%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU572^1 : 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 : n014.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 08:30:07 AM UTC 2026
% Result : Theorem 0.64s 0.38s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 21 unt; 0 typ; 6 def)
% Number of atoms : 1975 ( 536 equ; 0 cnn)
% Maximal formula atoms : 90 ( 31 avg)
% Number of connectives : 1089 ( 73 ~; 62 |; 368 &; 214 @)
% ( 10 <=>; 362 =>; 0 <=; 0 <~>)
% Maximal formula depth : 97 ( 15 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 : 227 ( 224 usr; 111 con; 0-4 aty)
% Number of variables : 84 ( 0 sgn 65 !; 19 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_106,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_107,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_108,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_109,type,
vNOT: $o > $o ).
thf(func_def_110,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_111,type,
vAND: $o > $o > $o ).
thf(func_def_112,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_113,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_114,type,
vIMP: $o > $o > $o ).
thf(func_def_115,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_116,type,
sP0: $i > $i > $o ).
thf(func_def_117,type,
sP1: $i > $o ).
thf(func_def_118,type,
sP2: $o ).
thf(func_def_119,type,
sK3: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_120,type,
sK4: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_123,type,
sK7: $i > $o ).
thf(func_def_124,type,
sK8: $i > $o ).
thf(func_def_129,type,
sK13: $o ).
thf(func_def_135,type,
sK19: $i > $i > $i ).
thf(func_def_136,type,
sK20: $i > $i > $i ).
thf(func_def_139,type,
sK23: $i > $i > $i ).
thf(func_def_144,type,
sK28: $i > $i ).
thf(func_def_145,type,
sK29: $i > $i ).
thf(func_def_146,type,
sK30: $i > $o ).
thf(func_def_149,type,
sK33: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_150,type,
sK34: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_151,type,
sK35: $i > $o ).
thf(func_def_152,type,
sK36: $i > $o ).
thf(func_def_159,type,
sK43: $i > $i ).
thf(func_def_161,type,
sK45: $o ).
thf(func_def_176,type,
sK60: $i > $o ).
thf(func_def_177,type,
sK61: $i > $o ).
thf(func_def_178,type,
sK62: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_179,type,
sK63: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_180,type,
sK64: $i > $i > $i ).
thf(func_def_185,type,
sK69: $i > ( $i > $o ) > $i ).
thf(func_def_186,type,
sK70: $i > $o ).
thf(func_def_191,type,
sK75: $i > $o ).
thf(func_def_192,type,
sK76: $i > $o ).
thf(func_def_194,type,
sK78: $i > ( $i > $o ) > $i ).
thf(func_def_197,type,
sK81: $i > $o ).
thf(func_def_199,type,
sK83: $i > $o ).
thf(func_def_200,type,
sK84: $i > $o ).
thf(func_def_203,type,
sK87: ( $i > $o ) > $i ).
thf(func_def_204,type,
sK88: $i > $o ).
thf(func_def_205,type,
sK89: $i > $i ).
thf(func_def_206,type,
sK90: $i > $i ).
thf(func_def_208,type,
sK92: $i > $o ).
thf(func_def_210,type,
sK94: ( $i > $o ) > $i ).
thf(func_def_211,type,
sK95: ( $i > $o ) > $i ).
thf(func_def_212,type,
sK96: $i > $i > $i ).
thf(func_def_224,type,
sK108: $o ).
thf(func_def_225,type,
sK109: ( $i > $i > $o ) > $i > $i ).
thf(func_def_226,type,
sK110: ( $i > $i > $o ) > $i > $i ).
thf(func_def_227,type,
sK111: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_229,type,
sK113: $i > $i > $o ).
thf(func_def_230,type,
sK114: $i > $i ).
thf(func_def_231,type,
sK115: $i > $i ).
thf(func_def_232,type,
sK116: $i > $o ).
thf(func_def_235,type,
sK119: $i > ( $i > $o ) > $i ).
thf(func_def_241,type,
sK125: $o ).
thf(func_def_242,type,
sK126: $o > $i > $i > $i ).
thf(func_def_246,type,
sK130: $i > $i > $i ).
thf(func_def_252,type,
sK136: $o ).
thf(func_def_255,type,
sK139: $i > $o ).
thf(func_def_261,type,
sK145: $i > $i > $i ).
thf(func_def_265,type,
sK149: $i > $i ).
thf(func_def_267,type,
sK151: $i > $i ).
thf(func_def_268,type,
sK152: $i > $i ).
thf(func_def_269,type,
sK153: $i > $i ).
thf(func_def_270,type,
sK154: $i > $i ).
thf(func_def_271,type,
sK155: $i > $i ).
thf(func_def_272,type,
sK156: $i > $i > $i > $i ).
thf(func_def_273,type,
sK157: $i > $i ).
thf(func_def_274,type,
sK158: $i > $i ).
thf(func_def_275,type,
sK159: $i > $i ).
thf(func_def_276,type,
sK160: $i > $i ).
thf(func_def_277,type,
sK161: $i > $i > $i ).
thf(func_def_278,type,
sK162: $i > $i > $i ).
thf(func_def_279,type,
sK163: $i > $i > $i > $i ).
thf(func_def_280,type,
sK164: $i > $i > $i > $i ).
thf(func_def_281,type,
sK165: $i > $i > $i > $i ).
thf(func_def_282,type,
sK166: $i > $i > $i ).
thf(func_def_283,type,
sK167: $i > $i > $i ).
thf(func_def_284,type,
sK168: $i > $i > $i ).
thf(func_def_285,type,
sK169: ( $i > $o ) > $i > $i ).
thf(func_def_287,type,
sK171: $i > $o ).
thf(func_def_289,type,
sK173: $i > $o ).
thf(func_def_292,type,
sK176: $i > ( $i > $o ) > $i ).
thf(func_def_293,type,
sK177: $o ).
thf(func_def_295,type,
sK179: $i > $i ).
thf(func_def_299,type,
sK183: $i > $i ).
thf(func_def_304,type,
sK188: $i > $o ).
thf(func_def_307,type,
sK191: $i > ( $i > $o ) > $i ).
thf(func_def_310,type,
sK194: ( $i > $o ) > $i > $i ).
thf(func_def_312,type,
sK196: $i > $o ).
thf(func_def_314,type,
sK198: $i > $o ).
thf(func_def_318,type,
sK202: $i > $o ).
thf(func_def_324,type,
sK208: $i > $o ).
thf(func_def_328,type,
sK212: $i > $o ).
thf(func_def_329,type,
sK213: $i > $i ).
thf(func_def_330,type,
sK214: ( $i > $o ) > $i ).
thf(func_def_346,type,
sK230: $i > $o ).
thf(func_def_348,type,
sK232: ( $i > $o ) > $i > $i ).
thf(func_def_360,type,
sK244: ( $i > $o ) > $i ).
thf(func_def_361,type,
sK245: $i > $o ).
thf(func_def_362,type,
sK246: $i > $o ).
thf(func_def_365,type,
sK249: $i > $i > $i ).
thf(f89,axiom,
( subsetTrans
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(f90,axiom,
( setadjoinSub
= ( ! [X0: $i,X1: $i] : ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(f91,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
=> ! [X2: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X2 )
=> ( subset @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(f92,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
=> ! [X2: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X2 )
=> ( subset @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f91]) ).
thf(f162,plain,
( setadjoinSub
= ( ! [X0: $i,X1: $i] : ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f90]) ).
thf(f163,plain,
( ! [X1: $i,X0: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinSub = $true ) ),
inference(fool_elimination,[],[f162]) ).
thf(f211,plain,
( subsetTrans
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( subset @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f89]) ).
thf(f212,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( subset @ X2 @ X0 )
= $true )
=> ( ( ( subset @ X0 @ X1 )
= $true )
=> ( $true
= ( subset @ X2 @ X1 ) ) ) )
<=> ( subsetTrans = $true ) ),
inference(fool_elimination,[],[f211]) ).
thf(f238,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X0 )
=> ( subset @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f92]) ).
thf(f239,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 )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( subset @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f238]) ).
thf(f331,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X2 @ X0 )
!= $true ) )
<=> ( subsetTrans = $true ) ),
inference(ennf_transformation,[],[f212]) ).
thf(f332,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X2 @ X0 )
!= $true )
| ( $true
= ( subset @ X2 @ X1 ) ) )
<=> ( subsetTrans = $true ) ),
inference(flattening,[],[f331]) ).
thf(f366,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true )
& ( ( subset @ X1 @ X0 )
= $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,[],[f239]) ).
thf(f367,plain,
( ( powersetAx = $true )
& ( setunion__Cong = $true )
& ( dsetconstrI = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI2 = $true )
& ( subsetE = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan2 = $true )
& ( omega__Cong = $true )
& ( setadjoinSub = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) )
& ( eqimpsubset2 = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( notequalI2 = $true )
& ( dsetconstrER = $true )
& ( omegaIndAx = $true )
& ( prop2set2propI = $true )
& ( vacuousDall = $true )
& ( setadjoinIL = $true )
& ( subPowSU = $true )
& ( setadjoinOr = $true )
& ( emptyE1 = $true )
& ( in__Cong = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( setunionAx = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrEL = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( descr__Cong = $true )
& ( subsetTrans = $true )
& ( exuE2 = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( notequalI1 = $true )
& ( setextAx = $true )
& ( eqinunit = $true )
& ( subsetE2 = $true )
& ( setadjoinE = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( setadjoinAx = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( uniqinunit = $true )
& ( emptyset__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( exuI1 = $true )
& ( upairsetE = $true )
& ( emptysetsubset = $true )
& ( omega0Ax = $true )
& ( notdexE = $true )
& ( noeltsimpempty = $true )
& ( singletonsswitch = $true )
& ( notinemptyset = $true )
& ( setoftrueEq = $true )
& ( powersetE = $true )
& ( notdallE = $true )
& ( exu__Cong = $true )
& ( setbeta = $true )
& ( exuE3u = $true )
& ( exuE1 = $true )
& ( prop2setI = $true )
& ( subsetRefl = $true )
& ( wellorderingAx = $true )
& ( upairsetIR = $true )
& ( nonemptyE1 = $true )
& ( exuEu = $true )
& ( eqimpsubset1 = $true )
& ( subsetI1 = $true )
& ( nonemptyI1 = $true )
& ( exuE3e = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( setadjoin__Cong = $true )
& ( emptysetE = $true )
& ( setunionE = $true )
& ( powerset__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( notsubsetI = $true ) ),
inference(flattening,[],[f366]) ).
thf(f576,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X2 @ X0 )
!= $true )
| ( $true
= ( subset @ X2 @ X1 ) ) )
| ( subsetTrans != $true ) )
& ( ( subsetTrans = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X2 @ X0 )
= $true )
& ( $true
!= ( subset @ X2 @ X1 ) ) ) ) ),
inference(nnf_transformation,[],[f332]) ).
thf(f577,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X1 @ X2 )
= $true ) )
| ( subsetTrans != $true ) )
& ( ( subsetTrans = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
& ( ( subset @ X4 @ X3 )
= $true )
& ( ( subset @ X4 @ X5 )
!= $true ) ) ) ),
inference(rectify,[],[f576]) ).
thf(f578,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X1 @ X2 )
= $true ) )
| ( subsetTrans != $true ) )
& ( ( subsetTrans = $true )
| ( ( ( subset @ sK180 @ sK182 )
= $true )
& ( $true
= ( subset @ sK181 @ sK180 ) )
& ( $true
!= ( subset @ sK181 @ sK182 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180,sK181,sK182]),skolemize(X3,sK180),skolemize(X4,sK181),skolemize(X5,sK182)],[f577]) ).
thf(f600,plain,
( ( powersetAx = $true )
& ( setunion__Cong = $true )
& ( dsetconstrI = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI2 = $true )
& ( subsetE = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan2 = $true )
& ( omega__Cong = $true )
& ( setadjoinSub = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true )
& ( ( subset @ X0 @ X2 )
= $true ) )
& ( eqimpsubset2 = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( notequalI2 = $true )
& ( dsetconstrER = $true )
& ( omegaIndAx = $true )
& ( prop2set2propI = $true )
& ( vacuousDall = $true )
& ( setadjoinIL = $true )
& ( subPowSU = $true )
& ( setadjoinOr = $true )
& ( emptyE1 = $true )
& ( in__Cong = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( setunionAx = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrEL = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( descr__Cong = $true )
& ( subsetTrans = $true )
& ( exuE2 = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( notequalI1 = $true )
& ( setextAx = $true )
& ( eqinunit = $true )
& ( subsetE2 = $true )
& ( setadjoinE = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( setadjoinAx = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( uniqinunit = $true )
& ( emptyset__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( exuI1 = $true )
& ( upairsetE = $true )
& ( emptysetsubset = $true )
& ( omega0Ax = $true )
& ( notdexE = $true )
& ( noeltsimpempty = $true )
& ( singletonsswitch = $true )
& ( notinemptyset = $true )
& ( setoftrueEq = $true )
& ( powersetE = $true )
& ( notdallE = $true )
& ( exu__Cong = $true )
& ( setbeta = $true )
& ( exuE3u = $true )
& ( exuE1 = $true )
& ( prop2setI = $true )
& ( subsetRefl = $true )
& ( wellorderingAx = $true )
& ( upairsetIR = $true )
& ( nonemptyE1 = $true )
& ( exuEu = $true )
& ( eqimpsubset1 = $true )
& ( subsetI1 = $true )
& ( nonemptyI1 = $true )
& ( exuE3e = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( setadjoin__Cong = $true )
& ( emptysetE = $true )
& ( setunionE = $true )
& ( powerset__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( notsubsetI = $true ) ),
inference(rectify,[],[f367]) ).
thf(f601,plain,
( ( powersetAx = $true )
& ( setunion__Cong = $true )
& ( dsetconstrI = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI2 = $true )
& ( subsetE = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan2 = $true )
& ( omega__Cong = $true )
& ( setadjoinSub = $true )
& ( ( subset @ sK204 @ ( setadjoin @ sK205 @ sK206 ) )
!= $true )
& ( ( subset @ sK204 @ sK206 )
= $true )
& ( eqimpsubset2 = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( notequalI2 = $true )
& ( dsetconstrER = $true )
& ( omegaIndAx = $true )
& ( prop2set2propI = $true )
& ( vacuousDall = $true )
& ( setadjoinIL = $true )
& ( subPowSU = $true )
& ( setadjoinOr = $true )
& ( emptyE1 = $true )
& ( in__Cong = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( setunionAx = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrEL = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( descr__Cong = $true )
& ( subsetTrans = $true )
& ( exuE2 = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( notequalI1 = $true )
& ( setextAx = $true )
& ( eqinunit = $true )
& ( subsetE2 = $true )
& ( setadjoinE = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( setadjoinAx = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( uniqinunit = $true )
& ( emptyset__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( exuI1 = $true )
& ( upairsetE = $true )
& ( emptysetsubset = $true )
& ( omega0Ax = $true )
& ( notdexE = $true )
& ( noeltsimpempty = $true )
& ( singletonsswitch = $true )
& ( notinemptyset = $true )
& ( setoftrueEq = $true )
& ( powersetE = $true )
& ( notdallE = $true )
& ( exu__Cong = $true )
& ( setbeta = $true )
& ( exuE3u = $true )
& ( exuE1 = $true )
& ( prop2setI = $true )
& ( subsetRefl = $true )
& ( wellorderingAx = $true )
& ( upairsetIR = $true )
& ( nonemptyE1 = $true )
& ( exuEu = $true )
& ( eqimpsubset1 = $true )
& ( subsetI1 = $true )
& ( nonemptyI1 = $true )
& ( exuE3e = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( setadjoin__Cong = $true )
& ( emptysetE = $true )
& ( setunionE = $true )
& ( powerset__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( notsubsetI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204,sK205,sK206]),skolemize(X0,sK204),skolemize(X1,sK205),skolemize(X2,sK206)],[f600]) ).
thf(f614,plain,
( ( ! [X1: $i,X0: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinSub != $true ) )
& ( ( setadjoinSub = $true )
| ? [X1: $i,X0: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f163]) ).
thf(f615,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinSub != $true ) )
& ( ( setadjoinSub = $true )
| ? [X2: $i,X3: $i] :
( ( subset @ X2 @ ( setadjoin @ X3 @ X2 ) )
!= $true ) ) ),
inference(rectify,[],[f614]) ).
thf(f616,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinSub != $true ) )
& ( ( setadjoinSub = $true )
| ( ( subset @ sK218 @ ( setadjoin @ sK219 @ sK218 ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218,sK219]),skolemize(X2,sK218),skolemize(X3,sK219)],[f615]) ).
thf(f942,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( ( subset @ X0 @ X2 )
!= $true )
| ( subsetTrans != $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f578]) ).
thf(f1026,plain,
subsetTrans = $true,
inference(cnf_transformation,[],[f601]) ).
thf(f1048,plain,
( ( subset @ sK204 @ sK206 )
= $true ),
inference(cnf_transformation,[],[f601]) ).
thf(f1049,plain,
( ( subset @ sK204 @ ( setadjoin @ sK205 @ sK206 ) )
!= $true ),
inference(cnf_transformation,[],[f601]) ).
thf(f1050,plain,
setadjoinSub = $true,
inference(cnf_transformation,[],[f601]) ).
thf(f1080,plain,
! [X0: $i,X1: $i] :
( ( setadjoinSub != $true )
| ( $true
= ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f616]) ).
thf(f1392,definition,
( spl252_31
<=> ( setadjoinSub = $true ) ),
introduced(definition,[new_symbols(definition,[spl252_31])],[avatar_definition]) ).
thf(f1395,plain,
spl252_31,
inference(avatar_split_clause,[],[f1050,f1392]) ).
thf(f1561,definition,
( spl252_70
<=> ( subsetTrans = $true ) ),
introduced(definition,[new_symbols(definition,[spl252_70])],[avatar_definition]) ).
thf(f1565,definition,
( spl252_71
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl252_71])],[avatar_definition]) ).
thf(f1566,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( ( subset @ X0 @ X2 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ~ spl252_71 ),
inference(avatar_component_clause,[],[f1565]) ).
thf(f1567,plain,
( ~ spl252_70
| spl252_71 ),
inference(avatar_split_clause,[],[f942,f1565,f1561]) ).
thf(f2563,definition,
( spl252_287
<=> ( ( subset @ sK204 @ ( setadjoin @ sK205 @ sK206 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl252_287])],[avatar_definition]) ).
thf(f2565,plain,
( ( ( subset @ sK204 @ ( setadjoin @ sK205 @ sK206 ) )
!= $true )
| spl252_287 ),
inference(avatar_component_clause,[],[f2563]) ).
thf(f2566,plain,
~ spl252_287,
inference(avatar_split_clause,[],[f1049,f2563]) ).
thf(f2776,definition,
( spl252_332
<=> ( ( subset @ sK204 @ sK206 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl252_332])],[avatar_definition]) ).
thf(f2778,plain,
( ( ( subset @ sK204 @ sK206 )
= $true )
| ~ spl252_332 ),
inference(avatar_component_clause,[],[f2776]) ).
thf(f2779,plain,
spl252_332,
inference(avatar_split_clause,[],[f1048,f2776]) ).
thf(f3239,definition,
( spl252_428
<=> ! [X0: $i,X1: $i] :
( $true
= ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl252_428])],[avatar_definition]) ).
thf(f3240,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X0 @ ( setadjoin @ X1 @ X0 ) ) )
| ~ spl252_428 ),
inference(avatar_component_clause,[],[f3239]) ).
thf(f3241,plain,
( spl252_428
| ~ spl252_31 ),
inference(avatar_split_clause,[],[f1080,f1392,f3239]) ).
thf(f3305,plain,
spl252_70,
inference(avatar_split_clause,[],[f1026,f1561]) ).
thf(f3574,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ ( setadjoin @ sK205 @ sK206 ) )
!= $true )
| ( ( subset @ sK204 @ X0 )
!= $true ) )
| ~ spl252_71
| spl252_287 ),
inference(superposition,[],[f2565,f1566]) ).
thf(f3575,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ ( setadjoin @ sK205 @ sK206 ) )
!= $true )
| ( ( subset @ sK204 @ X0 )
!= $true ) )
| ~ spl252_71
| spl252_287 ),
inference(trivial_inequality_removal,[],[f3574]) ).
thf(f3598,plain,
( ( $true != $true )
| ( ( subset @ sK204 @ sK206 )
!= $true )
| ~ spl252_71
| spl252_287
| ~ spl252_428 ),
inference(superposition,[],[f3575,f3240]) ).
thf(f3604,plain,
( ( ( subset @ sK204 @ sK206 )
!= $true )
| ~ spl252_71
| spl252_287
| ~ spl252_428 ),
inference(trivial_inequality_removal,[],[f3598]) ).
thf(f3611,plain,
( $false
| ~ spl252_71
| spl252_287
| ~ spl252_332
| ~ spl252_428 ),
inference(forward_subsumption_resolution,[],[f3604,f2778]) ).
thf(f3612,plain,
( ~ spl252_71
| spl252_287
| ~ spl252_332
| ~ spl252_428 ),
inference(avatar_contradiction_clause,[],[f3611]) ).
cnf(s15,plain,
spl252_31,
inference(sat_conversion,[],[f1395]) ).
cnf(s44,plain,
( ~ spl252_70
| spl252_71 ),
inference(sat_conversion,[],[f1567]) ).
cnf(s253,plain,
~ spl252_287,
inference(sat_conversion,[],[f2566]) ).
cnf(s307,plain,
spl252_332,
inference(sat_conversion,[],[f2779]) ).
cnf(s430,plain,
( ~ spl252_31
| spl252_428 ),
inference(sat_conversion,[],[f3241]) ).
cnf(s448,plain,
spl252_70,
inference(sat_conversion,[],[f3305]) ).
cnf(s458,plain,
( ~ spl252_71
| spl252_287
| ~ spl252_332
| ~ spl252_428 ),
inference(sat_conversion,[],[f3612]) ).
cnf(s556,plain,
spl252_71,
inference(rat,[],[s44,s448]) ).
cnf(s557,plain,
~ spl252_428,
inference(rat,[],[s458,s253,s307,s556]) ).
cnf(s559,plain,
~ spl252_31,
inference(rat,[],[s430,s557]) ).
cnf(s578,plain,
$false,
inference(rat,[],[s15,s559]) ).
thf(f3613,plain,
$false,
inference(avatar_sat_refutation,[],[s578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU572^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:51:00 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.38 % (2696001)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.64/0.38 % (2696011)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4112291762:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.64/0.38 % (2696012)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.64/0.38 % (2696012)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
% 0.64/0.38 % (2696006)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2923771321:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.64/0.38 % (2696007)lrs+10_16_si=on:nwc=1.5:random_seed=994362795:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.64/0.38 % (2696008)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3219495738:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.64/0.38 % (2696010)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2343869626:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.64/0.38 % (2696009)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=1253463488: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)
% 0.64/0.38 % (2696012)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=3686767573:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.64/0.38 % (2696008)Instruction limit reached!
% 0.64/0.38 % (2696008)------------------------------
% 0.64/0.38 % (2696008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696008)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696008)Termination reason: Instruction limit
% 0.64/0.38 % (2696008)Termination phase: shuffling
% 0.64/0.38 % (2696008)Time elapsed: 0.002 s
% 0.64/0.38 % (2696008)Peak memory usage: 10 MB
% 0.64/0.38 % (2696008)Instructions burned: 4 (million)
% 0.64/0.38 % (2696007)Instruction limit reached!
% 0.64/0.38 % (2696007)------------------------------
% 0.64/0.38 % (2696007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696007)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696007)Termination reason: Instruction limit
% 0.64/0.38 % (2696007)Termination phase: Property scanning
% 0.64/0.38 % (2696007)Time elapsed: 0.008 s
% 0.64/0.38 % (2696007)Peak memory usage: 10 MB
% 0.64/0.38 % (2696007)Instructions burned: 19 (million)
% 0.64/0.38 % (2696011)Instruction limit reached!
% 0.64/0.38 % (2696011)------------------------------
% 0.64/0.38 % (2696011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696011)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696011)Termination reason: Instruction limit
% 0.64/0.38 % (2696011)Termination phase: Saturation
% 0.64/0.38 % (2696011)Time elapsed: 0.019 s
% 0.64/0.38 % (2696011)Peak memory usage: 13 MB
% 0.64/0.38 % (2696011)Instructions burned: 76 (million)
% 0.64/0.38 % (2696010)Instruction limit reached!
% 0.64/0.38 % (2696010)------------------------------
% 0.64/0.38 % (2696010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696010)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696010)Termination reason: Instruction limit
% 0.64/0.38 % (2696010)Termination phase: Property scanning
% 0.64/0.38 % (2696010)Time elapsed: 0.013 s
% 0.64/0.38 % (2696010)Peak memory usage: 11 MB
% 0.64/0.38 % (2696010)Instructions burned: 26 (million)
% 0.64/0.38 % (2696022)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.38 % (2696020)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=388928779:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.38 % (2696022)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3621929996:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.64/0.38 % (2696020)Instruction limit reached!
% 0.64/0.38 % (2696020)------------------------------
% 0.64/0.38 % (2696020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696020)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696020)Termination reason: Instruction limit
% 0.64/0.38 % (2696020)Termination phase: shuffling
% 0.64/0.38 % (2696020)Time elapsed: 0.003 s
% 0.64/0.38 % (2696020)Peak memory usage: 10 MB
% 0.64/0.38 % (2696020)Instructions burned: 6 (million)
% 0.64/0.38 % (2696022)Instruction limit reached!
% 0.64/0.38 % (2696022)------------------------------
% 0.64/0.38 % (2696022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696022)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696022)Termination reason: Instruction limit
% 0.64/0.38 % (2696022)Termination phase: Property scanning
% 0.64/0.38 % (2696022)Time elapsed: 0.003 s
% 0.64/0.38 % (2696022)Peak memory usage: 10 MB
% 0.64/0.38 % (2696022)Instructions burned: 15 (million)
% 0.64/0.38 % (2696021)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1180263702:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.64/0.38 % (2696021)Instruction limit reached!
% 0.64/0.38 % (2696021)------------------------------
% 0.64/0.38 % (2696021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696021)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696021)Termination reason: Instruction limit
% 0.64/0.38 % (2696021)Termination phase: shuffling
% 0.64/0.38 % (2696021)Time elapsed: 0.003 s
% 0.64/0.38 % (2696021)Peak memory usage: 10 MB
% 0.64/0.38 % (2696021)Instructions burned: 6 (million)
% 0.64/0.38 % (2696023)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2093912470:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.64/0.38 % (2696026)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
% 0.64/0.38 % (2696026)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.38 % (2696026)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2375127746:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.64/0.38 % (2696023)Instruction limit reached!
% 0.64/0.38 % (2696023)------------------------------
% 0.64/0.38 % (2696023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696023)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696023)Termination reason: Instruction limit
% 0.64/0.38 % (2696023)Termination phase: Property scanning
% 0.64/0.38 % (2696023)Time elapsed: 0.005 s
% 0.64/0.38 % (2696023)Peak memory usage: 10 MB
% 0.64/0.38 % (2696023)Instructions burned: 12 (million)
% 0.64/0.38 % (2696006)Instruction limit reached!
% 0.64/0.38 % (2696006)------------------------------
% 0.64/0.38 % (2696006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696006)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696006)Termination reason: Instruction limit
% 0.64/0.38 % (2696006)Termination phase: Saturation
% 0.64/0.38 % (2696006)Time elapsed: 0.041 s
% 0.64/0.38 % (2696006)Peak memory usage: 13 MB
% 0.64/0.38 % (2696006)Instructions burned: 88 (million)
% 0.64/0.38 % (2696026)Instruction limit reached!
% 0.64/0.38 % (2696026)------------------------------
% 0.64/0.38 % (2696026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696026)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696026)Termination reason: Instruction limit
% 0.64/0.38 % (2696026)Termination phase: Property scanning
% 0.64/0.38 % (2696026)Time elapsed: 0.006 s
% 0.64/0.38 % (2696026)Peak memory usage: 10 MB
% 0.64/0.38 % (2696026)Instructions burned: 28 (million)
% 0.64/0.38 % (2696027)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=2872801639:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.64/0.38 % (2696029)lrs+10_1_si=on:cs=on:random_seed=3790541130:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.64/0.38 % (2696034)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3739851948:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.64/0.38 % (2696032)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.64/0.38 % (2696029)Instruction limit reached!
% 0.64/0.38 % (2696029)------------------------------
% 0.64/0.38 % (2696029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696029)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696029)Termination reason: Instruction limit
% 0.64/0.38 % (2696029)Termination phase: shuffling
% 0.64/0.38 % (2696029)Time elapsed: 0.004 s
% 0.64/0.38 % (2696029)Peak memory usage: 10 MB
% 0.64/0.38 % (2696029)Instructions burned: 9 (million)
% 0.64/0.38 % (2696032)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=1705665424:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.38 % (2696009) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2696001-2696009"...
% 0.64/0.38 % (2696032)Instruction limit reached!
% 0.64/0.38 % (2696032)------------------------------
% 0.64/0.38 % (2696032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696032)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696032)Termination reason: Instruction limit
% 0.64/0.38 % (2696032)Termination phase: shuffling
% 0.64/0.38 % (2696032)Time elapsed: 0.002 s
% 0.64/0.38 % (2696032)Peak memory usage: 10 MB
% 0.64/0.38 % (2696032)Instructions burned: 4 (million)
% 0.64/0.38 % (2696033)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2437560544:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.64/0.38 % (2696009)...printing done.
% 0.64/0.38 % (2696009)Refutation found. Thanks to Tanya!
% 0.64/0.38 % SZS status Theorem for theBenchmark
% 0.64/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/0.38 % (2696009)------------------------------
% 0.64/0.38 % (2696009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (2696009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (2696009)CaDiCaL version: 2.1.3
% 0.64/0.38 % (2696009)Termination reason: Refutation
% 0.64/0.38 % (2696009)Time elapsed: 0.062 s
% 0.64/0.38 % (2696009)Peak memory usage: 15 MB
% 0.64/0.38 % (2696009)Instructions burned: 118 (million)
% 0.64/0.38 % (2696001)Success in time 0.113 s
% 0.64/0.38 % Vampire exiting
%------------------------------------------------------------------------------