(f341,plain,
( ( prop2set2propI = $true )
& ( subsetI1 = $true )
& ( descr__Cong = $true )
& ( uniqinunit = $true )
& ( noeltsimpempty = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinE = $true )
& ( emptyE1 = $true )
& ( eqimpsubset2 = $true )
& ( descrp = $true )
& ( dsetconstrEL = $true )
& ( subPowSU = $true )
& ( notequalI1 = $true )
& ( prop2setE = $true )
& ( eqimpsubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( sepSubset = $true )
& ( nonemptyImpWitness = $true )
& ( powersetI1 = $true )
& ( setadjoinSub = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true ) )
& ( exu__Cong = $true )
& ( emptyinPowerset = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset3 = $true )
& ( setext = $true )
& ( subsetE = $true )
& ( binunionIR = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( in__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( subsetE2 = $true )
& ( setadjoinIR = $true )
& ( vacuousDall = $true )
& ( powerset__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( emptyI = $true )
& ( emptysetE = $true )
& ( powersetI = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( subsetI2 = $true )
& ( exuE1 = $true )
& ( upairset2IR = $true )
& ( powersetAx = $true )
& ( binunionEcases = $true )
& ( subsetRefl = $true )
& ( nonemptyI = $true )
& ( setadjoinIL = $true )
& ( setunion__Cong = $true )
& ( exuE3e = $true )
& ( binintersectI = $true )
& ( notinsingleton = $true )
& ( exuE3u = $true )
& ( quantDeMorgan3 = $true )
& ( exuI3 = $true )
& ( emptyset__Cong = $true )
& ( notsubsetI = $true )
& ( setadjoinSub2 = $true )
& ( binunionRsub = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( binunionIL = $true )
& ( exuI1 = $true )
& ( setbeta = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( binunionLsub = $true )
& ( omegaIndAx = $true )
& ( singletonsswitch = $true )
& ( replAx = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( emptyinunitempty = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( foundationAx = $true )
& ( exuEu = $true )
& ( powersetsubset = $true )
& ( setunionI = $true )
& ( binintersectLsub = $true )
& ( setadjoinOr = $true )
& ( upairsetIR = $true )
& ( notdallE = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( prop2setI = $true )
& ( eqinunit = $true )
& ( exuE2 = $true )
& ( setunionE = $true )
& ( subset2powerset = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( subsetTrans = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrI = $true )
& ( binintersectEL = $true )
& ( quantDeMorgan2 = $true )
& ( sepInPowerset = $true )
& ( exuI2 = $true )
& ( emptysetAx = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstr__Cong = $true )
& ( binunionE = $true )
& ( dsetconstrER = $true )
& ( upairsetE = $true )
& ( binintersectSubset2 = $true )
& ( setextsub = $true ) ),
inference(flattening,[],[f340]) ).
thf(f342,plain,
( ( prop2set2propI = $true )
& ( subsetI1 = $true )
& ( descr__Cong = $true )
& ( uniqinunit = $true )
& ( noeltsimpempty = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinE = $true )
& ( emptyE1 = $true )
& ( eqimpsubset2 = $true )
& ( descrp = $true )
& ( dsetconstrEL = $true )
& ( subPowSU = $true )
& ( notequalI1 = $true )
& ( prop2setE = $true )
& ( eqimpsubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( sepSubset = $true )
& ( nonemptyImpWitness = $true )
& ( powersetI1 = $true )
& ( setadjoinSub = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true ) )
& ( exu__Cong = $true )
& ( emptyinPowerset = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset3 = $true )
& ( setext = $true )
& ( subsetE = $true )
& ( binunionIR = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( in__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( subsetE2 = $true )
& ( setadjoinIR = $true )
& ( vacuousDall = $true )
& ( powerset__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( emptyI = $true )
& ( emptysetE = $true )
& ( powersetI = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( subsetI2 = $true )
& ( exuE1 = $true )
& ( upairset2IR = $true )
& ( powersetAx = $true )
& ( binunionEcases = $true )
& ( subsetRefl = $true )
& ( nonemptyI = $true )
& ( setadjoinIL = $true )
& ( setunion__Cong = $true )
& ( exuE3e = $true )
& ( binintersectI = $true )
& ( notinsingleton = $true )
& ( exuE3u = $true )
& ( quantDeMorgan3 = $true )
& ( exuI3 = $true )
& ( emptyset__Cong = $true )
& ( notsubsetI = $true )
& ( setadjoinSub2 = $true )
& ( binunionRsub = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( binunionIL = $true )
& ( exuI1 = $true )
& ( setbeta = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( binunionLsub = $true )
& ( omegaIndAx = $true )
& ( singletonsswitch = $true )
& ( replAx = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( emptyinunitempty = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( foundationAx = $true )
& ( exuEu = $true )
& ( powersetsubset = $true )
& ( setunionI = $true )
& ( binintersectLsub = $true )
& ( setadjoinOr = $true )
& ( upairsetIR = $true )
& ( notdallE = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( prop2setI = $true )
& ( eqinunit = $true )
& ( exuE2 = $true )
& ( setunionE = $true )
& ( subset2powerset = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( subsetTrans = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrI = $true )
& ( binintersectEL = $true )
& ( quantDeMorgan2 = $true )
& ( sepInPowerset = $true )
& ( exuI2 = $true )
& ( emptysetAx = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstr__Cong = $true )
& ( binunionE = $true )
& ( dsetconstrER = $true )
& ( upairsetE = $true )
& ( binintersectSubset2 = $true )
& ( setextsub = $true ) ),
inference(rectify,[],[f341]) ).
thf(f343,plain,
( ( prop2set2propI = $true )
& ( subsetI1 = $true )
& ( descr__Cong = $true )
& ( uniqinunit = $true )
& ( noeltsimpempty = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinE = $true )
& ( emptyE1 = $true )
& ( eqimpsubset2 = $true )
& ( descrp = $true )
& ( dsetconstrEL = $true )
& ( subPowSU = $true )
& ( notequalI1 = $true )
& ( prop2setE = $true )
& ( eqimpsubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( sepSubset = $true )
& ( nonemptyImpWitness = $true )
& ( powersetI1 = $true )
& ( setadjoinSub = $true )
& ( ( in @ sK1 @ sK0 )
!= $true )
& ( ( in @ sK1 @ ( binintersect @ sK2 @ sK0 ) )
= $true )
& ( exu__Cong = $true )
& ( emptyinPowerset = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset3 = $true )
& ( setext = $true )
& ( subsetE = $true )
& ( binunionIR = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( in__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( subsetE2 = $true )
& ( setadjoinIR = $true )
& ( vacuousDall = $true )
& ( powerset__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( emptyI = $true )
& ( emptysetE = $true )
& ( powersetI = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( subsetI2 = $true )
& ( exuE1 = $true )
& ( upairset2IR = $true )
& ( powersetAx = $true )
& ( binunionEcases = $true )
& ( subsetRefl = $true )
& ( nonemptyI = $true )
& ( setadjoinIL = $true )
& ( setunion__Cong = $true )
& ( exuE3e = $true )
& ( binintersectI = $true )
& ( notinsingleton = $true )
& ( exuE3u = $true )
& ( quantDeMorgan3 = $true )
& ( exuI3 = $true )
& ( emptyset__Cong = $true )
& ( notsubsetI = $true )
& ( setadjoinSub2 = $true )
& ( binunionRsub = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( binunionIL = $true )
& ( exuI1 = $true )
& ( setbeta = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( binunionLsub = $true )
& ( omegaIndAx = $true )
& ( singletonsswitch = $true )
& ( replAx = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( emptyinunitempty = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( foundationAx = $true )
& ( exuEu = $true )
& ( powersetsubset = $true )
& ( setunionI = $true )
& ( binintersectLsub = $true )
& ( setadjoinOr = $true )
& ( upairsetIR = $true )
& ( notdallE = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( prop2setI = $true )
& ( eqinunit = $true )
& ( exuE2 = $true )
& ( setunionE = $true )
& ( subset2powerset = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( subsetTrans = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrI = $true )
& ( binintersectEL = $true )
& ( quantDeMorgan2 = $true )
& ( sepInPowerset = $true )
& ( exuI2 = $true )
& ( emptysetAx = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstr__Cong = $true )
& ( binunionE = $true )
& ( dsetconstrER = $true )
& ( upairsetE = $true )
& ( binintersectSubset2 = $true )
& ( setextsub = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f342]) ).
thf(f379,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f275]) ).
thf(f409,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f343]) ).
thf(f497,plain,
( ( in @ sK1 @ ( binintersect @ sK2 @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f343]) ).
thf(f498,plain,
( ( in @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f343]) ).
thf(f552,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f197]) ).
thf(f608,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f379,f409]) ).
thf(f635,plain,
( ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK2
@ sK0 ) )
= $true ),
inference(definition_unfolding,[],[f497,f552]) ).
thf(f685,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f608]) ).
thf(f686,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f685]) ).
thf(f687,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f686]) ).
thf(f688,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f687]) ).
thf(f689,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f688]) ).
thf(f690,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ X3 ) )
= $true ),
inference(beta-eta_normalization,[],[f689]) ).
thf(f691,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( ( X1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f690]) ).
thf(f910,plain,
( $true
= ( in @ sK1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f635]) ).
thf(f2666,plain,
( ( ( ^ [Y0: $i] : ( in @ Y0 @ sK0 )
@ sK1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[],[f691,f910]) ).
thf(f2670,plain,
( ( ^ [Y0: $i] : ( in @ Y0 @ sK0 )
@ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f2666]) ).
thf(f2671,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(beta-eta_normalization,[],[f2670]) ).
thf(f2679,plain,
$false,
inference(forward_subsumption_resolution,[],[f2671,f498]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU595^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.19 % Computer : n013.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Sep 29 13:55:23 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.23 Running higher-order theorem proving
% 0.13/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/0.39 % (2155228)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.77/0.39 % (2155233)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1904251693:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.77/0.39 % (2155234)lrs+10_16_si=on:nwc=1.5:random_seed=2774912315:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.77/0.39 % (2155235)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3442816466:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.77/0.39 % (2155239)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.77/0.39 % (2155239)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
% 0.77/0.39 % (2155237)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1692266071:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.77/0.39 % (2155236)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=2936670465: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)
% 0.77/0.39 % (2155235)Instruction limit reached!
% 0.77/0.39 % (2155235)------------------------------
% 0.77/0.39 % (2155235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.39 % (2155235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.39 % (2155235)CaDiCaL version: 2.1.3
% 0.77/0.39 % (2155235)Termination reason: Instruction limit
% 0.77/0.39 % (2155235)Termination phase: shuffling
% 0.77/0.39 % (2155235)Time elapsed: 0.002 s
% 0.77/0.39 % (2155235)Peak memory usage: 10 MB
% 0.77/0.39 % (2155235)Instructions burned: 3 (million)
% 0.77/0.39 % (2155239)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=1296224237:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.77/0.39 % (2155234)Instruction limit reached!
% 0.77/0.39 % (2155234)------------------------------
% 0.77/0.39 % (2155234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.39 % (2155234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.39 % (2155234)CaDiCaL version: 2.1.3
% 0.77/0.39 % (2155234)Termination reason: Instruction limit
% 0.77/0.39 % (2155234)Termination phase: Property scanning
% 0.77/0.39 % (2155234)Time elapsed: 0.008 s
% 0.77/0.39 % (2155234)Peak memory usage: 10 MB
% 0.77/0.39 % (2155234)Instructions burned: 18 (million)
% 0.77/0.39 % (2155238)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2537251695:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.77/0.39 % (2155237)Instruction limit reached!
% 0.77/0.39 % (2155237)------------------------------
% 0.77/0.39 % (2155237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.39 % (2155237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.39 % (2155237)CaDiCaL version: 2.1.3
% 0.77/0.39 % (2155237)Termination reason: Instruction limit
% 0.77/0.39 % (2155237)Termination phase: Preprocessing 3
% 0.77/0.39 % (2155237)Time elapsed: 0.013 s
% 0.77/0.39 % (2155237)Peak memory usage: 11 MB
% 0.77/0.39 % (2155237)Instructions burned: 25 (million)
% 0.77/0.39 % (2155233)Instruction limit reached!
% 0.77/0.39 % (2155233)------------------------------
% 0.77/0.39 % (2155233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.39 % (2155233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.39 % (2155233)CaDiCaL version: 2.1.3
% 0.77/0.39 % (2155233)Termination reason: Instruction limit
% 0.77/0.39 % (2155233)Termination phase: Saturation
% 0.77/0.39 % (2155233)Time elapsed: 0.030 s
% 0.77/0.39 % (2155233)Peak memory usage: 13 MB
% 0.77/0.39 % (2155233)Instructions burned: 90 (million)
% 0.77/0.39 % (2155245)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=658783330:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.77/0.39 % (2155245)Instruction limit reached!
% 0.77/0.39 % (2155245)------------------------------
% 0.77/0.39 % (2155245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2155245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2155245)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2155245)Termination reason: Instruction limit
% 0.77/0.43 % (2155245)Termination phase: shuffling
% 0.77/0.43 % (2155245)Time elapsed: 0.002 s
% 0.77/0.43 % (2155245)Peak memory usage: 10 MB
% 0.77/0.43 % (2155245)Instructions burned: 4 (million)
% 0.77/0.43 % (2155247)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3217840697:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.77/0.43 % (2155249)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.77/0.43 % (2155247)Instruction limit reached!
% 0.77/0.43 % (2155247)------------------------------
% 0.77/0.43 % (2155247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2155247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2155247)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2155247)Termination reason: Instruction limit
% 0.77/0.43 % (2155247)Termination phase: shuffling
% 0.77/0.43 % (2155247)Time elapsed: 0.003 s
% 0.77/0.43 % (2155247)Peak memory usage: 10 MB
% 0.77/0.43 % (2155247)Instructions burned: 6 (million)
% 0.77/0.43 % (2155250)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2326015075:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.77/0.43 % (2155249)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3651319309:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.77/0.43 % (2155250)Instruction limit reached!
% 0.77/0.43 % (2155250)------------------------------
% 0.77/0.43 % (2155250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2155250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2155250)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2155250)Termination reason: Instruction limit
% 0.77/0.43 % (2155250)Termination phase: Property scanning
% 0.77/0.43 % (2155250)Time elapsed: 0.003 s
% 0.77/0.43 % (2155250)Peak memory usage: 10 MB
% 0.77/0.43 % (2155250)Instructions burned: 16 (million)
% 0.77/0.43 % (2155249)Instruction limit reached!
% 0.77/0.43 % (2155249)------------------------------
% 0.77/0.43 % (2155249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2155249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2155249)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2155249)Termination reason: Instruction limit
% 0.77/0.43 % (2155249)Termination phase: shuffling
% 0.77/0.43 % (2155249)Time elapsed: 0.003 s
% 0.77/0.43 % (2155249)Peak memory usage: 10 MB
% 0.77/0.43 % (2155249)Instructions burned: 7 (million)
% 0.77/0.43 % (2155253)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
% 0.77/0.43 % (2155253)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.77/0.43 % (2155253)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2602497641:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.77/0.43 % (2155257)lrs+10_1_si=on:cs=on:random_seed=742928759:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.77/0.43 % (2155258)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.77/0.43 % (2155257)Instruction limit reached!
% 0.77/0.43 % (2155257)------------------------------
% 0.77/0.43 % (2155257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2155257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2155257)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2155257)Termination reason: Instruction limit
% 0.77/0.43 % (2155257)Termination phase: shuffling
% 0.77/0.43 % (2155257)Time elapsed: 0.003 s
% 0.77/0.43 % (2155257)Peak memory usage: 10 MB
% 0.77/0.43 % (2155257)Instructions burned: 12 (million)
% 0.77/0.43 % (2155254)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=3805169485:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.77/0.44 % (2155258)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=2142692960:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.77/0.44 % (2155258)Instruction limit reached!
% 0.77/0.44 % (2155258)------------------------------
% 0.77/0.44 % (2155258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155258)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155258)Termination reason: Instruction limit
% 0.77/0.44 % (2155258)Termination phase: shuffling
% 0.77/0.44 % (2155258)Time elapsed: 0.003 s
% 0.77/0.44 % (2155258)Peak memory usage: 10 MB
% 0.77/0.44 % (2155258)Instructions burned: 7 (million)
% 0.77/0.44 % (2155253)Instruction limit reached!
% 0.77/0.44 % (2155253)------------------------------
% 0.77/0.44 % (2155253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155253)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155253)Termination reason: Instruction limit
% 0.77/0.44 % (2155253)Termination phase: Property scanning
% 0.77/0.44 % (2155253)Time elapsed: 0.013 s
% 0.77/0.44 % (2155253)Peak memory usage: 10 MB
% 0.77/0.44 % (2155253)Instructions burned: 30 (million)
% 0.77/0.44 % (2155262)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1273995476:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.77/0.44 % (2155239)Instruction limit reached!
% 0.77/0.44 % (2155239)------------------------------
% 0.77/0.44 % (2155239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155239)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155239)Termination reason: Instruction limit
% 0.77/0.44 % (2155239)Termination phase: Saturation
% 0.77/0.44 % (2155239)Time elapsed: 0.067 s
% 0.77/0.44 % (2155239)Peak memory usage: 14 MB
% 0.77/0.44 % (2155239)Instructions burned: 157 (million)
% 0.77/0.44 % (2155238)Instruction limit reached!
% 0.77/0.44 % (2155238)------------------------------
% 0.77/0.44 % (2155238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155238)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155238)Termination reason: Instruction limit
% 0.77/0.44 % (2155238)Termination phase: Saturation
% 0.77/0.44 % (2155238)Time elapsed: 0.064 s
% 0.77/0.44 % (2155238)Peak memory usage: 13 MB
% 0.77/0.44 % (2155238)Instructions burned: 75 (million)
% 0.77/0.44 % (2155262)Instruction limit reached!
% 0.77/0.44 % (2155262)------------------------------
% 0.77/0.44 % (2155262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155262)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155262)Termination reason: Instruction limit
% 0.77/0.44 % (2155262)Termination phase: Property scanning
% 0.77/0.44 % (2155262)Time elapsed: 0.010 s
% 0.77/0.44 % (2155262)Peak memory usage: 11 MB
% 0.77/0.44 % (2155262)Instructions burned: 41 (million)
% 0.77/0.44 % (2155264)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2796623558:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.77/0.44 % (2155265)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=191293728:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.77/0.44 % (2155268)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2900268722:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.77/0.44 % (2155267)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2410257081:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.77/0.44 % (2155265)Instruction limit reached!
% 0.77/0.44 % (2155265)------------------------------
% 0.77/0.44 % (2155265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155265)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155265)Termination reason: Instruction limit
% 0.77/0.44 % (2155265)Termination phase: Preprocessing 3
% 0.77/0.44 % (2155265)Time elapsed: 0.012 s
% 0.77/0.44 % (2155265)Peak memory usage: 11 MB
% 0.77/0.44 % (2155265)Instructions burned: 25 (million)
% 0.77/0.44 % (2155254)Instruction limit reached!
% 0.77/0.44 % (2155254)------------------------------
% 0.77/0.44 % (2155254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155254)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155254)Termination reason: Instruction limit
% 0.77/0.44 % (2155254)Termination phase: Saturation
% 0.77/0.44 % (2155254)Time elapsed: 0.039 s
% 0.77/0.44 % (2155254)Peak memory usage: 13 MB
% 0.77/0.44 % (2155254)Instructions burned: 86 (million)
% 0.77/0.44 % (2155269)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4101009424:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.77/0.44 % (2155267)Instruction limit reached!
% 0.77/0.44 % (2155267)------------------------------
% 0.77/0.44 % (2155267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155267)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155267)Termination reason: Instruction limit
% 0.77/0.44 % (2155267)Termination phase: Property scanning
% 0.77/0.44 % (2155267)Time elapsed: 0.007 s
% 0.77/0.44 % (2155267)Peak memory usage: 10 MB
% 0.77/0.44 % (2155267)Instructions burned: 15 (million)
% 0.77/0.44 % (2155269)Instruction limit reached!
% 0.77/0.44 % (2155269)------------------------------
% 0.77/0.44 % (2155269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155269)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155269)Termination reason: Instruction limit
% 0.77/0.44 % (2155269)Termination phase: Property scanning
% 0.77/0.44 % (2155269)Time elapsed: 0.007 s
% 0.77/0.44 % (2155269)Peak memory usage: 10 MB
% 0.77/0.44 % (2155269)Instructions burned: 17 (million)
% 0.77/0.44 % (2155274)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1941379600: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)
% 0.77/0.44 % (2155275)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2302836875:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.77/0.44 % (2155274)Instruction limit reached!
% 0.77/0.44 % (2155274)------------------------------
% 0.77/0.44 % (2155274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155274)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155274)Termination reason: Instruction limit
% 0.77/0.44 % (2155274)Termination phase: shuffling
% 0.77/0.44 % (2155274)Time elapsed: 0.001 s
% 0.77/0.44 % (2155274)Peak memory usage: 10 MB
% 0.77/0.44 % (2155274)Instructions burned: 2 (million)
% 0.77/0.44 % (2155277)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=480897124:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.77/0.44 % (2155278)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3675940724:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.77/0.44 % (2155275)Instruction limit reached!
% 0.77/0.44 % (2155275)------------------------------
% 0.77/0.44 % (2155275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155275)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155275)Termination reason: Instruction limit
% 0.77/0.44 % (2155275)Termination phase: Property scanning
% 0.77/0.44 % (2155275)Time elapsed: 0.011 s
% 0.77/0.44 % (2155275)Peak memory usage: 10 MB
% 0.77/0.44 % (2155275)Instructions burned: 26 (million)
% 0.77/0.44 % (2155277)Instruction limit reached!
% 0.77/0.44 % (2155277)------------------------------
% 0.77/0.44 % (2155277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155277)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155277)Termination reason: Instruction limit
% 0.77/0.44 % (2155277)Termination phase: Property scanning
% 0.77/0.44 % (2155277)Time elapsed: 0.010 s
% 0.77/0.44 % (2155277)Peak memory usage: 11 MB
% 0.77/0.44 % (2155277)Instructions burned: 24 (million)
% 0.77/0.44 % (2155281)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
% 0.77/0.44 % (2155281)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.77/0.44 % (2155268) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2155228-2155268"...
% 0.77/0.44 % (2155268)...printing done.
% 0.77/0.44 % (2155281)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=2521017662:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.77/0.44 % (2155268)Refutation found. Thanks to Tanya!
% 0.77/0.44 % SZS status Theorem for theBenchmark
% 0.77/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.77/0.44 % (2155268)------------------------------
% 0.77/0.44 % (2155268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (2155268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (2155268)CaDiCaL version: 2.1.3
% 0.77/0.44 % (2155268)Termination reason: Refutation
% 0.77/0.44 % (2155268)Time elapsed: 0.043 s
% 0.77/0.44 % (2155268)Peak memory usage: 14 MB
% 0.77/0.44 % (2155268)Instructions burned: 155 (million)
% 0.77/0.44 % (2155228)Success in time 0.17 s
% 0.77/0.44 % Vampire exiting
%------------------------------------------------------------------------------