%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU605^1 : 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 : n002.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 08:30:17 AM UTC 2026
% Result : Theorem 0.65s 0.45s
% Output : Refutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 18 unt; 0 typ; 5 def)
% Number of atoms : 2905 ( 813 equ; 0 cnn)
% Maximal formula atoms : 124 ( 55 avg)
% Number of connectives : 1472 ( 64 ~; 49 |; 501 &; 226 @)
% ( 9 <=>; 623 =>; 0 <=; 0 <~>)
% Maximal formula depth : 131 ( 25 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 265 ( 262 usr; 142 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 51 !; 15 ?; 66 :)
% 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,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_143,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_144,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_145,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_146,type,
vAND: $o > $o > $o ).
thf(func_def_147,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_148,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_149,type,
vIMP: $o > $o > $o ).
thf(func_def_150,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_151,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_152,type,
vNOT: $o > $o ).
thf(func_def_153,type,
sP0: $i > $i > $o ).
thf(func_def_154,type,
sP1: $i > $o ).
thf(func_def_155,type,
sP2: $o ).
thf(func_def_158,type,
sK5: $i > $o ).
thf(func_def_164,type,
sK11: $i > $i ).
thf(func_def_165,type,
sK12: $i > $i ).
thf(func_def_166,type,
sK13: $i > $o ).
thf(func_def_169,type,
sK16: $i > $o ).
thf(func_def_172,type,
sK19: $o > $i > $i > $i ).
thf(func_def_175,type,
sK22: $o ).
thf(func_def_179,type,
sK26: $i > $o ).
thf(func_def_182,type,
sK29: $i > ( $i > $o ) > $i ).
thf(func_def_183,type,
sK30: $o ).
thf(func_def_186,type,
sK33: $i > $i > $i ).
thf(func_def_187,type,
sK34: $i > $i > $i ).
thf(func_def_191,type,
sK38: $i > $i ).
thf(func_def_197,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_199,type,
sK46: $i > $o ).
thf(func_def_204,type,
sK51: $i > $o ).
thf(func_def_205,type,
sK52: $i > $o ).
thf(func_def_209,type,
sK56: $i > $i > $i ).
thf(func_def_223,type,
sK70: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_224,type,
sK71: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_225,type,
sK72: $i > $o ).
thf(func_def_226,type,
sK73: $i > $o ).
thf(func_def_229,type,
sK76: $i > $o ).
thf(func_def_243,type,
sK90: $i > $i > $i ).
thf(func_def_253,type,
sK100: $o ).
thf(func_def_255,type,
sK102: $i > $i ).
thf(func_def_263,type,
sK110: ( $i > $o ) > $i ).
thf(func_def_264,type,
sK111: $i > $o ).
thf(func_def_265,type,
sK112: $i > $i ).
thf(func_def_267,type,
sK114: $i > $o ).
thf(func_def_272,type,
sK119: $i > $o ).
thf(func_def_273,type,
sK120: $i > $o ).
thf(func_def_274,type,
sK121: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_275,type,
sK122: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_279,type,
sK126: $o ).
thf(func_def_284,type,
sK131: $i > $i ).
thf(func_def_285,type,
sK132: ( $i > $o ) > $i > $i ).
thf(func_def_287,type,
sK134: $i > $o ).
thf(func_def_295,type,
sK142: $i > ( $i > $o ) > $i ).
thf(func_def_296,type,
sK143: $i > $o ).
thf(func_def_299,type,
sK146: $i > $o ).
thf(func_def_303,type,
sK150: $i > $i > $i ).
thf(func_def_313,type,
sK160: $i > $i ).
thf(func_def_316,type,
sK163: $i > $i > $i ).
thf(func_def_317,type,
sK164: $i > $i > $i ).
thf(func_def_318,type,
sK165: $i > $o ).
thf(func_def_321,type,
sK168: $o ).
thf(func_def_322,type,
sK169: $i > ( $i > $o ) > $i ).
thf(func_def_323,type,
sK170: $i > $o ).
thf(func_def_329,type,
sK176: $i > $o ).
thf(func_def_331,type,
sK178: ( $i > $o ) > $i ).
thf(func_def_332,type,
sK179: $i > $o ).
thf(func_def_342,type,
sK189: ( $i > $o ) > $i ).
thf(func_def_343,type,
sK190: ( $i > $o ) > $i ).
thf(func_def_344,type,
sK191: $i > $o ).
thf(func_def_347,type,
sK194: $i > $o ).
thf(func_def_349,type,
sK196: ( $i > $o ) > $i > $i ).
thf(func_def_354,type,
sK201: $i > $o ).
thf(func_def_364,type,
sK211: $i > $o ).
thf(func_def_370,type,
sK217: $i > $o ).
thf(func_def_371,type,
sK218: $i > $o ).
thf(func_def_372,type,
sK219: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_373,type,
sK220: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_380,type,
sK227: $o ).
thf(func_def_393,type,
sK240: $i > $i > $o ).
thf(func_def_395,type,
sK242: $i > $i ).
thf(func_def_396,type,
sK243: $i > $i ).
thf(func_def_397,type,
sK244: $i > ( $i > $i > $o ) > $i ).
thf(func_def_398,type,
sK245: $i > ( $i > $i > $o ) > $i ).
thf(func_def_399,type,
sK246: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_402,type,
sK249: $i > $i > $i ).
thf(func_def_407,type,
sK254: $i > ( $i > $o ) > $i ).
thf(func_def_408,type,
sK255: $i > $o ).
thf(func_def_415,type,
sK262: ( $i > $o ) > $i ).
thf(func_def_416,type,
sK263: $i > $o ).
thf(func_def_417,type,
sK264: $i > $i ).
thf(func_def_435,type,
sK282: $o ).
thf(func_def_437,type,
sK284: $i > $i ).
thf(func_def_439,type,
sK286: $i > $i ).
thf(func_def_440,type,
sK287: $i > $i ).
thf(func_def_441,type,
sK288: $i > $i ).
thf(func_def_442,type,
sK289: $i > $i ).
thf(func_def_443,type,
sK290: $i > $i ).
thf(func_def_444,type,
sK291: $i > $i > $i > $i ).
thf(func_def_445,type,
sK292: $i > $i ).
thf(func_def_446,type,
sK293: $i > $i ).
thf(func_def_447,type,
sK294: $i > $i ).
thf(func_def_448,type,
sK295: $i > $i ).
thf(func_def_449,type,
sK296: $i > $i > $i ).
thf(func_def_450,type,
sK297: $i > $i > $i > $i ).
thf(func_def_451,type,
sK298: $i > $i > $i > $i ).
thf(func_def_452,type,
sK299: $i > $i > $i > $i ).
thf(func_def_453,type,
sK300: $i > $i > $i ).
thf(func_def_454,type,
sK301: $i > $i > $i ).
thf(func_def_455,type,
sK302: $i > $i > $i ).
thf(func_def_456,type,
sK303: $i > $i > $i ).
thf(func_def_467,type,
sK314: $i > $o ).
thf(func_def_470,type,
sK317: $i > ( $i > $o ) > $i ).
thf(func_def_477,type,
sK324: $i > $i > $i ).
thf(f120,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f124,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
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ! [X1: $i,X2: $i,X0: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(f125,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
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ! [X1: $i,X2: $i,X0: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f124]) ).
thf(f317,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
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f125]) ).
thf(f318,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 )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f317]) ).
thf(f341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
inference(rectify,[],[f120]) ).
thf(f342,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f341]) ).
thf(f387,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 )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f318]) ).
thf(f391,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ),
inference(flattening,[],[f342]) ).
thf(f508,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $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,[],[f387]) ).
thf(f509,plain,
( ( exuE1 = $true )
& ( subsetTrans = $true )
& ( setunionI = $true )
& ( setadjoinAx = $true )
& ( descr__Cong = $true )
& ( powersetI1 = $true )
& ( subPowSU = $true )
& ( dsetconstrI = $true )
& ( sepInPowerset = $true )
& ( emptyinPowerset = $true )
& ( subsetE = $true )
& ( subset2powerset = $true )
& ( dsetconstr__Cong = $true )
& ( noeltsimpempty = $true )
& ( binintersectI = $true )
& ( nonemptyImpWitness = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( setadjoinSub2 = $true )
& ( binintersectSubset3 = $true )
& ( notinsingleton = $true )
& ( disjointsetsI1 = $true )
& ( notequalI1 = $true )
& ( nonemptyI1 = $true )
& ( powersetE1 = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( setoftrueEq = $true )
& ( notdexE = $true )
& ( setext = $true )
& ( binintersectLsub = $true )
& ( setminusI = $true )
& ( notinemptyset = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( powersetsubset = $true )
& ( exu__Cong = $true )
& ( binintersectER = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( notdallE = $true )
& ( emptyI = $true )
& ( quantDeMorgan2 = $true )
& ( vacuousDall = $true )
& ( omegaIndAx = $true )
& ( setadjoinOr = $true )
& ( emptyset__Cong = $true )
& ( binunionIR = $true )
& ( setextAx = $true )
& ( powersetAx = $true )
& ( binintersectSubset5 = $true )
& ( upairset2IR = $true )
& ( in__Cong = $true )
& ( powersetI = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrEL = $true )
& ( powerset__Cong = $true )
& ( subsetI1 = $true )
& ( emptysetE = $true )
& ( emptyE1 = $true )
& ( prop2setI = $true )
& ( setadjoinIR = $true )
& ( exuEu = $true )
& ( binintersectRsub = $true )
& ( subsetI2 = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( binunionLsub = $true )
& ( upairsetIR = $true )
& ( setminusER = $true )
& ( setunion__Cong = $true )
& ( exuE3u = $true )
& ( singletonsswitch = $true )
& ( setadjoinIL = $true )
& ( emptysetsubset = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( setadjoinE = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( notsubsetI = $true )
& ( descrp = $true )
& ( binintersectSubset4 = $true )
& ( inPowerset = $true )
& ( dsetconstrER = $true )
& ( eqimpsubset1 = $true )
& ( binunionEcases = $true )
& ( setadjoinSub = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionE = $true )
& ( exuE2 = $true )
& ( uniqinunit = $true )
& ( emptysetimpfalse = $true )
& ( omega__Cong = $true )
& ( binunionIL = $true )
& ( setminusSubset2 = $true )
& ( setextsub = $true )
& ( setunionAx = $true )
& ( bs114d = $true )
& ( prop2setE = $true )
& ( exuE3e = $true )
& ( subsetRefl = $true )
& ( binintersectEL = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
& ( setadjoin__Cong = $true )
& ( exuI2 = $true )
& ( foundationAx = $true )
& ( setbeta = $true )
& ( binintersectSubset1 = $true )
& ( sepSubset = $true )
& ( notequalI2 = $true )
& ( binintersectSubset2 = $true )
& ( replAx = $true )
& ( binunionE = $true ) ),
inference(flattening,[],[f508]) ).
thf(f515,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f391]) ).
thf(f516,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f515]) ).
thf(f661,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f516]) ).
thf(f662,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true ) ) ) ),
inference(rectify,[],[f661]) ).
thf(f663,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( $true
= ( in @ sK125 @ sK123 ) )
& ( ( in @ sK125 @ sK124 )
!= $true )
& ( ( in @ sK125 @ ( setminus @ sK123 @ sK124 ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123,sK124,sK125]),skolemize(X3,sK123),skolemize(X4,sK124),skolemize(X5,sK125)],[f662]) ).
thf(f691,plain,
( ( exuE1 = $true )
& ( subsetTrans = $true )
& ( setunionI = $true )
& ( setadjoinAx = $true )
& ( descr__Cong = $true )
& ( powersetI1 = $true )
& ( subPowSU = $true )
& ( dsetconstrI = $true )
& ( sepInPowerset = $true )
& ( emptyinPowerset = $true )
& ( subsetE = $true )
& ( subset2powerset = $true )
& ( dsetconstr__Cong = $true )
& ( noeltsimpempty = $true )
& ( binintersectI = $true )
& ( nonemptyImpWitness = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( setadjoinSub2 = $true )
& ( binintersectSubset3 = $true )
& ( notinsingleton = $true )
& ( disjointsetsI1 = $true )
& ( notequalI1 = $true )
& ( nonemptyI1 = $true )
& ( powersetE1 = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( setoftrueEq = $true )
& ( notdexE = $true )
& ( setext = $true )
& ( binintersectLsub = $true )
& ( setminusI = $true )
& ( notinemptyset = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( powersetsubset = $true )
& ( exu__Cong = $true )
& ( binintersectER = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( notdallE = $true )
& ( emptyI = $true )
& ( quantDeMorgan2 = $true )
& ( vacuousDall = $true )
& ( omegaIndAx = $true )
& ( setadjoinOr = $true )
& ( emptyset__Cong = $true )
& ( binunionIR = $true )
& ( setextAx = $true )
& ( powersetAx = $true )
& ( binintersectSubset5 = $true )
& ( upairset2IR = $true )
& ( in__Cong = $true )
& ( powersetI = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrEL = $true )
& ( powerset__Cong = $true )
& ( subsetI1 = $true )
& ( emptysetE = $true )
& ( emptyE1 = $true )
& ( prop2setI = $true )
& ( setadjoinIR = $true )
& ( exuEu = $true )
& ( binintersectRsub = $true )
& ( subsetI2 = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( binunionLsub = $true )
& ( upairsetIR = $true )
& ( setminusER = $true )
& ( setunion__Cong = $true )
& ( exuE3u = $true )
& ( singletonsswitch = $true )
& ( setadjoinIL = $true )
& ( emptysetsubset = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( setadjoinE = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( notsubsetI = $true )
& ( descrp = $true )
& ( binintersectSubset4 = $true )
& ( inPowerset = $true )
& ( dsetconstrER = $true )
& ( eqimpsubset1 = $true )
& ( binunionEcases = $true )
& ( setadjoinSub = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionE = $true )
& ( exuE2 = $true )
& ( uniqinunit = $true )
& ( emptysetimpfalse = $true )
& ( omega__Cong = $true )
& ( binunionIL = $true )
& ( setminusSubset2 = $true )
& ( setextsub = $true )
& ( setunionAx = $true )
& ( bs114d = $true )
& ( prop2setE = $true )
& ( exuE3e = $true )
& ( subsetRefl = $true )
& ( binintersectEL = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) )
& ( setadjoin__Cong = $true )
& ( exuI2 = $true )
& ( foundationAx = $true )
& ( setbeta = $true )
& ( binintersectSubset1 = $true )
& ( sepSubset = $true )
& ( notequalI2 = $true )
& ( binintersectSubset2 = $true )
& ( replAx = $true )
& ( binunionE = $true ) ),
inference(rectify,[],[f509]) ).
thf(f692,plain,
( ( exuE1 = $true )
& ( subsetTrans = $true )
& ( setunionI = $true )
& ( setadjoinAx = $true )
& ( descr__Cong = $true )
& ( powersetI1 = $true )
& ( subPowSU = $true )
& ( dsetconstrI = $true )
& ( sepInPowerset = $true )
& ( emptyinPowerset = $true )
& ( subsetE = $true )
& ( subset2powerset = $true )
& ( dsetconstr__Cong = $true )
& ( noeltsimpempty = $true )
& ( binintersectI = $true )
& ( nonemptyImpWitness = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( setadjoinSub2 = $true )
& ( binintersectSubset3 = $true )
& ( notinsingleton = $true )
& ( disjointsetsI1 = $true )
& ( notequalI1 = $true )
& ( nonemptyI1 = $true )
& ( powersetE1 = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( setoftrueEq = $true )
& ( notdexE = $true )
& ( setext = $true )
& ( binintersectLsub = $true )
& ( setminusI = $true )
& ( notinemptyset = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( powersetsubset = $true )
& ( exu__Cong = $true )
& ( binintersectER = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( notdallE = $true )
& ( emptyI = $true )
& ( quantDeMorgan2 = $true )
& ( vacuousDall = $true )
& ( omegaIndAx = $true )
& ( setadjoinOr = $true )
& ( emptyset__Cong = $true )
& ( binunionIR = $true )
& ( setextAx = $true )
& ( powersetAx = $true )
& ( binintersectSubset5 = $true )
& ( upairset2IR = $true )
& ( in__Cong = $true )
& ( powersetI = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrEL = $true )
& ( powerset__Cong = $true )
& ( subsetI1 = $true )
& ( emptysetE = $true )
& ( emptyE1 = $true )
& ( prop2setI = $true )
& ( setadjoinIR = $true )
& ( exuEu = $true )
& ( binintersectRsub = $true )
& ( subsetI2 = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( binunionLsub = $true )
& ( upairsetIR = $true )
& ( setminusER = $true )
& ( setunion__Cong = $true )
& ( exuE3u = $true )
& ( singletonsswitch = $true )
& ( setadjoinIL = $true )
& ( emptysetsubset = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( setadjoinE = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( notsubsetI = $true )
& ( descrp = $true )
& ( binintersectSubset4 = $true )
& ( inPowerset = $true )
& ( dsetconstrER = $true )
& ( eqimpsubset1 = $true )
& ( binunionEcases = $true )
& ( setadjoinSub = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionE = $true )
& ( exuE2 = $true )
& ( uniqinunit = $true )
& ( emptysetimpfalse = $true )
& ( omega__Cong = $true )
& ( binunionIL = $true )
& ( setminusSubset2 = $true )
& ( setextsub = $true )
& ( setunionAx = $true )
& ( bs114d = $true )
& ( prop2setE = $true )
& ( exuE3e = $true )
& ( subsetRefl = $true )
& ( binintersectEL = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ( $true
!= ( in @ sK151 @ ( setminus @ sK153 @ sK152 ) ) )
& ( ( in @ sK151 @ sK153 )
= $true )
& ( ( in @ sK151 @ sK152 )
!= $true )
& ( setadjoin__Cong = $true )
& ( exuI2 = $true )
& ( foundationAx = $true )
& ( setbeta = $true )
& ( binintersectSubset1 = $true )
& ( sepSubset = $true )
& ( notequalI2 = $true )
& ( binintersectSubset2 = $true )
& ( replAx = $true )
& ( binunionE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151,sK152,sK153]),skolemize(X0,sK151),skolemize(X1,sK152),skolemize(X2,sK153)],[f691]) ).
thf(f1053,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( setminusI != $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f663]) ).
thf(f1102,plain,
( ( in @ sK151 @ sK152 )
!= $true ),
inference(cnf_transformation,[],[f692]) ).
thf(f1103,plain,
( ( in @ sK151 @ sK153 )
= $true ),
inference(cnf_transformation,[],[f692]) ).
thf(f1104,plain,
( $true
!= ( in @ sK151 @ ( setminus @ sK153 @ sK152 ) ) ),
inference(cnf_transformation,[],[f692]) ).
thf(f1184,plain,
setminusI = $true,
inference(cnf_transformation,[],[f692]) ).
thf(f1634,definition,
( spl331_1
<=> ( ( in @ sK151 @ sK152 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl331_1])],[avatar_definition]) ).
thf(f1636,plain,
( ( ( in @ sK151 @ sK152 )
!= $true )
| spl331_1 ),
inference(avatar_component_clause,[],[f1634]) ).
thf(f1637,plain,
~ spl331_1,
inference(avatar_split_clause,[],[f1102,f1634]) ).
thf(f2380,definition,
( spl331_172
<=> ( ( in @ sK151 @ sK153 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl331_172])],[avatar_definition]) ).
thf(f2382,plain,
( ( ( in @ sK151 @ sK153 )
= $true )
| ~ spl331_172 ),
inference(avatar_component_clause,[],[f2380]) ).
thf(f2383,plain,
spl331_172,
inference(avatar_split_clause,[],[f1103,f2380]) ).
thf(f2477,definition,
( spl331_194
<=> ( setminusI = $true ) ),
introduced(definition,[new_symbols(definition,[spl331_194])],[avatar_definition]) ).
thf(f2647,definition,
( spl331_230
<=> ( $true
= ( in @ sK151 @ ( setminus @ sK153 @ sK152 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl331_230])],[avatar_definition]) ).
thf(f2649,plain,
( ( $true
!= ( in @ sK151 @ ( setminus @ sK153 @ sK152 ) ) )
| spl331_230 ),
inference(avatar_component_clause,[],[f2647]) ).
thf(f2650,plain,
~ spl331_230,
inference(avatar_split_clause,[],[f1104,f2647]) ).
thf(f2993,definition,
( spl331_306
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl331_306])],[avatar_definition]) ).
thf(f2994,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ~ spl331_306 ),
inference(avatar_component_clause,[],[f2993]) ).
thf(f2995,plain,
( ~ spl331_194
| spl331_306 ),
inference(avatar_split_clause,[],[f1053,f2993,f2477]) ).
thf(f4163,plain,
spl331_194,
inference(avatar_split_clause,[],[f1184,f2477]) ).
thf(f5606,plain,
( ( $true != $true )
| ( ( in @ sK151 @ sK153 )
!= $true )
| ( ( in @ sK151 @ sK152 )
= $true )
| spl331_230
| ~ spl331_306 ),
inference(superposition,[],[f2649,f2994]) ).
thf(f5608,plain,
( ( ( in @ sK151 @ sK152 )
= $true )
| ( ( in @ sK151 @ sK153 )
!= $true )
| spl331_230
| ~ spl331_306 ),
inference(trivial_inequality_removal,[],[f5606]) ).
thf(f5622,plain,
( ( ( in @ sK151 @ sK153 )
!= $true )
| spl331_1
| spl331_230
| ~ spl331_306 ),
inference(forward_subsumption_resolution,[],[f5608,f1636]) ).
thf(f5623,plain,
( $false
| spl331_1
| ~ spl331_172
| spl331_230
| ~ spl331_306 ),
inference(forward_subsumption_resolution,[],[f5622,f2382]) ).
thf(f5624,plain,
( spl331_1
| ~ spl331_172
| spl331_230
| ~ spl331_306 ),
inference(avatar_contradiction_clause,[],[f5623]) ).
cnf(s1,plain,
~ spl331_1,
inference(sat_conversion,[],[f1637]) ).
cnf(s112,plain,
spl331_172,
inference(sat_conversion,[],[f2383]) ).
cnf(s164,plain,
~ spl331_230,
inference(sat_conversion,[],[f2650]) ).
cnf(s231,plain,
( ~ spl331_194
| spl331_306 ),
inference(sat_conversion,[],[f2995]) ).
cnf(s545,plain,
spl331_194,
inference(sat_conversion,[],[f4163]) ).
cnf(s608,plain,
( spl331_1
| ~ spl331_172
| spl331_230
| ~ spl331_306 ),
inference(sat_conversion,[],[f5624]) ).
cnf(s681,plain,
spl331_306,
inference(rat,[],[s231,s545]) ).
cnf(s720,plain,
spl331_1,
inference(rat,[],[s608,s681,s164,s112]) ).
cnf(s767,plain,
$false,
inference(rat,[],[s1,s720]) ).
thf(f5625,plain,
$false,
inference(avatar_sat_refutation,[],[s767]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU605^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n002.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:59:38 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.21/0.27 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
% 0.65/0.42 % (1326093)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.65/0.42 % (1326101)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=4220923827: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)
% 0.65/0.42 % (1326099)lrs+10_16_si=on:nwc=1.5:random_seed=3519949540:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.65/0.42 % (1326100)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2413184139:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.65/0.42 % (1326102)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3676127232:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.65/0.42 % (1326098)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3310149012:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.65/0.42 % (1326104)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.65/0.42 % (1326104)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
% 0.65/0.42 % (1326100)Instruction limit reached!
% 0.65/0.42 % (1326100)------------------------------
% 0.65/0.42 % (1326100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.42 % (1326100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.42 % (1326100)CaDiCaL version: 2.1.3
% 0.65/0.42 % (1326100)Termination reason: Instruction limit
% 0.65/0.42 % (1326100)Termination phase: shuffling
% 0.65/0.42 % (1326100)Time elapsed: 0.002 s
% 0.65/0.42 % (1326100)Peak memory usage: 10 MB
% 0.65/0.42 % (1326100)Instructions burned: 4 (million)
% 0.65/0.42 % (1326103)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2437259736:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.65/0.42 % (1326104)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=3476780789:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.65/0.42 % (1326099)Instruction limit reached!
% 0.65/0.42 % (1326099)------------------------------
% 0.65/0.42 % (1326099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.42 % (1326099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.42 % (1326099)CaDiCaL version: 2.1.3
% 0.65/0.42 % (1326099)Termination reason: Instruction limit
% 0.65/0.42 % (1326099)Termination phase: Property scanning
% 0.65/0.42 % (1326099)Time elapsed: 0.009 s
% 0.65/0.42 % (1326099)Peak memory usage: 10 MB
% 0.65/0.42 % (1326099)Instructions burned: 19 (million)
% 0.65/0.42 % (1326102)Instruction limit reached!
% 0.65/0.42 % (1326102)------------------------------
% 0.65/0.42 % (1326102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.42 % (1326102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.42 % (1326102)CaDiCaL version: 2.1.3
% 0.65/0.42 % (1326102)Termination reason: Instruction limit
% 0.65/0.42 % (1326102)Termination phase: Preprocessing 3
% 0.65/0.42 % (1326102)Time elapsed: 0.012 s
% 0.65/0.42 % (1326102)Peak memory usage: 11 MB
% 0.65/0.42 % (1326102)Instructions burned: 25 (million)
% 0.65/0.42 % (1326114)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.42 % (1326113)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3064597400:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.65/0.42 % (1326110)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2513468817:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.42 % (1326113)Instruction limit reached!
% 0.65/0.42 % (1326113)------------------------------
% 0.65/0.42 % (1326113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.42 % (1326113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.42 % (1326113)CaDiCaL version: 2.1.3
% 0.65/0.42 % (1326113)Termination reason: Instruction limit
% 0.65/0.45 % (1326113)Termination phase: shuffling
% 0.65/0.45 % (1326113)Time elapsed: 0.003 s
% 0.65/0.45 % (1326113)Peak memory usage: 10 MB
% 0.65/0.45 % (1326113)Instructions burned: 5 (million)
% 0.65/0.45 % (1326114)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=340282233:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.65/0.45 % (1326110)Instruction limit reached!
% 0.65/0.45 % (1326110)------------------------------
% 0.65/0.45 % (1326110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326110)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326110)Termination reason: Instruction limit
% 0.65/0.45 % (1326110)Termination phase: shuffling
% 0.65/0.45 % (1326110)Time elapsed: 0.002 s
% 0.65/0.45 % (1326110)Peak memory usage: 10 MB
% 0.65/0.45 % (1326110)Instructions burned: 2 (million)
% 0.65/0.45 % (1326114)Instruction limit reached!
% 0.65/0.45 % (1326114)------------------------------
% 0.65/0.45 % (1326114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326114)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326114)Termination reason: Instruction limit
% 0.65/0.45 % (1326114)Termination phase: shuffling
% 0.65/0.45 % (1326114)Time elapsed: 0.003 s
% 0.65/0.45 % (1326114)Peak memory usage: 10 MB
% 0.65/0.45 % (1326114)Instructions burned: 7 (million)
% 0.65/0.45 % (1326098)Instruction limit reached!
% 0.65/0.45 % (1326098)------------------------------
% 0.65/0.45 % (1326098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326098)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326098)Termination reason: Instruction limit
% 0.65/0.45 % (1326098)Termination phase: Saturation
% 0.65/0.45 % (1326098)Time elapsed: 0.039 s
% 0.65/0.45 % (1326098)Peak memory usage: 13 MB
% 0.65/0.45 % (1326098)Instructions burned: 89 (million)
% 0.65/0.45 % (1326103)Instruction limit reached!
% 0.65/0.45 % (1326103)------------------------------
% 0.65/0.45 % (1326103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326103)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326103)Termination reason: Instruction limit
% 0.65/0.45 % (1326103)Termination phase: Saturation
% 0.65/0.45 % (1326103)Time elapsed: 0.035 s
% 0.65/0.45 % (1326103)Peak memory usage: 13 MB
% 0.65/0.45 % (1326103)Instructions burned: 76 (million)
% 0.65/0.45 % (1326118)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1221388358:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.65/0.45 % (1326121)lrs+10_1_si=on:cs=on:random_seed=685590765:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.65/0.45 % (1326118)Instruction limit reached!
% 0.65/0.45 % (1326118)------------------------------
% 0.65/0.45 % (1326118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326118)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326118)Termination reason: Instruction limit
% 0.65/0.45 % (1326118)Termination phase: Property scanning
% 0.65/0.45 % (1326118)Time elapsed: 0.006 s
% 0.65/0.45 % (1326118)Peak memory usage: 10 MB
% 0.65/0.45 % (1326118)Instructions burned: 14 (million)
% 0.65/0.45 % (1326120)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=2468345586:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.65/0.45 % (1326121)Instruction limit reached!
% 0.65/0.45 % (1326121)------------------------------
% 0.65/0.45 % (1326121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326121)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326121)Termination reason: Instruction limit
% 0.65/0.45 % (1326121)Termination phase: shuffling
% 0.65/0.45 % (1326121)Time elapsed: 0.004 s
% 0.65/0.45 % (1326121)Peak memory usage: 10 MB
% 0.65/0.45 % (1326121)Instructions burned: 8 (million)
% 0.65/0.45 % (1326119)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
% 0.65/0.45 % (1326122)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.65/0.45 % (1326119)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.45 % (1326119)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=428411644:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.65/0.45 % (1326122)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=3649766444:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.45 % (1326122)Instruction limit reached!
% 0.65/0.45 % (1326122)------------------------------
% 0.65/0.45 % (1326122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326122)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326122)Termination reason: Instruction limit
% 0.65/0.45 % (1326122)Termination phase: shuffling
% 0.65/0.45 % (1326122)Time elapsed: 0.003 s
% 0.65/0.45 % (1326122)Peak memory usage: 10 MB
% 0.65/0.45 % (1326122)Instructions burned: 3 (million)
% 0.65/0.45 % (1326125)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=198681121:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.65/0.45 % (1326119)Instruction limit reached!
% 0.65/0.45 % (1326119)------------------------------
% 0.65/0.45 % (1326119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326119)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326119)Termination reason: Instruction limit
% 0.65/0.45 % (1326119)Termination phase: Property scanning
% 0.65/0.45 % (1326119)Time elapsed: 0.012 s
% 0.65/0.45 % (1326119)Peak memory usage: 11 MB
% 0.65/0.45 % (1326119)Instructions burned: 29 (million)
% 0.65/0.45 % (1326127)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2650379308:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.65/0.45 % (1326104)Instruction limit reached!
% 0.65/0.45 % (1326104)------------------------------
% 0.65/0.45 % (1326104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326104)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326104)Termination reason: Instruction limit
% 0.65/0.45 % (1326104)Termination phase: Saturation
% 0.65/0.45 % (1326104)Time elapsed: 0.082 s
% 0.65/0.45 % (1326104)Peak memory usage: 14 MB
% 0.65/0.45 % (1326104)Instructions burned: 159 (million)
% 0.65/0.45 % (1326130)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=274596767:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.65/0.45 % (1326125)Instruction limit reached!
% 0.65/0.45 % (1326125)------------------------------
% 0.65/0.45 % (1326125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326125)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326125)Termination reason: Instruction limit
% 0.65/0.45 % (1326125)Termination phase: Property scanning
% 0.65/0.45 % (1326125)Time elapsed: 0.019 s
% 0.65/0.45 % (1326125)Peak memory usage: 12 MB
% 0.65/0.45 % (1326125)Instructions burned: 39 (million)
% 0.65/0.45 % (1326132)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1115384297:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.45 % (1326130)Instruction limit reached!
% 0.65/0.45 % (1326130)------------------------------
% 0.65/0.45 % (1326130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326130)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326130)Termination reason: Instruction limit
% 0.65/0.45 % (1326130)Termination phase: Preprocessing 3
% 0.65/0.45 % (1326130)Time elapsed: 0.012 s
% 0.65/0.45 % (1326130)Peak memory usage: 11 MB
% 0.65/0.45 % (1326130)Instructions burned: 25 (million)
% 0.65/0.45 % (1326120)Instruction limit reached!
% 0.65/0.45 % (1326120)------------------------------
% 0.65/0.45 % (1326120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326120)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326120)Termination reason: Instruction limit
% 0.65/0.45 % (1326120)Termination phase: Saturation
% 0.65/0.45 % (1326120)Time elapsed: 0.052 s
% 0.65/0.45 % (1326120)Peak memory usage: 13 MB
% 0.65/0.45 % (1326120)Instructions burned: 86 (million)
% 0.65/0.45 % (1326132)Instruction limit reached!
% 0.65/0.45 % (1326132)------------------------------
% 0.65/0.45 % (1326132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326132)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326132)Termination reason: Instruction limit
% 0.65/0.45 % (1326132)Termination phase: Property scanning
% 0.65/0.45 % (1326132)Time elapsed: 0.014 s
% 0.65/0.45 % (1326132)Peak memory usage: 10 MB
% 0.65/0.45 % (1326132)Instructions burned: 15 (million)
% 0.65/0.45 % (1326136)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4226518828:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.65/0.45 % (1326134)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1946185561:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.65/0.45 % (1326136)Instruction limit reached!
% 0.65/0.45 % (1326136)------------------------------
% 0.65/0.45 % (1326136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326136)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326136)Termination reason: Instruction limit
% 0.65/0.45 % (1326136)Termination phase: Property scanning
% 0.65/0.45 % (1326136)Time elapsed: 0.007 s
% 0.65/0.45 % (1326136)Peak memory usage: 10 MB
% 0.65/0.45 % (1326136)Instructions burned: 16 (million)
% 0.65/0.45 % (1326101) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1326093-1326101"...
% 0.65/0.45 % (1326101)...printing done.
% 0.65/0.45 % (1326101)Refutation found. Thanks to Tanya!
% 0.65/0.45 % SZS status Theorem for theBenchmark
% 0.65/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.65/0.45 % (1326101)------------------------------
% 0.65/0.45 % (1326101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1326101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1326101)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1326101)Termination reason: Refutation
% 0.65/0.45 % (1326101)Time elapsed: 0.130 s
% 0.65/0.45 % (1326101)Peak memory usage: 17 MB
% 0.65/0.45 % (1326101)Instructions burned: 243 (million)
% 0.65/0.45 % (1326093)Success in time 0.169 s
% 0.65/0.45 % Vampire exiting
%------------------------------------------------------------------------------