%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU614^1 : 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 : n005.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 08:30:20 AM UTC 2026
% Result : Theorem 0.62s 0.38s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 31 unt; 0 typ; 10 def)
% Number of atoms : 3475 ( 983 equ; 0 cnn)
% Maximal formula atoms : 133 ( 36 avg)
% Number of connectives : 1863 ( 148 ~; 109 |; 569 &; 328 @)
% ( 18 <=>; 691 =>; 0 <=; 0 <~>)
% Maximal formula depth : 141 ( 17 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 : 284 ( 281 usr; 160 con; 0-4 aty)
% Number of variables : 107 ( 0 sgn 86 !; 21 ?; 107 :)
% 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_153,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_154,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_155,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_156,type,
vAND: $o > $o > $o ).
thf(func_def_157,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_158,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_159,type,
vIMP: $o > $o > $o ).
thf(func_def_160,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_161,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_162,type,
vNOT: $o > $o ).
thf(func_def_163,type,
sP0: $i > $i > $o ).
thf(func_def_164,type,
sP1: $i > $o ).
thf(func_def_165,type,
sP2: $o ).
thf(func_def_169,type,
sK6: $i > $o ).
thf(func_def_171,type,
sK8: $i > $o ).
thf(func_def_182,type,
sK19: $i > $i ).
thf(func_def_183,type,
sK20: $i > $i ).
thf(func_def_193,type,
sK30: $i > $o ).
thf(func_def_208,type,
sK45: ( $i > $i > $o ) > $i > $i ).
thf(func_def_209,type,
sK46: ( $i > $i > $o ) > $i > $i ).
thf(func_def_210,type,
sK47: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_212,type,
sK49: $i > $i > $o ).
thf(func_def_213,type,
sK50: $i > $i ).
thf(func_def_214,type,
sK51: $i > $i ).
thf(func_def_215,type,
sK52: $i > $o ).
thf(func_def_216,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_226,type,
sK63: $o ).
thf(func_def_230,type,
sK67: $i > $o ).
thf(func_def_231,type,
sK68: $i > $o ).
thf(func_def_232,type,
sK69: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_233,type,
sK70: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_242,type,
sK79: $o ).
thf(func_def_244,type,
sK81: $i > $i ).
thf(func_def_245,type,
sK82: $i > $i > $i ).
thf(func_def_252,type,
sK89: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK90: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_254,type,
sK91: $i > $o ).
thf(func_def_255,type,
sK92: $i > $o ).
thf(func_def_262,type,
sK99: $i > $o ).
thf(func_def_271,type,
sK108: $i > $o ).
thf(func_def_272,type,
sK109: $i > $i ).
thf(func_def_273,type,
sK110: ( $i > $o ) > $i ).
thf(func_def_276,type,
sK113: $i > $i > $i ).
thf(func_def_280,type,
sK117: $o ).
thf(func_def_283,type,
sK120: $i > $i > $i ).
thf(func_def_292,type,
sK129: $i > $i > $i ).
thf(func_def_296,type,
sK133: $i > $i > $i ).
thf(func_def_297,type,
sK134: $i > $i > $i ).
thf(func_def_300,type,
sK137: $i > ( $i > $o ) > $i ).
thf(func_def_301,type,
sK138: $i > $o ).
thf(func_def_311,type,
sK148: $i > $i > $i ).
thf(func_def_316,type,
sK153: $i > $o ).
thf(func_def_321,type,
sK158: $i > $i ).
thf(func_def_322,type,
sK159: $i > $i ).
thf(func_def_323,type,
sK160: $i > $i ).
thf(func_def_324,type,
sK161: $i > $i ).
thf(func_def_325,type,
sK162: $i > $i ).
thf(func_def_326,type,
sK163: $i > $i > $i > $i ).
thf(func_def_327,type,
sK164: $i > $i ).
thf(func_def_328,type,
sK165: $i > $i ).
thf(func_def_329,type,
sK166: $i > $i ).
thf(func_def_330,type,
sK167: $i > $i ).
thf(func_def_331,type,
sK168: $i > $i > $i ).
thf(func_def_332,type,
sK169: $i > $i > $i > $i ).
thf(func_def_333,type,
sK170: $i > $i > $i > $i ).
thf(func_def_334,type,
sK171: $i > $i > $i > $i ).
thf(func_def_335,type,
sK172: $i > $i > $i ).
thf(func_def_336,type,
sK173: $i > $i > $i ).
thf(func_def_337,type,
sK174: $i > $i > $i ).
thf(func_def_338,type,
sK175: $i > $i > $i ).
thf(func_def_349,type,
sK186: $i > $o ).
thf(func_def_354,type,
sK191: $o ).
thf(func_def_361,type,
sK198: $i > $i > $i ).
thf(func_def_372,type,
sK209: $i > $o ).
thf(func_def_375,type,
sK212: $i > ( $i > $o ) > $i ).
thf(func_def_377,type,
sK214: $i > $o ).
thf(func_def_379,type,
sK216: $o ).
thf(func_def_382,type,
sK219: $i > $o ).
thf(func_def_383,type,
sK220: $i > $o ).
thf(func_def_384,type,
sK221: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_385,type,
sK222: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_387,type,
sK224: $i > $o ).
thf(func_def_396,type,
sK233: $o > $i > $i > $i ).
thf(func_def_399,type,
sK236: $o ).
thf(func_def_401,type,
sK238: $i > $i ).
thf(func_def_402,type,
sK239: $i > $o ).
thf(func_def_409,type,
sK246: $o ).
thf(func_def_419,type,
sK256: $i > $o ).
thf(func_def_440,type,
sK277: $i > $o ).
thf(func_def_441,type,
sK278: $i > $i ).
thf(func_def_442,type,
sK279: ( $i > $o ) > $i ).
thf(func_def_444,type,
sK281: $i > $i ).
thf(func_def_446,type,
sK283: $i > $o ).
thf(func_def_448,type,
sK285: ( $i > $o ) > $i > $i ).
thf(func_def_453,type,
sK290: $i > $o ).
thf(func_def_464,type,
sK301: $i > ( $i > $o ) > $i ).
thf(func_def_465,type,
sK302: $i > $o ).
thf(func_def_468,type,
sK305: $i > $o ).
thf(func_def_470,type,
sK307: $i > ( $i > $o ) > $i ).
thf(func_def_486,type,
sK323: ( $i > $o ) > $i > $i ).
thf(func_def_488,type,
sK325: $i > $o ).
thf(func_def_491,type,
sK328: $i > $i ).
thf(func_def_495,type,
sK332: $i > $i > $i ).
thf(func_def_497,type,
sK334: $i > $o ).
thf(func_def_500,type,
sK337: $i > ( $i > $o ) > $i ).
thf(func_def_501,type,
sK338: $i > $o ).
thf(func_def_504,type,
sK341: $i > ( $i > $o ) > $i ).
thf(func_def_505,type,
sK342: $i > $o ).
thf(func_def_512,type,
sK349: ( $i > $o ) > $i ).
thf(func_def_513,type,
sK350: ( $i > $o ) > $i ).
thf(func_def_514,type,
sK351: $i > $o ).
thf(func_def_516,type,
sK353: $i > $i ).
thf(func_def_519,type,
sK356: $o ).
thf(f3,axiom,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(f94,axiom,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) )
= subsetemptysetimpeq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(f130,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) )
= symdiffE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(f133,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
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(f134,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
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f133]) ).
thf(f208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X0 @ X2 ) )
=> ! [X3: $o] :
( ( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> X3 ) )
=> ( ( ~ ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> X3 ) )
=> X3 ) ) )
= symdiffE ),
inference(rectify,[],[f130]) ).
thf(f209,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
=> ! [X3: $o] :
( ( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) )
<=> ( symdiffE = $true ) ),
inference(fool_elimination,[],[f208]) ).
thf(f230,plain,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[],[f3]) ).
thf(f231,plain,
( ( emptysetAx = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(fool_elimination,[],[f230]) ).
thf(f355,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ ( symdiff @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f134]) ).
thf(f356,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ ( symdiff @ X1 @ X0 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f355]) ).
thf(f369,plain,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) )
= subsetemptysetimpeq ),
inference(rectify,[],[f94]) ).
thf(f370,plain,
( ( subsetemptysetimpeq = $true )
<=> ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
=> ( emptyset = X0 ) ) ),
inference(fool_elimination,[],[f369]) ).
thf(f401,plain,
( ( symdiffE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
=> ! [X3: $o] :
( ( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ),
inference(flattening,[],[f209]) ).
thf(f405,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( emptysetAx = $true ) ),
inference(flattening,[],[f231]) ).
thf(f422,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 )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ ( symdiff @ X1 @ X0 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f356]) ).
thf(f481,plain,
( ( symdiffE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
| ( ( $true != X3 )
& ( ( in @ X1 @ X2 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
| ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) ),
inference(ennf_transformation,[],[f401]) ).
thf(f482,plain,
( ( symdiffE = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
| ( ( ( in @ X1 @ X0 )
= $true )
& ( $true != X3 )
& ( ( in @ X1 @ X2 )
!= $true ) ) )
| ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) ),
inference(flattening,[],[f481]) ).
thf(f504,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( symdiff @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $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,[],[f422]) ).
thf(f505,plain,
( ( prop2set2propI = $true )
& ( eqimpsubset1 = $true )
& ( emptyE1 = $true )
& ( setminusELneg = $true )
& ( emptyinunitempty = $true )
& ( binunionIL = $true )
& ( upairsetIL = $true )
& ( notinemptyset = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinIL = $true )
& ( inCongP = $true )
& ( replAx = $true )
& ( setadjoinAx = $true )
& ( setminusEL = $true )
& ( nonemptyI = $true )
& ( powersetI = $true )
& ( symdiffE = $true )
& ( sepInPowerset = $true )
& ( dsetconstr__Cong = $true )
& ( subPowSU = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( symdiff @ X1 @ X0 ) )
= $true ) )
& ( setminusSubset1 = $true )
& ( omegaSAx = $true )
& ( omega__Cong = $true )
& ( symdiffI1 = $true )
& ( emptysetsubset = $true )
& ( notsubsetI = $true )
& ( foundationAx = $true )
& ( descr__Cong = $true )
& ( prop2setI = $true )
& ( setunionAx = $true )
& ( setminusI = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset3 = $true )
& ( binunionLsub = $true )
& ( bs114d = $true )
& ( setminusILneg = $true )
& ( setminusLsub = $true )
& ( binintersectLsub = $true )
& ( emptysetAx = $true )
& ( exuI1 = $true )
& ( exuI3 = $true )
& ( exuE3u = $true )
& ( noeltsimpempty = $true )
& ( upairsetIR = $true )
& ( setunionE = $true )
& ( emptyInPowerset = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( quantDeMorgan1 = $true )
& ( upairset2IR = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinSub2 = $true )
& ( omegaIndAx = $true )
& ( dsetconstrI = $true )
& ( sepSubset = $true )
& ( emptyinPowerset = $true )
& ( exuEu = $true )
& ( notequalI1 = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( exuE3e = $true )
& ( binunionRsub = $true )
& ( emptyI = $true )
& ( binintersectEL = $true )
& ( setextAx = $true )
& ( binunionE = $true )
& ( setextsub = $true )
& ( setminusER = $true )
& ( binintersectRsub = $true )
& ( singletonsswitch = $true )
& ( wellorderingAx = $true )
& ( setminusSubset2 = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset4 = $true )
& ( subsetTrans = $true )
& ( setunionI = $true )
& ( powersetsubset = $true )
& ( subset2powerset = $true )
& ( inPowerset = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset2 = $true )
& ( binunionIR = $true )
& ( setext = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( subsetRefl = $true )
& ( exu__Cong = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIR = $true )
& ( exuE2 = $true )
& ( nonemptyImpWitness = $true )
& ( descrp = $true )
& ( binintersectER = $true )
& ( notdexE = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( in__Cong = $true )
& ( omega0Ax = $true )
& ( symdiffI2 = $true )
& ( disjointsetsI1 = $true )
& ( powerset__Cong = $true )
& ( powersetE = $true )
& ( dsetconstrEL = $true )
& ( setbeta = $true )
& ( setminusERneg = $true )
& ( setadjoinE = $true )
& ( nonemptyE1 = $true )
& ( notinsingleton = $true )
& ( setunion__Cong = $true )
& ( eqimpsubset2 = $true )
& ( binintersectI = $true )
& ( setadjoin__Cong = $true )
& ( uniqinunit = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset1 = $true )
& ( subsetE2 = $true )
& ( setadjoinOr = $true )
& ( setoftrueEq = $true )
& ( powersetI1 = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI2 = $true )
& ( binunionEcases = $true )
& ( vacuousDall = $true )
& ( notdallE = $true ) ),
inference(flattening,[],[f504]) ).
thf(f543,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
<=> ( subsetemptysetimpeq = $true ) ),
inference(ennf_transformation,[],[f370]) ).
thf(f704,plain,
( ( ( symdiffE = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true ) )
& ( ( ( in @ X1 @ X0 )
!= $true )
| ( $true = X3 )
| ( ( in @ X1 @ X2 )
= $true ) ) )
& ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
| ( ( ( in @ X1 @ X0 )
= $true )
& ( $true != X3 )
& ( ( in @ X1 @ X2 )
!= $true ) ) )
| ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) )
| ( symdiffE != $true ) ) ),
inference(nnf_transformation,[],[f482]) ).
thf(f705,plain,
( ( ( symdiffE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( ( in @ X2 @ X0 )
!= $true )
| ( $true = X3 )
| ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $o] :
( ( $true = X7 )
| ( ( $true != X7 )
& ( ( in @ X6 @ X5 )
= $true )
& ( ( in @ X6 @ X4 )
!= $true ) )
| ( ( ( in @ X6 @ X4 )
= $true )
& ( $true != X7 )
& ( ( in @ X6 @ X5 )
!= $true ) ) )
| ( $true
!= ( in @ X6 @ ( symdiff @ X4 @ X5 ) ) ) )
| ( symdiffE != $true ) ) ),
inference(rectify,[],[f704]) ).
thf(f706,plain,
( ( ( symdiffE = $true )
| ( ( sK117 != $true )
& ( ( sK117 = $true )
| ( $true
!= ( in @ sK116 @ sK115 ) )
| ( ( in @ sK116 @ sK114 )
= $true ) )
& ( ( ( in @ sK116 @ sK114 )
!= $true )
| ( sK117 = $true )
| ( $true
= ( in @ sK116 @ sK115 ) ) )
& ( ( in @ sK116 @ ( symdiff @ sK114 @ sK115 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $o] :
( ( $true = X7 )
| ( ( $true != X7 )
& ( ( in @ X6 @ X5 )
= $true )
& ( ( in @ X6 @ X4 )
!= $true ) )
| ( ( ( in @ X6 @ X4 )
= $true )
& ( $true != X7 )
& ( ( in @ X6 @ X5 )
!= $true ) ) )
| ( $true
!= ( in @ X6 @ ( symdiff @ X4 @ X5 ) ) ) )
| ( symdiffE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114,sK115,sK116,sK117]),skolemize(X0,sK114),skolemize(X1,sK115),skolemize(X2,sK116),skolemize(X3,sK117)],[f705]) ).
thf(f775,plain,
( ( prop2set2propI = $true )
& ( eqimpsubset1 = $true )
& ( emptyE1 = $true )
& ( setminusELneg = $true )
& ( emptyinunitempty = $true )
& ( binunionIL = $true )
& ( upairsetIL = $true )
& ( notinemptyset = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinIL = $true )
& ( inCongP = $true )
& ( replAx = $true )
& ( setadjoinAx = $true )
& ( setminusEL = $true )
& ( nonemptyI = $true )
& ( powersetI = $true )
& ( symdiffE = $true )
& ( sepInPowerset = $true )
& ( dsetconstr__Cong = $true )
& ( subPowSU = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) )
& ( setminusSubset1 = $true )
& ( omegaSAx = $true )
& ( omega__Cong = $true )
& ( symdiffI1 = $true )
& ( emptysetsubset = $true )
& ( notsubsetI = $true )
& ( foundationAx = $true )
& ( descr__Cong = $true )
& ( prop2setI = $true )
& ( setunionAx = $true )
& ( setminusI = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset3 = $true )
& ( binunionLsub = $true )
& ( bs114d = $true )
& ( setminusILneg = $true )
& ( setminusLsub = $true )
& ( binintersectLsub = $true )
& ( emptysetAx = $true )
& ( exuI1 = $true )
& ( exuI3 = $true )
& ( exuE3u = $true )
& ( noeltsimpempty = $true )
& ( upairsetIR = $true )
& ( setunionE = $true )
& ( emptyInPowerset = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( quantDeMorgan1 = $true )
& ( upairset2IR = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinSub2 = $true )
& ( omegaIndAx = $true )
& ( dsetconstrI = $true )
& ( sepSubset = $true )
& ( emptyinPowerset = $true )
& ( exuEu = $true )
& ( notequalI1 = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( exuE3e = $true )
& ( binunionRsub = $true )
& ( emptyI = $true )
& ( binintersectEL = $true )
& ( setextAx = $true )
& ( binunionE = $true )
& ( setextsub = $true )
& ( setminusER = $true )
& ( binintersectRsub = $true )
& ( singletonsswitch = $true )
& ( wellorderingAx = $true )
& ( setminusSubset2 = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset4 = $true )
& ( subsetTrans = $true )
& ( setunionI = $true )
& ( powersetsubset = $true )
& ( subset2powerset = $true )
& ( inPowerset = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset2 = $true )
& ( binunionIR = $true )
& ( setext = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( subsetRefl = $true )
& ( exu__Cong = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIR = $true )
& ( exuE2 = $true )
& ( nonemptyImpWitness = $true )
& ( descrp = $true )
& ( binintersectER = $true )
& ( notdexE = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( in__Cong = $true )
& ( omega0Ax = $true )
& ( symdiffI2 = $true )
& ( disjointsetsI1 = $true )
& ( powerset__Cong = $true )
& ( powersetE = $true )
& ( dsetconstrEL = $true )
& ( setbeta = $true )
& ( setminusERneg = $true )
& ( setadjoinE = $true )
& ( nonemptyE1 = $true )
& ( notinsingleton = $true )
& ( setunion__Cong = $true )
& ( eqimpsubset2 = $true )
& ( binintersectI = $true )
& ( setadjoin__Cong = $true )
& ( uniqinunit = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset1 = $true )
& ( subsetE2 = $true )
& ( setadjoinOr = $true )
& ( setoftrueEq = $true )
& ( powersetI1 = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI2 = $true )
& ( binunionEcases = $true )
& ( vacuousDall = $true )
& ( notdallE = $true ) ),
inference(rectify,[],[f505]) ).
thf(f776,plain,
( ( prop2set2propI = $true )
& ( eqimpsubset1 = $true )
& ( emptyE1 = $true )
& ( setminusELneg = $true )
& ( emptyinunitempty = $true )
& ( binunionIL = $true )
& ( upairsetIL = $true )
& ( notinemptyset = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinIL = $true )
& ( inCongP = $true )
& ( replAx = $true )
& ( setadjoinAx = $true )
& ( setminusEL = $true )
& ( nonemptyI = $true )
& ( powersetI = $true )
& ( symdiffE = $true )
& ( sepInPowerset = $true )
& ( dsetconstr__Cong = $true )
& ( subPowSU = $true )
& ( $true
= ( in @ sK193 @ sK194 ) )
& ( ( in @ sK193 @ sK192 )
= $true )
& ( ( in @ sK193 @ ( symdiff @ sK194 @ sK192 ) )
= $true )
& ( setminusSubset1 = $true )
& ( omegaSAx = $true )
& ( omega__Cong = $true )
& ( symdiffI1 = $true )
& ( emptysetsubset = $true )
& ( notsubsetI = $true )
& ( foundationAx = $true )
& ( descr__Cong = $true )
& ( prop2setI = $true )
& ( setunionAx = $true )
& ( setminusI = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset3 = $true )
& ( binunionLsub = $true )
& ( bs114d = $true )
& ( setminusILneg = $true )
& ( setminusLsub = $true )
& ( binintersectLsub = $true )
& ( emptysetAx = $true )
& ( exuI1 = $true )
& ( exuI3 = $true )
& ( exuE3u = $true )
& ( noeltsimpempty = $true )
& ( upairsetIR = $true )
& ( setunionE = $true )
& ( emptyInPowerset = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( quantDeMorgan1 = $true )
& ( upairset2IR = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinSub2 = $true )
& ( omegaIndAx = $true )
& ( dsetconstrI = $true )
& ( sepSubset = $true )
& ( emptyinPowerset = $true )
& ( exuEu = $true )
& ( notequalI1 = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( exuE3e = $true )
& ( binunionRsub = $true )
& ( emptyI = $true )
& ( binintersectEL = $true )
& ( setextAx = $true )
& ( binunionE = $true )
& ( setextsub = $true )
& ( setminusER = $true )
& ( binintersectRsub = $true )
& ( singletonsswitch = $true )
& ( wellorderingAx = $true )
& ( setminusSubset2 = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset4 = $true )
& ( subsetTrans = $true )
& ( setunionI = $true )
& ( powersetsubset = $true )
& ( subset2powerset = $true )
& ( inPowerset = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset2 = $true )
& ( binunionIR = $true )
& ( setext = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( subsetRefl = $true )
& ( exu__Cong = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIR = $true )
& ( exuE2 = $true )
& ( nonemptyImpWitness = $true )
& ( descrp = $true )
& ( binintersectER = $true )
& ( notdexE = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( in__Cong = $true )
& ( omega0Ax = $true )
& ( symdiffI2 = $true )
& ( disjointsetsI1 = $true )
& ( powerset__Cong = $true )
& ( powersetE = $true )
& ( dsetconstrEL = $true )
& ( setbeta = $true )
& ( setminusERneg = $true )
& ( setadjoinE = $true )
& ( nonemptyE1 = $true )
& ( notinsingleton = $true )
& ( setunion__Cong = $true )
& ( eqimpsubset2 = $true )
& ( binintersectI = $true )
& ( setadjoin__Cong = $true )
& ( uniqinunit = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset1 = $true )
& ( subsetE2 = $true )
& ( setadjoinOr = $true )
& ( setoftrueEq = $true )
& ( powersetI1 = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI2 = $true )
& ( binunionEcases = $true )
& ( vacuousDall = $true )
& ( notdallE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK192,sK193,sK194]),skolemize(X0,sK192),skolemize(X1,sK193),skolemize(X2,sK194)],[f775]) ).
thf(f847,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) ) ),
inference(nnf_transformation,[],[f405]) ).
thf(f848,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ? [X1: $i] :
( ( in @ X1 @ emptyset )
= $true ) ) ),
inference(rectify,[],[f847]) ).
thf(f849,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ( ( in @ sK257 @ emptyset )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(X1,sK257)],[f848]) ).
thf(f928,plain,
( ( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ? [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
& ( emptyset != X0 ) ) ) ),
inference(nnf_transformation,[],[f543]) ).
thf(f929,plain,
( ( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ? [X1: $i] :
( ( ( subset @ X1 @ emptyset )
= $true )
& ( emptyset != X1 ) ) ) ),
inference(rectify,[],[f928]) ).
thf(f930,plain,
( ( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ( ( ( subset @ sK329 @ emptyset )
= $true )
& ( emptyset != sK329 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(X1,sK329)],[f929]) ).
thf(f1111,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( symdiffE != $true )
| ( ( in @ X6 @ X5 )
!= $true )
| ( $true = X7 )
| ( $true
!= ( in @ X6 @ ( symdiff @ X4 @ X5 ) ) ) ),
inference(cnf_transformation,[],[f706]) ).
thf(f1295,plain,
subsetemptysetimpeq = $true,
inference(cnf_transformation,[],[f776]) ).
thf(f1338,plain,
emptysetAx = $true,
inference(cnf_transformation,[],[f776]) ).
thf(f1359,plain,
( ( in @ sK193 @ ( symdiff @ sK194 @ sK192 ) )
= $true ),
inference(cnf_transformation,[],[f776]) ).
thf(f1360,plain,
( ( in @ sK193 @ sK192 )
= $true ),
inference(cnf_transformation,[],[f776]) ).
thf(f1361,plain,
( $true
= ( in @ sK193 @ sK194 ) ),
inference(cnf_transformation,[],[f776]) ).
thf(f1365,plain,
symdiffE = $true,
inference(cnf_transformation,[],[f776]) ).
thf(f1473,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) ),
inference(cnf_transformation,[],[f849]) ).
thf(f1565,plain,
! [X0: $i] :
( ( emptyset = X0 )
| ( subsetemptysetimpeq != $true )
| ( ( subset @ X0 @ emptyset )
!= $true ) ),
inference(cnf_transformation,[],[f930]) ).
thf(f1895,definition,
( spl357_31
<=> ! [X7: $o] : ( $true = X7 ) ),
introduced(definition,[new_symbols(definition,[spl357_31])],[avatar_definition]) ).
thf(f1896,plain,
( ! [X7: $o] : ( $true = X7 )
| ~ spl357_31 ),
inference(avatar_component_clause,[],[f1895]) ).
thf(f1919,definition,
( spl357_37
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl357_37])],[avatar_definition]) ).
thf(f1920,plain,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ~ spl357_37 ),
inference(avatar_component_clause,[],[f1919]) ).
thf(f2170,definition,
( spl357_95
<=> ( symdiffE = $true ) ),
introduced(definition,[new_symbols(definition,[spl357_95])],[avatar_definition]) ).
thf(f2381,plain,
spl357_95,
inference(avatar_split_clause,[],[f1365,f2170]) ).
thf(f2540,definition,
( spl357_178
<=> ! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( $true
!= ( in @ X6 @ ( symdiff @ X4 @ X5 ) ) )
| ( ( in @ X6 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl357_178])],[avatar_definition]) ).
thf(f2541,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( symdiff @ X4 @ X5 ) ) )
| ( ( in @ X6 @ X4 )
!= $true )
| ( ( in @ X6 @ X5 )
!= $true ) )
| ~ spl357_178 ),
inference(avatar_component_clause,[],[f2540]) ).
thf(f2542,plain,
( ~ spl357_95
| spl357_31
| spl357_178 ),
inference(avatar_split_clause,[],[f1111,f2540,f1895,f2170]) ).
thf(f2612,definition,
( spl357_194
<=> ( ( in @ sK193 @ ( symdiff @ sK194 @ sK192 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl357_194])],[avatar_definition]) ).
thf(f2614,plain,
( ( ( in @ sK193 @ ( symdiff @ sK194 @ sK192 ) )
= $true )
| ~ spl357_194 ),
inference(avatar_component_clause,[],[f2612]) ).
thf(f2615,plain,
spl357_194,
inference(avatar_split_clause,[],[f1359,f2612]) ).
thf(f2724,definition,
( spl357_219
<=> ( ( in @ sK193 @ sK192 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl357_219])],[avatar_definition]) ).
thf(f2726,plain,
( ( ( in @ sK193 @ sK192 )
= $true )
| ~ spl357_219 ),
inference(avatar_component_clause,[],[f2724]) ).
thf(f2727,plain,
spl357_219,
inference(avatar_split_clause,[],[f1360,f2724]) ).
thf(f2864,definition,
( spl357_250
<=> ( subsetemptysetimpeq = $true ) ),
introduced(definition,[new_symbols(definition,[spl357_250])],[avatar_definition]) ).
thf(f2867,plain,
spl357_250,
inference(avatar_split_clause,[],[f1295,f2864]) ).
thf(f2906,definition,
( spl357_259
<=> ( emptysetAx = $true ) ),
introduced(definition,[new_symbols(definition,[spl357_259])],[avatar_definition]) ).
thf(f2909,plain,
( spl357_37
| ~ spl357_259 ),
inference(avatar_split_clause,[],[f1473,f2906,f1919]) ).
thf(f3617,definition,
( spl357_407
<=> ! [X0: $i] :
( ( emptyset = X0 )
| ( ( subset @ X0 @ emptyset )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl357_407])],[avatar_definition]) ).
thf(f3618,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
| ~ spl357_407 ),
inference(avatar_component_clause,[],[f3617]) ).
thf(f3619,plain,
( ~ spl357_250
| spl357_407 ),
inference(avatar_split_clause,[],[f1565,f3617,f2864]) ).
thf(f3961,definition,
( spl357_478
<=> ( $true
= ( in @ sK193 @ sK194 ) ) ),
introduced(definition,[new_symbols(definition,[spl357_478])],[avatar_definition]) ).
thf(f3963,plain,
( ( $true
= ( in @ sK193 @ sK194 ) )
| ~ spl357_478 ),
inference(avatar_component_clause,[],[f3961]) ).
thf(f3964,plain,
spl357_478,
inference(avatar_split_clause,[],[f1361,f3961]) ).
thf(f4565,plain,
spl357_259,
inference(avatar_split_clause,[],[f1338,f2906]) ).
thf(f4658,plain,
( ! [X0: $i] : ( emptyset = X0 )
| ~ spl357_31
| ~ spl357_407 ),
inference(forward_subsumption_resolution,[],[f3618,f1896]) ).
thf(f4660,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
| ~ spl357_31
| ~ spl357_37
| ~ spl357_407 ),
inference(superposition,[],[f1920,f4658]) ).
thf(f4661,plain,
( $false
| ~ spl357_31
| ~ spl357_37
| ~ spl357_407 ),
inference(forward_subsumption_resolution,[],[f4660,f1896]) ).
thf(f4662,plain,
( ~ spl357_31
| ~ spl357_37
| ~ spl357_407 ),
inference(avatar_contradiction_clause,[],[f4661]) ).
thf(f4668,plain,
( ( $true
!= ( in @ sK193 @ sK194 ) )
| ( $true != $true )
| ( ( in @ sK193 @ sK192 )
!= $true )
| ~ spl357_178
| ~ spl357_194 ),
inference(superposition,[],[f2541,f2614]) ).
thf(f4669,plain,
( ( $true
!= ( in @ sK193 @ sK194 ) )
| ( ( in @ sK193 @ sK192 )
!= $true )
| ~ spl357_178
| ~ spl357_194 ),
inference(trivial_inequality_removal,[],[f4668]) ).
thf(f4670,plain,
( ( ( in @ sK193 @ sK192 )
!= $true )
| ~ spl357_178
| ~ spl357_194
| ~ spl357_478 ),
inference(forward_subsumption_resolution,[],[f4669,f3963]) ).
thf(f4671,plain,
( $false
| ~ spl357_178
| ~ spl357_194
| ~ spl357_219
| ~ spl357_478 ),
inference(forward_subsumption_resolution,[],[f4670,f2726]) ).
thf(f4672,plain,
( ~ spl357_178
| ~ spl357_194
| ~ spl357_219
| ~ spl357_478 ),
inference(avatar_contradiction_clause,[],[f4671]) ).
cnf(s84,plain,
spl357_95,
inference(sat_conversion,[],[f2381]) ).
cnf(s115,plain,
( spl357_31
| ~ spl357_95
| spl357_178 ),
inference(sat_conversion,[],[f2542]) ).
cnf(s127,plain,
spl357_194,
inference(sat_conversion,[],[f2615]) ).
cnf(s150,plain,
spl357_219,
inference(sat_conversion,[],[f2727]) ).
cnf(s177,plain,
spl357_250,
inference(sat_conversion,[],[f2867]) ).
cnf(s187,plain,
( spl357_37
| ~ spl357_259 ),
inference(sat_conversion,[],[f2909]) ).
cnf(s354,plain,
( ~ spl357_250
| spl357_407 ),
inference(sat_conversion,[],[f3619]) ).
cnf(s445,plain,
spl357_478,
inference(sat_conversion,[],[f3964]) ).
cnf(s610,plain,
spl357_259,
inference(sat_conversion,[],[f4565]) ).
cnf(s626,plain,
( ~ spl357_31
| ~ spl357_37
| ~ spl357_407 ),
inference(sat_conversion,[],[f4662]) ).
cnf(s627,plain,
( ~ spl357_178
| ~ spl357_194
| ~ spl357_219
| ~ spl357_478 ),
inference(sat_conversion,[],[f4672]) ).
cnf(s710,plain,
spl357_37,
inference(rat,[],[s187,s610]) ).
cnf(s717,plain,
spl357_407,
inference(rat,[],[s354,s177]) ).
cnf(s718,plain,
~ spl357_31,
inference(rat,[],[s626,s710,s717]) ).
cnf(s735,plain,
~ spl357_178,
inference(rat,[],[s627,s445,s150,s127]) ).
cnf(s737,plain,
~ spl357_95,
inference(rat,[],[s115,s735,s718]) ).
cnf(s748,plain,
$false,
inference(rat,[],[s84,s737]) ).
thf(f4673,plain,
$false,
inference(avatar_sat_refutation,[],[s748]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU614^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:58:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.25 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
% 0.62/0.38 % (1707374)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.62/0.38 % (1707404)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.62/0.38 % (1707404)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
% 0.62/0.38 % (1707404)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=2292209303:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.62/0.38 % (1707398)lrs+10_16_si=on:nwc=1.5:random_seed=458026734:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.62/0.38 % (1707397)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=538656000:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.62/0.38 % (1707399)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4033425095:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.62/0.38 % (1707403)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2499248255:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.62/0.38 % (1707400)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=2674085121: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)
% 0.62/0.38 % (1707402)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=150621885:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.62/0.38 % (1707399)Instruction limit reached!
% 0.62/0.38 % (1707399)------------------------------
% 0.62/0.38 % (1707399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707399)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707399)Termination reason: Instruction limit
% 0.62/0.38 % (1707399)Termination phase: shuffling
% 0.62/0.38 % (1707399)Time elapsed: 0.002 s
% 0.62/0.38 % (1707399)Peak memory usage: 10 MB
% 0.62/0.38 % (1707399)Instructions burned: 4 (million)
% 0.62/0.38 % (1707398)Instruction limit reached!
% 0.62/0.38 % (1707398)------------------------------
% 0.62/0.38 % (1707398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707398)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707398)Termination reason: Instruction limit
% 0.62/0.38 % (1707398)Termination phase: Property scanning
% 0.62/0.38 % (1707398)Time elapsed: 0.009 s
% 0.62/0.38 % (1707398)Peak memory usage: 10 MB
% 0.62/0.38 % (1707398)Instructions burned: 20 (million)
% 0.62/0.38 % (1707402)Instruction limit reached!
% 0.62/0.38 % (1707402)------------------------------
% 0.62/0.38 % (1707402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707402)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707402)Termination reason: Instruction limit
% 0.62/0.38 % (1707402)Termination phase: Preprocessing 3
% 0.62/0.38 % (1707402)Time elapsed: 0.013 s
% 0.62/0.38 % (1707402)Peak memory usage: 11 MB
% 0.62/0.38 % (1707402)Instructions burned: 26 (million)
% 0.62/0.38 % (1707426)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3372913275:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.62/0.38 % (1707426)Instruction limit reached!
% 0.62/0.38 % (1707426)------------------------------
% 0.62/0.38 % (1707426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707426)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707426)Termination reason: Instruction limit
% 0.62/0.38 % (1707426)Termination phase: shuffling
% 0.62/0.38 % (1707426)Time elapsed: 0.004 s
% 0.62/0.38 % (1707426)Peak memory usage: 10 MB
% 0.62/0.38 % (1707426)Instructions burned: 9 (million)
% 0.62/0.38 % (1707430)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.62/0.38 % (1707404)Instruction limit reached!
% 0.62/0.38 % (1707404)------------------------------
% 0.62/0.38 % (1707404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707404)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707404)Termination reason: Instruction limit
% 0.62/0.38 % (1707404)Termination phase: Saturation
% 0.62/0.38 % (1707404)Time elapsed: 0.038 s
% 0.62/0.38 % (1707404)Peak memory usage: 13 MB
% 0.62/0.38 % (1707404)Instructions burned: 161 (million)
% 0.62/0.38 % (1707429)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1604752104:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.62/0.38 % (1707430)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3816428968:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.62/0.38 % (1707403)Instruction limit reached!
% 0.62/0.38 % (1707403)------------------------------
% 0.62/0.38 % (1707403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707403)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707403)Termination reason: Instruction limit
% 0.62/0.38 % (1707403)Termination phase: Saturation
% 0.62/0.38 % (1707403)Time elapsed: 0.034 s
% 0.62/0.38 % (1707403)Peak memory usage: 12 MB
% 0.62/0.38 % (1707403)Instructions burned: 75 (million)
% 0.62/0.38 % (1707429)Instruction limit reached!
% 0.62/0.38 % (1707429)------------------------------
% 0.62/0.38 % (1707429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707429)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707429)Termination reason: Instruction limit
% 0.62/0.38 % (1707429)Termination phase: shuffling
% 0.62/0.38 % (1707429)Time elapsed: 0.003 s
% 0.62/0.38 % (1707429)Peak memory usage: 10 MB
% 0.62/0.38 % (1707429)Instructions burned: 6 (million)
% 0.62/0.38 % (1707430)Instruction limit reached!
% 0.62/0.38 % (1707430)------------------------------
% 0.62/0.38 % (1707430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707430)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707430)Termination reason: Instruction limit
% 0.62/0.38 % (1707430)Termination phase: shuffling
% 0.62/0.38 % (1707430)Time elapsed: 0.005 s
% 0.62/0.38 % (1707430)Peak memory usage: 10 MB
% 0.62/0.38 % (1707430)Instructions burned: 11 (million)
% 0.62/0.38 % (1707397)Instruction limit reached!
% 0.62/0.38 % (1707397)------------------------------
% 0.62/0.38 % (1707397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707397)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707397)Termination reason: Instruction limit
% 0.62/0.38 % (1707397)Termination phase: Saturation
% 0.62/0.38 % (1707397)Time elapsed: 0.040 s
% 0.62/0.38 % (1707397)Peak memory usage: 13 MB
% 0.62/0.38 % (1707397)Instructions burned: 87 (million)
% 0.62/0.38 % (1707439)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
% 0.62/0.38 % (1707439)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.62/0.38 % (1707439)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1745577985:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.62/0.38 % (1707436)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2120461991:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.62/0.38 % (1707439)Instruction limit reached!
% 0.62/0.38 % (1707439)------------------------------
% 0.62/0.38 % (1707439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707439)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707439)Termination reason: Instruction limit
% 0.62/0.38 % (1707439)Termination phase: Property scanning
% 0.62/0.38 % (1707439)Time elapsed: 0.007 s
% 0.62/0.38 % (1707439)Peak memory usage: 10 MB
% 0.62/0.38 % (1707439)Instructions burned: 29 (million)
% 0.62/0.38 % (1707436)Instruction limit reached!
% 0.62/0.38 % (1707436)------------------------------
% 0.62/0.38 % (1707436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707436)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707436)Termination reason: Instruction limit
% 0.62/0.38 % (1707436)Termination phase: shuffling
% 0.62/0.38 % (1707436)Time elapsed: 0.006 s
% 0.62/0.38 % (1707436)Peak memory usage: 10 MB
% 0.62/0.38 % (1707436)Instructions burned: 12 (million)
% 0.62/0.38 % (1707441)lrs+10_1_si=on:cs=on:random_seed=135791685:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.62/0.38 % (1707440)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=457185952:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.62/0.38 % (1707442)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.62/0.38 % (1707442)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=3074453843:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.62/0.38 % (1707441)Instruction limit reached!
% 0.62/0.38 % (1707441)------------------------------
% 0.62/0.38 % (1707441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707441)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707441)Termination reason: Instruction limit
% 0.62/0.38 % (1707441)Termination phase: shuffling
% 0.62/0.38 % (1707441)Time elapsed: 0.004 s
% 0.62/0.38 % (1707441)Peak memory usage: 10 MB
% 0.62/0.38 % (1707441)Instructions burned: 9 (million)
% 0.62/0.38 % (1707443)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3955907598:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.62/0.38 % (1707442)Instruction limit reached!
% 0.62/0.38 % (1707442)------------------------------
% 0.62/0.38 % (1707442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707442)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707442)Termination reason: Instruction limit
% 0.62/0.38 % (1707442)Termination phase: shuffling
% 0.62/0.38 % (1707442)Time elapsed: 0.002 s
% 0.62/0.38 % (1707442)Peak memory usage: 10 MB
% 0.62/0.38 % (1707442)Instructions burned: 4 (million)
% 0.62/0.38 % (1707400) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1707374-1707400"...
% 0.62/0.38 % (1707446)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3750518838:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.62/0.38 % (1707400)...printing done.
% 0.62/0.38 % (1707400)Refutation found. Thanks to Tanya!
% 0.62/0.38 % SZS status Theorem for theBenchmark
% 0.62/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.62/0.38 % (1707400)------------------------------
% 0.62/0.38 % (1707400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.38 % (1707400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.38 % (1707400)CaDiCaL version: 2.1.3
% 0.62/0.38 % (1707400)Termination reason: Refutation
% 0.62/0.38 % (1707400)Time elapsed: 0.069 s
% 0.62/0.38 % (1707400)Peak memory usage: 16 MB
% 0.62/0.38 % (1707400)Instructions burned: 135 (million)
% 0.62/0.38 % (1707374)Success in time 0.119 s
% 0.62/0.38 % Vampire exiting
%------------------------------------------------------------------------------