%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU623^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:30:22 AM UTC 2026
% Result : Theorem 0.40s 0.25s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 29 unt; 0 typ; 10 def)
% Number of atoms : 3086 ( 829 equ; 0 cnn)
% Maximal formula atoms : 142 ( 33 avg)
% Number of connectives : 1709 ( 97 ~; 85 |; 578 &; 364 @)
% ( 16 <=>; 569 =>; 0 <=; 0 <~>)
% Maximal formula depth : 149 ( 16 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 : 299 ( 296 usr; 171 con; 0-4 aty)
% Number of variables : 105 ( 0 sgn 82 !; 23 ?; 105 :)
% 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_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_164,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_167,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_168,type,
vAND: $o > $o > $o ).
thf(func_def_169,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_170,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_171,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_172,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_173,type,
vIMP: $o > $o > $o ).
thf(func_def_174,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_175,type,
vNOT: $o > $o ).
thf(func_def_176,type,
sP0: $i > $i > $o ).
thf(func_def_177,type,
sP1: $i > $o ).
thf(func_def_178,type,
sP2: $o ).
thf(func_def_187,type,
sK11: $i > $i > $i ).
thf(func_def_188,type,
sK12: $i > $i > $i ).
thf(func_def_201,type,
sK25: $i > $o ).
thf(func_def_204,type,
sK28: $i > ( $i > $o ) > $i ).
thf(func_def_214,type,
sK38: ( $i > $o ) > $i ).
thf(func_def_215,type,
sK39: $i > $o ).
thf(func_def_216,type,
sK40: $i > $i ).
thf(func_def_229,type,
sK53: $i > $o ).
thf(func_def_230,type,
sK54: $i > $o ).
thf(func_def_232,type,
sK56: $i > $i ).
thf(func_def_235,type,
sK59: $i > $i ).
thf(func_def_239,type,
sK63: $o ).
thf(func_def_240,type,
sK64: $i > $o ).
thf(func_def_242,type,
sK66: ( $i > $o ) > $i ).
thf(func_def_243,type,
sK67: ( $i > $o ) > $i ).
thf(func_def_250,type,
sK74: $i > $i ).
thf(func_def_260,type,
sK84: ( $i > $o ) > $i ).
thf(func_def_261,type,
sK85: $i > $o ).
thf(func_def_264,type,
sK88: ( $i > $o ) > $i ).
thf(func_def_265,type,
sK89: $i > $o ).
thf(func_def_266,type,
sK90: $i > $i ).
thf(func_def_267,type,
sK91: $i > $o ).
thf(func_def_270,type,
sK94: $i > $o ).
thf(func_def_295,type,
sK119: $o ).
thf(func_def_310,type,
sK134: $i > $i > $i ).
thf(func_def_320,type,
sK144: $i > $i ).
thf(func_def_325,type,
sK149: $i > $o ).
thf(func_def_327,type,
sK151: ( $i > $o ) > $i > $i ).
thf(func_def_329,type,
sK153: $i > $o ).
thf(func_def_334,type,
sK158: $o ).
thf(func_def_340,type,
sK164: $i > $o ).
thf(func_def_345,type,
sK169: $i > $i > $i ).
thf(func_def_348,type,
sK172: $i > ( $i > $o ) > $i ).
thf(func_def_349,type,
sK173: $i > $o ).
thf(func_def_352,type,
sK176: $i > $o ).
thf(func_def_353,type,
sK177: $i > $o ).
thf(func_def_354,type,
sK178: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_355,type,
sK179: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_365,type,
sK189: $i > $o ).
thf(func_def_366,type,
sK190: $i > $o ).
thf(func_def_367,type,
sK191: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_368,type,
sK192: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_371,type,
sK195: $i > ( $i > $o ) > $i ).
thf(func_def_372,type,
sK196: $i > $o ).
thf(func_def_377,type,
sK201: $i > $i > $i ).
thf(func_def_382,type,
sK206: $i > $o ).
thf(func_def_387,type,
sK211: $i > $o ).
thf(func_def_390,type,
sK214: $i > ( $i > $o ) > $i ).
thf(func_def_400,type,
sK224: $i > $o ).
thf(func_def_408,type,
sK232: $i > $i ).
thf(func_def_409,type,
sK233: $o > $i > $i > $i ).
thf(func_def_412,type,
sK236: $o ).
thf(func_def_418,type,
sK242: $i > $o ).
thf(func_def_422,type,
sK246: $i > $o ).
thf(func_def_424,type,
sK248: ( $i > $o ) > $i > $i ).
thf(func_def_429,type,
sK253: $i > $i ).
thf(func_def_430,type,
sK254: $i > $i ).
thf(func_def_431,type,
sK255: $i > $i ).
thf(func_def_432,type,
sK256: $i > $i ).
thf(func_def_433,type,
sK257: $i > $i ).
thf(func_def_434,type,
sK258: $i > $i > $i > $i ).
thf(func_def_435,type,
sK259: $i > $i ).
thf(func_def_436,type,
sK260: $i > $i ).
thf(func_def_437,type,
sK261: $i > $i ).
thf(func_def_438,type,
sK262: $i > $i ).
thf(func_def_439,type,
sK263: $i > $i > $i ).
thf(func_def_440,type,
sK264: $i > $i > $i ).
thf(func_def_441,type,
sK265: $i > $i > $i > $i ).
thf(func_def_442,type,
sK266: $i > $i > $i > $i ).
thf(func_def_443,type,
sK267: $i > $i > $i > $i ).
thf(func_def_444,type,
sK268: $i > $i > $i ).
thf(func_def_445,type,
sK269: $i > $i > $i ).
thf(func_def_446,type,
sK270: $i > $i > $i ).
thf(func_def_450,type,
sK274: $i > $i > $i ).
thf(func_def_464,type,
sK288: $o ).
thf(func_def_473,type,
sK297: $i > $o ).
thf(func_def_476,type,
sK300: $i > $i ).
thf(func_def_478,type,
sK302: $i > ( $i > $i > $o ) > $i ).
thf(func_def_479,type,
sK303: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_480,type,
sK304: $i > ( $i > $i > $o ) > $i ).
thf(func_def_481,type,
sK305: $i > $i > $o ).
thf(func_def_483,type,
sK307: $i > $i ).
thf(func_def_484,type,
sK308: $i > $i ).
thf(func_def_487,type,
sK311: $i > $i > $i ).
thf(func_def_493,type,
sK317: $i > $i > $i ).
thf(func_def_494,type,
sK318: $i > $o ).
thf(func_def_497,type,
sK321: $o ).
thf(func_def_507,type,
sK331: $i > $i > $i ).
thf(func_def_512,type,
sK336: $i > ( $i > $o ) > $i ).
thf(func_def_513,type,
sK337: $i > $o ).
thf(func_def_518,type,
sK342: $i > $o ).
thf(func_def_522,type,
sK346: $i > $o ).
thf(func_def_523,type,
sK347: $i > $o ).
thf(func_def_524,type,
sK348: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_525,type,
sK349: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_526,type,
sK350: $i > ( $i > $o ) > $i ).
thf(func_def_527,type,
sK351: $i > $o ).
thf(func_def_533,type,
sK357: $o ).
thf(func_def_545,type,
sK369: $o ).
thf(func_def_547,type,
sK371: $i > $i ).
thf(f92,axiom,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= subset2powerset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(f101,axiom,
( binunionIL
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(f143,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
=> ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 ) )
= singletonsubset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(f145,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
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(f146,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
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f145]) ).
thf(f189,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= subset2powerset ),
inference(rectify,[],[f92]) ).
thf(f190,plain,
( ( subset2powerset = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f189]) ).
thf(f211,plain,
( binunionIL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f101]) ).
thf(f212,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) )
<=> ( binunionIL = $true ) ),
inference(fool_elimination,[],[f211]) ).
thf(f294,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
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f146]) ).
thf(f295,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 )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f294]) ).
thf(f322,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
=> ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 ) )
= singletonsubset ),
inference(rectify,[],[f143]) ).
thf(f323,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true ) )
<=> ( singletonsubset = $true ) ),
inference(fool_elimination,[],[f322]) ).
thf(f494,plain,
( ( binunionIL = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f212]) ).
thf(f546,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
<=> ( subset2powerset = $true ) ),
inference(ennf_transformation,[],[f190]) ).
thf(f572,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( singletonsubset = $true ) ),
inference(ennf_transformation,[],[f323]) ).
thf(f593,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) )
!= $true ) )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( 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,[],[f295]) ).
thf(f594,plain,
( ( eqimpsubset2 = $true )
& ( in__Cong = $true )
& ( upairsetIL = $true )
& ( exuE1 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionIR = $true )
& ( noeltsimpempty = $true )
& ( setminusSubset2 = $true )
& ( subsetE2 = $true )
& ( powersetI = $true )
& ( sepSubset = $true )
& ( emptyE1 = $true )
& ( exuI2 = $true )
& ( exu__Cong = $true )
& ( omegaIndAx = $true )
& ( emptysetimpfalse = $true )
& ( exuE2 = $true )
& ( exuI1 = $true )
& ( setminusIRneg = $true )
& ( powerset__Cong = $true )
& ( exuE3e = $true )
& ( setukpairIR = $true )
& ( omega0Ax = $true )
& ( notequalI1 = $true )
& ( binintersectSubset4 = $true )
& ( powersetsubset = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( singletonsubset = $true )
& ( upairset2IR = $true )
& ( notinsingleton = $true )
& ( notdallE = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE1 = $true )
& ( exuEu = $true )
& ( binintersectSubset1 = $true )
& ( symdiffI2 = $true )
& ( powersetI1 = $true )
& ( setextAx = $true )
& ( binintersectSubset3 = $true )
& ( binintersectI = $true )
& ( binunionEcases = $true )
& ( subsetE = $true )
& ( setminusI = $true )
& ( setadjoin__Cong = $true )
& ( powersetE = $true )
& ( dsetconstrER = $true )
& ( setminusELneg = $true )
& ( setunionAx = $true )
& ( setunionE = $true )
& ( binunionLsub = $true )
& ( inCongP = $true )
& ( notdexE = $true )
& ( subsetRefl = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( setoftrueEq = $true )
& ( exuE3u = $true )
& ( singletoninpowerset = $true )
& ( binunionRsub = $true )
& ( emptysetE = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( setunionI = $true )
& ( symdiffIneg1 = $true )
& ( subsetI2 = $true )
& ( sepInPowerset = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan3 = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset5 = $true )
& ( wellorderingAx = $true )
& ( dsetconstr__Cong = $true )
& ( uniqinunit = $true )
& ( exuI3 = $true )
& ( setukpairIL = $true )
& ( inPowerset = $true )
& ( setminusERneg = $true )
& ( binintersectRsub = $true )
& ( bs114d = $true )
& ( subsetTrans = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinIL = $true )
& ( setext = $true )
& ( setminusLsub = $true )
& ( setunion__Cong = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) )
!= $true ) )
& ( powersetAx = $true )
& ( notsubsetI = $true )
& ( omega__Cong = $true )
& ( nonemptyI = $true )
& ( kpairiskpair = $true )
& ( eqinunit = $true )
& ( setextsub = $true )
& ( binintersectLsub = $true )
& ( vacuousDall = $true )
& ( descr__Cong = $true )
& ( upairsetIR = $true )
& ( prop2setI = $true )
& ( symdiffI1 = $true )
& ( binintersectEL = $true )
& ( emptyinPowerset = $true )
& ( singletonsswitch = $true )
& ( subset2powerset = $true )
& ( prop2set2propI = $true )
& ( emptyset__Cong = $true )
& ( symdiffE = $true )
& ( prop2setE = $true )
& ( binunionIL = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub = $true )
& ( setadjoinOr = $true )
& ( setadjoinSub2 = $true )
& ( upairsetE = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset1 = $true )
& ( setminusILneg = $true )
& ( symdiffIneg2 = $true )
& ( secondinupair = $true )
& ( foundationAx = $true )
& ( descrp = $true )
& ( setadjoinE = $true )
& ( subPowSU = $true )
& ( emptysetsubset = $true )
& ( emptyinunitempty = $true )
& ( setbeta = $true )
& ( binunionE = $true )
& ( setminusEL = $true )
& ( kpairp = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetAx = $true )
& ( setminusER = $true )
& ( notequalI2 = $true ) ),
inference(flattening,[],[f593]) ).
thf(f759,plain,
( ( ( binunionIL = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(nnf_transformation,[],[f494]) ).
thf(f760,plain,
( ( ( binunionIL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(rectify,[],[f759]) ).
thf(f761,plain,
( ( ( binunionIL = $true )
| ( ( ( in @ sK130 @ sK131 )
= $true )
& ( ( in @ sK130 @ ( binunion @ sK131 @ sK129 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129,sK130,sK131]),skolemize(X0,sK129),skolemize(X1,sK130),skolemize(X2,sK131)],[f760]) ).
thf(f919,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( singletonsubset != $true ) )
& ( ( singletonsubset = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f572]) ).
thf(f920,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( singletonsubset != $true ) )
& ( ( singletonsubset = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
!= $true )
& ( ( in @ X2 @ X3 )
= $true ) ) ) ),
inference(rectify,[],[f919]) ).
thf(f921,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( singletonsubset != $true ) )
& ( ( singletonsubset = $true )
| ( ( ( subset @ ( setadjoin @ sK276 @ emptyset ) @ sK277 )
!= $true )
& ( ( in @ sK276 @ sK277 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276,sK277]),skolemize(X2,sK276),skolemize(X3,sK277)],[f920]) ).
thf(f1007,plain,
( ( eqimpsubset2 = $true )
& ( in__Cong = $true )
& ( upairsetIL = $true )
& ( exuE1 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionIR = $true )
& ( noeltsimpempty = $true )
& ( setminusSubset2 = $true )
& ( subsetE2 = $true )
& ( powersetI = $true )
& ( sepSubset = $true )
& ( emptyE1 = $true )
& ( exuI2 = $true )
& ( exu__Cong = $true )
& ( omegaIndAx = $true )
& ( emptysetimpfalse = $true )
& ( exuE2 = $true )
& ( exuI1 = $true )
& ( setminusIRneg = $true )
& ( powerset__Cong = $true )
& ( exuE3e = $true )
& ( setukpairIR = $true )
& ( omega0Ax = $true )
& ( notequalI1 = $true )
& ( binintersectSubset4 = $true )
& ( powersetsubset = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( singletonsubset = $true )
& ( upairset2IR = $true )
& ( notinsingleton = $true )
& ( notdallE = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE1 = $true )
& ( exuEu = $true )
& ( binintersectSubset1 = $true )
& ( symdiffI2 = $true )
& ( powersetI1 = $true )
& ( setextAx = $true )
& ( binintersectSubset3 = $true )
& ( binintersectI = $true )
& ( binunionEcases = $true )
& ( subsetE = $true )
& ( setminusI = $true )
& ( setadjoin__Cong = $true )
& ( powersetE = $true )
& ( dsetconstrER = $true )
& ( setminusELneg = $true )
& ( setunionAx = $true )
& ( setunionE = $true )
& ( binunionLsub = $true )
& ( inCongP = $true )
& ( notdexE = $true )
& ( subsetRefl = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( setoftrueEq = $true )
& ( exuE3u = $true )
& ( singletoninpowerset = $true )
& ( binunionRsub = $true )
& ( emptysetE = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( setunionI = $true )
& ( symdiffIneg1 = $true )
& ( subsetI2 = $true )
& ( sepInPowerset = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan3 = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset5 = $true )
& ( wellorderingAx = $true )
& ( dsetconstr__Cong = $true )
& ( uniqinunit = $true )
& ( exuI3 = $true )
& ( setukpairIL = $true )
& ( inPowerset = $true )
& ( setminusERneg = $true )
& ( binintersectRsub = $true )
& ( bs114d = $true )
& ( subsetTrans = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinIL = $true )
& ( setext = $true )
& ( setminusLsub = $true )
& ( setunion__Cong = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true ) )
& ( powersetAx = $true )
& ( notsubsetI = $true )
& ( omega__Cong = $true )
& ( nonemptyI = $true )
& ( kpairiskpair = $true )
& ( eqinunit = $true )
& ( setextsub = $true )
& ( binintersectLsub = $true )
& ( vacuousDall = $true )
& ( descr__Cong = $true )
& ( upairsetIR = $true )
& ( prop2setI = $true )
& ( symdiffI1 = $true )
& ( binintersectEL = $true )
& ( emptyinPowerset = $true )
& ( singletonsswitch = $true )
& ( subset2powerset = $true )
& ( prop2set2propI = $true )
& ( emptyset__Cong = $true )
& ( symdiffE = $true )
& ( prop2setE = $true )
& ( binunionIL = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub = $true )
& ( setadjoinOr = $true )
& ( setadjoinSub2 = $true )
& ( upairsetE = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset1 = $true )
& ( setminusILneg = $true )
& ( symdiffIneg2 = $true )
& ( secondinupair = $true )
& ( foundationAx = $true )
& ( descrp = $true )
& ( setadjoinE = $true )
& ( subPowSU = $true )
& ( emptysetsubset = $true )
& ( emptyinunitempty = $true )
& ( setbeta = $true )
& ( binunionE = $true )
& ( setminusEL = $true )
& ( kpairp = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetAx = $true )
& ( setminusER = $true )
& ( notequalI2 = $true ) ),
inference(rectify,[],[f594]) ).
thf(f1008,plain,
( ( eqimpsubset2 = $true )
& ( in__Cong = $true )
& ( upairsetIL = $true )
& ( exuE1 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionIR = $true )
& ( noeltsimpempty = $true )
& ( setminusSubset2 = $true )
& ( subsetE2 = $true )
& ( powersetI = $true )
& ( sepSubset = $true )
& ( emptyE1 = $true )
& ( exuI2 = $true )
& ( exu__Cong = $true )
& ( omegaIndAx = $true )
& ( emptysetimpfalse = $true )
& ( exuE2 = $true )
& ( exuI1 = $true )
& ( setminusIRneg = $true )
& ( powerset__Cong = $true )
& ( exuE3e = $true )
& ( setukpairIR = $true )
& ( omega0Ax = $true )
& ( notequalI1 = $true )
& ( binintersectSubset4 = $true )
& ( powersetsubset = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( singletonsubset = $true )
& ( upairset2IR = $true )
& ( notinsingleton = $true )
& ( notdallE = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE1 = $true )
& ( exuEu = $true )
& ( binintersectSubset1 = $true )
& ( symdiffI2 = $true )
& ( powersetI1 = $true )
& ( setextAx = $true )
& ( binintersectSubset3 = $true )
& ( binintersectI = $true )
& ( binunionEcases = $true )
& ( subsetE = $true )
& ( setminusI = $true )
& ( setadjoin__Cong = $true )
& ( powersetE = $true )
& ( dsetconstrER = $true )
& ( setminusELneg = $true )
& ( setunionAx = $true )
& ( setunionE = $true )
& ( binunionLsub = $true )
& ( inCongP = $true )
& ( notdexE = $true )
& ( subsetRefl = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( setoftrueEq = $true )
& ( exuE3u = $true )
& ( singletoninpowerset = $true )
& ( binunionRsub = $true )
& ( emptysetE = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( setunionI = $true )
& ( symdiffIneg1 = $true )
& ( subsetI2 = $true )
& ( sepInPowerset = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan3 = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset5 = $true )
& ( wellorderingAx = $true )
& ( dsetconstr__Cong = $true )
& ( uniqinunit = $true )
& ( exuI3 = $true )
& ( setukpairIL = $true )
& ( inPowerset = $true )
& ( setminusERneg = $true )
& ( binintersectRsub = $true )
& ( bs114d = $true )
& ( subsetTrans = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinIL = $true )
& ( setext = $true )
& ( setminusLsub = $true )
& ( setunion__Cong = $true )
& ( $true
= ( in @ sK361 @ sK359 ) )
& ( ( in @ ( setadjoin @ sK361 @ emptyset ) @ ( powerset @ ( binunion @ sK359 @ sK360 ) ) )
!= $true )
& ( powersetAx = $true )
& ( notsubsetI = $true )
& ( omega__Cong = $true )
& ( nonemptyI = $true )
& ( kpairiskpair = $true )
& ( eqinunit = $true )
& ( setextsub = $true )
& ( binintersectLsub = $true )
& ( vacuousDall = $true )
& ( descr__Cong = $true )
& ( upairsetIR = $true )
& ( prop2setI = $true )
& ( symdiffI1 = $true )
& ( binintersectEL = $true )
& ( emptyinPowerset = $true )
& ( singletonsswitch = $true )
& ( subset2powerset = $true )
& ( prop2set2propI = $true )
& ( emptyset__Cong = $true )
& ( symdiffE = $true )
& ( prop2setE = $true )
& ( binunionIL = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub = $true )
& ( setadjoinOr = $true )
& ( setadjoinSub2 = $true )
& ( upairsetE = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset1 = $true )
& ( setminusILneg = $true )
& ( symdiffIneg2 = $true )
& ( secondinupair = $true )
& ( foundationAx = $true )
& ( descrp = $true )
& ( setadjoinE = $true )
& ( subPowSU = $true )
& ( emptysetsubset = $true )
& ( emptyinunitempty = $true )
& ( setbeta = $true )
& ( binunionE = $true )
& ( setminusEL = $true )
& ( kpairp = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetAx = $true )
& ( setminusER = $true )
& ( notequalI2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK359,sK360,sK361]),skolemize(X0,sK359),skolemize(X1,sK360),skolemize(X2,sK361)],[f1007]) ).
thf(f1024,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( subset2powerset != $true ) )
& ( ( subset2powerset = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f546]) ).
thf(f1025,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( subset2powerset != $true ) )
& ( ( subset2powerset = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X2 @ ( powerset @ X3 ) )
!= $true ) ) ) ),
inference(rectify,[],[f1024]) ).
thf(f1026,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( subset2powerset != $true ) )
& ( ( subset2powerset = $true )
| ( ( ( subset @ sK375 @ sK376 )
= $true )
& ( ( in @ sK375 @ ( powerset @ sK376 ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK375,sK376]),skolemize(X2,sK375),skolemize(X3,sK376)],[f1025]) ).
thf(f1216,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( binunionIL != $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true ) ),
inference(cnf_transformation,[],[f761]) ).
thf(f1434,plain,
! [X0: $i,X1: $i] :
( ( singletonsubset != $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f921]) ).
thf(f1579,plain,
binunionIL = $true,
inference(cnf_transformation,[],[f1008]) ).
thf(f1584,plain,
subset2powerset = $true,
inference(cnf_transformation,[],[f1008]) ).
thf(f1601,plain,
( ( in @ ( setadjoin @ sK361 @ emptyset ) @ ( powerset @ ( binunion @ sK359 @ sK360 ) ) )
!= $true ),
inference(cnf_transformation,[],[f1008]) ).
thf(f1602,plain,
( $true
= ( in @ sK361 @ sK359 ) ),
inference(cnf_transformation,[],[f1008]) ).
thf(f1664,plain,
singletonsubset = $true,
inference(cnf_transformation,[],[f1008]) ).
thf(f1712,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( subset2powerset != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f1026]) ).
thf(f2006,definition,
( spl377_33
<=> ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl377_33])],[avatar_definition]) ).
thf(f2007,plain,
( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X3 ) )
= $true )
| ( ( subset @ X2 @ X3 )
!= $true ) )
| ~ spl377_33 ),
inference(avatar_component_clause,[],[f2006]) ).
thf(f2142,definition,
( spl377_64
<=> ( $true
= ( in @ sK361 @ sK359 ) ) ),
introduced(definition,[new_symbols(definition,[spl377_64])],[avatar_definition]) ).
thf(f2144,plain,
( ( $true
= ( in @ sK361 @ sK359 ) )
| ~ spl377_64 ),
inference(avatar_component_clause,[],[f2142]) ).
thf(f2145,plain,
spl377_64,
inference(avatar_split_clause,[],[f1602,f2142]) ).
thf(f2285,definition,
( spl377_97
<=> ( binunionIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl377_97])],[avatar_definition]) ).
thf(f2288,plain,
spl377_97,
inference(avatar_split_clause,[],[f1579,f2285]) ).
thf(f2334,definition,
( spl377_107
<=> ( subset2powerset = $true ) ),
introduced(definition,[new_symbols(definition,[spl377_107])],[avatar_definition]) ).
thf(f2961,definition,
( spl377_247
<=> ( singletonsubset = $true ) ),
introduced(definition,[new_symbols(definition,[spl377_247])],[avatar_definition]) ).
thf(f2964,plain,
spl377_247,
inference(avatar_split_clause,[],[f1664,f2961]) ).
thf(f3679,plain,
( spl377_33
| ~ spl377_107 ),
inference(avatar_split_clause,[],[f1712,f2334,f2006]) ).
thf(f4087,definition,
( spl377_487
<=> ( ( in @ ( setadjoin @ sK361 @ emptyset ) @ ( powerset @ ( binunion @ sK359 @ sK360 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl377_487])],[avatar_definition]) ).
thf(f4089,plain,
( ( ( in @ ( setadjoin @ sK361 @ emptyset ) @ ( powerset @ ( binunion @ sK359 @ sK360 ) ) )
!= $true )
| spl377_487 ),
inference(avatar_component_clause,[],[f4087]) ).
thf(f4090,plain,
~ spl377_487,
inference(avatar_split_clause,[],[f1601,f4087]) ).
thf(f4207,definition,
( spl377_510
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl377_510])],[avatar_definition]) ).
thf(f4208,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ~ spl377_510 ),
inference(avatar_component_clause,[],[f4207]) ).
thf(f4209,plain,
( spl377_510
| ~ spl377_97 ),
inference(avatar_split_clause,[],[f1216,f2285,f4207]) ).
thf(f4568,definition,
( spl377_581
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl377_581])],[avatar_definition]) ).
thf(f4569,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ~ spl377_581 ),
inference(avatar_component_clause,[],[f4568]) ).
thf(f4570,plain,
( spl377_581
| ~ spl377_247 ),
inference(avatar_split_clause,[],[f1434,f2961,f4568]) ).
thf(f4822,plain,
spl377_107,
inference(avatar_split_clause,[],[f1584,f2334]) ).
thf(f5180,plain,
( ( $true != $true )
| ( $true
!= ( subset @ ( setadjoin @ sK361 @ emptyset ) @ ( binunion @ sK359 @ sK360 ) ) )
| ~ spl377_33
| spl377_487 ),
inference(superposition,[],[f4089,f2007]) ).
thf(f5186,plain,
( ( $true
!= ( subset @ ( setadjoin @ sK361 @ emptyset ) @ ( binunion @ sK359 @ sK360 ) ) )
| ~ spl377_33
| spl377_487 ),
inference(trivial_inequality_removal,[],[f5180]) ).
thf(f5191,definition,
( spl377_647
<=> ( $true
= ( subset @ ( setadjoin @ sK361 @ emptyset ) @ ( binunion @ sK359 @ sK360 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl377_647])],[avatar_definition]) ).
thf(f5193,plain,
( ( $true
!= ( subset @ ( setadjoin @ sK361 @ emptyset ) @ ( binunion @ sK359 @ sK360 ) ) )
| spl377_647 ),
inference(avatar_component_clause,[],[f5191]) ).
thf(f5194,plain,
( ~ spl377_647
| ~ spl377_33
| spl377_487 ),
inference(avatar_split_clause,[],[f5186,f4087,f2006,f5191]) ).
thf(f5554,plain,
( ( ( in @ sK361 @ ( binunion @ sK359 @ sK360 ) )
!= $true )
| ( $true != $true )
| ~ spl377_581
| spl377_647 ),
inference(superposition,[],[f5193,f4569]) ).
thf(f5557,plain,
( ( ( in @ sK361 @ ( binunion @ sK359 @ sK360 ) )
!= $true )
| ~ spl377_581
| spl377_647 ),
inference(trivial_inequality_removal,[],[f5554]) ).
thf(f5560,definition,
( spl377_654
<=> ( ( in @ sK361 @ ( binunion @ sK359 @ sK360 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl377_654])],[avatar_definition]) ).
thf(f5562,plain,
( ( ( in @ sK361 @ ( binunion @ sK359 @ sK360 ) )
!= $true )
| spl377_654 ),
inference(avatar_component_clause,[],[f5560]) ).
thf(f5563,plain,
( ~ spl377_654
| ~ spl377_581
| spl377_647 ),
inference(avatar_split_clause,[],[f5557,f5191,f4568,f5560]) ).
thf(f5670,plain,
( ( $true
!= ( in @ sK361 @ sK359 ) )
| ( $true != $true )
| ~ spl377_510
| spl377_654 ),
inference(superposition,[],[f5562,f4208]) ).
thf(f5674,plain,
( ( $true
!= ( in @ sK361 @ sK359 ) )
| ~ spl377_510
| spl377_654 ),
inference(trivial_inequality_removal,[],[f5670]) ).
thf(f5681,plain,
( $false
| ~ spl377_64
| ~ spl377_510
| spl377_654 ),
inference(forward_subsumption_resolution,[],[f5674,f2144]) ).
thf(f5682,plain,
( ~ spl377_64
| ~ spl377_510
| spl377_654 ),
inference(avatar_contradiction_clause,[],[f5681]) ).
cnf(s39,plain,
spl377_64,
inference(sat_conversion,[],[f2145]) ).
cnf(s59,plain,
spl377_97,
inference(sat_conversion,[],[f2288]) ).
cnf(s174,plain,
spl377_247,
inference(sat_conversion,[],[f2964]) ).
cnf(s326,plain,
( spl377_33
| ~ spl377_107 ),
inference(sat_conversion,[],[f3679]) ).
cnf(s428,plain,
~ spl377_487,
inference(sat_conversion,[],[f4090]) ).
cnf(s462,plain,
( ~ spl377_97
| spl377_510 ),
inference(sat_conversion,[],[f4209]) ).
cnf(s568,plain,
( ~ spl377_247
| spl377_581 ),
inference(sat_conversion,[],[f4570]) ).
cnf(s642,plain,
spl377_107,
inference(sat_conversion,[],[f4822]) ).
cnf(s669,plain,
( ~ spl377_33
| spl377_487
| ~ spl377_647 ),
inference(sat_conversion,[],[f5194]) ).
cnf(s677,plain,
( ~ spl377_581
| spl377_647
| ~ spl377_654 ),
inference(sat_conversion,[],[f5563]) ).
cnf(s680,plain,
( ~ spl377_64
| ~ spl377_510
| spl377_654 ),
inference(sat_conversion,[],[f5682]) ).
cnf(s724,plain,
spl377_33,
inference(rat,[],[s326,s642]) ).
cnf(s725,plain,
~ spl377_647,
inference(rat,[],[s669,s428,s724]) ).
cnf(s767,plain,
spl377_581,
inference(rat,[],[s568,s174]) ).
cnf(s768,plain,
~ spl377_654,
inference(rat,[],[s677,s725,s767]) ).
cnf(s816,plain,
spl377_510,
inference(rat,[],[s462,s59]) ).
cnf(s817,plain,
~ spl377_64,
inference(rat,[],[s680,s768,s816]) ).
cnf(s827,plain,
$false,
inference(rat,[],[s39,s817]) ).
thf(f5683,plain,
$false,
inference(avatar_sat_refutation,[],[s827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU623^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 13:58:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.14 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.24 % (148736)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.24 % (148747)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.24 % (148747)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
% 0.08/0.24 % (148742)lrs+10_16_si=on:nwc=1.5:random_seed=1703819217:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.24 % (148743)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=868738981:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.24 % (148745)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=272722703:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.24 % (148741)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1456195280:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.24 % (148746)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=595371414:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.24 % (148744)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=611423479: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)
% 0.08/0.24 % (148747)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=2572990078:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.24 % (148743)Instruction limit reached!
% 0.08/0.24 % (148743)------------------------------
% 0.08/0.24 % (148743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (148743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (148743)CaDiCaL version: 2.1.3
% 0.08/0.24 % (148743)Termination reason: Instruction limit
% 0.08/0.24 % (148743)Termination phase: shuffling
% 0.08/0.24 % (148743)Time elapsed: 0.003 s
% 0.08/0.24 % (148743)Peak memory usage: 10 MB
% 0.08/0.24 % (148743)Instructions burned: 14 (million)
% 0.08/0.24 % (148742)Instruction limit reached!
% 0.08/0.24 % (148742)------------------------------
% 0.08/0.24 % (148742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (148742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (148742)CaDiCaL version: 2.1.3
% 0.08/0.24 % (148742)Termination reason: Instruction limit
% 0.08/0.24 % (148742)Termination phase: Property scanning
% 0.08/0.24 % (148742)Time elapsed: 0.005 s
% 0.08/0.24 % (148742)Peak memory usage: 10 MB
% 0.08/0.24 % (148742)Instructions burned: 20 (million)
% 0.08/0.24 % (148745)Instruction limit reached!
% 0.08/0.24 % (148745)------------------------------
% 0.08/0.24 % (148745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (148745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (148745)CaDiCaL version: 2.1.3
% 0.08/0.24 % (148745)Termination reason: Instruction limit
% 0.08/0.24 % (148745)Termination phase: Preprocessing 3
% 0.08/0.24 % (148745)Time elapsed: 0.007 s
% 0.08/0.24 % (148745)Peak memory usage: 11 MB
% 0.08/0.24 % (148745)Instructions burned: 27 (million)
% 0.08/0.24 % (148755)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=740466830:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.08/0.24 % (148756)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=747826272:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.08/0.24 % (148757)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.08/0.24 % (148755)Instruction limit reached!
% 0.08/0.24 % (148755)------------------------------
% 0.08/0.24 % (148755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (148755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (148757)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1865045829:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.40/0.25 % (148755)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148755)Termination reason: Instruction limit
% 0.40/0.25 % (148755)Termination phase: shuffling
% 0.40/0.25 % (148755)Time elapsed: 0.002 s
% 0.40/0.25 % (148755)Peak memory usage: 10 MB
% 0.40/0.25 % (148755)Instructions burned: 9 (million)
% 0.40/0.25 % (148756)Instruction limit reached!
% 0.40/0.25 % (148756)------------------------------
% 0.40/0.25 % (148756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148756)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148756)Termination reason: Instruction limit
% 0.40/0.25 % (148756)Termination phase: shuffling
% 0.40/0.25 % (148756)Time elapsed: 0.002 s
% 0.40/0.25 % (148756)Peak memory usage: 10 MB
% 0.40/0.25 % (148756)Instructions burned: 9 (million)
% 0.40/0.25 % (148746)Instruction limit reached!
% 0.40/0.25 % (148746)------------------------------
% 0.40/0.25 % (148746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148746)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148746)Termination reason: Instruction limit
% 0.40/0.25 % (148746)Termination phase: Property scanning
% 0.40/0.25 % (148746)Time elapsed: 0.018 s
% 0.40/0.25 % (148746)Peak memory usage: 12 MB
% 0.40/0.25 % (148746)Instructions burned: 78 (million)
% 0.40/0.25 % (148757)Instruction limit reached!
% 0.40/0.25 % (148757)------------------------------
% 0.40/0.25 % (148757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148757)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148757)Termination reason: Instruction limit
% 0.40/0.25 % (148757)Termination phase: shuffling
% 0.40/0.25 % (148757)Time elapsed: 0.002 s
% 0.40/0.25 % (148757)Peak memory usage: 10 MB
% 0.40/0.25 % (148757)Instructions burned: 7 (million)
% 0.40/0.25 % (148741)Instruction limit reached!
% 0.40/0.25 % (148741)------------------------------
% 0.40/0.25 % (148741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148741)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148741)Termination reason: Instruction limit
% 0.40/0.25 % (148741)Termination phase: Saturation
% 0.40/0.25 % (148741)Time elapsed: 0.022 s
% 0.40/0.25 % (148741)Peak memory usage: 13 MB
% 0.40/0.25 % (148741)Instructions burned: 91 (million)
% 0.40/0.25 % (148762)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
% 0.40/0.25 % (148762)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.40/0.25 % (148761)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=945729669:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.40/0.25 % (148762)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=934130605:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.40/0.25 % (148763)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=4215151045:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.40/0.25 % (148764)lrs+10_1_si=on:cs=on:random_seed=2906486878:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.40/0.25 % (148765)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.40/0.25 % (148761)Instruction limit reached!
% 0.40/0.25 % (148761)------------------------------
% 0.40/0.25 % (148761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148761)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148761)Termination reason: Instruction limit
% 0.40/0.25 % (148761)Termination phase: shuffling
% 0.40/0.25 % (148761)Time elapsed: 0.003 s
% 0.40/0.25 % (148761)Peak memory usage: 10 MB
% 0.40/0.25 % (148761)Instructions burned: 13 (million)
% 0.40/0.25 % (148764)Instruction limit reached!
% 0.40/0.25 % (148764)------------------------------
% 0.40/0.25 % (148764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148764)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148764)Termination reason: Instruction limit
% 0.40/0.25 % (148764)Termination phase: shuffling
% 0.40/0.25 % (148764)Time elapsed: 0.002 s
% 0.40/0.25 % (148764)Peak memory usage: 10 MB
% 0.40/0.25 % (148765)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=3136288060:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.40/0.25 % (148764)Instructions burned: 10 (million)
% 0.40/0.25 % (148762)Instruction limit reached!
% 0.40/0.25 % (148762)------------------------------
% 0.40/0.25 % (148762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148762)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148762)Termination reason: Instruction limit
% 0.40/0.25 % (148762)Termination phase: Property scanning
% 0.40/0.25 % (148762)Time elapsed: 0.006 s
% 0.40/0.25 % (148762)Peak memory usage: 10 MB
% 0.40/0.25 % (148762)Instructions burned: 30 (million)
% 0.40/0.25 % (148747)Instruction limit reached!
% 0.40/0.25 % (148747)------------------------------
% 0.40/0.25 % (148747)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148747)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148747)Termination reason: Instruction limit
% 0.40/0.25 % (148747)Termination phase: Saturation
% 0.40/0.25 % (148747)Time elapsed: 0.036 s
% 0.40/0.25 % (148747)Peak memory usage: 14 MB
% 0.40/0.25 % (148747)Instructions burned: 159 (million)
% 0.40/0.25 % (148765)Instruction limit reached!
% 0.40/0.25 % (148765)------------------------------
% 0.40/0.25 % (148765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148765)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148765)Termination reason: Instruction limit
% 0.40/0.25 % (148765)Termination phase: shuffling
% 0.40/0.25 % (148765)Time elapsed: 0.005 s
% 0.40/0.25 % (148765)Peak memory usage: 10 MB
% 0.40/0.25 % (148765)Instructions burned: 5 (million)
% 0.40/0.25 % (148770)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2525414697:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.40/0.25 % (148772)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=993775988:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.40/0.25 % (148773)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2701317227:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.40/0.25 % (148763)Instruction limit reached!
% 0.40/0.25 % (148763)------------------------------
% 0.40/0.25 % (148763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148763)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148763)Termination reason: Instruction limit
% 0.40/0.25 % (148763)Termination phase: Saturation
% 0.40/0.25 % (148763)Time elapsed: 0.020 s
% 0.40/0.25 % (148763)Peak memory usage: 13 MB
% 0.40/0.25 % (148763)Instructions burned: 89 (million)
% 0.40/0.25 % (148775)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1318911470:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.40/0.25 % (148773)Instruction limit reached!
% 0.40/0.25 % (148773)------------------------------
% 0.40/0.25 % (148773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148773)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148773)Termination reason: Instruction limit
% 0.40/0.25 % (148773)Termination phase: Preprocessing 3
% 0.40/0.25 % (148773)Time elapsed: 0.007 s
% 0.40/0.25 % (148773)Peak memory usage: 11 MB
% 0.40/0.25 % (148773)Instructions burned: 28 (million)
% 0.40/0.25 % (148770)Instruction limit reached!
% 0.40/0.25 % (148770)------------------------------
% 0.40/0.25 % (148770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148770)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148770)Termination reason: Instruction limit
% 0.40/0.25 % (148770)Termination phase: Preprocessing 3
% 0.40/0.25 % (148770)Time elapsed: 0.011 s
% 0.40/0.25 % (148770)Peak memory usage: 11 MB
% 0.40/0.25 % (148770)Instructions burned: 41 (million)
% 0.40/0.25 % (148774)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1185054545:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.40/0.25 % (148744) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-148736-148744"...
% 0.40/0.25 % (148744)...printing done.
% 0.40/0.25 % (148780)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3454713027:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.40/0.25 % (148744)Refutation found. Thanks to Tanya!
% 0.40/0.25 % SZS status Theorem for theBenchmark
% 0.40/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.40/0.25 % (148744)------------------------------
% 0.40/0.25 % (148744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.25 % (148744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.25 % (148744)CaDiCaL version: 2.1.3
% 0.40/0.25 % (148744)Termination reason: Refutation
% 0.40/0.25 % (148744)Time elapsed: 0.060 s
% 0.40/0.25 % (148744)Peak memory usage: 16 MB
% 0.40/0.25 % (148744)Instructions burned: 212 (million)
% 0.40/0.25 % (148736)Success in time 0.097 s
% 0.40/0.25 % Vampire exiting
%------------------------------------------------------------------------------